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Big Ideas Math Book 1st Grade Answer Key Chapter 11 Represent and Interpret Data

Take the given pdf as a reference and score maximum marks in the exams. Big Ideas Math Answers Grade 1 Ch 11 Represent and Interpret Data helps you built self-confidence in yourself. Unlimited practice will make you master maths. In this chapter we will discuss the topics like Sort and Organize Data, Read and Interpret Picture Graphs, Bar Graphs, etc. It is necessary to practice with the Big Ideas Math Book 1st Grade Answer Key Chapter 11 Represent and Interpret Data to score maximum marks in the exams.

• Represent and Interpret Data Vocabulary

Lesson: 1 Sort and Organize Data

• Lesson 11.1 Sort and Organize Data
• Sort and Organize Data Practice 11.1

Lesson: 2 Read and Interpret Picture Graphs

• Lesson 11.2 Read and Interpret Picture Graphs
• Read and Interpret Picture Graphs Practice 11.2

Lesson: 3 Read and Interpret Bar Graphs

• Lesson 11.3 Read and Interpret Bar Graphs
• Read and Interpret Bar Graphs Practice 11.3

Lesson: 4 Represent Data

• Lesson 11.4 Represent Data
• Represent Data Practice 11.4

Lesson: 5 Solve Problems Involving Data

• Lesson 11.5 Solve Problems Involving Data
• Solve Problems Involving Data Practice 11.5

Performance Task

• Represent and Interpret Data Performance Task
• Represent and Interpret Data Chapter Practice
• Represent and Interpret Data Cumulative Practice

Represent and Interpret Data Vocabulary

Organize It

Review Words:
category
mark

Use the review words to complete the graphic organizer.

Answer:

Define It

Use your vocabulary cards to match.

Answer:

Explanation:
Bar chart – A bar graph can be defined as a chart or a graphical representation of data, quantities or numbers using bars or strips.
Picture graph – A picture graph, or pictograph, is a graph used to display information that uses images or symbols to represent data.
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.

Lesson 11.1 Sort and Organize Data

Explore and Grow

Explain how you can sort the objects.

Answer:

Explanation:
Here we can classify the given data in two tabular forms .
In First tabular column we can classify it based on favorite item.
we have pencils – 3 ; Crayons – 3 and Markers – 3
In Second tabular column we can classify it based on favorite Color.
we have yellow color – 3 items , Green color – 3 items and Blue color – 3 items.

Show and Grow

Question 1.
Complete the tally chart.

Answer:

Explanation:
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.
As per the above given figure we can see the number of stickers in the given figure
we observe
The number of umbrellas – 4
The number of bucket – 5
The number of Crab – 6

Apply and Grow: Practice

Question 2.
Complete the tally chart.

Answer:

Explanation:
As per the above given figure we can see the number of balls in the given figure
we observe
The number of balls Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.
The number of Foot balls – 5 + 3 = 8
The number of Soccer ball – 5
The number of Basket ball – 3

Question 3.
MP Reasoning
Which sentences are correct?

There are 7 tigers. The numbers of foxes and raccoons are the same.
There are 7 foxes. There are 3 raccoons.
Answer:
The numbers of foxes and raccoons are the same and There are 7 foxes are true statements as per the given information in the tabular column .
Explanation:
There are 7 tigers statement is false because as per the tabular column there are 10 tigers
There are 3 raccoons statement is false because as per the tabular column there are 7 raccoons

Think and Grow: Modeling Real Life

How many sunny days are there? ________ days
Is the number of cloudy days greater than or less than the number of rainy days?
greater than           less than
Answer:
Number of sunny days =  5 + 3 = 8
Number of cloudy days = 4
Number of rainy days = 3
Therefore Number of cloudy days are greater than Number of rainy days.
4 > 3 .
Explanation:
The above chart is represented in tally chart
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.

Show and Grow

Question 4.

