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Practice with the help of enVision Math Common Core Grade 6 Answer Key Topic 8 Display, Describe and Summarize Data regularly and improve your accuracy in solving questions.

Envision Math Common Core 6th Grade Answers Key Topic 8 Display, Describe, And Summarize Data

Topic 8 Essential Question

How can data be described by a single number? How can tables and graphs be used to represent data and answer questions?

3-ACT MATH

Vocal Range
Have you ever disagreed with the judge on a reality TV show? Reality TV competitions rely on the different opinions of the judges to make the show more exciting. There are lots of factors to consider when comparing two contestants on a show. Think about this during the 3-Act Mathematical Modeling lesson.

Topic 8 enVision STEM Project

Did You Know?
Earthquakes are caused by the sudden release of energy in the Earth’s crust when friction between tectonic plates causes rocks to break along fault lines.
RING OF FIRE
PACIFIC OCEAN
Nearly 80% of Earth’s largest earthquakes occur along the “Ring of Fire.”
Many tectonic plates meet in this horseshoeshaped region around the Pacific Ocean.


The shape of a pagoda is known for resisting damage from earthquakes.

Your Task: Shake It Up
Engineers design sturdy bridges, buildings, dams and other structures that can withstand earthquakes. They also devise detection devices to predict earthquakes. You and your classmates will gather and display data about earthquake frequency and magnitude. You will analyze the data and determine what constraints engineers must consider when designing roadways, bridges, homes, and other structures.

Topic 8 Get Ready!

Review What You Know!

Vocabulary
Choose the best term from the box to complete each sentence.

• bar graph
• data
• dot plot
• tally chart

Question 1.
_______ are pieces of gathered information.

Answer:
Data are pieces of gathered information.

Explanation:
In the above-given question,
given that,
data are pieces of gathered information.
for example:

Question 2.
Display data as marks above a number line in a _________.

Answer:
Display data as marks above a number line in a line plot.

Explanation:
In the above-given question,
given that,
Display data as marks above a number line in a line plot.
for example:
negative integers on the left side in a number line.
positive integers on the right side in a number line.

Question 3.
Use the lengths of bars to show and compare data in a __________.

Answer:
Use the lengths of bars to show and compare data in a bar chart.

Explanation:
In the above-given question,
given that,
use the lengths of bars to show and compare data in a bar chart.
for example:
the student marks are given on the bar graph.
the students on the x-axis.
the marks on the y-axis.
scale: 1 unit = 5 marks.

Summarize Data

Use the number of text messages Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
Question 4.
What is the least value?

Answer:
The least value is 2.

Explanation:
In the above-given question,
given that,
Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
from the given data,
the least value is 2.
there are 2 two’s in the data.

Question 5.
What is the greatest value?

Answer:
The greatest value is 12.

Explanation:
In the above-given question,
given that,
Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
from the given data,
the greatest value is 12.
there is one 12 in the data.

Question 6.
What numbers are repeated?

Answer:
6 and 2 are repeating.

Explanation:
In the above-given question,
given that,
Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
from the given data,
6 is repeating 3 times.
2 is repeating 2 times.
6 and 2 are repeating.

Question 7.
How many text messages did Henry send in all?

Answer:
The number of text messages did Henry send in all = 9.

Explanation:
In the above-given question,
given that,
Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
from the given data,
the number of text messages did Henry send in all = 9.
among those numbers 6 and 2 are repeating.

Display Data
Question 8.
The table shows the time students spend doing chores each day. Draw a dot plot to show the data.

Answer:
20 is repeating 3 times.
25 is repeating 2 times.
30 is repeating 2 times.
40 is repeating 2 times.

Explanation:
In the above-given question,
given that,
the table shows the time students spend doing chores each day.
minutes doing chores each day.
20, 25, 45, 20, 30, 40, 30, 25, 20, 15, 35, 40.
20 is repeating 3 times.
25 is repeating 2 times.
30 is repeating 2 times.
40 is repeating 2 times.

Analyze Data

Use the graph to answer the questions about a student’s test performance.

Question 9.
How many more points were earned on Test 3 than on Test 1?

Answer:
The more points that were earned on Test 3 than on Test 1 is 5.

Explanation:
In the above-given question,
given that,
the test score in the social studies are given.
the test number is on the x-axis.
the scores are on the y-axis.
test 1 the number of points is 90.
test 3 the number of points is 95.
95 – 90 = 5.
so the more points that were earned on test 3 than on test 1 is 5.

Question 10.
Which two tests have the least difference in score? What is the difference?

Answer:
The two tests that have the least difference in the score are Test 4 and Test 5.

Explanation:
In the above-given question,
given that,
the two tests that have the least difference in the score are Test 4 and Test 5.
on Test 4 the score is 98.
on test 5 the score is 99.
99 – 98 = 1.
so the two tests that have the least difference in the score are Test 4 and Test 5.

Question 11.
What is the greatest difference between two scores? How do you know?

Answer:
The greatest difference between the two scores is 11.

Explanation:
In the above-given question,
given that,
The greatest difference between the two scores is Test 2 and Test 5.
on Test 2 the score is 88.
on Test 5 the score is 99.
99 – 88 = 11.
so the greatest difference between the two scores is 11.

Language Development
Complete the graphic organizer. Write the definition of each measure in your own words.

Pick A Project

PROJECT 8A
If you recorded a video blog, what would it be about?
PROJECT: EXPLORE VIDEO BLOGS

PROJECT 8B
How many different breakfast cereals have you tasted?
PROJECT: INVESTIGATE CEREALS

PROJECT 8C
How far could you bike before needing to rest?
PROJECT: ANALYZE A TIME TRIAL

PROJECT 8D
If you could change something at your school, what would it be?
PROJECT: SURVEY YOUR SCHOOL

Lesson 8.1 Recognize Statistical Questions

Solve & Discuss It!
Ms. Jackson wrote a question on the board. Then she collected student responses to the question and recorded them in a tally chart. What question could she have asked? Is there more than one possible response to the question? Explain

I can… identify and write statistical questions.

Answer:
Yes, there is more than one possible response.

Explanation:
In the above-given question,
given that,
Ms. Jackson wrote a question on the board.
Then she collected student responses to the question and recorded them in a tally chart.
so there is more than one possible response.

Make Sense and Persevere
What other questions could you ask that would result in a variety of numerical answers?

Focus on math practices
Reasoning Suppose Ms. Jackson wants to know the amount of time her students spent outdoors the previous afternoon. What question might she ask each student to gather the data?

Answer:
the number of  0 books is 3.
the number of 2nd books is 1.
the number of 3 books is 3.
the number of 4 books is 2.
the number of 5 books is 1.

Explanation:
In the above-given question,
given that,
Ms. Jackson wants to know the amount of time her students spent outdoors the previous afternoon.
the number of  0 books is 3.
the number of 2nd books is 1.
the number of 3 books is 3.
the number of 4 books is 2.
the number of 5 books is 1.

Essential Question
How are statistical questions different from other questions?

Try It!

Is the question What was the high temperature on March 8 of last year? a statistical question? Explain.

Answer:
The high temperature on March 8 of last year is 90 degrees.

Explanation:
In the above-given question,
given that,
the high temperature on March 8 of last year is 90 degrees.

Convince Me! How could you change the question above to make it a statistical question?

Try It!

What is another statistical question Lucia might ask about the exercise the students in her class do each week?
Answer:

Try It!

How could Dante change his statistical question so that there would be more than two possible answers?
Answer:

KEY CONCEPT
To recognize and write statistical questions, determine whether the question has only one answer or several different answers. Statistical questions have a variety of different answers.
How many nickels are in a dollar? Not statistical
Which former U.S. president appears on a nickel? Not statistical
How many nickels do students carry in their backpacks? Statistical

Do You Understand?
Question 1.
Essential Question How are statistical questions different from other questions?

Answer:
Statistical questions are different from other questions.

Explanation:
In the above-given question,
given that,
statistical questions have a variety of different answers.
statistical questions example:
how many nickels do students carry in their backpacks?
non-statistical questions example:
How many nickels are in a dollar? Not statistical.

Question 2.
Generalize How does examining the answers to a question help you determine if the question is a statistical question?

Answer:
The number of nickels does students carry in their backpacks.

Explanation:
In the above-given question,
given that,
the number of nickels do students carry in their backpacks.
statistical questions example:
how many nickels do students carry in their backpacks?

Question 3.
Write a question about movies that your classmates saw last month. Is the question you wrote a statistical question? Justify your response.

Answer:
The movie that your classmates saw last month is vakelsaab.

Explanation:
In the above-given question,
given that,
the movie that your classmates saw last month is vakelsaab.
the question is a statistical question.

Question 4.
Choose which is a statistical question: What are the ages of the students in this class? or How many pennies equal 1 dollar? Explain.

Answer:
The ages of the students in this class = 12, 13, and 14.

Explanation:
In the above-given question,
given that,
the statistical questions are:
the ages of the students in this class.
the ages of the students in this class = 12, 13, and 14.

Do You Know How?
Question 5.
Determine which of the questions below are statistical questions.
a. In which months are the birthdays of everyone in your class?

Answer:
The birthday of everyone in your class is march, September, and August.

Explanation:
In the above-given question,
given that,
the birthdays of everyone in my class are:
one of a friend is in march.
one of my friends is in September.
my birthday is in august.

b. Does Sue wear glasses?

Answer:
Yes, sue wears glasses.

Explanation:
In the above-given question,
given that,
sue wears glasses.
sue buys 3 pairs of glasses.
so he will wear glasses.

c. Who is the current president of the United States?

Answer:
The current president of the united states is Joe Biden.

Explanation:
In the above-given question,
given that,
the current president of the united states is Joe Biden.

d. How tall are the students in Grade 6?

Answer:
The students in Grade 6 are 4 feet high.

Explanation:
In the above-given question,
given that,
the students in Grade 6 are 4 feet high.
some of the students in Grade 6 are also 3.8 feet high.
so the students in Grade 6 are 4 feet high.

e. What is the least populated state?

Answer:
The least populated state is

Explanation:
In the above-given question,
given that,
the least populated state is
the population in the state is

f. How many fish are in the pond?

Answer:
The number of fish is in the pond is 9.

Explanation:
In the above-given question,
given that,
in the pond, there are many numbers of fishes and also frogs.
the number of fish is in the pond is 9.
the number of frogs in the pond is 6.

Question 6.
Mr. Borden asked his students, How far from school do you live? Is his question a statistical question? Explain.

Answer:
Yes, it is a statistical question.

Explanation:
In the above-given question,
given that,
the far from school do i live is 3 km.
so it is a statistical question.

Question 7.
Mr. Borden also asked his students, How do you get to school each day? Is this question statistical? Explain.

Answer:
No, this is not a statistical question.

Explanation:
In the above-given question,
given that,
I will go to school each day by cycle.
I will go to school by either cycle or bike.
so it is not a statistical question.

Practice & Problem Solving

In 8 and 9, write a statistical question that you could ask to gather data on each topic.
Question 8.
Number of pets classmates own

Answer:
The number of pets classmates own is 4.

Explanation:
In the above-given question,
given that,
the number of pets classmates own.
the number of dogs is 4.
so the number of pets classmates own is 4.

Question 9.
Heights of different household plants

Answer:
The height of the plants is 2, 1, and 1/2 in.

Explanation:
In the above-given question,
given that,
there are 5 varieties of household plants.
the height of 2 plants is 2 in.
the height of the other 2 plants is 1 in.
the height of 1 plant is 1/2 inch.

Question 10.
Kim asked her classmates, How many siblings do you have? She collected the following responses: 0, 1, 2, 1, 2, 0, 3, 1, 0, 5, 5, 1, 3, 1, 0, 2, 4, 1, 3, 0. Make a dot plot to display the data.

Answer:
The number of siblings does Kim have = 6.

Explanation:
In the above-given question,
given that,
Kim asked her classmates.
she collected the responses 0,1, 2, 1, 2, 0, 3, 1, 0, 5, 5, 1, 3, 1, 0, 2, 4, 1, 3, 0.
the number of plots on 0 is 5.
the number of plots on 1 is 6.
the number of plots on 2 is 3.
the number of plots on 3 is 3.
the number of plots on 4 is 1.
the number of plots on 5 is 5.
so the number of siblings does Kim have = 6.

Question 11.
Sergei asked his classmates, Will you take Spanish or French next year? He collected these responses: 15 classmates chose Spanish and 13 chose French. Make a frequency table to display the data.

Answer:
The number of classmates who choose both languages is 28.

Explanation:
In the above-given question,
given that,
Sergei asked his classmates.
15 classmates chose Spanish and 13 chose French.
so the number of classmates who choose both languages is 28.

Question 12.
Is the following a statistical question? Explain. How many plays do students see in a year?

Answer:
The number of plays does students see in a year is 3.

Explanation:
In the above-given question,
given that,
the number of plays does students see in a year is 3.
the total number of students in a year is 6.
so the number of plays do students see in a year is 3.

Question 13.
Is the following a statistical question? Explain. How do shoppers in a town pay for groceries?

Answer:

In 14 and 15, use the dot plot at the right.
Question 14.
Make Sense and Persevere What statistical question could have been asked to collect the data shown in the dot plot?

Answer:
The time spent on 60 minutes is 2.

Explanation:
In the above-given question,
given that,
the time spent on Homework is given.
the time spent on 0 minutes is 1.
the time spent on 10 minutes is 2.
the time spent on 20 minutes is 3.
the time spent on 30 minutes is 5.
the time spent on 40 minutes is 4.
the time spent on 50 minutes is 3.
the time spent on 60 minutes is 2.

Question 15.
Higher Order Thinking If the data in the dot plot show how many minutes students spent on homework the previous night, how many hours in all did these students spend doing homework? Did a typical student from this group spend more or fewer than 20 minutes on homework?

Answer:

Explanation:
In the above-given question,
given that,

Question 16.
Vocabulary Wyatt says that a statistical question must have a numerical answer. Do you agree with Wyatt? Explain.
Answer:

Question 17.
Reasoning Ms. Miller asks parents, Do you support switching to a new lunch vendor for our school program? How many different responses could she get? Is this a statistical question?
Answer:

Assessment Practice

Question 18.
Ms. Williams asked each student in her class these two questions:

• How many digits are in a phone number, including the area code?
• In a typical week, on how many days do you spend some time watching television?

Which of the questions that Ms. Williams asked is a statistical question? Explain.

Answer:
How many digits are in a phone number, including the area code?

Explanation:
In the above-given question,
given that,
Ms. Williams asked is a statistical question?
there are 12 digits are in a phone number, including the area code.
so How many digits are in a phone number, including the area code.

Question 19.
Select all of the statistical questions.
☐ What is your favorite color?
☐ Does Carmen wear braces?
☐ How many books did you read last week?
☐ Which U.S. state has the largest land area?
☐ Should the basketball team purchase new uniforms?

Answer:
Options A and D are correct.

Explanation:
In the above-given question,
given that,
the questions satisfy the statistical questions.
what is your favorite color?
How many books did you read last week?
which U.S state has the largest land area.
so options A and D are correct.

Lesson 8.2 Summarize Data Using Mean, Median, Mode, and Range

Solve & Discuss It!
Eight students were surveyed about the number of hours they spend each week reading for fun. Order their responses from least to greatest values. What do you notice about the number of hours these students spent reading each week?

I can… identify the mean, median, mode, and range of a data set.

Look for Relationships
How does ordering the responses from least to greatest help you analyze the data set?

Focus on math practices
Critique Reasoning Jamal says that the middle value in a data set is the number that occurs most often. Evan disagrees. Why does Jamal say what he says and why does Evan disagree? Explain.

Essential Question
How can you use a single measure to describe a data set?

Try It!

The next week, Maria bowls a 151-point game. The other bowlers match their scores. What is the new mean final score for the team? Explain.
Answer:

Convince Me! How did the mean final score change from the Example to the Try It!?

Try It!

Nadia’s grades on four quizzes were 95, 75, 85, and 95. Find the mean, median, and mode for Nadia’s grades.

Answer:
Mean = 87.5.
median = 90.
mode = 95.

Explanation:
In the above-given question,
given that,
Nadia’s grades on four quizzes were 95, 75, 85, and 95.
the mean is sum/n.
mean = 87.5.
median = 75, 85, 95, 95.
median = 180/2.
median = 90.
mode = the number that appears the most.
mode = 95.

Try It!

Find the mean, median, mode, and range for the following set of data.
4, 6, 8, 3, 2, 1, 0, 12, 9

Answer:
Mean = 5, median = 2, mode = no, and range = 12.

Explanation:
In the above-given question,
given that,
the data is 4, 6, 8, 3, 2, 1, 0, 12, 9.
mean = sum/n.
mean = 4 + 6 + 8 + 3 + 2 + 1 + 0 + 12 + 9/9.
mean = 45/9.
mean = 5.
median = 2.
mode = no.
range = 12 – 0.
range = 12.

KEY CONCEPT
You can summarize a set of data using a measure of center, such as the mean, median, or mode, or a measure of variability, such as the range.

The average number of hours of TV watched each week is 12.5 hours. The range of hours watched is 14 hours.

Do You Understand?
Question 1.
Essential Question How can you use a single measure to describe a data set?
Answer:

Question 2.
Maddie scored 3 goals, 2 goals, and 4 goals during her last three soccer games. How can you find the mean, or average, number of goals Maddie scored?

Answer:
Mean = 3.

Explanation:
In the above-given question,
given that,
Maddie scored 3 goals, 2 goals, and 4 goals during her last three soccer games.
mean = 3 + 2 + 4/3.
mean = 9/3.
mean = 3.

Question 3.
Use Structure Why is it important to order the data when finding the median?

Answer:
median is the number that is the middle of the middle value.

Explanation:
In the above-given question,
given that,
median is the number that is the middle of the middle value.
for example:
11, 7, 11, 18, 9, 7, 6, 23, 7.
6, 7, 7, 7, 9, 11, 11, 18, 23.
median = 9.

Do You Know How?
The table shows data about the students in three classes.

Question 4.
What is the mean number of boys in the three classes? What is the mean number of girls in the three classes?

Answer:
The mean number of girls in the three classes = 14.

Explanation:
In the above-given question,
given that,
the girls in the class are 14, 12, and 16.
mean = 14 + 12 + 16/3.
mean = 42/3.
mean = 14.
so the mean number of girls in the three classes = 14.

Question 5.
What is the mode of the number of girls in the three classes?

Answer:
The mode of the number of girls in three classes = no.

Explanation:
In the above-given question,
given that,
the girls in the class are 14, 12, and 16.
mode = no.
no number is repeating.
so the mode of the number of girls in three classes = 0.

Question 6.
What is the median number of students in the three classes?

Answer:
The median number of students in the three classes = 13.

Explanation:
In the above-given question,
given that,
the students in the class are 12, 15, 12, 14, 12, and 16.
median = 12, 12, 12, 14, 15, 16.
median = 26/2.
median = 13.
so the median number of students in the three classes = 13.

Practice & Problem Solving

In 7-10, use the data shown in the table to find each mean.

Question 7.
Technical marks from judges

Answer:
Technical marks from judges = 5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.

Explanation:
In the above-given question,
given that,
the technical marks of A, B, C, D, E, F, G.
5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.
so the technical marks from judges = 5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.

Question 8.
Presentation marks from judges

Answer:
presentation marks from judges = 5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.

Explanation:
In the above-given question,
given that,
the presentation marks of A, B, C, D, E, F, G.
5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.
so the presentation marks from judges = 5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.

Question 9.
Find the combined marks, or total score, awarded by each of the 7 judges. Record your answers in the table.

Answer:
The total score awarded by each of the 7 judges = 79.1.

Explanation:
In the above-given question,
given that,
the technical marks of A, B, C, D, E, F, G.
5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.
the presentation marks of A, B, C, D, E, F, G.
5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.
total score = 11.3, 11.5, 11.1, 11.2 , 11.4, 10.9, 11.7.
total score = 79.1.

Question 10.
What is the mean total score awarded by the judges?

Answer:
The mean total score awarded by the judges = 11.3.

Explanation:
In the above-given question,
given that,

the technical marks of A, B, C, D, E, F, G.
5.9, 5.8, 5.8, 5.6, 5.9, 5.6, 6.0.
the presentation marks of A, B, C, D, E, F, G.
5.4, 5.7, 5.3, 5.6, 5.5, 5.3, 5.7.
total score = 11.3, 11.5, 11.1, 11.2 , 11.4, 10.9, 11.7.
mean = 79.1/7.
mean = 11.3.
so the mean total score awarded by the judges = 11.3.

In 11-14, use the data in the table.

States Traveled to or Lived In
Question 11.
Order the data from least to greatest.

Answer:
The order from least to greatest = 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.

Explanation:
In the above-given question,
given that,
the states traveled to or lived in.
1, 3, 5, 2, 5, 2, 10, 7, 1, 2, 4, 1, 2, 7, 12.
the order from least to greatest is:
1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.
so the order from least to greatest = 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.

Question 12.
What are the median, mode, and range of the data?

Answer:
The median, mode, and range = 4.2, 2, 11.

Explanation:
In the above-given question,
given that,
1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 7, 7, 10, 12.
mean = 64/15.
mean = 4.2.
mode = 2.
range = 12 – 1.
range = 11.

Question 13.
Use Structure The student who traveled to 3 states visited 3 new states during a vacation. Does increasing the 3 to 6 change the median? If so, how?

Answer:
median = 6.

Explanation:
In the above-given question,
given that,
The student who traveled to 3 states visited 3 new states during a vacation.
3 + 3 = 6.
6 – 3 = 3.
median = 6.

Question 14.
Look for Relationships Does increasing the 3 to 6 change the mode? If so, how?
Answer:

In 15-17, use the data table.

Question 15.
What is the average low temperature forecasted for the five days?

Answer:
The average low temperature forecasted for the five days = 40.75.

Explanation:
In the above-given question,
given that,
the average temperature on Monday is 42.
Tuesday is 44.
Wednesday is 45.
Thursday 34.
Friday is 40.
44 + 45 + 34 + 40 = 163/4.
average low temperature = 40.75.

Question 16.
What is the average high temperature forecasted for the five days?

Answer:
The average high temperature forecasted for the five days = 53.4.

Explanation:
In the above-given question,
given that,
the average high temperature on Monday is 55.
Tuesday is 57.
Wednesday is 60.
Thursday 45.
Friday is 50.
the average high temperature = 55 + 57 + 60 + 45 + 50.
average = 267/5.
average = 53.4.

Question 17.
The forecast for Wednesday is later changed to a high of 70°F. Without calculating the new mean, describe how this changes the mean high temperature for the 5 days.

Answer:
The high temperature for the 5 days = 14.

Explanation:
In the above-given question,
given that,
The forecast for Wednesday is later changed to a high of 70°F.
the mean high temperature for the 5 days.
mean = 70/5.
mean = 14.

Question 18.
Vocabulary What term is used to describe the difference between the greatest and the least values of a data set?

Answer:
The term is used to describe the difference between the greatest and the least values of a data set are range.

Explanation:
In the above-given question,
given that,
the term is used to describe the difference between the greatest and the least values of a data set are range.
for example:
11, 7, 11, 18, 9, 7, 6, 23, 7.
large = 23 and small = 6.
range = 23 – 6.
range = 17.

Question 19.
Critique Reasoning Lewis thinks that since the data 5, 0, 4, 0, 0 has a mode of 0, the data has no mode. Critique Lewis’s reasoning.

Answer:
Data has no mode.

Explanation:
In the above-given question,
given that,
the data is 5, 0, 4, 0, and 0.
mode = 0.
so the data has no mode.

Question 20.
Chester scored 84, 88, and 80 on his first 3 math tests. How can you find Chester’s mean, or average, score on these tests?

Answer:
The mean = 84.

Explanation:
In the above-given question,
given that,
Chester scored 84, 88, and 80 on his first 3 math tests.
mean = 84 + 88 + 80/3.
mean = 84.

Question 21.
Reasoning Use the information in Exercise 20. Suppose Chester scores a 90 on his next test. Without doing any calculations, will Chester’s mean score increase, decrease, or stay the same? Explain.

Answer:
Mean = 85.5.

Explanation:
In the above-given question,
given that,
Suppose Chester scores a 90 on his next test.
mean = 84 + 88 + 80 + 90/4.
mean = 342/4.
mean = 85.5.