How many sunflowers are there? ___________ sunflowers
Is the number of roses greater than or less than the number of daisies?
greater than           less than
Answer:
Number of sunflowers = 2
Number of roses = 5 + 1 = 6
Number of daisies =5 + 2 = 7
The Number of roses are lesser than number of daises
6 > 7
Explanation:
The above chart is represented in tally chart
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.

Sort and Organize Data Practice 11.1

Question 1.
Complete the tally chart.

Answer:

Explanation:
As per the above given figure we can see the number of Insects
we observe
The number of Insects in Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.
The number of Caterpillars =5 + 2 = 7
The number of Flies = 5 + 3 = 8
The number of lady bugs = 2

Question 2.
MP Reasoning
Which sentences are correct?

9 students like princess movies.
4 students like superhero movies.
Princess movies are the most favorite
Answer:
9 students like princess movies is correct
Princess movies are the most favorite is correct
Explanation:
As per the given tally chart of Favorite movie we notice
The number of students like super heroes movies= 5
The number of students like Princess movies = 5 + 4 = 9
The number of students like Mystery movies = 5
Princess movies are the most favorite is correct because more number of students likes this movie

Question 3.
Modeling Real Life
Use the tally chart.

How many students chose fruit? ________ students
Is the number of students who chose yogurt greater than or less than the number of students who chose cereal?
greater than               less than
Answer:
Number of students chose fruit = 4 students.
Number of students chose Yogurt = 5 students.
Number of students chose Cereal = 5 + 1 = 6 students.
Number of students chose Yogurt are less than Number of students chose Cereal
5 < 6

Review & Refresh

Compare.

Question 4.
45 ○ 55
Answer:
45 < 55

Question 5.
74 ○ 47
Answer:
74 > 47

Question 6.
22 ○ 22
Answer:
22 = 22

Lesson 11.2 Read and Interpret Picture Graphs

Explore and Grow

How are the graphs similar? How are they different?


Each ○ = 1 counter.
Answer:
The First picture is the Tally chart of Yellow and Red color counters.
Tally chart marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.
In this tally chart we see Red color shows group of five counters and another 1 counter total = 5 + 1 = 6 counters.
Yellow color shows four counters with four vertical lines.
The second graph is the Picture graph. A picture graph, or pictograph, is a graph used to display information that uses images or symbols to represent data.
In this each counter is marked as ○. In this picture chart we notice the red color counter has 6 counters marked with 6 ○.
In the yellow color we have 4 counters marked with four ○ .
In both the charts the representation is different from each other .

Show and Grow

Question 1.

Each = 1 student.
How many students chose museum? _________
Which trip is the least favorite?
Answer:
As we have 8 in the museum row that means 8 students chose the museum trip
as Each = 1 student
Number of students chose museum = 8
Number of students chose Zoo = 6
Number of students chose play = 2
The trip which is least favorite is play as only two students chooses it .

Apply and Grow: Practice

Question 2.

Each = 1 student.
How many students chose pasta? _________
How many students chose soup? _________
Which lunch is the least favorite?
Answer:
As per the above picture graph we know Each = 1 student.
Number of students chose pasta = 5
Number of students chose soup = 3
Number of students chose Taco = 8
Explanation:
The least favorite lunch is soup because less students chooses it compared to pasta and Taco
Only 3 students chooses soup so it is least Favorite.

Question 3.
Writing
In Exercise 2. how do you know which lunch is the most favorite?

________________________________________

________________________________________

________________________________________
Answer:
Number of students chose pasta = 5
Number of students chose soup = 3
Number of students chose Taco = 8
Taco is the favorite lunch
Explanation:
Taco lunch is chose by 8 number of students compared to soup and pasta 5 and 3 respectively.

Think and Grow: Modeling Real Life

Each = 1 student.
Is the number of students who chose rides greater than, less than, or equal to the number of students who chose animals?
greater than         less than             equal to
Answer:
Number of students chose Rides are greater than number of students chose animals .
Explanation:
Each = 1 student.
Number of students chooses Rides = 5
Number of students chooses Animals = 2
Number of students chooses Games = 4
Number of students chose Rides are greater than number of students chose animals .
5 > 2 .