Question 22.
On Monday, Jeremiah collects data on the number of cars that pass through an intersection each hour from 6 A.M. to 10 A.m. He records the following data: 15, 27, 37, 29, and 12. If Jeremiah removes the 12 from his data set, will the mean change? Explain.

Answer:
Yes, the mean change.

Explanation:
In the above-given question,
given that,
On Monday, Jeremiah collects data on the number of cars that pass through an intersection each hour from 6 A.M. to 10 A.m.
He records the following data: 15, 27, 37, 29, and 12.
15 + 27 + 37 + 29.
mean = 15 + 27 + 37 + 29/4.
mean = 86.25.
so the mean will change.

Question 23.
On Tuesday, Jeremiah finds the mean number of cars that pass through the same intersection from 6 A.m. to 10 A.M. was 22. Using the data from Exercise 22, how many fewer cars passed through the intersection on Tuesday?

Answer:
The fewer cars passed through the intersection on Tuesday = 30.

Explanation:
In the above-given question,
given that,
On Tuesday, Jeremiah finds the mean number of cars that pass through the same intersection from 6 A.m. to 10 A.M.
He records the following data: 15, 27, 37, 29, and 12.
15 + 27 + 37 + 29 + 12.
mean = 15 + 27 + 37 + 29 + 12/4.
mean = 30.

In 24-26, use the data table.

Question 24.
What are the median, mode, and range of these data?

Answer:
The mean, mode, and range = 18.25, 0, and 52.

Explanation:
In the above-given question,
given that,
Known numbers of the moons of the planets are given.
mercury – 0.
venus – 0.
Earth – 1.
Mars – 2.
Jupiter – 50.
Saturn = 53.
Uranus = 27.
Neptune = 13.
mean = 146/8.
mean = 18.25.
mode = 0.
range = 53 – 1.
range = 52.

Question 25.
What is the mean number of moons for the 8 planets, rounded to the nearest whole number?

Answer:
The mean number of moons for the 8 planets = 18.25.

Explanation:
In the above-given question,
given that,
Known numbers of the moons of the planets are given.
mercury – 0.
venus – 0.
Earth – 1.
Mars – 2.
Jupiter – 50.
Saturn = 53.
Uranus = 27.
Neptune = 13.
mean = 146/8.
mean = 18.25.

Question 26.
If you include Pluto’s moons in the data, the median is 5.
a. How many moons does Pluto have? Explain.

Answer:
The number of moons does pluto have = 0.

Explanation:
In the above-given question,
given that,
pluto is a dwarf planet.
there is no planets for pluto.
so the number of moons does pluto have = 0.

b. Would including Pluto affect the range of the data? Explain.
Answer:

Question 27.
Higher Order Thinking is the median always, sometimes, or never one of the data values? Explain.
Answer:

Question 28.
Critique Reasoning Maria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4. Is she correct? Explain why or why not.

Answer:
Yes, mean is 5.

Explanation:
In the above-given question,
given that,
Maria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4.
mean = 7 + 8 + 3 + 2 /4.
mean = 20/4.
mean = 5.

Assessment Practice

Question 29.
The cost of 8 different sets of golf clubs is shown in the data table. A new brand of golf clubs for $533 is now being sold at the shop. Which of the following statements about the data is true?

A. The mean cost will decrease.
B. The range of the costs will increase.
C. The mean cost will stay the same.
D. The range of the costs will stay the same.

Answer:
Option A, B, and D are correct.

Explanation:
In the above-given that,
given that,
The cost of 8 different sets of golf clubs is shown in the data table.
A new brand of golf clubs for $533 is now being sold at the shop.
so options A, B, and D are correct.

Lesson 8.3 Display Data in Box Plots

Solve & Discuss It!
To track how many raisins are needed for packaging, a quality control inspector at a food processing plant collected data for the number of raisins in small boxes. Describe the data, including minimum value, maximum value, and median. Then describe what you notice about the values between the minimum and the median, and between the median and maximum.

I can… make and interpret box plots.

Reasoning
How can ordering the numbers of raisins in small boxes from least to greatest help you find the median?

Focus on math practices
Construct Arguments The median of the first half of the data is 26.5, and the median of the second half of the data is 30.5. Why would this information be helpful and what do those medians show? Explain.

Essential Question
Why is a box plot useful for representing certain types of data?

Try It!

The lengths in inches of 11 fish that Helen caught last year are listed below.
7, 8, 12, 12, 12, 13, 14, 15, 16, 17, 22
Circle the first quartile, median, and third quartile.

Answer:
The length in inches of 11 fish that Helen caught last year is 13.4.

Explanation:
In the above-given question,
given that,
The length in inches of 11 fish that Helen caught last year is
mean = 7 + 8 + 12 + 12 + 12 + 13 + 14 + 15 + 16 + 17 + 22.
mean = 148/11.
mean = 13.4.
so the length in inches of 11 fish that Helen caught last year is 13.4.

Convince Me! How is the distribution of Helen’s data this year different from Helen’s data last year? Draw a box +HHH H HHHHHHHH plot of last year’s data and use it to support your answer.

Try It!

The ages of 12 volunteers participating in a beach clean-up are shown:
15, 27, 9, 15, 21, 9, 21, 9, 15, 21, 21, 24
Record the ages in a box plot.

Answer:
Mean = 17.25.

Explanation:
In the above-given question,
given that,
The ages of 12 volunteers participating in a beach clean-up are shown.
15, 27, 9, 15, 21, 9, 21, 9, 15, 21, 21, 24.
mean = 207/ 12.
mean = 17.25.

KEY CONCEPT
A box plot shows a distribution of data values on a number line. A box plot visually represents a data set divided into four equal parts.

Do You Understand?
Question 1.
Essential Question Why is a box plot useful for representing certain types of data?

Answer:
A box plot shows a distribution of data values on a number line.
A box plot visually represents a data set divided into four equal parts.

Explanation:
In the above-given question,
given that,
A box plot shows a distribution of data values on a number line.
A box plot visually represents a data set divided into four equal parts.
quartiles divide data into quarters or equal group.
median is also the second quartile.
quartile is divided into 3 parts.

Question 2.
What values are included inside the box of a box plot?

Answer:
A box plot shows a distribution of data values on a number line.
A box plot visually represents a data set divided into four equal parts.

Explanation:
In the above-given question,
given that,
A box plot shows a distribution of data values on a number line.
A box plot visually represents a data set divided into four equal parts.
quartiles divide data into quarters or equal group.
median is also the second quartile.

Question 3.
Critique Reasoning A box plot shows the distribution of the costs of used books. The box of the box plot starts at $2 and ends at $5. Alex says this means that about one-quarter of the books cost between $2 and $5. Is Alex correct? Explain.

Answer:
Yes, Alex is correct.

Explanation:
In the above-given question,
given that,
A box plot shows the distribution of the costs of used books.
The box of the box plot starts at $2 and ends at $5.
Alex says this means that about one-quarter of the books cost between $2 and $5.
$2 is on the first quartile.
$5 is on the third quartile.
so Alex is correct.

Do You Know How?
Sarah’s scores on tests were 79, 75, 82, 90, 73, 82, 78, 85, and 78. In 4-8, use the data.
Question 4.
What are the minimum and maximum test scores?

Answer:
The minimum and maximum test scores are 73 and 90.

Explanation:
In the above-given question,
given that,
Sarah’s scores on tests were 79, 75, 82, 90, 73, 82, 78, 85, and 78.
the minimum test score is 73.
the maximum test score is 90.
so the minimum and maximum test scores are 73 and 90.

Question 5.
Find the median.

Answer:
Median = 78.

Explanation:
In the above-given question,
given that,
the median is the number which is in the middle or the middle value.
Sarah’s scores on tests were 79, 75, 82, 90, 73, 82, 78, 85, and 78.
median = 78.

Question 6.
Find the first and the third quartiles.

Answer:
The first quartile is $2 and the third quartile is $5.

Explanation:
In the above-given question,
given that,
A box plot shows the distribution of the costs of used books.
The box of the box plot starts at $2 and ends at $5.
Alex says this means that about one-quarter of the books cost between $2 and $5.
$2 is on the first quartile.
$5 is on the third quartile.

Question 7.
Draw a box plot that shows the distribution of Sarah’s test scores.
Answer:

Question 8.
Eric is in Sarah’s class. This box plot shows his scores on the same nine tests. How do Eric’s scores compare to Sarah’s?

Answer:
Eric’s tests is 85.

Explanation:
In the above-given question,
given that,
Eric is in Sarah’s class.
This box plot shows his scores on the same nine tests.
85/9 = 9.4.
Eric’s tests is 85.

Practice & Problem Solving

Multimedia Leveled Practice in 9 and 10, use this data set, which shows how many minutes Enzo practiced violin each day for 10 days.
40, 25, 45, 55, 30, 25, 30, 50, 30, 40
Question 9.
Find the statistical measures that you need to make a box plot of Enzo’s practice times.

Answer:
Median = 30.

Explanation:
In the above-given question,
given that,
which shows how many minutes Enzo practiced violin each day for 10 days.
40, 25, 45, 55, 30, 25, 30, 50, 30, 40.
minimum is 25.
first quartile = 30.
Median = 30.
third quartile = 45.
maximum = 55.

Question 10.
Complete the box plot to represent Enzo’s practice times.

Answer:
The missing values are 30, 30, 30, 40, 55.

Explanation:
In the above-given question,
given that,
40, 25, 45, 55, 30, 25, 30, 50, 30, 40.
minimum is 25.
first quartile = 30.
Median = 30.
third quartile = 45.
maximum = 55.

In 11 and 12, use this data set, which shows the prices, in dollars, of tickets to 10 plays at the community theater.
14, 22, 8, 14, 16, 8, 20, 14, 10, 18
Question 11.
Find the minimum, maximum, median, and quartile ticket prices.

Answer:
Minimum = 14.
Median = 14.
Maximum = 18.
First quartile = 10.
Third quartile = 18.

Explanation:
In the above-given question,
given that,
the data is 14, 22, 8, 14, 16, 8, 20, 14, 10, 18.
the order is 8, 8, 10, 14, 14, 14, 16, 18, 20, 22.
minimum = 14.
maximum = 18.
median = 14.
first quartile = 10.
third quartile = 18.

Question 12.
Make a box plot to display the ticket prices.
Answer:

In 13 and 14, draw box plots using the data provided.
Question 13.
The sprint times, in seconds, of students who tried out for the track team:
44, 40, 40, 42, 49, 43, 41, 47, 54, 48, 42, 52, 48

Answer:
Minimum = 40.
Median = 43.5.
Maximum = 54.
First quartile = 42.
Third quartile = 52.

Explanation:
In the above-given question,
given that,
the sprint times in seconds, of students who tried out for the track team:
44, 40, 40, 42, 49, 43, 41, 47, 54, 48, 42, 52, 48.
the order is 40, 40, 41, 42, 42, 43, 44, 47, 48, 49, 52, 54.
minimum = 40.
maximum = 54.
median = 43.5.
first quartile = 41.
third quartile = 52.

Question 14.
Scores earned on science tests:
73, 78, 66, 61, 85, 90, 99, 76, 64, 70, 72, 72, 93, 81

Answer:
Minimum = 40.
Median = 43.5.
Maximum = 54.
First quartile = 42.
Third quartile = 52.

Explanation:
In the above-given question,
given that,
the scores earned on science tests:
73, 78, 66, 61, 85, 90, 99, 76, 64, 70, 72, 72, 93, 81.
the order is 70, 72, 72, 73, 76, 78, 81, 85, 90, 93, 99.
minimum = 70.
maximum = 99.
median = 78.
first quartile = 72.
third quartile = 93.

In 15 and 16, use the box plot to answer the question.
Question 15.
How many words per minute does the fastest keyboarder type?

Answer:
The words per minute do the fastest keyboarder type = 75.

Explanation:
In the above-given question,
given that,
the keyboarding speeds and words per minute.
the data is 20, 30, 40, 50, 60, 70, 80, 90, 100, 110.
1 minute = 60 seconds.
the box plot is on 75.
so the words per minute do the fastest keyboarder type = 75.

Question 16.
How many words per minute do the fastest 50% of keyboarders type?

Answer:
The number of words per minute does the fastest 50% of keyboarders type = 70.

Explanation:
In the above-given question,
given that,
the keyboarding speeds and words per minute.
the data is 20, 30, 40, 50, 60, 70, 80, 90, 100, 110.
1 minute = 60 seconds.
the box plot is on 70.
so the number of words per minute does the fastest 50% of keyboarders type = 70.

Question 17.
Reasoning the price per share of Electric Company’s stock during 9 days, rounded to the nearest dollar, was as follows: $16, $17, $16, $16, $18, $18, $21, $22, $19.
Use a box plot to determine how much greater the third quartile’s price per share was than the first quartile’s price per share.

Answer:
third quartile’s price is 5 times greater than the first quartile’s price.

Explanation:
In the above-given question,
given that,
the price per share of Electric Company’s stock during 9 days, rounded to the nearest dollar, was as follows: $16, $17, $16, $16, $18, $18, $21, $22, $19.
the order is $16, $16, $16, $17, $18, $18, $19, $21, $22.
the first quartile = $16.
third quartile = $21.
$21 – $16 = $5.
so the third quartile’s price is 5 times greater than the first quartile’s price.

Question 18.
Make Sense and Persevere The temperature forecast for Topeka, Kansas, for the next 8 days is shown. Use a box plot to determine the range for the lower half of the temperatures.

Answer:
The range for the lower half of the temperatures = 7 degrees.

Explanation:
In the above-given question,
given that,
The temperature forecast for Topeka, Kansas, for the next 8 days is shown.
29 and 32 degrees on Sunday.
31 degrees on monday.
24 degrees on Tuesday.
26 degrees on Wednesday.
29 degrees on Thursday.
35 degrees on Friday.
27 degrees on Saturday.
range = 31 – 24.
range = 7.

Question 19.
Model with Math Coach Henderson clocked the speeds in miles per hour of pitches thrown during the first inning of a middle school baseball game, as shown at the right.

Draw a box plot to display the data and write two conclusions about the data shown in the box plot.

Answer:
Minimum = 45.3.
Maximum = 61.1.

Explanation:
In the above-given question,
given that,
speeds of pitches thrown in miles per hour.
45.3, 47, 48.1, 51.3, 55.8, 61.1, 48.5, 60.7, 49.
the order is 45.3, 47, 48.1, 48.5, 49, 51.3, 55.8, 60.7, 61.1.
minimum = 45.3.
maximum = 61.1.

Question 20.
Critique Reasoning Tanya recorded the ages of 10 local babysitters: 20, 16, 18, 13, 14, 13, 12, 16, 22, 18. She says that the box plot below shows the distribution of ages. What error did she make?

Answer:
The error is 13.

Explanation:
In the above-given question,
given that,
Tanya recorded the ages of 10 local babysitters: 20, 16, 18, 13, 14, 13, 12, 16, 22, 18.
the order is 12, 13, 13, 14, 16, 16, 18, 20, 22.
she says that the box plot shows the distribution of ages.
the age in years = 10, 12, 14, 16, 18, 20, 22, 24.
there is no 13 in the data.
so the erroe is 13.

Question 21.
Higher Order Thinking Alana made this box plot to represent classroom attendance last month. Without seeing the values, what conclusions can you make about whether attendance was mostly high or low last month? Explain.

Answer:
The attendance was mostly high.

Explanation:
In the above-given question,
given that,
Alana made this box plot to represent classroom attendance last month.
the attendance was mostly high last month.
because the line plot and box are shown in last.
so the attendance was mostly high.

Assessment Practice

Question 22.
Use the data given to complete the box plot.
The ages in years of the students in Caryn’s gymnastics class are shown in the table.

Complete the box plot to show the distribution of the students’ ages.

Answer:
minimum = 6.
maximum = 18.
median = 11.
first quartile = 9.
third quartile = 12.

Explanation:
In the above-given question,
given that,
ages of students in years are given.
the data is 12, 11, 9, 18, 10, 11, 7, 16, 14, 11, 6.
the order is 6, 7, 9, 10, 11, 11, 11, 12, 14, 16, 18.
minimum = 6.
maximum = 18.
median = 11.
first quartile = 9.
third quartile = 12.

Lesson 8.4 Display Data in Frequency Tables and Histograms

Explore It!
The students in a sixth-grade class recorded the number of letters in their first and last names combined.

I can… make and analyze frequency tables and histograms.

A. How can the data be organized? Describe one way to organize the data.

Answer:
The data can be organized in two ways.

Explanation:
In the above-given question,
given that,
the data can be organized in two ways.
they are:
frequency tables and the histograms.

B. Describe another way to organize the data.

Answer:
Another way to organize the data is histograms.

Explanation:
In the above-given question,
given that,
the data can be organized in two ways.
they are:
frequency tables and the histograms

C. Compare the two ways. What do you notice about the data in each way?
Answer:

Focus on math practices
Generalize What generalization can you make about the data set?

Essential Question
How can a frequency table or histogram help you organize and analyze data?

Try It!

This histogram shows a different way to represent Mr. Maxwell’s data. Fill in the boxes with appropriate times and shade the bars for the last three intervals. How have the intervals changed?

Answer:
The missing values are 18:00, 19:00, 16:59, and 19:59.

Explanation:
In the above-given question,
given that,
This histogram shows a different way to represent Mr. Maxwell’s data.
the number of runners is 5.
the number of minutes is 14:00, 15:00, 16:00…..
so the missing values are 18:00, 19:00, 16:59, and 19:59.

Convince Me! How is the analysis of the information displayed different between the two histograms?

Try It!

How many students sent between 20 and 59 texts?

Answer:
The number of students who sent between 20 and 59 texts = 39.

Explanation:
In the above-given question,
given that,
the students are from 20 to 59.
59 – 20 = 39.
so the number of students who sent between 20 and 59 texts = 39.

Try It!

Does the histogram show the mode of the number of points Kendra scored in the games? Explain.
Answer:

KEY CONCEPT
Data displays can be used to help make sense of data.

Do You Understand?
Question 1.
Essential Question How can a frequency table or histogram help you organize and analyze data?

Answer:
We can use a frequency table to make a histogram.

Explanation:
In the above-given question,
given that,
bags of popcorn are sold each day.
the data is 62, 65, 58, 31, 64, 58, 66, 68, 56, 67, 68, 51.
we can organize the data in a frequency table.
we can also use a frequency table to make a histogram.

Question 2.
How is a histogram different from a bar graph?

Answer:
The histogram and bar graph are the same.

Explanation:
In the above-given question,
given that,
the histogram is converted by a frequency table.
the bar graph is also converted by a frequency table.
so both the histogram and bar graph are the same.

Question 3.
What types of numerical data sets are easier to display using a histogram instead of a dot plot? Explain.

Answer:

Explanation:
the numerical data sets are easier to display using a histogram instead of a dot plot in a frequency table.

Explanation:
In the above-given question,
given that,
bags of popcorn are sold each day.
the data is 62, 65, 58, 31, 64, 58, 66, 68, 56, 67, 68, 51.
we can organize the data in a frequency table.
so the numerical data sets are easier to display using a histogram instead of a dot plot in a frequency table.

Question 4.
Reasoning How are frequency tables and histograms alike and how are they different?
Answer:

Do You Know How?
Question 5.
A data set contains ages ranging from 6 to 27.
6, 11, 9, 13, 18, 15, 21, 15, 17, 24, 27, 12
Complete the frequency table and histogram.

Answer:
The missing frequency are 1, 5, 2, 2, and 1.

Explanation:
In the above-given question,
given that,
A data set contains ages ranging from 6 to 27.
6, 11, 9, 13, 18, 15, 21, 15, 17, 24, 27, 12.
6 to 10 = 1.
11 to 15 = 5.
16 to 20 = 2.
21 to 25 = 2.
26 to 30 = 1.

Practice & Problem Solving

Leveled Practice In 6-11, use the data in the chart.

Question 6.
Complete the frequency table below for the number of songs stored on phones.

Answer:
The missing frequency is 5, 7, 2, 0.

Explanation:
In the above-given question,
given that,
the number of songs on the phones.
the data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
the song range from 100 – 149 = 5.
range from 150 – 199 = 5.
range from 200 – 249 = 7.
range from 250 – 299 = 2.
range from 300 – 349 = 0.
so the missing frequency is 5, 7, 2, 0.

Question 7.
Use your frequency table to complete the histogram.

Answer:

Question 8.
How many people have between 150 and 199 songs stored on their phones?

Answer:
The number of people has between 150 and 199 is 5.

Explanation:
In the above-given question,
given that,
the number of songs on the phones.
the data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
range from 150 – 199 = 5.
so the number of people has between 150 and 199 is 5.

Question 9.
Do more than half of the phones have fewer than 149 songs stored on them?

Answer:
Yes, more than half of the phones have fewer than 149 songs stored on them.

Explanation:
In the above-given question,
given that,
the number of songs on the phones.
the data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
the song range from 100 – 149 = 5.
range from 150 – 199 = 5.
range from 200 – 249 = 7.
range from 250 – 299 = 2.
range from 300 – 349 = 0.
the number of songs stored on them = 19.
so more than half of the phones have fewer than 149 songs stored on them.

Question 10.
Is the greatest number of songs stored on phones between 200 and 249 songs?

Answer:
Yes, the greatest number of songs stored on phones is between 200 and 249 songs = 7.

Explanation:
In the above-given question,
given that,
the number of songs on the phones.
the data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
the song range from 100 – 149 = 5.
range from 150 – 199 = 5.
range from 200 – 249 = 7.
range from 250 – 299 = 2.
range from 300 – 349 = 0.
so the greatest number of songs stored on phones is between 200 and 249 songs = 7.

Question 11.
Are there more phones that have between 200 and 249 songs stored on them than have between 150 and 199 songs?

Answer:
There are more phones that have between 200 and 249 = 7.

Explanation:
In the above-given question,
given that,
the number of songs on the phones.
the data is 125, 289, 115, 203, 192, 178, 256, 248, 165, 233, 147, 209, 225, 184, 156, 201, 143, 125, 263, 210.
the song range from 100 – 149 = 5.
range from 150 – 199 = 5.
range from 200 – 249 = 7.
range from 250 – 299 = 2.
range from 300 – 349 = 0.
so there are more phones that have between 200 and 249 = 7.

In 12-14, use the data in the histogram.

Question 12.
How many students in Ms. Gioia’s class took the science test?

Answer:
The number of students in Ms. Gioia’s class who took the science test = 6.

Explanation:
In the above-given question,
given that,
the number of students is 6.
the science test scores are 71 to 75, 76 60 80, 86 to 90, 91 to 95, and 96 to 100.
so the number of students in Ms. Gioia’s class who took the science test = 6.

Question 13.
How many more students had scores that were 80 or lower than had scores that were higher than 90?

Answer:
The number of students who had scored that were 80 or lower than 90 = 8.

Explanation:
In the above-given question,
given that,
the number of students is 6.
the science test scores are 71 to 75, 76 60 80, 86 to 90, 91 to 95, and 96 to 100.
the number of students who had scored that were 80 or lower than 90 = 8.

Question 14.
Be Precise Can you tell from the histogram how many students scored 83 on the test? Explain.

Answer:
The number of students who scored 83 on the test = 0.

Explanation:
In the above-given question,
given that,
the number of students is 6.
the science test scores are 71 to 75, 76 60 80, 86 to 90, 91 to 95, and 96 to 100.
the number of students who had scored that were 80 or lower than 90 = 8.
so the number of students who scored 83 on the test = 0.

In 15-17, use the data in the chart.

Question 15.
Reasoning Todd wants to know how many people took 20 seconds or more to stop a bike safely. Would a frequency table or a histogram be the better way to show this? Explain.

Answer:

Question 16.
Higher Order Thinking When organizing the data, what interval should Todd use? Explain.
Answer:

Question 17.
Model with Math Make a frequency table and histogram for the data.

Answer:

Assessment Practice

Question 18.
Use the data given to complete the histogram. Lissa recorded the time, in minutes, it took her to complete her homework each night for one month. 5, 7, 8, 10, 10, 11, 13, 14, 15, 15, 18, 19, 20, 20, 25, 26, 29, 31, 33, 35, 38, 40, 40, 42, 48, 50, 51, 55, 58, 71

Answer:
range from 0 to 14 is 7.
range from 15 to 29 is 9.
range from 30 to 44 is 7.
range from 45 to 59 is 5.
range from 60 to 74 is 1.

Explanation:
In the above-given question,
given that,
Lissa recorded the time, in minutes, it took her to complete her homework each night for one month.
5, 7, 8, 10, 10, 11, 13, 14, 15, 15, 18, 19, 20, 20, 25, 26, 29, 31, 33, 35, 38, 40, 40, 42, 48, 50, 51, 55, 58, 71.
the number of nights is 10, 20, 30, 40, 50, and 60.
range from 0 to 14 is 7.
range from 15 to 29 is 9.
range from 30 to 44 is 7.
range from 45 to 59 is 5.
range from 60 to 74 is 1.

Topic 8 Mid-Topic Checkpoint

Question 1.
Vocabulary Which of the following describes the mean of a data set? Lesson 8-2
A. The data value that occurs most often
B. The middle data value
C. The sum of the data values divided by the total number of data values
D. The difference of the greatest and least data values

Answer:
Option c is correct.

Explanation:
In the above-given question,
given that,
for example:
11, 7, 11, 18, 9, 7, 6, 23, 7.
the total value of the numbers divided by how many numbers there are.
99/9 = 11.
so option c is correct.

Question 2.
A P.E. teacher recorded how many sit-ups the students in her class did in one minute. Select all the statements that describe the data. Lesson 8-4

☐ Every student did at least 10 sit-ups in one minute.
☐ Two students did 50 or more sit-ups in one minute.
☐ Eight more students did 30 to 39 sit-ups than did 10 to 19 sit-ups.
☐ More than half of the students did 40 or more sit-ups in one minute.
☐ There are 30 students in the class.

Answer:
Options A and D are correct.

Explanation:
In the above-given question,
given that,
A P.E. teacher recorded how many sit-ups the students in her class did in one minute.
situps per minute are given per minute.
every student did at least 10 sit-ups in one minute.
more than half of the students did 40 or more sit-ups in one minute.
so options A and D are correct.

In 3 and 4, determine whether each question is statistical or not statistical. Explain.
Question 3.
How many pages did Liz read yesterday? Lesson 8-1

Answer:
The number of pages did Liz read yesterday is 3.

Explanation:
In the above-given question,
given that,
the question is statistical.
the number of pages did Liz read yesterday is 3.

Question 4.
How many books did each of the students in grade 6 read last year? Lesson 8-1

Answer:
The number of books did each of the students in grade 6 read last year = 6.

Explanation:
In the above-given question,
given that,
in grade 6 there are 3 students.
each student read 2 books.
3 x 2 = 6.
so the number of books did each of the students in grade 6 read last year = 6.

In 5 and 6, use the table of cousins’ ages at a family reunion.

Question 5.
Make a box plot of the ages. Lesson 8-3

Answer:
minimum = 9.
maximum = 21.

Explanation:
In the above-given question,
given that,
the cousins’ ages in years.
the data is 10, 9, 10, 14, 21, 11, 16, 10, 16.
order is 9, 10, 10, 10, 11, 14, 16, 16, 21.
minimum = 9.
maximum = 21.

Question 6.
One 8-year-old cousin could not make it to the reunion. Select all the ways the measures of center of the data set change if she had attended the reunion. Lesson 8-2
☐ The median increases by 1
☐ The mode decreases by 1
☐ The mean increases by 0.5
☐ The mean decreases by 0.5
☐ The median decreases by 0.5

Answer:
The median increases by 1.

Explanation:
In the above-given question,
given that,
One 8-year-old cousin could not make it to the reunion.
the cousins’ ages in years.
the data is 10, 9, 10, 14, 21, 11, 16, 10, 16.
order is 9, 10, 10, 10, 11, 14, 16, 16, 21.
so the median increases by 1.

Topic 8 Mid-Topic Performance Task

Antonia surveys a group of students entered in a school science fair. Her results are shown.

PART A
What statistical question could Antonia have asked to gather these data? Explain why the question is a statistical question.

Answer:
minimum = 2.
maximum = 22.
first quartile = 5.
third quartile = 20.

Explanation:
In the above-given question,
given that,
Antonia surveys a group of students who entered a school science fair.
hours spent on the project is given.
the data is 8, 12, 10, 5, 2, 10, 17, 20, 14, 22.
order is 2, 5, 8, 10, 12, 14, 17, 20, 22.
minimum = 2.
maximum = 22.
first quartile = 5.
third quartile = 20.

PART B
Find the mean, median, mode, and range of Antonia’s data. Draw lines to match each measure to its value.

Answer:
mean = 55.
median = 6.
mode = 10.
range = 20.

Explanation:
In the above-given question,
given that,
Antonia surveys a group of students who entered a school science fair.
hours spent on the project is given.
the data is 8, 12, 10, 5, 2, 10, 17, 20, 14, 22.
order is 2, 5, 8, 10, 12, 14, 17, 20, 22.
mean = 110/2 = 55.
mode = 10.
median = 2 +10/2.
median = 6.
range = 22 – 2.
range = 20.

PART C
Choose reasonable intervals and then make a frequency table and a histogram to show Antonia’s data.

Answer:

Lesson 8.5 Summarize Data Using Measures of Variability

Solve & Discuss It!
Suppose you collected data from 11 people about the number of pieces of fruit they have eaten in the past week. The median number is 6 pieces of fruit. Make two possible dot plots that could be used to display the data–one in which the data vary a little and one in which the data vary a lot. Explain how you created your dot plots.

I can… use measures of variability to describe a data set.

Reasoning
How can you find values that have the same median?

Focus on math practices
Critique Reasoning Jackline says that only 3 people surveyed ate more than six pieces of fruit in the past week. Do you agree? Explain why or why not.

Essential Question
How can the variability of data be described using a single number?

Try It!

Ann’s vocabulary quiz scores are 75, 81, and 90. The mean score is 82. What is the mean absolute deviation?

Answer:
The missing Absolute deviation is 7, 1, -8.

Explanation:
In the above-given question,
given that,
Ann’s vocabulary quiz scores are 75, 81, and 90.
The mean score is 82.
absolute deviation is 82 – 75 = 7.
absolute deviation is 82 – 81 = 1.
absolute deviation is 82 – 90 = -8.

Convince Me! Can the mean absolute deviation ever have a negative value? Explain.

Try It!

The dot plot shows the distribution of Ann’s health quiz scores. How can the IQR describe her scores?

Answer:
The more number of students are 92%.

Explanation:
In the above-given question,
The dot plot shows the distribution of Ann’s health quiz scores.
Ann’s health quiz scores in percentages.
the more number of students are 92 %.
there are two students on 92%.
one student on 84, 86, 88, 90, and 94.

Try It!

Jonah’s team scored 36, 37, 38, 38, 41, 46, 47, 47, and 48 points in the last nine games. Find the IQR and range of the points Jonah’s team scored in its last nine games. Are these good measures for describing the points scored?

Answer:
Yes, these are good measures for describing the points.

Explanation:
In the above-given question,
given that,
Jonah’s team scored 36, 37, 38, 38, 41, 46, 47, 47, and 48 points in the last nine games.
the data is 36, 37, 38, 38, 41, 46, 47, 47, and 48.
range = 48 – 36.
range = 12.

KEY CONCEPT
The mean absolute deviation and the interquartile range each use a single number to describe the variability, or spread, of a data set. The mean absolute deviation (MAD) tells you how far the data are spread out from the mean. The interquartile range (IQR) tells you how far the middle of the data is spread out from the median.

Do You Understand?
Question 1.
Essential Question How can the variability of data be described using a single number?
Answer:

Question 2.
What does the IQR show that the range does not show?

Answer:
The interquartile range (IQR) tells you how far the middle of the data is spread out from the median.

Explanation:
In the above-given question,
given that,
the interquartile range (IQR) tells you how far the middle of the data is spread out from the median.
there are 10 numbers on the number line.
interquartile range is between 4 and 6.
IQR = 6 – 4.
IQR = 2.

Question 3.
Reasoning Two data sets have the same mean, 8. However, the MAD of Data Set A is 2 and the MAD of Data Set B is 4. What does this indicate about the variability of the data sets?

Answer:
This indicate the variability of the data set is less than 8.

Explanation:
In the above-given question,
given that,
Two data sets have the same mean, 8.
the MAD of Data set A is 2.
the MAD of Data set B is 4.
4 + 2 = 6.

Do You Know How?
In 4-7, use these data. Davita works at a shoe store. She measured the feet of nine customers and found that their shoe sizes were 4, 5, 5, 6, 7, 8, 8, 10, and 10.
Question 4.
Find the mean.

Answer:
Mean = 31.5.

Explanation:
In the above-given question,
given that,
Davita works at a shoe store.
the data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
mean = 63/2.
mean = 31.5.

Question 5.
Find the sum of the absolute deviations from the mean.

Answer:
The sum of the absolute deviations from the mean = 7.

Explanation:
In the above-given question,
given that,
Davita works at a shoe store.
the data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
ADM = 63/9.
63/9 = 7.
so the sum of the absolute deviations from the mean = 7.

Question 6.
Find the mean absolute deviation. Explain how you found the MAD.

Answer:
The sum of the absolute deviations from the mean = 7.

Explanation:
In the above-given question,
given that,
Davita works at a shoe store.
the data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
ADM = 63/9.
63/9 = 7.
so the sum of the absolute deviations from the mean = 7.

Question 7.
Find the range and IQR. How is each calculated?

Answer:
The range = 6.

Explanation:
In the above-given question,
given that,
Davita works at a shoe store.
the data is 4, 5, 5, 6, 7, 8, 8, 10, and 10.
range = 10 – 4.
range = 6.
so the range = 6.

Practice & Problem Solving

Question 8.
Leveled Practice The mean of the data set is 3. Find the absolute deviation of each of the green values.

a. The absolute deviation of 1 is _______.

Answer:
The absolute deviation of 1 is 2.

Explanation:
In the above-given question,
given that,
The mean of the data set is 3.
the absolute deviation of 1 is 2.
the numbers on the number line is 7.
the numbers are from 0 to 7.
the absolute deviation of 1 is 2.

b. The absolute deviation of 2 is _______.

Answer:
The absolute deviation of 2 is 2.

Explanation:
In the above-given question,
given that,
The mean of the data set is 3.
the absolute deviation of 2 is 2.
the numbers on the number line is 7.
the numbers are from 0 to 7.
the absolute deviation of 2 is 2.

c. The absolute deviation of 5 is _______.

Answer:
The absolute deviation of 5 is 1.

Explanation:
In the above-given question,
given that,
The mean of the data set is 3.
the absolute deviation of 5 is 1.
the numbers on the number line is 7.
the numbers are from 0 to 7.
the absolute deviation of 5 is 1.

In 9 and 10, use the data table showing the number of miles that Jill biked on 9 days.

Question 9.
Find the mean.

Answer:
Mean = 8.

Explanation:
In the above-given question,
given that,
the number of miles that Jill biked on 9 days.
miles biked are given.
the data is 5, 9, 11, 10, 8, 6, 7, 12, and 4.
mean = 72/9.
mean = 8.

Question 10.
Find the MAD of this data set. What does this tell you about the number of miles that Jill biked?

Answer:
MAD = 8.

Explanation:
In the above-given question,
given that,
the number of miles that Jill biked on 9 days.
miles biked are given.
the data is 5, 9, 11, 10, 8, 6, 7, 12, and 4.
mean = 72/9.
mean = 8.

In 11 and 12, use the data shown in the dot plot.

Question 11.
What are the mean and the MAD?

Answer:
Mean = 14.

Explanation:
In the above-given question,
given that,
Ages of park volunteers are given.
the data is 10, 11, 12, 13, 14, 15, 16, 17, 18.
mean = 126/9.
mean = 14.

Question 12.
Describe the variability of the data.

Answer:
Range = 8.

Explanation:
In the above-given question,
given that,
Ages of park volunteers are given.
the data is 10, 11, 12, 13, 14, 15, 16, 17, 18.
range = 18 – 10.
range = 8.

In 13 and 14, use the data shown in the box plot.

Question 13.
What are the range and the IQR?

Answer:
Range = 10.

Explanation:
In the above-given question,
given that,
Heights of volleyball players(in.).
the numbers on the line are:
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70.
range = maximum – minimum.
range = 70 – 60.
range = 10.

Question 14.
Describe the variability of the data.

Answer:
IQR = 3.

Explanation:
In the above-given question,
given that,
Heights of volleyball players(in.).
the numbers on the line are:
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70.
IQR = 66 – 63.
IQR = 3.

Question 15.
The data set shows prices for concert tickets in 10 different cities in Florida.

a. Find the IQR of the data set.

Answer:
IQR of the data set = 8.

Explanation:
In the above-given question,
given that,
The data set shows prices for concert tickets in 10 different cities in Florida.
the data is 45, 50, 35, 37, 29, 36, 24, 25, 27, 43.
the order is 24, 25, 27, 29, 35, 36, 37, 43, 45, and 50.
IQR = 37 – 29.
IQR = 8.

b. How do prices vary within the middle 50%?
Answer:

Question 16.
Reasoning The MAD of the data set in the table is about 6.7. Does the value 4 deviate more or less than most of the values in the table? Explain.

Answer:
Mean = 16.

Explanation:
In the above-given question,
given that,
The MAD of the data set in the table is about 6.7.
the data is 4, 28, 25, 19, 7, 13, 16, 22, 10.
order is 4, 7, 10, 13, 16, 19, 22, 25, 28.
mean = 144/9.
mean = 16.

In 17-19, use the data set shown in the table.

Question 17.
Vocabulary What is the term used to describe the range of the middle half of the data set? Find that value for this data.

Answer:
Range = 11.

Explanation:
In the above-given question,
given that,
the term used to describe the range of the middle half of the data set.
temperatures are shown.
11, 17, 20, 16, 19, 16, 15, 22.
range = 22 – 11.
range = 11.

Question 18.
Critique Reasoning Dina said that the greatest absolute deviation will be found from the highest temperature because it has to be the farthest from the mean. Is she correct? Explain.

Answer:
MAD = 17.

Explanation:
In the above-given question,
given that,
11, 17, 20, 16, 19, 16, 15, 22.
MAD = 11 + 17 + 20 +16 + 19 + 16 + 15 + 22.
MAD = 136/8.
MAD = 17.

Question 19.
Higher Order Thinking What is the MAD for the data and what does it tell you about the temperatures?
Answer:

Assessment Practice

Question 20.
Harlo recorded the tide, in feet, every hour during an 8-hour period as shown in the table.

PART A
What is the MAD for the data set?

Answer:
MAD = 21.

Explanation:
In the above-given question,
given that,
Harlo recorded the tide, in feet, every hour during an 8-hour period.
the tides in feet are 3, 7, 11, 15, 20, 31, 39, 42.
MAD = 168/8.
MAD = 21.

PART B
Select all the statements that best describe the IQR, MAD, and variability of the data set.
☐ The middle 50% of the data is spread out more than the average variation.
☐ The IQR is greater than the MAD.
☐ The middle 25% of the data is spread out more than the average variation.
☐ The IQR is less than the MAD.
☐ The MAD shows that the tides generally varied greatly from the mean.

Answer:
Options B and E are correct.

Explanation:
In the above-given question,
Harlo recorded the tide, in feet, every hour during an 8-hour period.
the tides in feet are 3, 7, 11, 15, 20, 31, 39, 42.
MAD = 168/8.
MAD = 21.
so options B and E are correct.

Lesson 8.6 Choose Appropriate Statistical Measures

Solve & Discuss It!
The prices in dollars of athletic shoes in one store are shown below. Does the mean, median, or mode best describe the typical price for shoes at this store?

I can… select and use appropriate statistical measures.

Look for Relationships
How can you use the spread and clustering of data to help decide which statistical measures to use?

Focus on math practices
Construct Arguments which measure would the store most likely use in its advertising? Explain why this measure should be used.

Essential Question
Why is one statistical measure more useful than another to describe a given situation?

Try It!

If Gary scored a 70 on his next weekly quiz, how would that affect his mean score?
Answer:

Convince Me! Gary says that he usually scores 98 on his weekly quiz. What measure of center did Gary use? Explain.

Try It!

Suppose the French teacher says that she will drop each student’s lowest quiz score. Would the MAD now be a good measure of variability for John’s quiz scores? Calculate the MAD without John’s lowest score and use it to justify your answer.
John’s lowest score is ______.
Without the lowest score, John’s mean score is _______.

Answer:
MAD = 5.

Explanation:
In the above-given question,
given that,
I am assuming the data is 1, 2, 3, 4, 5, 6, 7, 8, 9.
MAD = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9/9.
MAD = 45/9.
MAD = 5.

KEY CONCEPT
The statistical measure that is most appropriate to describe the center and variability of a data set should be chosen based on an analysis of the spread, clustering, and outliers in the data set.
The mean is a good choice to describe the center of a data together.
When the mean is used, the mean absolute deviation (MAD) is a good choice to describe the variability.

The median is a good choice to describe the center of a data set set when the data are clustered when the data contain an outlier.
When the median is used, the interquartile range (IQR) is a good choice to describe the variability.

The mode is sometimes a good choice to describe the center of a data set if the data is not numeric or does not fall in intervals.

Do You Understand?
Question 1.
Essential Question Why is one statistical measure more useful than another to describe a given situation?

Answer:
The statistical measure that is most appropriate to describe the center and variability of a data set should be chosen based on an analysis of the spread, clustering, and outliers in the data set.

Explanation:
In the above-given question,
given that,
The mean is a good choice to describe the center of a data together.
When the mean is used, the mean absolute deviation (MAD) is a good choice to describe the variability.
The median is a good choice to describe the center of a data set set when the data are clustered when the data contain an outlier.
When the median is used, the interquartile range (IQR) is a good choice to describe the variability.

Question 2.
Reasoning You cannot find a good measure of center for a data set. What is probably true of the data set?

Answer:
Yes, we cannot find a good measure of center for a data set.

Explanation:
In the above-given question,
given that,
The mean is a good choice to describe the center of a data together.
When the mean is used, the mean absolute deviation (MAD) is a good choice to describe the variability.
The median is a good choice to describe the center of a data set set when the data are clustered when the data contain an outlier.
When the median is used, the interquartile range (IQR) is a good choice to describe the variability.
so we cannot find a good measure of center for a data set.

Do You Know How?
In 3-5, use the basketball team’s scores for one season: 44, 43, 42, 40, 42, 45, 39, 38, 18.
Question 3.
Find the mean, median, and mode of the scores.

Answer:
Mean = 39.
median = 42.
mode = 42.

Explanation:
In the above-given question,
given that,
the data is 44, 43, 42, 40, 42, 45, 39, 38, 18.
mean = 44 + 43 + 42 + 40 + 42 + 45 + 39 + 38 + 18.
mean = 351/9.
mean = 39.
mode = 42.
median = 42.

Question 4.
Is the median or mean the best measure of center for these data? Explain.

Answer:
Median is the best measure of center for the data.

Explanation:
In the above-given question,
given that,
the data is 44, 43, 42, 40, 42, 45, 39, 38, 18.
mean = 44 + 43 + 42 + 40 + 42 + 45 + 39 + 38 + 18.
mean = 351/9.
mean = 39.
mode = 42.
median = 42.
so median is the best measure of center for the data.

Question 5.
Find the measure of variability that best describes the data set.
Answer:

Practice & Problem Solving

In 6-8, use the data to answer the questions. Each of five different stores sell a quart of milk for one of the following prices: $1.50, $1.55, $1.80, $1.70, $1.50.
Question 6.
What are the mean, median, and mode of the data?

Answer:
Mean = $1.61.
median = $1.80.
mode = $1.50.

Explanation:
In the above-given question,
given that,
the data is $1.50, $1.55, $1.80, $1.70, $1.50.
mean = 8.05/5.
mean = $1.61.
median = $1.80.
mode = $1.50.

Question 7.
Which measure of center best describes these data? Which measure of variability?

Answer:
Mean describes the center of the data.

Explanation:
In the above-given question,
given that,
the data is $1.50, $1.55, $1.80, $1.70, $1.50.
mean = 8.05/5.
mean = $1.61.
median = $1.80.
mode = $1.50.

Question 8.
Find the best measure of variability for these data. Describe the variability.

Answer:
The best measure of variability for these data = median.

Explanation:
In the above-given question,
given that,
the data is $1.50, $1.55, $1.80, $1.70, $1.50.
mean = 8.05/5.
mean = $1.61.
median = $1.80.
mode = $1.50.

In 9-11, use the dot plot at the right.
The dot plot shows the hourly wages of cashiers at a supermarket.

Question 9.
a. Is the median, mean, or mode the best measure of center for these data? Explain.

Answer:
mean = 10.4.
median = 11.
mode = 10.

Explanation:
In the above-given question,
given that,
the data is 9, 9.5, 10, 10, 10, 10, 10.5, 11, 11, 11, 11.5, 11.5, 12, 12, 16.
mean = 156/15.
mean = 10.4.
median = 11.
mode = 10.

b. Find that measure of center.

Answer:
The measure of center = mean.

Explanation:
In the above-given question,
given that,
the data is 9, 9.5, 10, 10, 10, 10, 10.5, 11, 11, 11, 11.5, 11.5, 12, 12, 16.
mean = 156/15.
mean = 10.4.
median = 11.
mode = 10.

Question 10.
Identify a good measure of variability for these data. Find the value.

Answer:
The good measure of variability of data is median.

Explanation:
In the above-given question,
given that,
the data is 9, 9.5, 10, 10, 10, 10, 10.5, 11, 11, 11, 11.5, 11.5, 12, 12, 16.
mean = 156/15.
mean = 10.4.
median = 11.
mode = 10.

Question 11.
Write a sentence describing the variability of the wages.
Answer:

Question 12.
Critique Reasoning Hayden looks at the dot plot. He believes that the data set contains outliers and argues that the best measure of variability is the IQR because the median is a good measure to describe a data set that contains outliers. Is Hayden correct? Explain.

Answer:
Median = 5.

Explanation:
In the above-given question,
given that,
Hayden looks at the dot plot.
the total goals at Hockey games are given.
the number of goals are:
0, 1, 2, 3, 4, 5, 6.
the number of goals on 0 are 3.
number of goals on 1 are 2.
the number of goals on 5 are 4.
the number of goals on 6 are 2.
1, 1, 2, 5, 5, 5, 5, 5, 4, 6, 6.
median = 5.

In 13-16, use the table at the right.
The table shows measures of center based on 5 data points for attendance at a national skateboarding competition.

Question 13.
Vocabulary What is the term and the value of the middle number of the data set?

Answer:
The term and the value of the middle number of the data set = 14000.

Explanation:
In the above-given question,
given that,
mean = 14000.
median = 13000.
mode = 12500.
the term and the value of the middle number of the data set = 14000.

Question 14.
Make Sense and Persevere Which value in the data set occurs at least twice? Can it occur 3 times? Explain.
Answer:

Question 15.
Reasoning Why must the other two numbers in the data set be greater than or equal to 13,000?
Answer:

Question 16.
Model with Math What must be the sum of the two remaining numbers, x and y? Write an equation to show how to find this sum.
Answer:

In 17 and 18, use the table.

Question 17.
Be Precise The coach needs to choose the top bowler for the next meet. If the coach bases her decision on the player with the best average, whom should she choose? Justify your answer using measures of center.

Answer:
The coach bases her decision on the player with the best average = 192.

Explanation:
In the above-given question,
given that,
Game scores for the Bravo bowling team.
Jessie 150, 145, 181, 235, 196, 211, 204, 221, 185.
Sam 186, 187, 192, 195, 194, 157, 162, 200.
the coach bases her decision on the player with the best average.
mean = 150 + 145 + 181 + 235 + 196 + 211 + 204 + 221 + 185.
mean = 1728/9.
mean = 192.

Question 18.
Higher Order Thinking If the coach bases her decision on the player who is most consistent, whom should she choose? Justify your answer using measures of variability.
Answer:

Assessment Practice

Question 19.
The table at the right shows the winning bowling scores during the last five bowling events. Select the statements that best describe the data.

☐ There are outliers in the data set.
☐ The mean best describes the center of the data.
☐ The MAD is 11.92 points and the IQR is 27.5 points.
☐ The MAD best describes the variability.
☐ The IQR best describes the spread.

Answer:
Option B is correct.

Explanation:
In the above-given question,
given that,
the data is 121, 159, 146, 132, 149.
mean = 707/5.
mean = 141.4.
median = 146.
range = 146.
so option B is correct.

Lesson 8.7 Summarize Data Distributions

Explain It!
George tosses two six-sided number cubes 20 times. He records his results in a dot plot.
I can… summarize numerical data sets.

A. Describe the shape of the data distribution.

Answer:
A distribution can show gaps, clusters, or outliers.

Explanation:
In the above-given question,
given that,
A distribution can show gaps, clusters, or outliers.
It may spread out more to one side.
When the data are not symmetric, use the median and interquartile range (IQR) to describe the data.

B. Critique Reasoning George says that he expects to roll a sum of 11 on his next roll. Do you agree? Justify your reasoning.

Answer:
No, I wont agree.

Explanation:
In the above-given question,
given that,
A distribution can show gaps, clusters, or outliers.
It may spread out more to one side.
When the data are not symmetric, use the median and interquartile range (IQR) to describe the data.
the next roll is 5 + 6 + 3.
so I wont agree.

Focus on math practices
Construct Arguments Suppose George tossed the number cubes 20 more times and added the data to his dot plot. Would you expect the shape of the distribution to be different? Construct an argument that supports your reasoning.

Essential Question
How can you summarize a data distribution?

Try It!

Does the shape of the distribution match what you found when you used measures of center and variability? Explain.
Answer:

Convince Me! What are some factors that might explain why some plants grew more or less than others in the science lab?

Try It!

Why does it make sense to look at the overall shape before deciding which measures to use?
Answer:

KEY CONCEPT
To describe a set of data, look at the shape and observe how the data are clustered or spread out.
A distribution can be symmetric and clustered in the center. When the data are symmetric, use the mean and mean absolute deviation (MAD) to describe the data.

A distribution can show gaps, clusters, or outliers. It may spread out more to one side. When the data are not symmetric, use the median and interquartile range (IQR) to describe the data.

Do You Understand?
Question 1.
Essential Question How can you summarize a data distribution?

Answer:
A distribution can show gaps, clusters, or outliers.

Explanation:
In the above-given question,
given that,
A distribution can show gaps, clusters, or outliers.
It may spread out more to one side.
When the data are not symmetric, use the median and interquartile range (IQR) to describe the data.

Question 2.
Reasoning This data set has an outlier.
0, 40, 50, 60, 60, 70, 80, 80
How would the median and the mean be affected if the outlier was removed?

Answer:
Mean = 63.3.
median = 70.

Explanation:
In the above-given question,
given that,
the data is 0, 40, 50, 60, 70, 80, 80.
mean = 40 + 50 + 60 + 70 + 80 + 80/6.
mean = 380/6.
mean = 63.3.
median = 60 + 80/2.
median = 70.

Do You Know How?
Question 3.
Five different students measured the length of a shadow in inches as follows: 38, 38, 37, 38, 381. Make a generalization about the data distribution of the shadow measurements.

Answer:
Mean =106.4.
median = 37.

Explanation:
In the above-given question,
given that,
Five different students measured the length of a shadow in inches as follows: 38, 38, 37, 38, 381.
mean = 532/5.
mean = 106.4.
median = 37.

Question 4.
What are the mean, the median, and the interquartile range of the data set in Exercise 3?

Answer:
Mean =106.4.
median = 37.

Explanation:
In the above-given question,
given that,
Five different students measured the length of a shadow in inches as follows: 38, 38, 37, 38, 381.
mean = 532/5.
mean = 106.4.
median = 37.

Practice & Problem Solving

In 5-8, use the data table.

Question 5.
What are the mean and the median?

Answer:
Mean =106.4.
median = 7.

Explanation:
In the above-given question,
given that,
number of home runs hit by players on My team.
player numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Home runs: 21, 9, 12, 20, 7, 11, 9, 10, 9,
mean = 108/9.
mean = 12.
median = 7.

Question 6.
Draw a box plot of the data.
Answer:

Question 7.
Describe the overall shape of the data.
Answer:

Question 8.
Make a generalization about the data distribution.
Answer:

Question 9.
Be Precise A doctor asked 15 people how many hours they spend exercising each week. The dot plot displays the data.

What do any clusters and gaps in the dot plot tell you about the exercise habits of these people?

Answer:
There are gaps between 0 – 3 and 6 – 9.

Explanation:
In the above-given question,
given that,
A doctor asked 15 people how many hours they spend exercising each week.
the number of hours are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
there are gaps in between 0 and 3.
there are also gaps in between 6 and 9.

Question 10.
Look for Relationships Describe the pattern in the dot plot. Then write about a situation that this data could represent. Explain why your situation has this pattern.

Answer:
There is one gap between 2 and 4.

Explanation:
In the above-given question,
given that,
times nedded in hours are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
there is only one gaps between 2 and 4.

In 11 and 12, use the data in the table.

Question 11.
Model with Math Make a box plot for the data. What are the median, first quartile, third quartile, and interquartile range?

Answer:
Median = $101.5.
Fiest quartile = $38,000.
third quartile = $435,000.

Explanation:
In the above-given question,
given that,
salary of the adults are:
adult 1: $35,000.
adult 2: $46,000.
adult 3: $38,000.
adult 4: $34,000.
adult 5: $52,000.
adult 6: $99,000.
adult 7: $64,000.
adult 8: $435,000.
adult 9: $22,000.
adult 10: $88,000.
median = 52 + 99.
median = 101.5.

Question 12.
Higher Order Thinking Which data value most affects your choice of a measure of center to describe the data? Explain.
Answer:

In 13-15, use the data in the dot plot.

Question 13.
Describe the shape of the data.
Answer:

Question 14.
Describe the typical quiz scores of the students. Explain your choice of measure.
Answer:

Question 15.
Describe the variability of the quiz scores.
Answer:

Assessment Practice

Question 16.
Which statement about this data distribution is NOT true?

A. The interquartile range is 4.
B. The median is the preferable measure of center.
C. The data cluster from 2 to 7.
D. The distribution is symmetrical.

Answer:
Option B is not correct.

Explanation:
In the above-given question,
given that,
number of miles students ran in a week:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
the interquartile range is 4.
the data cluster from 2 to 7.
the distribution is symmetrical.

3-ACT MATH

3-Act Mathematical Modeling: Vocal Range

ACT 1
Question 1.
After watching the video, what is the first question that comes to mind?
Answer:

Question 2.
Write the Main Question you will answer.
Answer:

Question 3.
Make a prediction to answer this Main Question.
The person who should win the competition is _________.
Answer:

Question 4.
Construct Arguments Explain how you arrived at your prediction.

Answer:

ACT 2
Question 5.
What information in this situation would be helpful to know? How would you use that information?

Answer:

Question 6.
Use Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
Answer:

Question 7.
Model with Math Represent the situation using mathematics. Use your representation to answer the Main Question.
Answer:

Question 8.
What is your answer to the Main Question? Does it differ from your initial prediction? Explain.

Answer:

АСТ 3
Question 9.
Write the answer you saw in the video.

Answer:

Question 10.
Reasoning Does your answer match the answer in the video? If not, what are some reasons that would explain the difference?
Answer:

Question 11.
Make Sense and Persevere Would you change your model now that you know the answer? Explain.

Answer:

Reflect
Question 12.
Model with Math Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
Answer:

Question 13.
Use Appropriate Tools What tools or technology did you use to answer the Main Question? What other tools did your classmates use?
Answer:

SEQUEL
Question 14.
Be Precise Design your own singing competition. Explain how you would score each performance and how you would use those scores to choose a winner. Use a different method than you did to answer the Main Question.

Answer:

Topic 8 Review

Essential Question
How can data be described by a single number? How can tables and graphs be used to represent data and answer questions?

Vocabulary Review
Write always, sometimes, or never for each statement.
Question 1.
Intervals in a frequency table go beyond the values in a data set. ________

Answer:
Sometimes,Intervals in a frequency table go beyond the values in a data set.

Explanation:
In the above-given question,
given that,
sometimes in a frequency table go beyond the values in a data set.

Question 2.
You can calculate the IQR from a box plot. __________

Answer:
Yes, we can always calculate the IQR from a box plot.

Explanation:
In the above-given question,
given that,
so we can calculate the IQR from a box plot.

Question 3.
You can calculate the mean from a histogram. _________

Answer:
Yes, we can always calculate the mean from a histogram.

Explanation:
In the above-given question,
given that,
yes, we can always calculate the mean from a histogram.

Question 4.
The MAD is a negative value. _______

Answer:
Sometimes MAD is a negative value.

Explanation:
In the above-given question,
given that,
yes, sometimes MAD is a negative value.

Question 5.
The range is a measure of variability _________

Answer:
Sometimes the range is a measure of variability.

Explanation:
In the above-given question,
given that,
yes, sometimes the range is a measure of variability.

Question 6.
The mean, median, and mode are the same value. ________

Answer:
Never the mean, median, and mode are the same value.

Explanation:
In the above-given question,
given that,
never the mean, median, and mode are the same value.

Use Vocabulary in Writing
Describe measures of variability and when you would use them to summarize a data set. Use vocabulary words in your explanation.
Answer:

Concepts and Skills Review

Lesson 8.1 Recognize Statistical Questions

Quick Review
A statistical question anticipates that there will be a variety of answers.

Example
Ramon surveyed his classmates to determine the answer to the statistical question “How many hours do my classmates spend online each week?” The question yielded a variety of numerical answers. Ramon made this dot plot to display the data.

Practice
In 1-4, tell whether each question is statistical.
Question 1.
How many stations are there in a subway system?

Answer:
There are 3 stations are there in a subway system.

Explanation:
In the above-given question,
given that,
there are 3 stations are there in a subway system.
for example:
the statistical question is a direct question.
the non statistical question is an indirect question.

Question 2.
How would passengers of a subway system rate the quality of service on a scale of 1 to 10?

Answer:
The passengers of a subway system rate the quality of service on a scale of 8.

Explanation:
In the above-given question,
given that,
for example:
the passengers of a subway system rate the quality of service on a scale of 8.

Question 3.
How many passengers travel on each of the Green, Blue, Red, and Orange Lines of the subway system each day?

Answer:
The number of passengers travels on each of the Green, Blue, Red, and Orange lines of the subway system each day = 12.

Explanation:
In the above-given question,
given that,
for example:
in green the number of passengers travel = 3.
blue = 3.
red = 3.
orange = 3.
3 + 3 + 3 + 3 = 12.

Question 4.
How much does it cost for a ticket to ride the subway from Station A to Station B?

Answer:
The cost of the ticket from Station A to Station B = $40.

Explanation:
In the above-given question,
given that,
the cost of the ticket from Station A to Station B = $40.

Lesson 8.2 Summarize Data Using Mean, Median, Mode, and Range

Quick Review
The mean is the sum of all the values in a data set divided by the total number of values in the set. The median is the middle data value in a set arranged in numerical order. The mode is the value that occurs most often in a set. The range is the difference between the highest and lowest values in a set.

Example
Find the mean, median, mode, and range of the following set of data.

Mean: 125
Mode: 124
Median: 124
Range: 9

Practice
In 1-6, find the mean, median, mode, and range of each data set.
Question 1.
2, 5, 5

Answer:
mean = 4.
median = 5.
mode = 2.

Explanation:
In the above-given question,
given that,
the data is 2, 5, 5.
mean = 12/3.
mean = 4.
median = 5.
mode = 2.

Question 2.
11, 13, 13, 11, 13

Answer:
mean = 12.2.
median = 13.
mode = 13.

Explanation:
In the above-given question,
given that,
the data is 11, 13, 13, 11, 13.
mean = 61/5.
mean = 12.2.
median = 13.
mode = 13.

Question 3.
27, 26, 25, 20

Answer:
mean = 24.5.
median = 25.5.
mode = 0.

Explanation:
In the above-given question,
given that,
the data is 27, 26, 25, 20.
mean = 98/4.
mean = 24.5.
median = 25.5.
mode = 0.

Question 4.
100, 200, 500, 300, 500

Answer:
mean = 320.
median = 500.
mode = 500.

Explanation:
In the above-given question,
given that,
the data is 100, 200, 500, 300, 500.
mean = 1600/5.
mean = 320.
median = 500.
mode = 500.

Question 5.
1.4, 1.3, 1.1, 1.4, 1.9, 1.8, 1.7, 1.4

Answer:
mean = 1.5.
median = .65.
mode = 1.4.

Explanation:
In the above-given question,
given that,
the data is 1.4, 1.3, 1.1, 1.4, 1.9, 1.8, 1.7, 1.4.
mean = 12/8.
mean = 1.5.
median = 1.65.
mode = 1.4.

Question 6.
450, 0, 500, 750, 0

Answer:
mean = 566.
median = 500.
mode = 0.

Explanation:
In the above-given question,
given that,
the data is 450, 500, 750.
mean = 1700/3.
mean = 566.
median = 500.
mode = 0.

Lesson 8.3 Display Data in Box Plots

Quick Review
Quartiles divide a data set into four equal groups. A box plot uses the minimum, first quartile, median, third quartile, and maximum values in a data set to show how the data are distributed.

Example
Make a box plot of the distances, in feet, that seven paper airplanes flew: 60, 75, 45, 55, 70, 40, 65.

Practice
In 1 and 2, use the data to create a box plot.
Question 1.
27, 31, 30, 33, 29, 25, 28

Answer:
mean = 29.
median = 33.
mode = 0.

Explanation:
In the above-given question,
given that,
the data is 27, 31, 30, 33, 29, 25, 28.
mean = 203/7.
mean = 29.
median = 33.
mode = 0.

Question 2.
3, 1, 3, 7, 5, 2, 3, 6, 3

Answer:
mean = 3.6.
median = 5.
mode = 3.

Explanation:
In the above-given question,
given that,
the data is 3, 1, 3, 7, 5, 2, 3, 6, 3.
mean = 33/9.
mean = 3.6.
median = 5.
mode = 3.

Lesson 8.4 Display Data in Frequency Tables and Histograms

Quick Review
A frequency table shows the number of times a data value or a range of data values occurs in a data set. A histogram is a graph that uses bars to show the frequency of equal ranges or groups of data.

Example
Organize the ages of the campers listed below in a frequency table.
12, 14, 12, 14, 10, 11, 15, 13, 13, 11, 12, 12, 7, 14, 12
Divide the data into equal intervals and mark the frequency of the data using tally marks. Then write the frequency.

Practice
Question 1.
Represent the data in the frequency table on the left in a histogram.

Answer:
The data in the frequency table is 1.

Explanation:
In the above-given question,
given that,
the ages of the campers are:
12, 14, 12, 14, 10, 11, 15, 13, 13, 11, 12, 12, 7, 14, 12.
the frequency of 6-8 is 1.
the frequency of 9-11 is 3.
the frequency of 12-14 is 10.
the frequency of 15-17 is 1.

Lesson 8.5 Summarize Data Using Measures of Variability

Quick Review
The mean absolute deviation (MAD) describes how spread out data values are from the mean. The interquartile range (IQR) describes the difference between the third quartile and the first quartile.

Example
Find the MAD of the data set.
6, 7, 8, 8, 8, 11
Mean = 8
The absolute deviations from the mean are 2, 1, 0, 0, 0, and 3, and their sum is 6.
SO, MAD = \(\frac{6}{6}\) = 1.

Practice
In 1-3, find the mean and the MAD for each data set.
Question 1.
5, 12, 0,7

Answer:
Mean = 8.
MAD = 8.

Explanation:
In the above-given question,
given that,
the data is 5, 12, 0, 7.
mean = 24/3.
mean = 8.
MAD = 8.

Question 2.
8, 14, 22, 16

Answer:
Mean = 15.
MAD = 15.

Explanation:
In the above-given question,
given that,
the data is 8, 14, 22, 16.
mean = 60/4.
mean = 15.
MAD = 15.

Question 3.
1.25, 2.5, 3

Answer:
Mean = 2.25.
MAD = 2.25.

Explanation:
In the above-given question,
given that,
the data is 1.25, 2.5, 3.
mean = 6.75/3.
mean = 2.25.
MAD = 2.25.

In 4 and 5, find the median, first quartile, third quartile, and IQR for each data set.
Question 4.
10, 20, 35, 45, 45, 50

Answer:
Median = 35.
first quartile = 20.
third quartile = 45.

Explanation:
In the above-given question,
given that,
the data is 10, 20, 35, 45, 50.
median = 35.
first quartile = 20.
third quartile = 45.

Question 5.
24, 12, 30, 17, 32, 13, 19

Answer:
Median = 17.
first quartile = 12.
third quartile = 13.

Explanation:
In the above-given question,
given that,
the data is 24, 12, 30, 17, 32, 13, 19.
median = 17.
first quartile = 12.
third quartile = 13.

Lessons 8.6 And 8.7 Choose Appropriate Statistical Measures and Summarize Data Distributions

Quick Review
You can summarize data by finding the measure of center and the measure of variability. Use the IQR when the median is an appropriate measure of center, and the MAD when the mean is an appropriate measure of center.

Example
Use statistical measures to summarize the data set shown.

The mean and MAD are good measures to describe this data set.
The mean test score is 78 points. The MAD is 10.4, so most test scores are within 10.4 points of the mean.

Practice
In 1-3, use the data below.

Question 1.
Describe the overall shape of the data. Include any outliers.

Answer:
The number of outliers are 4.

Explanation:
In the above-given question,
given that,
game sales and number sold each week.
64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104.
there are outliers on 88, 92, 96, 100, 104, 68.
there is gaps from 68 to 88.
so the number of outliers are 4.

Question 2.
Which measure of center and measure of variability best describe the data set? Explain.
Answer:

Question 3.
Summarize the data set.
Answer:

Topic 8 Fluency Practice

Riddle Rearranging
Find each sum or difference. Then arrange the answers in order from least to greatest. The letters will spell out the answer to the riddle below.
I can… add and subtract decimals.

What place’s name is only two words long but has hundreds of letters in it?

Answer:
O, P, S, T, O, F, F, I, C, E.

Explanation:
In the above-given question,
given that,
14.56 + 9.471 = 24.031.
33.582 – 2.8 = 30.782.
8.999 + 2.3 = 11.299.
45.74 – 22.08 = 23.66.
1.43 + 12.89 = 14.32.
20.4 – 11.81 = 8.59.
25.35 – 2.5 = 22.85.
2.456 – 7 = -4.544.
7.074 + 12.75 = 19.824.
80 – 66.7 = 13.3.
so from least to greatest = O, P, S, T, O, F, F, I, C, E.

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• Topic 3 Addition Facts to 20: Use Strategies
• Topic 4 Subtraction Facts to 20: Use Strategies
• Topic 5 Work with Addition and Subtraction Equations
• Topic 6 Represent and Interpret Data
• Topic 7 Extend the Counting Sequence

enVision Math Common Core 1st Grade Volume 2 Answer Key | enVision Math Common Core Grade 1 Volume 2 Answers

• Topic 8 Understand Place Value
• Topic 9 Compare Two-Digit Numbers
• Topic 10 Use Models and Strategies to Add Tens and Ones
• Topic 11 Use Models and Strategies to Subtract Tens
• Topic 12 Measure Lengths
• Topic 13 Time and Money
• Topic 14 Reason with Shapes and Their Attributes
• Topic 15 Equal Shares of Circles and Rectangles

Want to seek math homework help to complete your complex assignments? Check out the enVision Math Answer Key and finish your homework or assignments.

enVision Math Common Core Grade 8 Answers | enVision Math Common Core 8th Grade Textbook Answer Key

enVision Math Common Core Grade 8 Volume 1 Answer Key | enVision Math Common Core 8th Grade Volume 1 Answers

• Topic 1 Real Numbers
• Topic 2 Analyze and Solve Linear Equations
• Topic 3 Use Functions to Model Relationships
• Topic 4 Investigate Bivariate Data

enVision Math Common Core 8th Grade Volume 2 Answer Key | enVision Math Common Core Grade 8 Volume 2 Answers

• Topic 5 Analyze and Solve Systems of Linear Equations
• Topic 6 Congruence and Similarity
• Topic 7 Understand and Apply the Pythagorean Theorem
• Topic 8 Solve Problems Involving Surface Area and Volume

Want to seek math homework help to complete your complex assignments? Check out the enVision Math Answer Key and finish your homework or assignments.

enVision Math Common Core Grade Kindergarten Answers | enVision Math Common Core Grade K Textbook Answer Key

enVision Math Common Core Kindergarten Volume 1 Answer Key | enVision Math Common Core Grade K Volume 1 Answers

• Topic 1 Numbers 0 to 5
• Topic 2 Compare Numbers 0 to 5
• Topic 3 Numbers 6 to 10
• Topic 4 Compare Numbers 0 to 10
• Topic 5 Classify and Count Data
• Topic 6 Understand Addition
• Topic 7 Understand Subtraction
• Topic 8 More Addition and Subtraction

enVision Math Common Core Grade K Volume 2 Answer Key | enVision Math Common Core Kindergarten Volume 2 Answers

• Topic 9 Count Numbers to 20
• Topic 10 Compose and Decompose Numbers 11 to 19
• Topic 11 Count Numbers to 100
• Topic 12 Identify and Describe Shapes
• Topic 13 Analyze, Compare, and Create Shapes
• Topic 14 Describe and Compare Measurable Attributes

Want to seek math homework help to complete your complex assignments? Check out the enVision Math Answer Key and finish your homework or assignments.

enVision Math Common Core Grade 6 Answers | enVision Math Common Core 6th Grade Textbook Answer Key

enVision Math Common Core Grade 6 Volume 1 Answer Key | enVision Math Common Core 6th Grade Volume 1 Answers

• Topic 1 Use Positive Rational Numbers
• Topic 2 Integers and Rational Numbers
• Topic 3 Numeric and Algebraic Expressions
• Topic 4 Represent and Solve Equations and Inequalities

Envision Math Common Core 6th Grade Volume 2 Answer Key | Envision Math Common Core Grade 6 Volume 2 Answers

• Topic 5 Understand and Use Ratio and Rate
• Topic 6 Understand and Use Percent
• Topic 7 Solve Area, Surface Area, and Volume Problems
• Topic 8 Display, Describe and Summarize Data

Practice with the help of enVision Math Common Core Grade 1 Answer Key Topic 14 Reason with Shapes and Their Attributes regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 14 Reason with Shapes and Their Attributes

Essential Question:
How can you define shapes and compose new shapes?

Find Out Talk to friends and relatives about everyday objects that have special shapes. Discuss how the shape is important for its use.
Journal: Make a Book Show what you found out. In your book, also:

• Draw different buildings using circles, squares, rectangles, cylinders, and rectangular prisms.
• In your drawings, show how shapes can be put together to make new shapes.

Review What You Know

Vocabulary
Question 1.
Scott sorted these shapes. Put an X on the one that does not belong.

Answer:

Explanation:
In the above image we can observe 4 shapes one is square, second is rectangle, third is also rectangle and fourth is circle. Both Square and rectangle have four edges and four vertices. Circle has 0 edges and 0 vertices. So draw X on the circle which is different from the above three shapes.
Question 2.
Circle the object that is a different shape.

Answer:

Explanation:
In the above image we can observe four shapes. First shape is different from the remaining three shapes. So circle first shape.

Question 3.
Circle the triangle.

Answer:

Explanation:
In the above image we can observe four different shapes one is circle and second one is rectangle and third is square, fourth is triangle. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Here we have to draw a circle for triangle. So draw a circle for triangle.

Same and Different
Question 4.
Draw a shape that is the same as the one below.

Answer:

Explanation:
Here we have to draw a shape that is same as the one above in the question. We can observe the circle shape in the above image. So drawn a circle shape which is similar to the above image.

Question 5.
Draw a shape that is different from the one below.

Answer:

The above shape is right angled triangle which is different from the above shape.
Explanation:
Here we have to draw a shape which is different from the square shape. In geometry, a square is a regular quadrilateral, it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length.
Here I drawn right angled triangle. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
C1ount by 1s
Question 6.
Write the missing numbers.
1, ______, 3, 4, _______
Answer:
1, 2, 3, 4, 5
The missing numbers are 2, 5
Explanation:
In the above number series we can observe 1, ______, 3, 4, _______. We have to find the missing numbers in the series. The missing numbers are 2, 5. The number series is 1, 2, 3, 4, 5.

Pick a Project

PROJECT 14A
Have you ever seen a building this crooked? Project: Build a Strong Tower

PROJECT 14B
Where can you see your reflection? Project: Reflect Shapes

PROJECT 14C
How can lots of little tiles make one big piece of art? Project: Design a Tile Picture

PROJECT 14D
What is a robot?
Project: Design and Build a Robot

Lesson 14.1 Use Attributes to Define Two Dimensional (2-D) Shapes

Solve & Share
Tell how the 4 shapes are alike. Tell how the 4 shapes are different. Use a measuring tool to help..

I can … use attributes to describe shapes.

Visual Learning Bridge

Convince Me! Look at the blue triangle above. How would you define it by how it looks?

Guided Practice

For each shape, tell how many straight sides or vertices, and if it is closed or not.
Question 1.

Answer:

Explanation:
In the above image we can observe trapezium shape. A trapezium is a quadrilateral, which is defined as a shape with four sides, which has one set of parallel sides. The trapezium is basically a types of quadrilaterals, with exactly one pair of parallel sides. Trapezium has four straight sides and it is a closed shape.

Question 2.

How many vertices? ________
Closed? _______
Answer:
There are 2 vertices for the above image.
The above image is not a closed shape.
Explanation:
The above shape is not a triangle because it is not a closed shape and it has 2 vertices.

Question 3.

How many straight sides? __________
Closed? ___________
Answer:
The above shape is hexagon. It has 6 straight sides.
The above shape is a closed shape.
Explanation:
The above shape is hexagon. Hexagon is a closed geometric figure having six angles and six sides. It has six straight sides and it is a closed shape.

Independent Practice

Draw each shape.
Question 4.
Draw a closed shape with 3 vertices.
Answer:

Right angled triangle is a closed shape with three vertices.
Explanation:
A Right angled triangle is a closed shape with three vertices. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Question 5.
Draw a closed shape with 0 straight sides.
Answer:

Circle is a closed shape with 0 straight sides.
Explanation:
Circle is a closed shape with 0 straight sides. It is one of the 2D shapes.

Question 6.
Draw a closed shape with more than 3 vertices.
Answer:

Square is a closed shape with more than 3 vertices.
Explanation:
Square is a closed shape with more than 3 vertices. In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. Square has 4 vertices and a closed shape.

Question 7.
Circle the closed shapes.

Answer:

Explanation:
In the above image we can observe different types of shapes. Some are closed shapes some are not closed shapes. The closed figures are triangle, circle, and parallelogram. So draw a circle for the closed shapes.

Question 8.
Higher Order Thinking Look at the shapes in each group. Explain how the shapes are sorted.

Answer:
In Group 1 all triangles are sorted with different shape and size. And all triangle shapes are closed figures.
In Group 2 only two shapes are closed figures. The closed shapes are circle and hexagon. Remaining two shapes are not closed shapes.

Problem Solving

Solve each problem below.
Question 9.
Be Precise Circle 3 shapes that have the same number of vertices and sides.

Answer:

Explanation:
In the above image we can observe different types of shapes. The shapes are Hexagon, rectangle, square, triangle, circle. Square and rectangle have four sides and four vertices. Draw a circle for square and rectangle.

Question 10.
Be Precise Circle 3 shapes that do NOT have any vertices.

Answer:

Explanation:
In the above image, we can observe different types of shapes. There are hexagons, squares, circles, and rhombus. Hexagon has six vertices and the square has four vertices, the circle has no vertices, and the rhombus has four vertices. So draw a circle for circle shape.

Question 11.
Higher Order Thinking Think about a 2-D shape. Write a riddle about the shape for a partner to solve.
Answer:

Question 12.
Assessment Practice I have 6 vertices. I am a closed figure. Which shape or shapes can I NOT be? Choose three that apply.

Answer:

Explanation:
In the above image, we can observe two closed shapes and two open shapes. The closed shapes are hexagon and triangle. Hexagon has 6 vertices and a closed figure. But here asked the shape should not be a hexagon. So select the remaining three shapes.

Lesson 14.2 Defining and Non-Defining Attributes of 2-D Shapes

Solve & Share
Tell how the 5 shapes are alike. Tell how the 5 shapes are different. Use a tool to help.

I can … define 2-D shapes by their attributes.

Visual Learning Bridge

Convince Me! Why is this shape NOT a square?

Answer:
It’s a rectangle.

Explanation:
The shown image is not square, because the image shows opposite sides are parallel which represents a rectangle.

Guided Practice

Circle the words that are true for Practice the shape.
Question 1.

are blue.
have 4 equal sides.
are closed shapes.
are small.
have 4 square corners.
Answer:

Explanation:
In the above image we can observe two square shapes. Draw a circle for these words. All squares have 4 equal sides. All squares are closed shapes and all squares have 4 square corners.

Independent Practice

Circle the words that are true for each shape.
Question 2.

All triangles:
are orange.
have 3 sides.
have 3 equal sides.
are tall.
are closed figures.
Answer:

Explanation:
In the above image we can observe a triangle. Draw a circle for these words. All triangles have 3 sides and all triangles are closed figures.

Question 3.

All circles:
are blue.
have 0 vertices.
are small.
have 0 straight sides.
Answer:

Explanation:
In the above image we can observe a circle. Draw a circle for these words. All circles have 0 vertices and all circles have 0 straight sides.

Question 4.
Higher Order Thinking Tim says that this is a rectangle. Is he correct? Tell why or why not.

Answer:
The above image is not a rectangle because it is not a closed shape.
Explanation:
Rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. The rectangle is a closed figure. The above image is not a closed figure so the above shape is not a rectangle.

Problem Solving

Solve each problem below.
Question 5.
Use Tools Do all rectangles have equal sides? Circle Yes or No.
Yes
No
Choose a tool to show how you know.
Answer:
No.

Explanation:
No, all rectangles do not have equal sides.

Question 6.
Higher Order Thinking Jake says both of these shapes are hexagons because they are closed, have 6 straight sides, and are red. Do you agree? Explain.

Answer:
Hexagonal shape is a two-dimensional geometrical shape which is made of six sides, having the same or different dimensions of length. Hexagon is a closed figure.
The above shapes are hexagons. Hexagon is a closed shape and it has 6 straight sides. Color, overall size, or position do not define a shape. So I am not agree with Jake.

Question 7.
Assessment Practice Tanya says that this shape is NOT a square. Do you agree? Circle Yes or No.
Yes
No
Explain why or why not.

Answer:

The above image is a square.
Explanation:
A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. The above shape is square because it has four equal sides.

Lesson 14.3 Build and Draw 2-D Shapes by Attributes

Solve & Share
Find square corners and rectangle shapes in the classroom. Tell your partner why a shape you find is a rectangle. Count how many square corners you find. Use the chart to help keep track.

I can … use different materials to make shapes.

Visual Learning Bridge

Convince Me! Sue made the gray shape on the right. Is it also a hexagon? Tell how you know.

Guided Practice

Make a square. Use materials your teacher gives you. Glue or tape the square in the box. Explain how you know it is a square.
Question 1.
Answer:
As we have glued the square in the box and all the sides are equal. So we know it is a square.

Independent Practice

Use materials your teacher gives you to make each shape. Glue or tape the shape in the box. Explain how you know the shape is correct.
Question 2.
Make a circle.
Answer:

Question 3.
Make a rectangle.
Answer:

Question 4.
Higher Order Thinking Carlos made the shapes below. He says they are both squares. Is he correct? Explain.

Answer:
Carlos is not correct because in the above two images first, one is the square and the second one is a rectangle.
Explanation:
The first shape is square because the square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length.
The second shape is a rectangle because it is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Problem Solving

Draw a picture to solve each problem below. Use pattern blocks to help you.
Question 5.
Reasoning Sandy makes a closed shape with 4 equal sides. What shape did she make?
Draw the shape Sandy made.
Answer:

Sandy made a square shape. It is a closed shape with 4 equal sides.
Explanation:
Sandy made a square shape because it is a closed shape with four equal sides. A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length

Question 6.
Reasoning Miguel makes a closed shape with 3 straight sides and 3 vertices. What shape did Miguel make?
Draw the shape Miguel made.
Answer:

Miguel made a triangle. It is a closed shape with 3 straight sides and 3 vertices.
Explanation:
Miguel made a triangle. Because it is a closed shape with 3 straight sides and 3 vertices. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Question 7.
Higher Order Thinking Use a piece of paper to make a square. Then turn the square into a triangle. What did you do? Explain.
Answer:
We have turned the square into a triangle.

Question 8.
Assessment Practice Mark wants to use straws to make a hexagon. Use the dots to draw straight lines that show Mark how the hexagon would look.

Answer:

Explanation:
Mark used the dots to draw straight lines to draw the hexagon. The hexagon shape is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Here Mark drew the hexagon with the help of dots and straight lines.

Lesson 14.4 Compose 2-D Shapes

Solve & Share
Use shapes to make a . Write how many of each shape you use. Then add the three numbers to find how many pieces in all. See if you can make the hexagon with less than 15 pieces in all!

________ pieces in all
I can .. put shapes together to make another shape.

Visual Learning Bridge

Convince Me! How can you make a large shape using smaller shapes?

Guided Practice

Use pattern blocks to make the large triangle shape.
Question 1.
Complete the chart.

Answer:

Independent Practice

Use the smaller shapes to make larger shapes.
Question 2.
Complete the chart to show a list of ways you can make the hexagon. Use pattern blocks to help.

Answer:

Question 3.
Use to make a . Draw the in the space below.
Answer:

Question 4.
Higher Order Thinking Use 3 pattern blocks to make a new shape. Trace the pattern blocks. What shapes did you use? What shape did you make?
Answer:

Problem Solving

Use smaller shapes to make bigger shapes.
Question 5.
Make Sense Two of which shape can make ?
Answer:

Question 6.
Make Sense Two of which shape can make ?
Answer:

Question 7.
Higher Order Thinking Name and draw the shape you will make if you put the orange pattern blocks together with their full sides touching. Explain how you know.

Answer:

If I put the orange pattern blocks together with their full sides touching then we got the shape as a rectangle.
Explanation:
In the above image, we can observe two shapes which are squares. A square has four equal sides and four equal angles. When we combine these two squares then we get a rectangle shape. A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Question 8.
Assessment Practice Nicole wants to make a hexagon. She has I Which set of other shapes could she use to complete the ?

Answer:

Lesson 14.5 Compose New 2-D Shapes from 2-D Shapes

Solve & Share
Use exactly 10 pattern blocks to make a picture of a boat. Trace the shapes in the space below to show your boat.
Then use what you know about tens. How many pattern blocks would you need to make 6 boats?

I can … use shapes to make different shapes.

It would take _________ pattern blocks to make 6 boats.

Visual Learning Bridge

Convince Me! Use pattern blocks to make a picture of a tree. What shapes did you use? Explain.

Guided Practice

Start with a triangle and use pattern blocks to make a picture. Trace around your shapes to show your picture. Write how many of each shape you used.
Question 1.

Independent Practice

Use any of the pattern blocks shown to make pictures. Practice Trace around your shapes to show your pictures. Write how many of each shape you used for each picture.
Question 2.

Answer:

Question 3.

Answer:

Problem Solving

Solve the problems below.
Question 4.
Model Dana started making a flower using these pattern blocks. Draw more leaves and petals to help her finish.

Answer:

Question 5.
Higher Order Thinking Use pattern blocks to make a picture of a fish.
Answer:

Question 6.
Assessment Practice Jeff is making a model of this arrow. Which shape does he need to add to his model to finish it?

Answer:

He needs to add a triangle to his model to finish the arrow.
Explanation:
Jeff needs to add one shape to the above arrow. Here we have four options. Option A is a hexagon and option B is a trapezium, option C is a parallelogram, and option D is a triangle. Here triangle is the correct match to the above image. So Jeff needs to add a triangle to his model to finish the arrow. So make a tick mark to option D.

Lesson 14.6 Use Attributes to Define Three Dimensional (3-D) Shapes

Solve & Share
Can you find objects in the classroom that are shaped like the objects below? Find as many as you can and record the number of each shape you find. Circle the shape that you find the most.

I can … define 3-D shapes by their number of edges, vertices, and faces or flat surfaces.

Visual Learning Bridge

Convince Me! Do 3-D shapes always have either faces, flat surfaces, or vertices? Explain.

Guided Practice

Write how many faces or flat surfaces and vertices each 3-D shape has.
Question.

Answer:

Explanation:
1. A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section.
2. A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). A cone has one flat surface, one vertex, and 0 edges.

Independent Practice

Write how many faces or flat surfaces, vertices, and edge each object has.
Question.

Answer:

Explanation:
3. A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere. A Sphere has Zero vertices, zero faces, and zero edges.
4. In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex. It has 6 faces, 12 edges, and 8 vertices.
5. The above image has two flat surfaces, zero vertices, and 2 edges.

Question 6.
Higher Order Thinking Lily has an object that looks like a 3-D shape. The object has 2 flat surfaces and 0 vertices.
Draw an object that Lily could have.
Answer:

The above object has two flat surfaces and zero vertices. The object is a cylinder.
Explanation:
In mathematics, a cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. The cylinder has two flat surfaces and zero vertices.

Problem Solving

Solve each problem below.
Question 7.
This shape is a cone. Which shape below is also a cone? How do you know?

Answer:

Explanation:
In the above we can observe three shapes. First is cylinder, second is cone and third also cone. A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone. The circular base has measured value of radius. Cone has one flat surface and one vertex and zero edges.

Question 8.
Reasoning Nikki and Ben each buy I item from the store. Nikki’s item has 4 more edges than vertices. Ben’s item has the same number of flat surfaces and edges. Draw a circle around Nikki’s item. Draw a box around Ben’s item.

Answer:

Explanation:
Nikki and Ben each buy one item from the store. Nikki’s item has 4 more edges than vertices. Ben’s item has the same number of flat surfaces and edges.
Nikki’s item has 8 vertices and 12 edges. The shape is a rectangular prism. So draw a circle for Nikki’s item.
Ben item has 2 flat surfaces and 2 edges. Draw a box to the ben’s item.

Question 9.
Higher Order Thinking Draw and label a 3-D shape. Then write a sentence describing your 3-D shape.
Answer:

The above 3D shape is a cube.
Explanation:
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. It has 6 faces, 12 edges, and 8 vertices.

Question 10.
Assessment Practice I have 6 faces. I have 8 vertices. Which 3-D shape could I be? Choose two that apply.
☐ sphere
☐ cube
☐ rectangular prism
☐ cylinder
Answer:

Explanation:
A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section.
A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Lesson 14.7 Defining and Non-Defining Attributes of 3-D Shapes

Solve & Share
Measure the lengths of the cylinders. How could you make a tower 10 cubes tall using some of the cylinders? Tell what shape the tower would be.

I can … choose the defining attributes of 3-D shapes.

Visual Learning Bridge

Convince Me! Write 2 things that are true about all rectangular prisms. Write 2 things that do not define rectangular prisms.

Guided Practice

Circle the words that are true for the shape.
Question 1.
All cones:

Independent Practice

Circle the words that are true for each shape.
Question 2.
All cubes:

have 12 edges.
have 8 vertices.
cannot roll.
are blue.
Answer:

Explanation:
A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. Draw a circle for the above words. All cubes have 12 edges and 8 vertices. All cubes cannot roll.

Question 3.
All cylinders:

have 2 flat surfaces.
cannot roll.
are red.
can roll.
Answer:

Explanation:
In mathematics, a cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. Draw a circle for the above words. All cylinder have two flat surface and all cylinders can roll.

Question 4.
en Vision® STEM Kevin wants to build a wall. Circle the 3-D shape or shapes he could stack to build the wall.

Answer:

Explanation:
STEM Kevin can build the wall with these two shape one is cube and other one is rectangular prism.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron. It has 6 faces, 12 edges, and 8 vertices.
A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section.
Problem Solving

Solve the problems below.
Question 5.
Explain Do all cubes have the same number of edges?
Yes
No
Answer:
Yes all cubes have the same number of edges.
Explanation:
A cube has sides of equal length and each vertex forms a right angle between the edges. Hence, a cube has 6 faces, 12 edges, and 8 vertices. So all cubes have the same number of edges.

Explain or draw a picture to show how you know.
Answer:

Explanation:
A cube has sides of equal length and each vertex forms a right angle between the edges. Hence, a cube has 6 faces, 12 edges, and 8 vertices.

Question 6.
Higher Order Thinking Steve says that both of these shapes are the same because they both have 6 faces and both are purple. Do you agree? Explain.

Answer:

Question 7.
Assessment Practice Match each shape with the words that describe it.

Answer:

Explanation:
A rectangular prism has 8 vertices. So match the rectangular prism with the 8 vertices.
A cube has 6 equal faces. So match the cube with the 6 equal faces.
A sphere has no flat surfaces or vertices. So match the sphere with the no flat surfaces or vertices.
A cone has one vertex. So match the cone with one vertex.

Lesson 14.8 Compose with 3-D Shapes

Solve & Share
Use green cubes to build two different rectangular prisms. Draw and write about the shapes you made. How many cubes did you use to build both rectangular prisms?

I can … put 3-D shapes together to make another 3-D shape.

Visual Learning Bridge

Convince Me! How can you find the 3-D shapes that make an object?

Guided Practice

Circle the 3-D shapes that could be put together to make the object.
Question 1.

Question 2.

Answer:

Explanation:
The 3-D shapes that makes an above object are rectangular prism and cube. Draw a circle for the 3-D shapes that could be put together to make the object are rectangular prism and cube.
A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

Independent Practice

Circle the 3-D shapes that could be put together to make the object.
Question 3.

Answer:

Explanation:
The 3-D shapes that makes an above object are rectangular prism, cube, cylinder, and sphere. Draw a circle for the 3-D shapes that could be put together to make the object are rectangular prism, cube, cylinder, and sphere.
A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section.
A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.
A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere.

Question 4.

Answer:

Explanation:
The 3-D shapes that makes an above object are rectangular prism, cylinder, and cone. Draw a circle for the 3-D shapes that could be put together to make the object are rectangular prism, cylinder, and cone.
A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section.
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.
A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone. The circular base has measured value of radius.

Question 5.

Answer:

Explanation:
The 3-D shapes that makes an above object are cylinders. Draw a circle for the 3-D shapes that could be put together to make the object are cylinder.
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.
Question 6.
Higher Order Thinking Jon wants to combine 6 green cubes to make a bigger cube. Can Jon do this? Explain. Use cubes to help.

Answer:

Jon can combine 6 green cubes to make bigger cube.
Explanation:
Jon can combine 6 green cubes to make bigger cube. In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron. It has 6 faces, 12 edges, and 8 vertices.

Problem Solving

Solve the problems below.
Question 7.
Make Sense Ralph made this shape below with 3-D shapes.

What 3-D shapes did Ralph use?
Answer:
Ralph used two cones and one cylinder.
Explanation:
Ralph used two cones and one cylinder.
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.
A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

Question 8.
Make Sense Kirsten has 12 ice cubes. She wants to combine the ice cubes to make an ice sculpture.

What 3-D shape could Kirsten make with the ice cubes?
Answer:
Kristen can make a 3D shape with ice cubes is rectangular prism.
Explanation:
A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross section. Rectangular prisms can be of two types, namely right rectangular prism and non-right rectangular prisms.

Question 9.
Higher Order Thinking Ellen uses two of the same shape to build a bigger 3-D shape. Her new figure has 2 flat surfaces and O vertices.
What 2 shapes did Ellen use?
_________________
What bigger shape did Ellen build?
__________________
Answer:
Ellen used two same shape cylinders to build a bigger 3D shape.
The bigger shape is cylinder. A cylinder has 2 flat surfaces and 0 vertices.
Explanation:
In mathematics, a cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.

Question 10.
Assessment Practice Which object could be made with a and a ?

Answer:

Explanation:
The object that could be made with both cone and cylinder is crayon. Put a tick mark to the option A.

Lesson 14.9 Problem Solving

Make Sense and Persevere
Solve & Share
Draw an X on all the objects that have flat surfaces that are circles. Tell how you know the flat surfaces are circles. Make sense of the problem by circling the words that are true about the objects you crossed out.

I can … make sense of problems.
Thinking Habits What am I asked to find? What else can I try if I get stuck?

Visual Learning Bridge

Convince Me! What words can always be used to describe a rectangular prism?

Guided Practice

Circle the words that are true of the shapes.
Question 1.
All of these shapes are squares.

Independent Practice

Circle the words that are true of the shapes. Then explain how you know.
Question 2.
All of these shapes are cones.

All cones:
are blue
have I flat surface
have I edge
have | vertex
Answer:

Explanation:
A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone. The circular base has measured value of radius. All cones have one flat surface and one vertex.

Question 3.
All of these shapes are hexagons.

All hexagons:
are small
have 6 sides
are blue
have 6 vertices
Answer:

Explanation:
Hexagon is a two-dimensional geometrical shape which is made of six sides, having the same or different dimensions of length. All hexagons have 6 sides and 6 vertices.

Problem Solving

Performance Task
Arts and Crafts Wes has cubes, spheres, cylinders, and cones. He wants to use these shapes to make art pieces for an arts and crafts sale at his school.

Wes wants to put together the right shapes for each piece of art.

Question 4.
Be Precise Wes wants to put together one shape that has 6 faces and one shape that has no flat surfaces. What shapes can he use? Explain.
Answer:
He uses cube and sphere. The one shape that has 6 faces is called as cube and the one shape that has no flat surfaces is called as sphere.
Explanation:
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere.

Question 5.
Reasoning Wes puts two cubes together to make a new shape. Tell what shape Wes made and one thing that is true about the new shape.
Answer:

Topic 14 Fluency Practice Activity

Show the Word
Color these sums and differences. Leave the rest white.

I can … add and subtract within 10.

The word is
________ __________ ____________
Answer:

The word is OFF
Explanation:
By coloring these sums and differences we got the word as OFF. For one I colored blue, for two I colored orange and for three I colored green.

Topic 14 Vocabulary Review

Understand Vocabulary
Word List
• 2-D shape
• 3-D shape
• attributes
• cone
• cube
• cylinder
• edge
• face
• flat surface
• rectangle
• rectangular prism
• side
• sphere
• square
• triangle
• vertex/ vertices

Question 1.
Put an X on the 2-D shape that has no vertices. Circle the 2-D shape that has 4 vertices and 4 equal sides.

Answer:

Explanation:
Here I put X to the circle because it has no vertices. A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.
Here I drawn a circle for square because it has four vertices and 4 equal sides. Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal.

Question 2.
Write what part of the shape is shown. Use the Word List.

Answer:
In the above image we can observe a flat surface of the cone.
Explanation:
In the above image the arrow points to the flat surface of the cone. A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex).
Question 3.
Complete the name of the shape. Use the Word List to help you.

________ prism
Answer:
The name of the above shape is rectangular prism.
Explanation:
In the above image we can observe a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces of the prism are rectangles. Both the bases of a rectangular prism must be a rectangle. Also, the other lateral faces will be rectangles. It is also called a cuboid.

Use Vocabulary in Writing
Question 4.
Draw some shapes. Label the shapes using words from the Word List.
Answer:

Explanation:
From the above word list I draw some shapes. Here I draw two 2D shapes and two 3D shapes. In 2D shapes I draw square and triangle. In 3D shapes I draw sphere and cone as we can observe in the above image.

Topic 14 Reteaching

Set A

You can define 2-D shapes by their attributes.
A hexagon must be a closed figure. It must have 6 sides and 6 vertices.

Color, overall size, or position do not define a shape.

Solve each problem below.
Question 1.
Circle the shape that has 4 straight sides and 4 vertices.

Answer:

Explanation:
In the above shapes I draw a circle for rectangle shape because it has four straight sides and 4 vertices. A rectangle is a two-dimensional figure, which has four sides (Quadrilateral) and four corners/vertices. All the interior angles are equal, which measures 90 degrees. The opposite sides of a rectangle are parallel and are of equal measure.

Question 2.
Circle the shape that has 0 vertices.

Answer:

Explanation:
In the above shapes I draw a circle for circle shape because it has 0 vertices. A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.

Set B

You can make 2-D shapes using different kinds of materials.

Use materials your teacher gives you to make a rectangle. Glue or tape it in the box.
Question 3.
Answer:

Set C

You can use pattern blocks to make a larger shape.

Question 4.
Make this shape in two different ways.

Answer:

Set D

You can use pattern blocks to make a picture.

Write the number of blocks you used.

Question 5.
Make a picture. Write how many of each block you used.

Answer:

Set E

Reteaching Continued
You can find faces, flat surfaces, edges, and vertices on 3-D shapes or objects.

Write how many flat surfaces, edges, and vertices for each shape.
Question 6.

_________ flat surfaces
________ vertices
________ edges
Answer:
A cylinder has 2 Flat surfaces, 0 vertices and 2 edges.
Explanation:
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. A cylinder has 2 Flat surfaces, 0 vertices and 2 edges.

Question 7.

_________ flat surfaces
________ vertices
________ edges
Answer:
A cone has 1 flat surfaces and 1 vertices and 0 edges.
Explanation:
A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). A cone has 1 flat surfaces and 1 vertices and 0 edges.

Set F

You can combine 3-D shapes to make bigger 3-D shapes. Combine 2 cubes.

Two shapes were combined to make a new shape. Write the number of flat surfaces, vertices, and edges for the new shape.
Question 8.

Answer:

Explanation:
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. A cylinder has a curved lateral surface and two circular faces at its ends. A cylinder has no corner or vertex. A cylinder has 2 circular edges.

Set G

All of these are cylinders.

Cylinders are defined by:
0 vertices and 2 flat surfaces.
Cylinders are NOT defined by:
Color or Direction

Finish the sentences to define spheres.

Question 9.
Spheres are defined by:
________ and _________.
Answer:
Spheres are defined by 0 vertices and 0 flat surfaces.
Explanation:
A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere. Sphere has 0 vertices and 0 flat surfaces.

Question 10.
Spheres are NOT defined by:
____________ or ___________.
Answer:
Spheres are not defined by color or directions.
Explanation:
A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere. Sphere has 0 vertices and 0 flat surfaces. Spheres are not defined by color or directions.

Set H

Thinking Habits
Persevere
What am I asked to find? What else can I try if I get stuck?

Circle the words that are true for all rectangles.

Question 11.
All rectangles:
have sides of different lengths.
are blue.
have 4 vertices.
Answer:

Explanation:
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square. It has 4 vertices.

Topic 14 Assessment Practice

Question 1.
Which shape has exactly 3 sides?
A. rectangle
B. triangle
C. circle
D. Square
Answer:
B. Triangle
Explanation:
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Triangle is a plane figure with three straight sides and three angles.

Question 2.
How do you know if a shape is a square?
A. The shape has 0 edges and 0 vertices.
B. The shape has 3 edges and 3 vertices.
C. The shape has 4 edges and 4 vertices.
D. The shape has 4 edges that are the same length and 4 vertices.
Answer:
D. The shape has 4 edges that are the same length and 4 vertices.
Explanation:
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. A square has 4 edges that are the same length and 4 vertices.

Question 3.
How many flat surfaces and edges does a cone have?
________ flat surface(s)
________ edge(s)
Answer:
Cone have 1 flat surface.
Cone have 0 edges.
Explanation:
A cone is a shape formed by using a set of line segments or the lines which connect a common point, called the apex or vertex, to all the points of a circular base (which does not contain the apex). A cone has 0 edges and has 1 flat surface.

Question 4.
Jaxon makes 3 triangles. Then he puts them together to make a new shape.
Draw a shape that Jaxon could have made.
Answer:

Question 5.
Complete the sentence. Then explain how you know you are correct.

This 3-D shape is a _________.
Answer:
This 3-D shape is a cylinder.
Explanation:
The above 3D shape is a cylinder. A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.

Question 6.
Jazmin is making a butterfly. Use pattern blocks to draw in the pieces she is still missing.

Answer:

Explanation:
Jazmin is making a butterfly. She missed some pieces. By using pattern blocks we can make a butterfly. The pattern blocks are trapezium and hexagon. She missed three pieces of hexagon and one piece of trapezium. By using these shapes we can complete the butterfly shape.

Question 7.
Choose two sets of shapes you can use to make .

Answer:

Question 8.
All of these shapes are triangles. Circle two ways to describe all triangles.

Answer:

Explanation:
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. All triangles have 3 sides and 3 vertices.

Question 9.
A. Which 3-D shape does NOT have a vertex?

Answer:

Explanation:
In the above image, we can observe 4 different 3D shapes. The shapes are cube, rectangular prism, cone, and cylinder. The cylinder has 0 vertices.

B. What is the name of the shape you chose in A?
Answer:
The name of the shape I choose in A is a cylinder.
Explanation:
In mathematics, a cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.

Question 10.
Circle the two 3-D shapes that can be used to make this object.

Answer:

Explanation:
The two 3D shapes that make the above objectives are rectangular prism and cube.
A rectangular prism has 8 vertices, 12 sides, and 6 rectangular faces. All the opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross-section.
In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges.

Question 11.
A. Which 2-D shape has no straight sides?

Answer:

Explanation:
In the above image, we can observe four different 2D shapes. The shapes are Hexagon, parallelogram, square, circle. The 2D shape that has no straight sides is the circle.

B. How many vertices does your answer to A have?
Answer:
0 vertices
Explanation:
The circle doesn’t have vertices.

Question 12.
Match each 3-D shape with one way to describe it. Use each description once.

Answer:

Explanation:
A cone has 1 vertex.
A sphere has no flat surfaces.
A rectangular prism has 12 edges.
A cube has 12 edges and 6 square faces.

Topic 14 Performance Task

Home Sweet Home! Leslie uses shapes to make this drawing of her house.

Question 1.
Color two of the rectangles in the drawing blue.
Answer:

Question 2.
Explain how you know that the two shapes are rectangles.
Answer:
As parallel sides are equal we can know that it is a rectangle

Question 3.
One of the windows of the house is in the shape of a hexagon.
Show 3 ways you could make a hexagon using smaller shapes. You can use pattern blocks to help you.

Answer:

Question 4.
Leslie has these tents in her backyard.

She says that the doors of both tents are the shape of a triangle because they have 3 sides and 3 vertices.
Do you agree with Leslie’s reasoning? Circle Yes or No.
Yes
No
Explain your answer.
Answer:
Yes.

Explanation:
As the tent is in triangle shape, so they have 3 sides and 3 vertices.

Question 5.
Leslie has a table in her house that is this shape.

Part A
What is the shape of her table?

Answer:
Rectangle.

Explanation:
The shape of her table is rectangle as the parallel sides are equal.

Part B
How many of each does her table have?
faces ________
edges ________
vertices ________

Answer:
Faces – 2.
Edges – 4.
Vertices – 4.

Explanation:
As the table is rectangle shape, so the number of faces of the rectangle is 2.
The edges of the rectangle is 4.
The vertices of the rectangle is 4.

Part C
What 3-D shapes could Leslie put together to make her table?
Answer:
Right rectangular prism.

Explanation:
The 3-D shapes could be right rectangular prism.

Practice with the help of enVision Math Common Core Grade 1 Answer Key Topic 11 Use Models and Strategies to Subtract Tens regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 11 Use Models and Strategies to Subtract Tens

enVision STEM Project: Tools Solve Problems

Find Out Talk to friends and relatives about different tools we use to solve problems. Ask them about tools they use in their everyday lives.
Journal: Make a Book Show what you found out. In your book, also:

• Draw some tools that solve simple problems. Make sure to describe the simple problems they solve.
• Make up and solve subtraction problems about tools.

Review What You Know

Vocabulary

Question 1.
How many tens are in this number?
23
__ tens
Answer:
2 tens .
Explanation :
23 have 2 is in tens place and 3 is in Ones place .

Question 2.
Use the hundred chart to count by 10s.

30, 40, 50, ___, ___
Answer:
30, 40, 50, 60, 70 .

Question 3.
Use the open number line to add.

7 + 9 = __
Answer:

Explanation :
Start at 7 and to add 9 make 9 jumps from 7 you land at 16 which is the sum .

Count Back to Subtract

Question 4.
Mark takes 8 pictures. Julia takes 3 fewer pictures than Mark. Count back to find how many pictures Julia took.
8, __, ___, __ __ pictures
Answer:
Number of Pictures taken by Mark = 8
Number of pictures taken by Julia = 3 fewer pictures than Mark = 8 – 3 = 5 Pictures .

Explanation :
Start at 8 and to subtract 3 from 8 . jump back 3 times you will land at 5 which is the difference .

Question 5.
Katie picks 15 flowers. Max picks 13 flowers. Count back to find how many fewer flowers Max picked than Katie.
15, ___, ___ ___ fewer flowers
Answer:
Number of Flowers Katie picks = 15 flowers
Number of flowers Max picks = 13 flowers
Number of fewer flowers Max picked than Katie = 15 – 13 = 2 flowers .
Therefore, Number of fewer flowers Max picked than Katie = 2 flowers  .

Explanation :
Count back
Start at 15 and count back and make 13 jumps as we are subtracting 13 .
you land at 2 , which is the difference .

Subtraction Facts

Question 6.
Find each difference.
12 – 4 = ___
14 – 7 = ___
19 – 9 = ___
Answer:
12 – 4 = 8
14 – 7 = 7
19 – 9 =10

Pick a Project

PROJECT 11A

Have you ever looked closely at money?
Project: Study Penny Collections

PROJECT 11B

Where are baby sea turtles born?
Project: Tell Sea Turtle Subtraction Stories

PROJECT 11C

What’s your favorite flavor of smoothie?
Project: Set Up a Smoothie Stand

3-ACT MATH PREVIEW

Math Modeling

So Many Colors

Before watching the video, think: When you clean up, how many toys can you clean up at the same time? How can you tell how many toys fit in a container?

Lesson 11.1 Subtract Tens Using Models

Solve & Share

How can thinking about 4 – 1 help you to find 40 – 10? Use place-value blocks to help you.

Answer :

Visual Learning Bridge

Convince Me!
When you solve 40 – 10, how does the tens digit change? How does the ones digit change?
Answer :
40 – 10 = 30
In tens digit only the tens values are subtracted and the ones digit will remain same as 0 .
In Ones digit only the subtracted values are written .

Guided Practice
Write the numbers to complete each equation.

Question 1.

Answer:

Explanation :
70 – 10 is like subtracting 1 ten from groups of 10 .
7 tens – 1 tens = 6 tens .

Question 2.

___ tens – ___ tens = ___ tens.
__ – __ = ___
Answer:

Explanation :
60 – 20 is like subtracting 1 ten from groups of 10 .
6 tens – 2 tens = 4 tens .

Independent Practice

Write the numbers to complete each equation.

Question 3.

___ tens – ___ tens = ___ tens.
__ – __ = ___
Answer:

Explanation :
80 – 30 is like subtracting 1 ten from groups of 10 .
8 tens – 3 tens = 5 tens .

Question 4.

___ tens – ___ tens = ___ tens.
__ – __ = ___
Answer:

Explanation :
50 – 10 is like subtracting 1 ten from groups of 10 .
5 tens – 1 tens = 4 tens .

Question 5.

___ tens – ___ tens = ___ tens.
__ – __ = ___
Answer:

Explanation :
80 – 20 is like subtracting 1 ten from groups of 10 .
8 tens – 2 tens = 6 tens .

Question 6.

___ tens – ___ tens = ___ tens.
__ – __ = ___
Answer :

Explanation :
60 – 30 is like subtracting 1 ten from groups of 10 .
6 tens – 3 tens = 3 tens .

Problem Solving

Solve each problem below.

Question 7.
Ethan has 30 crayons. He gives 10 crayons away. How many crayons does Ethan have now? Write the equation.
__ – ___ = ____ crayons
Answer :
Number of Crayons with Ethan = 30 crayons
Number of Crayons given away = 10 crayons .
Number of crayons with Ethan now = 30 – 10 = 20 crayons .

Question 8.
Algebra Jacob solved these problems. Did Jacob subtract 1 or 10?
Finish the equations.
50 – = 40
60 – = 59
Answer:

so, Jacob used both 10 and 1 to subtract the equations .
Explanation :
To get 40 as difference we need to subtract 10 from 50 .
To get 59 as difference we need to subtract 1 from 60 .

Question 9.
Higher Order Thinking Write and solve a story problem for 90 – 10.

Answer:

Question 10.
Assessment Practice 20 teddy bears are for sale at the store. Then, 10 teddy bears are sold.

How many teddy bears are on sale at the store now?

Answer:
Option c – 10
Explanation :
Number of teddy bears for sale = 20
Number of teddy bears are sold = 10
Number of teddy bears are left = 20 – 10 = 10 bears .

Lesson 11.2 Subtract Tens Using a Hundred Chart

Solve & Share

Use a hundred chart to find these differences. 50 – 30 = ? 30 – 20 = ? 80 – 10 = ? Explain.

Answer :

Visual Learning Bridge

Convince Me!
Find 80 – 50. Explain how you found the difference.
Answer :

Explanation :
Start at 80
For every ten we subtract, move up 1 row – to subtract 50 that is 5 tens we move up 5 rows .
after moving 5 rows we land at 30 which is the difference .

Guided Practice
Use the chart to subtract. Be ready to explain your work.

Question 1.
40 – 10 = 30
Answer :

Question 2.
40 – 20 = __
Answer:

Question 3.
30 – 20 = ___
Answer:

Question 4.
10 – 10 = ___
Answer:
10 – 10 = 0

Explanation :
start at 10
To subtract 10 from 10
cancel 10 numbers from 10 count back
it will land at 0 , the difference .

Independent Practice

Use the chart to subtract. Be ready to explain your work.

Question 5.
50 – 30 = ___
Answer:

Question 6.
80 – 60 = ___
Answer:

Question 7.
30 – 30 = ___
Answer:

Question 8.
90 – 30 = ___
Answer:

Question 9.
70 – 20 = ___
Answer:

Question 10.
20 – 10 = ___
Answer:

Question 11.
60 – 30 = ___
Answer:

Question 12.
90 – 50 = ___
Answer:

Question 13.
90 – 40 = ___
Answer:

Question 14.
80 – 40 = ___
Answer :

Algebra Find the missing numbers.

Question 15.
30 – ___ = 20
Answer:
30 – ___ = 20
30 – 20 = x
x = 10 .

Question 16.
___ – 30 = 10
Answer:
40
Explanation :
___ – 30 = 10
x – 30 = 10
x = 30 + 10
x = 40 .

Question 17.
___ – 50 = 20
Answer:
70
Explanation :
___ – 50 = 20
x – 50 = 20
x = 50 + 20
x = 70 .

Question 18.
20 – ___ = 0
Answer :
20
Explanation :
20 – ___ = 0
20 – x = 0
x = 20 .

Question 19.
___ – 20 = 30
Answer:
50
Explanation :
___ – 20 = 30
x – 20 = 30
x = 30 + 20
x = 50 .

Question 20.
70 – __ = 30
Answer:
40
Explanation :
70 – __ = 30
70 – x = 30
x = 70 -30
x = 40 .

Problem Solving

Use the chart to solve each problem. Show your work.

Question 21.
Use Tools Colvin throws a dart at a target 70 times. 10 times, he misses the target. How many times did he hit the target?
__ – ___ = ___
___ times
Answer:
Number of times he threw the dart = 70 times.
Number of times he misses the target = 10 times .
Number of times he targets = 70 – 10 = 60 times .

Question 22.
Use Tools Mal’s basketball team scores 40 points. They score 10 more points than the other team. How many points did the other team score?
__ – ___ = ___
___ points
Answer:
Score of Mal’s basketball team = 40 points .
Score of other team = 10 more points than the other team = 40 – 10 = 30 points .

Question 23.
Higher Order Thinking Circle any number in the last row of the partial hundred chart above. Subtract 30. Write your equation.
Answer:
Any number of last row of the partial hundred chart above = 70 .
70 – 30 = 40

Question 24.
Assessment Practice Leo makes 50 muffins for his class bake sale. He sells 10 muffins. How many muffins are left?
A. 10
B. 20
C. 30
D. 40
Answer:
Number of muffins baked = 50
Number of muffins for sold = 10
Number of muffins left = 50 – 10 = 40 . muffins .
Therefore, Number of muffins left = 40 muffins .

Lesson 11.3 Subtract Tens Using an Open Number Line

Solve & Share

Solve 50 – 20 by showing it on this open number line. Be ready to explain your work.

Answer :

Visual Learning Bridge

Convince Me!
How can you use an open number line to subtract tens?
Answer :
We can use open number line for subtraction by counting back .

Guided Practice

Use the open number line to subtract. Be ready to explain your work.

Question 1.
30 – 20 = ___

Answer:

30 – 20 = 10 .
Explanation :
Start at 30 . Use place value take 20 as 2 groups of 10 .
count back 2 10’s from 30 .
we land on 10 which is the difference .

Question 2.
90 – 50 = ___

Answer:

Explanation :
Start at 90 . Use place value take 50 as 5 groups of 10 .
count back 5 10’s from 90 .
we land on 40 which is the difference .

Independent Practice

Use the open number lines to subtract. Be ready to explain your work.

Question 3.
70 – 20 = ___

Answer:

Explanation :
Start at 70 . Use place value take 20 as 2 groups of 10 .
count back 2 10’s from 70 .
we land on 50 which is the difference .

Question 4.
60 – 10 = __

Answer:

Explanation :
Start at 60 . Use place value take 10 as 1 group of 10 .
count back 1 10’s from 60 .
we land on 50 which is the difference .

Question 5.
80 – 30 = __

Answer:

Explanation :
Start at 80 . Use place value take 30 as 3 groups of 10 .
count back 3 10’s from 80 .
we land on 50 which is the difference .

Question 6.
40 – 40 = ___

Answer:

Explanation :
Start at 40 . Use place value take 40 as 4 groups of 10 .
count back 4 10’s from 40 .
we land on 0 which is the difference .

Problem Solving

Use open number lines to solve the problems.

Question 7.
Model Dexter has 40 toothpicks. He uses 20 of them. How many toothpicks does he have left to use? Show your work.

___ – ___ = ___ Dexter has ___ toothpicks left.
Answer:
Total Number of tooth picks = 40
Number of tooth picks used = 20 .
Number of tooth picks left = 40 – 20 = 20  tooth picks .

Question 8.
Higher Order Thinking Write an equation for what this number line shows.

Answer:
50 – 30 = 20 .
Explanation :
started at 50 .
each jump represent – 10 .
3 jumps are made from 50 that is -30 .
lands on 20 which is the difference .

Question 9.
Assessment Practice Find 80 – 20. Explain your work.

Answer:

Explanation :
Start at 80 . Use place value take 20 as 2 groups of 10 .
count back 2 10’s from 80 .
we land on 60 which is the difference .

Lesson 1.4 Use Addition to Subtract Tens

Solve & Share

Mia has 70 stickers. Jack has 30 stickers. How many more stickers does Mia have than Jack has?

Answer :

Visual Learning Bridge

Convince Me!
How can using addition help you solve subtraction problems?
Answer :
With addition, the parts are known, but not the total; with subtraction, the total and one of the parts are known, but not the other part. Because of this relationship between the two operations, using addition is the most effective thinking strategy for helping students learn the basic subtraction facts .

Guided Practice
Use addition to solve each subtraction problem. Show how to find the missing addend on the open number line.

Question 1.

Answer:

Explanation :
Each jump represent + 10, 4 jumps are made 40 is added .
Start at 40 and make 4 jumps . You land on 80 , which is the sum .
From 80 , if we Subtract 40,we get 40 as difference.

Question 2.
30 + ___ = 90 so 90 – 30 = __

Answer:

Explanation :
Each jump represent + 10, 6 jumps are made 60 is added .
Start at 30 and make 6 jumps . You land on 90 , which is the sum .
From 90 , if we Subtract 30, we get 60 as difference .

Independent Practice

Use addition to solve each subtraction problem. Show how to find the missing addend on the open number line.

Question 3.
20+ ___ = 60, so 60 – 20 = ___

Answer:

Explanation :
Each jump represent + 10, 4 jumps are made 40 is added .
Start at 20 and make 4 jumps . You land on 60 , which is the sum .
From 60 , if we Subtract 20, we get 40 as difference .

Question 4.
30 + ___ = 80, so 80 – 30 = ___

Answer :

Explanation :
Each jump represent + 10, 5 jumps are made 50 is added .
Start at 30 and make 5 jumps . You land on 80 , which is the sum .
From 80 , if we subtract 30, we get 50 as difference .

Use addition to solve each subtraction problem. Draw a picture to show your thinking.

Question 5.
30 + ___ = 50, so 50 – 30 = ___

Answer :

Explanation :
Each jump represent + 10, 2 jumps are made 20 is added .
Start at 30 and make 2 jumps . You land on 50 , which is the sum .
From 50 , if we subtract 30, we get 20 as difference .

Question 6.
60 + __ = 80, so 80 – 60 = ___
Answer:

Explanation :
Each jump represent + 10, 2 jumps are made 20 is added .
Start at 60 and make 2 jumps . You land on 80 , which is the sum .
From 80 , if we subtract 60, we get 20 as difference .

Problem Solving

Write an equation and solve the problems below.

Question 7.
Reasoning Mr. Andrews collects 90 papers from his students. He has already graded 40 papers. How many papers does Mr. Andrews have left to grade?

__ papers
Answer:
Number of papers collected by Mr. Andrew = 90 papers
Number of papers graded = 40 papers .
Number of papers left to grade = 90 – 40 = 50 papers .
Therefore, Number of papers left to grade = 50 papers  .

Question 8.
Reasoning Stacy drives 40 miles to work. She has already driven some miles. Stacy has 20 miles left to drive. How many miles has Stacy already driven?

___ miles
Answer:
Number of miles Stacy drives = 40 miles .
Number of miles left to drive = 20 miles.
Number of miles driven by Stacy = 40 – 20 = 20 miles .
Therefore, Number of miles driven by Stacy = 20 miles .

Question 9.
Higher Order Thinking Sam has 4 cases of juice boxes. There are 10 juice boxes in each case. He brings 3 cases to share with his class.
Write and solve an equation to show how many juice boxes Sam has left.
__ – __ = ___
___ juice boxes
Answer:
Number of cases of juice boxes = 4
Number of juice boxes in each case = 10 .
Number of cases of juice boxes Sam took to share = 3
Number of cases of juice boxes left = 4 – 3 = 1 case .
Number of juice boxes in 1 case = 10 .juice boxes .
Therefore, Number of juice boxes left = 10 juice boxes .

Question 10.
Assessment Practice Dr. Tess had 20 patients to see today. She has already seen 10 of them. How many patients does Dr. Tess have left to see?
A 40
B 30
C 20
D 10
Answer:
Option D – 10 .
Explanation :
Number of patients = 20 .
Number of patients already seen by Dr . = 10 .
Number of patients left to see = 20 – 10 = 10 patients .

Lesson 11.5 Mental Math: Ten Less Than a Number

Solve & Share

Suppose you have 89 trading cards. How many cards would 10 more cards be? How many cards would 10 less cards be?

Answer :
89 + 10 = 99
tens digit value is increased by 1, 8tens + 1 tens = 9 tens
ones digit value remains same . 9 ones .
89 – 10 = 79
tens digit value is decreased by 1, 8tens – 1 tens = 7 tens
ones digit value remains same . 9 ones .
Explanation :
Adding 10 increases the the digit in the tens place by 1 (as long as it is not 9).
Subtracting 1 decreases the the digit in the tens place by 1 (as long as it is not 0).

Visual Learning Bridge

Convince Me!
Explain why only the tens digit changes when you subtract 10 from 76.
Answer :
Subtracting 10 from the 76 decreases one from the tens digit value
that is 7 – 1 = 6
and ones digit 6 remains the same as any number subtracted from 0 gives number itself .
so, no change takes place to the one’s digit value .
so, 76 – 10 = 66 .

Guided Practice
Use mental math to subtract. Use ten-frames if needed.

Question 1.

Answer:

Explanation :
26 is represented in ten frame .
to subtract 10 from 26 complete 1 ten frame is removed
then difference = 16 .

Question 2.

32 – 10 = ___
Answer:

Explanation :
32 is represented in ten frame .
to subtract 10 from 32 complete 1 ten frame is removed
then difference = 22 .

Question 3.
98 – 10 = ___
Answer:

Explanation :
98 is represented in ten frame .
to subtract 10 from 98 complete 1 ten frame is removed
then difference = 88 .

Question 4.
44 – 10 = __
Answer:

Explanation :
44 is represented in ten frame .
to subtract 10 from 44 complete 1 ten frame is removed
then difference = 34 .

Independent Practice

Use mental math to solve.

Question 5.
53 – 10 = ___
Answer:

Explanation :
53 is represented in ten frame .
to subtract 10 from 53 complete 1 ten frame is removed
then difference = 43 .

Question 6.
20 – 10 = __
Answer:

Explanation :
20 is represented in ten frame .
to subtract 10 from 20 complete 1 ten frame is removed
then difference = 10 .

Question 7.
32 – 10 = ___
Answer:

Explanation :
32 is represented in ten frame .
to subtract 10 from 32 complete 1 ten frame is removed
then difference = 22 .

Question 8.
80 – 10 = __
Answer:

Explanation :
80 is represented in ten frame .
to subtract 10 from 80 complete 1 ten frame is removed
then difference = 70 .

Question 9.
17 – 10 = ___
Answer:

Explanation :
17 is represented in ten frame .
to subtract 10 from 17 complete 1 ten frame is removed
then difference = 7 .

Question 10.
60 – 10 = ___
Answer:

Explanation :
60 is represented in ten frame .
to subtract 10 from 60 complete 1 ten frame is removed
then difference = 50 .

Question 11.
47 – 10 = ___
Answer:

Explanation :
47 is represented in ten frame .
to subtract 10 from 47 complete 1 ten frame is removed
then difference = 37 .

Question 12.
85 – 10 = ___
Answer:

Explanation :
85 is represented in ten frame .
to subtract 10 from 85 complete 1 ten frame is removed
then difference = 75 .

Question 13.
11 – 10 = ___
Answer:

Explanation :
11 is represented in ten frame .
to subtract 10 from 11 complete 1 ten frame is removed
then difference = 34 .

Question 14.
Number Sense Subtract using ten-frames and mental math. Complete the related addition equation.

Answer:

Explanation :
39 is represented in ten frame .
to subtract 10 from 39 complete 1 ten frame is removed
then difference = 29.

Problem Solving

Use mental math to solve the problems below.

Question 15.
Reasoning Jamal has 43 stamps on his desk. He puts 10 stamps in a notebook. How many stamps are left?

__ stamps
Answer:

Explanation :
Number of stamps on desk = 43 stamps.
Number of stamps kept in book = 10 stamps.
Number of stamps left over = 43 – 10 stamps = 33 stamps.

Question 16.
Vocabulary Ed brings 27 oranges home. His family eats 10 of them. How many oranges does Ed have left? Find the difference.
27 – 10 = ___
___ oranges
Answer:
Number of Oranges brought = 27
Number of Oranges family ate = 10
Number of oranges left = 27 – 10 = 17
Therefore, Number of oranges left = 17 oranges .

Question 17.
Higher Order Thinking Write a subtraction story about 56 – 10. Then solve your story.

Answer:
Addy have 56 mangos to sell . he sold 10 mangos, How many mangos did Addy left with ?
Answer :
Total Number of Mangoes = 56
Number of Mangoes sold = 10 .
Number of mangoes left = 56 – 10 = 46 mangoes .

Question 18.
Assessment Practice Use mental math to find 44 – 10.
A 54
B 45
C 43
D 34
Answer:
Option D – 34.
Explanation :
Subtracting 10 from the 44 decreases one from the tens digit value
that is 4 – 1 = 3
and ones digit 4 remains the same as any number subtracted from 0 gives number itself .
so, no change takes place to the one’s digit value .
so, 44 – 10 = 34 .

Lesson 11.6 Use Strategies to Practice Subtraction

Solve & Share

Make up a story about 60 – 40. Then solve the subtraction problem. Use the strategy you think works best.

Answer :

Visual Learning Bridge

Convince Me!
Which strategy would you use to solve 50 – 40? Explain why.
Answer :
Number line.

Explanation :
Each jump represent -10 .
Start at 50 and make 4 jumps that is – 40 .
it lands on 10 which is the difference .

Guided Practice
Use the partial hundred chart or another strategy to solve each subtraction problem.

Question 1.
70 – 10 = 60
Answer:

Question 2.
60 – 20 = __
Answer:

Question 3.
43 – 10 = ___
Answer:

Question 4.
70 – 30 = __
Answer:

Independent Practice

Use the strategy you think works best to solve each subtraction problem. Explain your reasoning.

Question 5.
90 – 40 = ___
Answer :

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .

Question 6.
40 – 20 = ___
Answer:

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .

Question 7.
80 – 60 = ___
Answer:

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .

Question 8.
50 – 20 = ___
Answer:

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .

Question 9.
74 – 10 = ___
Answer:

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .

Question 10.
80 – 40 = ___
Answer:

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .

Question 11.
enVision® STEM Students at a school plant flowers in a garden. They plant 50 flowers in a part that gets a lot of sunshine. They plant 30 flowers in a part that is shaded from the sun. How many fewer flowers did they plant in a shaded spot than in a sunny spot? Write an equation to show your work.
___ – ___ = ___ ___ fewer flowers
Answer :
Number of flower plants planted in sunshine = 50 flowers .
Number of flower plants planted in sunny spot = 30 flowers .
Number of fewer flower plants planted in shaded spot than in a sunny spot = 50 – 30 = 20 fewer flowers .
Therefore, 20 fewer flower plants are planted in shaded spot than in a sunny spot .

Problem Solving

Choose one of the strategies you learned to solve each subtraction problem.

Question 12.
Use Tools Charlie puts baseball cards into an album. He already put 10 cards in the album. He has 83 cards in all.
How many baseball cards does Charlie have left to put in the album?
__ cards
Answer:
Total Number of cards = 83 cards .
Number of cards kept in album = 10 cards .
Total number of cards left to put in album = 83 – 10 = 73 cards .
Explanation :

Question 13.
Use Tools Pearl’s basketball team scores 50 points in one game. They score some points in the first half. They score 20 points in the second half.
How many points did Pearl’s team score in the first half?
___ points
Answer:
Number of points scored by pearl’s team = 50 points .
Number of points in second half = 20
Number of points scored in first half = 50 – 20 = 30 points .
Explanation :

Question 14.
Higher Order Thinking Write a subtraction problem for which you would think addition to subtract. Explain why this would be a good strategy to use to solve this problem.
Answer:
Andy walks 80 miles from his house to school to park . he  walks 60 miles from school to park . How many miles did he walk from house to school?
Solution :
Number of miles andy walk = 80 miles.
Number of miles he walked from School to park = 60 miles.
Number of miles he walked from house to school = 80 – 60 = 20 .

Explanation :
Each jump represent + 10, 2 jumps are made 20 is added .
Start at 60 and make 2 jumps . You land on 80 , which is the sum .
From 80 , if we subtract 60, we get 20 as difference .

Question 15.
Assessment Practice Explain how you would use a hundred chart to solve 60 – 20.
Answer:

Lesson 11.7 Model with Math

Solve & Share

Val picks 40 strawberries. She shares 20 of them with her brother. How many strawberries did Val keep for herself?
How can modeling your thinking help you solve this problem?

Answer :

Thinking Habits
Can I use a drawing, diagram, graph, or table to model this problem? How can I make my model better if it doesn’t work?

Visual Learning Bridge

Convince Me!
In the example above, how do the boxes of 10 help model the problem?
Answer :
The sum is given in the multiples of ten so, each box represent 10 and 70 is represented as 7 boxes to subtract 40 we need to cancel 4 boxes .
it made calculation part easier and simple .

Guided Practice
Use drawings, models, or equations to solve.

Question 1.
A store has 60 muffins. It sells 30 of the muffins. How many muffins does the store have now?
30 muffins

Answer:
Number of muffins at store = 60 muffins .
Number of muffins sold = 30 muffins .
Number of muffins left out = 60 – 30 = 30 muffins .

Therefore, Number of muffins left out = 30 muffins .

Question 2.
Andy has 84 baseball cards. He has 10 more cards than Tia has. How many cards does Tia have?
___ cards
Answer:
Number of base ball cards with Andy = 84 .
Andy has 10 more cards than Tia that means Tia have 10 less cards than Andy
Number of base ball cards with Tia = 84 – 10 = 74 cards .

Independent Practice

Use drawings, models, or equations to solve. Explain your work.

Question 3.
Viola has 80 stickers. Dean has 60 stickers. How many more stickers does Viola have than Dean?
___ more stickers
Answer:
Number of Stickers with Viola = 80 stickers.
Number of stickers with Dean = 60 stickers .
Number of More stickers Viola have than Dean – 80 – 60 = 20 stickers .
Explanation :

Question 4.
Carla reads some pages in a book. She reads 20 pages less than Mary reads. Mary reads 50 pages. How many pages did Carla read?
__ pages
Answer:
Number of pages Read by Mary = 50 pages .
Carla reads 20 pages less than Mary reads
Number of pages read by Carla = 50 – 20 = 30 pages .

Question 5.
A store has 72 toy cars. It sells 10 cars. How many cars does the store have left?
___ cars
Answer:
Number of car toys = 72 .
Number of car toys sold = 10 .
Number of car toys left = 72 – 10 = 62 toys .
Therefore, Number of car toys left = 62 toys .

Problem Solving

Performance Task

Dog Walking James, Emily, and Simon walk dogs after school.
On Monday, they have 40 dogs to walk. James and Emily take 20 of the dogs for a walk. How many dogs are left for Simon to walk?

Answer:
Total Number of dogs = 40 dogs
Number of dogs James and Emily took for walking = 20 dogs .
Number of dogs left to take for walking by Simon = 40 – 20 = 20 dogs .
Therefore, Simon takes 20 dogs for walk .

Question 6.
Make Sense What problem do you need to solve?
Answer:
Number of dogs left to take for walking by Simon .

Question 7.

Use Tools What tool or tools can you use to solve this problem?
Answer:
Subtraction

Question 8.
Model Write an equation to show the problem. Then use pictures, words, or symbols to solve.

___ dogs
Answer:
Number of dogs left to take for walking by Simon = 40 – 20 = 20 dogs .

Topic 11 Fluency Practice Activity

Point & Tally

Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue.
Partner I and Partner 2 each point to a black number at the same time. Subtract Partner 2’s number from Partner 1’s number.
If the answer is on your color, you get a tally mark. Work until one partner gets twelve tally marks.

Topic Vocabulary Review

Understand Vocabulary

Question 1.
Subtract the tens shown by the model.

__ tens – __ tens = ___ tens
Answer:

Explanation :
60 – 30 is like subtracting 1 ten from groups of 10 .
6 tens – 3 tens = 3 tens .

Question 2.
Subtract the tens shown by the model.

__ tens – __ tens = ___ tens
Answer:

Explanation :
80 – 60 is like subtracting 1 ten from groups of 10 .
8 tens – 6 tens = 2 tens .

Question 3.
Circle the addition problem that could help you solve 50 – 30.
10 + 40 = 50
25 + 25 = 50
30 + 20 = 50
40 + 10 = 50
Answer:

Explanation :
50 – 30 = 20
20 + 30 = 50 .

Question 4.
Solve 40 – 20 using a partial hundred chart. Circle the difference.

Answer:

Question 5.
Use mental math to solve 70 – 10. Circle the difference.

Answer:
70 – 10 = 60

Explanation :
70 is represented in ten frame .
to subtract 10 from 70 complete 1 ten frame is removed
then difference = 60 .

Use Vocabulary in Writing

Question 6.
Solve 80 – 50 using an open number line. Explain how you solved it using terms from the Word List.

Answer:

Explanation :
Each jump represent – 10, 5 jumps are made that is -50 . .
Start at 80 and make 5 jumps . You land on 30 , which is the difference count back .

Topic 11 Reteaching

Set A

You can subtract tens.
40 – 30 = ?
You need to subtract 30, which is 3 tens.
Cross out that many tens.

Count the tens and ones that are left.
40 – 30 = 10

Cross out the tens. Write the difference.

Question 1.

60 – 40 = ___
Answer:

Explanation :
You need to subtract 40, which is 4 tens.
Cross out 4 tens.
Count the tens and ones that are left are 20 which is the difference .
60 – 40 = 20

Question 2.

50 – 20 = ___
Answer:

Explanation :
You need to subtract 20, which is 2 tens.
Cross out 2 tens.
Count the tens and ones that are left are 30 which is the difference .
50 – 20 = 30

Set B

You can use a hundred chart to subtract tens.
80 – 20 = ?

Use this partial hundred chart to subtract tens.

Question 3.
70 – 20 = ___
Answer:

Explanation :
Start at 70 .
For every 10 you subtract , move up 1 row .
20 , is 2 tens . so, move up 2 rows .
lands on 50 which is the difference .

Question 4.
60 – 10 = ___
Answer:
60 – 10 = 50 .

Explanation :
Start at 60 .
For every 10 you subtract , move up 1 row .
10 , is 1 tens . so, move up 1 rows .
lands on 50 which is the difference .

Set C

You can use mental math to subtract tens. Find 46 – 10.

Subtract. Use mental math.

Question 5.
62 – 10 = ___
Answer:
62 – 10 = 52 .

Explanation :
You need to subtract 10, which is 1 tens.
Cross out 1 tens.
6 tens – 1 tens = 5 tens .
so, 62 – 10 = 52 .

Question 6.
89 – 10 = ___
Answer:

Explanation :
You need to subtract 10, which is 1 tens.
Cross out 1 tens.
8 tens – 1 tens = 7 tens .
so, 89 – 10 = 79 .

Question 7.
27 – 10 = ___
Answer:

Explanation :
You need to subtract 10, which is 1 tens.
Cross out 1 tens.
2 tens – 1 tens = 1 tens .
so, 27 – 10 = 17 .

Set D

Thinking Habits
Model with Math

Can I use a drawing, diagram, table, or graph to model the problem? How can I make my model better if it doesn’t work?

Write an equation to solve. Use drawings or models to show your work.

Question 8.
A store has 50 toy boats. They sell 10 boats. How many toy boats does the store have now?
___ toy boats
Answer:
Number of toy boats = 50 .
Number of toy boats sold = 10 .
Number of toy boats left = 50 – 10 = 40 .

Topic 11 Assessment Practice

Question 1.
Use the partial hundred chart to subtract tens.

A 70
B 60
C 50
D 40
Answer:
Option C .

Explanation :
Start at 70 .
For every 20 you subtract , move up 2 rows .
20 , is 2 tens . so, move up 2 rows .
lands on 50 which is the difference .

Question 2.
Use the place-value blocks. Find the difference.
A 10
B 20
C 30
D 40
Answer:
Option A

Explanation :
You need to subtract 30, which is 3 tens.
Cross out 3 tens.
4 tens – 3 tens = 1 tens .
so, 40 – 30 = 10 .

Question 3.
Use the open number line to solve. Show your work. Explain how you used the number line to find the answer. 60 – 20 = ____

Answer :

Explanation :
Start at 60 . Use place value take 20 as 2 groups of 10 .
count back 2 10’s from 60 .
we land on 40 which is the difference .

Question 4.
Solve the problem. Use any strategy. Explain why you picked the strategy. Write an addition equation to check your answer.
70 – 60 = ___
Answer:

Explanation :
Start at 70 . Use place value take 60 as 6 groups of 10 .
count back 6 10’s from 70 .
we land on 10 which is the difference .

Use mental math to solve. Then write an addition equation to check your answer.

Question 5.
23 – 10 =
Answer:

Explanation :
23 is represented in ten frame .
to subtract 10 from 23 complete 1 ten frame is removed
then difference = 13 .

Question 6.
94 – 10 = ___
Answer:

Explanation :
94 is represented in ten frame .
to subtract 10 from 94 complete 1 ten frame is removed
then difference = 84 .

Question 7.
51 – 10 = ___
Answer:

Explanation :
23 is represented in ten frame .
to subtract 10 from 23 complete 1 ten frame is removed
then difference = 13 .

Use addition to solve each subtraction problem.

Question 8.
50 + ___ = 80, so 80 – 50 = ___.
Answer:
50 + 30 = 80,
so 80 – 50 = 30 .

Question 9.
20 + __ = 60, so 60 – 20 = ___.
Answer:
20 + 40  = 60,
so 60 – 20 = 40.

Question 10.
A store has 90 sleds. It sells 30 sleds. How many sleds does the store have left?
Write an equation and solve. Use drawings or models to show your work.
___ sleds
Answer:
Number of sleds = 90 .
Number of sleds sold = 30
Remaining Number of sleds = 90 – 30 = 60 .

Topic 11 Performance Task

Fred’s Farm
Fred sells different vegetables at his farm. He puts them in packages of 10.

Question 1.
Fred sells 3 packages of green peppers. How many green peppers does he have left to sell? Use the open number line to solve.

____ green Peppers
Answer:
Number of peppers in each bag contains = 10 peppers
Total number of green peppers = 7 bags .
Number of peppers bags sold = 3 bags .
Number of peppers bags left = 7 – 3 = 4 bags .

Question 2.
Fred feeds 10 carrots to his horse. How many carrots does he have left?
___ carrots
Answer:
Number of carrots = 6 bags
each bag contains 10 carrots .
Number of carrots = 6 × 10 = 60 carrots
Number of carrots feeds to Horse = 10
Number of carrots left = 60 – 10 = 50 carrots .

Question 3.
Fred sells 30 potatoes on Monday. He sells the rest on Tuesday. How many potatoes were sold on Tuesday?
Use the partial hundred chart to solve the problem. Write the missing numbers in the equation.

___ potatoes
Answer:
Total Number of potatoes = 60
Number of potatoes sold on Monday = 30 .
Number of potatoes sold on Tuesday = ? = 60 – 30 = 30 potatoes .

Explanation :
Hundred chart is the best for subtraction problems for tens . it just move up 1 row for every 10 we subtract .
30 is 3 tens move up 3 rows .
we get 30 as the difference .

Question 4.
Debbie buys 4 packages of carrots at the farm. She uses 10 carrots to make soup. How many carrots does she have left? Solve the problem. Use one of the strategies you learned. Show how you solved the problem.

___ carrots
Answer:
Number of carrots in each package = 10
Number of packages = 4
Number of carrots in 4 packages = 10 + 10 + 10 +10 = 40 carrots .
Number of carrots used for soup = 10
Number of carrots left = 40 -10 = 30 carrots .

Hundred chart is used to solve the above problem .

Question 5.
Ty buys 36 vegetables. Lee buys 10 fewer vegetables than Ty. How many vegetables does Lee buy?

Part A
What strategy could you use to solve the problem?
Answer :
Hundred chart strategy .
Part B
Write an equation and solve the problem. Show how you solved it.

___ vegetables
Answer :
Number of vegetables ty bought = 36
Number of vegetables lee buys = 10 fewer vegetables than Ty. = 36 – 10 = 26 .

26 vegetables .

Practice with the help of enVision Math Common Core Grade 1 Answer Key Topic 8 Understand Place Value regularly and improve your accuracy in solving questions.

enVision Math Common Core 1st Grade Answers Key Topic 8 Understand Place Value

enVision STEM Project: Daylight Throughout the Year
Find Out Talk to friends and relatives about why there is more daylight in summer than in winter.
Ask them to help you find information about the changes in daylight each season.

Journal: Make a Book Draw pictures of the tilting globe and the sun at different times of the year. In your book, also:

• Add labels to show summer and winter.
• Write a sentence to describe the pattern of the seasons in your own words.

Review What You Know

Vocabulary

Question 1.
Circle the tens digit.

Answer:

Explanation:
Given 2 digit number 48.
Two digit number have tens place and ones place.
4 is in tens place and 8 in ones place
4 is circled as tens digit.

Question 2.
Circle the ones digit.

Answer:

Explanation:
Given 2 digit number 76.
Two digit number have tens place and ones place.
7 is in tens place and 6 in ones place
6 is circled as ones digit.

Question 3.
Use the ten-frames to find the sum.
7 + 9 = ___

Answer:

Counting to 120

Question 4.
Write the number that comes next when counting forward by Is. Use a hundred chart to help you.
110, 111, 112, ____
Answer:
110, 111, 112, 113
Explanation:
Given
A sequence of  3 digit numbers
110, 111, 112, ____ and asked to find the 4th digit by counting forward by Is
3 digit number have hundreds place  tens place and ones place
Since counting forward by 1s
we add the 1 to the ones place of 3rd digit to get the 4th digit keeping the tens place and hundreds place constant.
112 + 001 = 113.
Missing number is 113.

Question 5.
Maria counts by 10s. She starts at 30. Write the missing numbers.
30, ___, ___
60, ___
Answer:
30, _40__, _50__
60, _70__
Explanation:
Maria counts by 10s
Given
30, ___, ___ and 2 number missing to find the missing number we add 1 to the tens place keeping ones place constant.
given
30 = 3 is tens digit and 0 ones digit.
Adding tens digit with 1
3 + 1 = 4, 4 + 1 = 5.
30, _40__,_50__
60 = 6 tens digit and 0 ones digit
60 + 10 = 70
60, _70__

Hundred Chart

Question 6.
Write the missing numbers in this part of the hundred chart.

Answer:

pick a Project

PROJECT 8A
What do you put on your hot dog?
Project: Act Out Serving Up Hot Dogs

Answer:
Topping on the Hot dog
1. Hot dog bun.
2. Veg- dog or Non- Veg dog
3. Onion
4. Jalapenos
5. Lattice
6. Herbs
7. Sauces.

PROJECT 8B
What is your favorite color?
Project: Make a Color Poster

PROJECT 8C
Can you eat a tiger?
Project: Play a Cracker Stack Game

PROJECT 8D
Which sea creatures have 10 legs?
Project: Make a Finger Painting

Answer:

Lesson 8.1 Make Numbers 11 to 19

Solve & Share

Use counters and ten-frames to show 12, then 15, and then 18. Draw your counters in the ten-frames below. Tell what is the same and different about each number you show.

Visual Learning Bridge

Answer:

Convince Me!
How could you use ten-frames to show 13 counters?
Answer:

Explanation:
one group of 10 ones = 1 ten
13 is made up of one group of 10 ones and 3 ones
13 is 1 ten and  3 ones.

Guided Practice

Use counters to make each number. Then write each number as I ten and some ones.

Question 1.
twelve
is 1 ten and ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
12 is made up of one group of 10 ones and 2 ones
12 = 10 + 2
12 is 1 ten and  2 ones.

Question 2.
fourteen
is 1 ten and ___ ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
14 is made up of one group of 10 ones and 4 ones
14 = 10 + 4
14 is 1 ten and  4 ones.

Question 3.
fifteen
is 1 ten and __ ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
15 is made up of one group of 10 ones and 5 ones
15 = 10 + 5
15 is 1 ten and  5 ones.

Independent Practice

Use counters to make each number. Then write the word or number.

Question 4.
sixteen
is ___ ten and 6 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
16 is made up of one group of 10 ones and 6 ones
16 = 10 + 6
16 is 1 ten and  6 ones.

Question 5.
____
is 1 ten and 8 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
18 is made up of one group of 10 ones and 8 ones
18 = 10 + 8
18 is 1 ten and  8 ones.

Question 6.
thirteen
is 1 ten and __ ones.
Answer:

is 1 ten and __ ones.
Explanation:
one group of 10 ones = 1 ten
13 is made up of one group of 10 ones and 3 ones
13 = 10 + 3
13 is 1 ten and 3 ones.

Question 7.
eleven
is ___ ten and 1 one.
Answer:

Explanation:
one group of 10 ones = 1 ten
11 is made up of one group of 10 ones and 1 ones
11 = 10 + 1
11 is 1 ten and  1 ones.

Question 8.
_____
is 1 and 7 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
17 is made up of one group of 10 ones and  7 ones
17 = 10 + 7
17 is 1 ten and  7 ones.

Question 9.
nineteen
is 1 ten and 9 ones.
Answer:

Explanation:
one group of 10 ones = 1 ten
19 is made up of one group of 10 ones and 9 ones
19 = 10 + 9
19 is 1 ten and  9 ones.

Question 10.
Vocabulary Circle the tens and ones that match the words shown.

Answer:

Explanation:
one group of 10 ones = 1 ten
12 is made up of one group of 10 ones and 2 ones
12 = 10 + 2
12 is 1 ten and 2  ones.
Explanation:
one group of 10 ones = 1 ten
15 is made up of one group of 10 ones and 5 ones
15 = 10 + 5
15 is 1 ten and  5 ones.

Problem Solving

Solve each problem below.

Question 11.
Use Tools Jill has 14 buttons and 2 boxes. She puts 10 buttons in one box. How many buttons does Jill put in the other box? Draw counters to solve. Write the numbers.
___ buttons
__ is ___ ten and __ ones.

Answer:

Question 12.
Higher Order Thinking Choose a number between 11 and 14. Draw a picture to show how to make the number with ten-frames. Write the number and the number word.

Answer:

Question 13.
Assessment Practice Match the groups or numbers on the left with the number word on the right.

Answer:

Lesson 8.2 Numbers Made with Tens

Solve & Share

How are 2 tens and 20 ones alike and different?
Use cubes to show your answer. Then draw your cubes.

Visual Learning Bridge

Answer:

Convince Me!
How many tens are in 90? How do you know?
Answer:

Explanation:
10 cubes make 1 ten.
To count the number of tens in 90
we count by 10’s as  10,20,30,40,50,60,70,80,90.
we count by tens as 1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens.
There are 90 cubes
90 is 9 tens and 0 ones.

Guided Practice

Use cubes. Count by 10s. Write the numbers.

Question 1

Answer:

Explanation:
10 cubes make 1 ten.
Here are 3 ten.
Count by 10’s to
10, 20, 30.
There are 30 cubes in all.
3 tens and 0 ones is 30.

Question 2.

___ tens and ___ ones is ____.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 5 ten.
Count by 10’s to
10, 20, 30, 40, 50.
There are 50 cubes in all.
5 tens and 0 ones is 50.

Independent Practice

Use cubes. Count by 10s. Draw the cubes. Write the numbers.

Question 3.

6 tens and 0 ones is ___.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 6 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60.
There are 60 cubes in all.
6 × 10 = 60.
6 tens and 0 ones is Sixty.

Question 4.

___ tens and ___ ones is 90.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 9 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70, 80, 90.
There are 90 cubes in all.
9 × 10 = 90.
9 tens and 0 ones is Ninety.

Question 5.

8 tens and 0 ones is ___.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 8 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70, 80.
There are 80 cubes in all.
8 × 10 = 80.
8 tens and 0 ones is Eighty.

Question 6.

__ tens and ___ ones is 70.
Answer:

Explanation:
10 cubes make 1 ten.
Here are 7 ten.
Count by 10’s to
10, 20, 30, 40, 50, 60, 70.
There are 70 cubes in all.
7 × 10 = 70.
7 tens and 0 ones is Seventy

Question 7.
Number Sense Joey has 2 tens. He wants to trade the tens for ones. How many ones should Joey get?
____ ones

Answer:
Number of tens Joey has = 2 tens
Joey wants to trade tens for ones.
1 ten = 10 ones
So, 2 tens  = 2 × 10 = 20 ones.
Joel gets 20 ones foe 2 tens.

Problem Solving

Solve the problems below.

Question 8.
Reasoning There are 2 buses. 10 people are in each bus. How many people ride in the buses? Count by 10s. Draw a picture to solve.

Answer:

Question 9.
Reasoning George has 3 boxes of pens. 10 pens are in each box. How many pens does George have?
___ pens
Answer:

Question 10.
Higher Order Thinking Brian has a book. He reads 10 pages every day. Show how many pages Brian reads in 5 days. Use pictures, numbers, or words.

Answer:

Question 11.
Assessment Practice
Beth has 4 jars. Each jar has 10 bouncy balls in it. How many bouncy balls does Beth have in all?


Answer:
Number of Jars Beth has = 4
Number of bouncy balls in each jar = 10
Total number of bouncy balls in the 4  jars = 10 + 10 + 10 + 10 = 40
4 × 10 = 40.
C)40 is the answer.
There are 40 bouncy balls in the jars.

Lesson 8.3 Count with Groups of Tens and Ones

Solve & Share

Tara has 34 cubes. How many groups of 10 can she make with the cubes? Show your work in the space below.

Answer:

Visual Learning Bridge

Convince Me!
Why does 37 have 3 groups of 10 and not 4 groups of 10?
Answer:
37 = 10 + 10 + 10 + 7
= 3 tens and 7 ones
= 3 groups of 10 and 7 ones.
4 groups of 10 = 10 + 10 + 10 + 10  = 40
So, 37 has 3 groups of 10 and 7 ones.

Guided Practice
Circle groups of 10. Write the numbers.

Question 1.

Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 5 sets of 5 cubes and 2 cubes
out of 5 set of 5 cubes 4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 5 + 2 = 7 ones.
2 groups of 10’s and 7 ones = 27 .

Question 2.

Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 7 sets of 5 cubes and 9 cubes
out of 7 set of 5 cubes 6 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
3 group of  10’s are formed.
The left over cubes are ones  = 5 + 4 = 9 ones.
3 groups of 10’s and 9 ones = 39.

Independent Practice

Circle the groups of 10. Write the numbers.

Question 3.

___ groups of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 8 sets of 5 cubes and 3 cubes
8 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
4 group of  10’s are formed.
The left over cubes are ones  = 3 = 3 ones.
4 groups of 10’s and 3 ones = 43.

Question 4.

___ groups of 10 and __ ones is ____.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 7 sets of 5 cubes
out of 7 set of 5 cubes 6 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
3 group of  10’s are formed.
The left over cubes are ones  = 5 = 5 ones.
3 groups of 10’s and 5 ones = 35.

Question 5.

___ group of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 3 sets of 5 cubes and 1 cubes
out of 3 set of 5 cubes 2 sets of 5 cubes make a
5 + 5 = 10
1 group of  10’s are formed.
The left over cubes are ones  = 5 + 1 = 6 ones.
1 groups of 10’s and 6 ones = 16.

Question 6.

___ groups of 10 and ___ ones is ___.

Write the number of groups of 10 and the number of ones. Then write the total.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 9 sets of 5 cubes and 3 cubes
out of 9 set of 5 cubes 8 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
5 + 5 = 10
4 group of  10’s are formed.
The left over cubes are ones  = 5 +3 = 8 ones.
4 groups of 10’s and 8 ones = 48.

Question 7.

___ groups of 10 and ___ ones is ___.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 5 sets of 5 cubes
out of 5 set of 5 cubes 4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 5  = 5 ones.
2 groups of 10’s and 5 ones = 25.

Question 8.

__ groups of 10 and ___ ones is __.
Answer:

Explanation:
2 sets of 5 cubes make 10.
Here 4 sets of 5 cubes
4 sets of 5 cubes make a
5 + 5 = 10
5 + 5 = 10
2 group of  10’s are formed.
The left over cubes are ones  = 2  = 2 ones.
2 groups of 10’s and 2 ones = 22.

Problem Solving

Draw a picture and write the numbers to solve each Solving problem below.

Question 9.
Model A monkey has 32 bananas. 10 bananas are in each bunch.

How many bunches are there? ____
How many bananas are left over? ___
Answer:

Question 10.
Model The dogs have 21 bones. 10 bones are in each bowl.

How many bowls are there? ____
How many bones are left over? ____
Answer:

Question 11.
Higher Order Thinking
Amil writes a number. His number has 5 groups of 10. His number has less than 9 ones. What number could Amil have written? ____
Answer:
Number of groups of 10’s Amil number has = 5
10 + 10 + 10 + 10 + 10 = 50
Number of ones Amil number has = less than 9
less than 9 may be = 1,2, 3, 4, 5, 6, 7, 8.
The number may be
5 groups of 10’s and 1 ones = 51
5 groups of 10’s and 2 ones = 52
5 groups of 10’s and 3 ones = 53
5 groups of 10’s and 4 ones = 54
5 groups of 10’s and 5 ones = 55
5 groups of 10’s and 6 ones = 56
5 groups of 10’s and 7 ones = 57
5 groups of 10’s and 8 ones = 58.
Amil number may be 51, 52, 53, 54, 55, 56, 57, 58.

Question 12.
Assessment Practice
A store has 5 bunches of grapes and 3 left over. Each bunch has 10 grapes. How many grapes are there in all? Explain.
Answer:
Number of bunches of grapes in the store = 5
Number of grapes in each bunch = 10 grapes
Number of left over = 3
Number of grapes in 5 bunches = 10 + 10 + 10 + 10 + 10 = 50 grapes.
Total number of grapes = 50 grapes and 3 left over is 53 grapes.

Lesson 8.4 Tens and Ones

Solve & Share

Estimate how many cubes are in your bag. Then empty the bag in the space below. Without counting each cube, estimate how many cubes there are. Write each estimate.

Now count the cubes and write the total number of cubes.

Estimate 1: ___ cubes
Estimate 2: ___ cubes
Actual amount: ___ cubes
Answer:

Visual Learning Bridge

Convince Me!
How are these numbers alike? How are they different?

Answer:
46 and 64 are two digit numbers
Two digit number have tens and ones.
Both the number have tens and ones digits only.
They are different as the place values of the number are different.
46 has 4 in tens place and 6 in ones place
64 has 6 in tens place and 4 in ones place .

Guided Practice
Use cubes. Count the tens and ones. Then write the numbers.

Question 1.

Answer:

Explanation:
Given
3 sets of 10 cubes in tens place
5 + 3 = 8 cubes in ones place
30 + 8 = 38.
3 tens and 8 ones  is 38.
3 in  38 is the tens digit
8 in 38 is the ones digit.

Question 2.

Answer:

Explanation:
Given
4 sets of 10 cubes in tens place
1 cubes in ones place
40 + 1 = 41
4 tens and 1 ones  is 41.
4 in  41 is the tens digit
1 in 41 is the ones digit.

Independent Practice

Use cubes. Count the tens and ones. Then write the numbers.

Question 3.

___ Ten and ___ ones is ___.
Answer:

Explanation:
Given
1 sets of 10 cubes in tens place
5 + 4 = 9 cubes in ones place
10 + 9 = 19
1 ten and 9 ones  is 19.
1 in  19 is the tens digit
9 in 19 is the ones digit.

Question 4.

___ tens and ___ ones is ___.
Answer:

Explanation:
Given
2 sets of 10 cubes in tens place
3 cubes in ones place
20 + 3 = 23
2 tens and 3 ones  is 23.
2 in  23 is the tens digit
3 in 23 is the ones digit.

Question 5.

___ tens and ___ ones is ___.
Answer:

Explanation:
Given
4 sets of 10 cubes in tens place
5 + 3 = 8 cubes in ones place
40 + 8 = 48
4 tens and 8 ones  is 48.
4 in  48 is the tens digit
8 in 48 is the ones digit.

Solve the problem below any way you choose.

Question 6.
Number Sense Bill writes a number. It has the same number of tens and ones. What could Bill’s number be?
Answer:
The number Bill wrote has same number of tens and ones.
Bills number may be any of these numbers.
1 ten and 1 one is 11
2 tens and 2 ones is 22
3 tens and 3 ones is 33
4 tens and 4 ones is 44
5 tens and 5 ones is 55
6 tens and  6 ones is 66
7 tens and  7 ones is 77
8 tens and 8 ones is 88
9 tens and 9 ones is 99.
Bill number may be 11, 22, 33, 44, 55, 66, 77, 88, 99.

Problem Solving

Solve each problem below.

Answer:

Question 7.
Reasoning Luz has juice boxes at her party. There are 3 packages of 10 and 7 extra juice boxes.
How many juice boxes are there in all?
Write the number of tens and ones. Then write the total number of juice boxes.

Answer:

Question 8.
Higher Order Thinking Draw a picture to show a number greater than 25 and less than 75. Then write the number.

Answer:

Question 9.
Assessment Practice Kai brought 2 packages of 10 juice boxes and 5 extra juice boxes. How many juice boxes did Kai bring? Write the number of tens and ones. Then write the total number of juice boxes.

Answer:

Lesson 8.5 Continue with Tens and Ones

Solve & Share

Laylani has 28 buttons. Draw her buttons so that a friend can see that there are 28 buttons without counting them one by one.

Answer:

Visual Learning Bridge

Convince Me!
When you draw to model a number, which digit tells you how many lines to draw? Which digit tells you how many dots to draw?
Answer:
When we draw a model a number
Tens place digit tells us to draw the number of lines.
Ones place digit tells us to draw the number of dots.

Guided Practice

Write the numbers and draw a model to show each number. Count by tens and ones to check.

Question 1.

Answer:

Explanation:
Given number 17
17 is 1 ten and 7 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
17 is represented with 1 line and 7 dots.

Question 2.
29 is ___ tens and ___ ones.

Answer:

Explanation:
Given number 29
29 is 2 ten and 9 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
29 is represented with 2 line and 9 dots.

Independent Practice

Write the numbers and draw a model to show each number. Count by tens and ones to check.

Question 3.
There are ___ tens and ___ ones in 43.
Answer:

There are 4 tens and 3 ones.
Explanation:
Given number 43
43 is 4 ten and 3 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
43 is represented with 4 line and 3 dots.

Question 4.
There are ___ tens and ___ ones in 86.
Answer:

Explanation:
Given number 86
86 is 8 ten and 6 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
86 is represented with 8 line and 6 dots.

Question 5.
There are ___ ten and __ ones in 15.
Answer:

Explanation:
Given number 15
15 is 1 ten and 5 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
15 is represented with 1 line and 5 dots.

Question 6.
There are ___ tens and ___ ones in 37.
Answer:

Explanation:
Given number 37
37 is 3 ten and 7 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
37 is represented with 3 line and 7 dots.

Question 7.
There are ___ tens and ___ ones in 62.
Answer:

Explanation:
Given number 62
62 is 6 ten and 2 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
62 is represented with 6 line and 2 dots.

Question 8.
There are ___ tens and __ ones in 24.
Answer:

Explanation:
Given number 24
24 is 2 ten and 4 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
24 is represented with 2 line and 4 dots.

Problem Solving

Solve the problems below.

Question 9.
Model Kevin draws the model below to show a number. What number is Kevin showing?

Answer:

Question 10.
enVision® STEM Gina is collecting
data on the number of hours of daylight in the fall and winter. She records data for 68 days. Draw a model to show 68.
Answer:

Question 11.
Higher Order Thinking Peyton starts drawing a model for the number 48, but she is interrupted. Help her finish her model.

Answer:

Question 12.
Assessment Practice Which number is represented here?

Answer:
Given
2 lines and 3 dots
Line represent Tens
Dot represents Ones.
2 lines = 10 + 10 = 20
3 dots  = 3
The number which is represented is 20 + 3 = 23.
Answer is C)23.

Lesson 8.6 Different Names for the Same Number

Solve & Share

Use cubes. Show two different ways to make 28. Draw each way in the spaces below.

Visual Learning Bridge

Convince Me!
How could you break apart 24 using only I ten? Explain.
Answer:
24 is 2 tens and 4 left over
24 is 2 tens and 4 ones
breaking 24 using only 1 ten
Breaking other  ten to make 10 more ones
24 is 1 ten and 14 ones.

Guided Practice

Count the tens and ones. Write different Practice ways to show the number.

Question 1.
Write two ways to break apart 34.

Answer:

Explanation:
Given a model of number 34 in two different ways
34 is represented as
34 is 3 tens and 4 ones in 1st case.
In 2nd case
out of 3 tens. 1 ten is broken down to make 10 more ones.
34 is 2 tens and 14 ones.

Independent Practice

Count the tens and ones. Write different ways to show each number.

Question 2.
Write two ways to break apart 21.

21 is ___ ten and __ one.
Answer:

Explanation:
Given to break apart 21 in two way
Case 1.
21 is represented as
21 is 2 tens and 1 ones
21 = 20 + 1
In 2nd case
out of 2 tens. 1 ten is broken down to make 10 more ones.
21 is 1 tens and 11 ones.
21 = 10 + 11.

Question 3.
Draw models and write two ways to break apart 59.

59 is ___ tens and ___ ones.

59 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 59 in two way
Case 1.
59 is represented as
59 is 5 tens and 9 ones
59 = 50 + 9
In 2nd case
out of 5 tens. 1 ten is broken down to make 10 more ones.
59 is 4 tens and 19 ones.
59 = 40 + 19 .

Write each number in two different ways. Use cubes to help if needed.

Question 4.
Show two ways to break apart 44.
44 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 44 in two way
Case 1.
44 is represented as
44 is 4 tens and 4 ones
44 = 40 + 4
In 2nd case
out of 4 tens. 1 ten is broken down to make 10 more ones.
44 is 3 tens and 14 ones.
44 = 30 + 14.

Question 5.
Show two ways to break apart 25.
25 is __ tens and __ones.
25 is __ tens and ___ ones.
Answer:

Explanation:
Given to break apart 25 in two way
Case 1.
25 is represented as
25 is 2 tens and 5 ones
25 = 20 + 5
In 2nd case
out of 2 tens. 1 ten is broken down to make 10 more ones.
25 is 1 tens and 15 ones.
25 = 10 + 15.

Problem Solving

Solve the problems below.

Question 6.
Explain Nate says 5 tens and 3 ones shows the same number as 3 tens and 13 ones. Do you agree? Explain.
Answer:

5 tens and 3 ones shows
50 + 3 = 53
3 tens and 13 ones shows
30 + 13 = 43
No, they both don’t show the same number.
To show the same number as
5 tens and 3 ones = 50 + 3 = 53
It should be 4 tens and 13 ones = 40 + 13 = 53 or
as given 3 tens and 13 ones add 10 more ones
3 tens and 23 ones = 30 + 23 = 53.

Question 7.
Number Sense Nancy shows a number as 4 tens and 16 ones. What number does she show?
Answer:
Nancy’s number shows 4 tens and 16 ones
4 tens and 16 ones = 40 + 16 = 56.
Nancy’s number is 56

Question 8.
What number is shown on the mat?

Answer:

Question 9.
Jeff picks 36 apples. He puts some of the apples in bags. Each bag holds 10 apples. Show two ways Jeff can put the apples in bags.

___ bags and __ apples left over
__ bags and __ apples left over
Answer:

Question 10.
Higher Order Thinking Meg breaks apart the number 80 three ways. What could be those ways?
___ tens and ___ ones
___ tens and ___ ones
___ tens and ___ ones
Answer:
Three ways Meg breaks apart the number 80 are
_80__ tens and _0__ ones
80 + 0 = 80
_70__ tens and _10__ ones
70 + 10 = 80
_60__ tens and _20__ ones
60 + 20 = 80.

Question 11.
Assessment Practice which is a way to break apart 38? Choose two that apply.
2 tens and 18 ones
2 tens and 8 ones
1 ten and 28 ones
8 tens and 3 ones
Answer:
The ways to break 38 are
3 tens and 8 ones
2 tens and 18 ones
1 ten and 28 ones
0 tens and 38 ones
In the above option given
2 tens and 18 ones is 38
1 ten and 28 ones is 38 make 38 other 2 options make
2 tens and 8 ones is 28
8 tens and 3 ones is 83.

Lesson 8.7 Look For and Use Structure

Solve & Share

Barry showed the number 42 with cubes. What are some of the ways he could have shown 42? Write the tens and ones to show the ways. Describe any patterns you see in the table.

Thinking Habits

Is there a pattern to the answers? How does the pattern help me? What do the answers have in common?

Visual Learning Bridge

Convince Me!
How can you help you. Talk to a partner about patterns use patterns to show all the ways to break apart a number into tens and ones?

Guided Practice

Make a list to solve. You can use cubes to help you. Talk to partner about patterns you see in your list.

Question 1.
Carly lists all the ways to 25 as tens and ones. What ways does she list?

Answer:

Explanation:
Here different way of 25 are represented
as you look at the ways you can notice a pattern
Ten decrease by 1 and Ones increase by 10.

Question 2.
Andy wants to show 31 as tens and ones. What are all the ways?

Answer:

Explanation:
Here different way of 31 are represented
as you look at the ways you can notice a pattern
Ten decrease by 1 and Ones increase by 10.

Independent Practice

Question 3.
Alma lists all the ways to show 46 as tens and ones. What ways does she list?

Answer:

Question 4.
Seth wants to show 33 as tens and ones. What are all the ways?

Answer:

Question 5.
Higher Order Thinking Dana says there are 4 ways to show 25 using tens and ones. Is she right? How do you know?

Answer:

Problem Solving

Performance Task

Bake Sale Rose brings 48 muffins to a bake sale. She only uses trays for groups of 10 muffins. Each plate holds only I muffin. How many trays and plates could Rose use to display the muffins?

Question 6.
Look For Patterns Fill in the table to show how many trays and plates Rose could use to display the muffins. Describe a pattern you see in the table.
Answer:

Question 7.
Reasoning Is there any way Rose can display her muffins using only trays? Explain how you know.
Answer:
No, Rose can not display her muffins using only trays.
Number of muffins Rose brought = 48
As she used trays for group of 10 muffins.
48 is 4 tens and 8 ones.
If she only uses trays then their will be 8 muffins left over. As she can only display 40 muffins in trays.

Topic 8 Fluency Practice Activity

Point&Tally

Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner I and Partner 2 each point to a black number at the same time. Both partners add those numbers.

If the answer is on your color, you get a tally mark. Work until one partner gets twelve tally marks.

TOPIC 8 Vocabulary Review

Understand Vocabulary

Question 1.
Write the number word that is one more than fourteen.
Answer:
one more than fourteen is fifteen
1 + 14 = 15.

Question 2.
Write the number word that is one fewer than eighteen.
Answer:
Seventeen is one fewer than eighteen.
18 – 1 = 17.

Question 3.
Circle the cubes that make 2 tens.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 2 tens
2 sets of 5 cubes make 1 ten
So, to make 2 tens we need 4 sets of 5 cubes.
4 sets of 5 cubes make 2 tens.

Question 4.
Circle the cubes that make 1 ten and 5 ones.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 1 tens  and 5 ones
2 sets of 5 cubes make 1 ten
So, to make 1 tens we need 2 sets of 5 cubes.
2 sets of 5 cubes make 1 tens.
1 set of 5 cubes make 5 ones.

Question 5.
Circle the cubes that make 3 tens and 3 ones.

Answer:

Explanation:
Given a set of 5 cubes.
There are 7 sets of 5 cubes.
To make 3 tens  and 3 ones
2 sets of 5 cubes make 1 ten
So, to make 3 tens we need 6 sets of 5 cubes.
6 sets of 5 cubes make 3 tens.
3 cubes make 3 ones.

Use Vocabulary in Writing

Question 6.
Ben shows 33 as 3 tens and 3 ones. Show 33 a different way. Use tens and ones. Explain using a word from the Word List.
Answer:

33 is 2 tens and 13 ones
33 is 2 groups of 10 and 13 ones left overs.

TOPIC 8 Reteaching

Set A

You can group objects by 10 to count.

Answer:

Circle groups of 10. Write the numbers.

Question 1.

___ is ___ groups of 10 and __ ones left over.
Answer:

Explanation:
Given a set of 5 cubes.
There are 5 sets of 5 cubes.
To make groups of 10
2 sets of 5 cubes make 10
So, to make 10 we join 2 sets 5 cubes.
We get 2 groups of 10 and 5 more cubes left over.
2 tens and 5 ones is 25.

Question 2.

___ is ___ groups of 10 and __ ones left over.
Answer:

Set B

You can show a two-digit number as tens and ones.

Count the tens and ones. Then write the number.
Answer:

Explanation:
Given a two digit number.
Two digit number has Tens and Ones.
Here given 4 tens cubes in tens place and 3 one cubes is the table.
4 tens = 40
3 ones = 3
4 tens and 3 one is 43.

Question 3.

Answer:

Explanation:
Given a two digit number.
Two digit number has Tens and Ones.
Here given 5 tens cubes in tens place and 4 one cubes is the table.
5 tens = 50
4 ones = 4
5 tens and 4 one is 54.

Set C

You can draw a model to show tens and ones.

Answer:

Draw a model to show tens and ones.

Question 4.
There are __ tens and __ ones in 78.
Answer:

Explanation:
Given number 78
78 is 7 ten and 8 ones.
Tens are represented with a LINE.
Ones are represented with DOTS.
78 is represented with 7 line and 8 dots.

Set D

Thinking Habits
Look For and Use Structure

Is there a pattern to the answers? How does the pattern help me? What do the answers have in common?

Use patterns and make a list to solve.

Question 5.
Lupita wants to show all the ways to break apart 54 as tens and ones. What are all the ways?

Answer:

Topic 8 Assessment Practice

Question 1.
A. Which of these is a way to show 16?
A. 1 ten and 11 ones
B. 1 ten and 6 ones
C. 16 tens and 0 ones
D. 9 tens and 5 ones
Answer:

A. 1 ten and 11 ones is 10 + 11 = 21
B. 1 ten and 6 ones is 10 + 6 = 16
C. 16 tens and 0 ones is 160 + 0 = 160
D. 9 tens and 5 ones is 90 + 5 = 95
way to show 16 is B.