Show and Grow

Question 4.

Each = 1 student.
Is the number of students who chose frog greater than, less than, or equal to the number of students who chose bear?
greater than         less than             equal to
Answer:
Number of students who chose frog are lesser than number of students chose bear.
Explanation:
Each = 1 student.
Number of students chooses frog = 3
Number of students chooses Bear = 6
3 < 6.
3 lesser than 6 so Number of students who chose frog are lesser than number of students chose bear.

Read and Interpret Picture Graphs Practice 11.2

Question 1.

Each = 1 student.
How many students chose summer? ________
How many students chose fall? _________
Which season is the least favorite?
Answer:
Each = 1 student.
Number of students chooses summer = 7
Number of students chooses Fall = 4
Winter is the least favorite among other seasons.
Explanation:
Number of students chose spring = 3
Number of students chooses summer = 7
Number of students chooses Fall = 4
Number of students chooses Winter = 1.
Among all 4 seasons only winter season is chosen by only one student compared to other seasons .

Question 2.
Writing
How do you know which category has the least when looking at a picture graph?

________________________________________

________________________________________

________________________________________
Answer:
Winter
Explanation:
Less number of means less number of students chosen so Winter is least favorite has it has only one .

Question 3.
Modeling Real Life
Use the picture graph.

Each = 1 student.
Is the number of students who chose water greater than, less than, or equal to the number of students who chose juice?
greater than         less than             equal to
Answer:
Number of students chooses water = Number of students chooses Juice .
Explanation:
Each = 1 student.
Number of students chooses water =4
Number of students chooses juice = 4
As both juice and water have equal number students that is 4 so both are equal .
Number of students chooses water = Number of students chooses Juice = 4

Review & Refresh

Question 4.
31 + 40 = ___________
Answer:

Explanation:
Step 1: Write the numbers one below the other as per the places of the digits.
Step 2 :Start adding from the ones digit. Write the sum under the ones digit.If the sum of the ones digit is greater than 9, write the ones digit of the sum under the ones and carry forward its tens digit to the tens column.
Step 3: Add the tens digits.(If there was a carry forward digit, add it along)

Numbers are arranged as shown in above picture . then add the numbers in one place 1 + 0 = 1
Then add the values in tens place 3 + 4 = 7.
Therefore sum = 71
Lesson 11.3 Read and Interpret Bar Graphs

Question 5.
62 + 20 = ___________
Answer:

Explanation:
Step 1: Write the numbers one below the other as per the places of the digits.
Step 2 :Start adding from the ones digit. Write the sum under the ones digit.If the sum of the ones digit is greater than 9, write the ones digit of the sum under the ones and carry forward its tens digit to the tens column.
Step 3: Add the tens digits.(If there was a carry forward digit, add it along)

Numbers are arranged as shown in above picture . then add the numbers in one place 2 + 0 = 2
Then add the values in tens place 6 + 2 = 8.
Therefore sum = 82

Explore and Grow

How are the graphs similar? How are they different?

Answer:
Picture Graph – A picture graph, or pictograph, is a graph used to display information that uses images or symbols to represent data.
Here as per the given diagram the representation is done with
Bar Graph – A bar graph can be defined as a chart or a graphical representation of data, quantities or numbers using bars or strips.
Here as per the given diagram the representation is done in strips with different colors .

Show and Grow

Question 1.

How many students chose coins? ______________
Which object is the least favorite?
Answer:
Number of students chooses coins = 6
The object which s least favorite is stickers
Explanation:
Number of students chooses Rocks = 4
Number of students chooses Stickers = 2
Number of students chooses Coins = 6
Compared with Rocks and Coins the stickers are chosen less that is only 2 students .
The object which s least favorite is stickers

Apply and Grow: practice

Question 2.

How many students chose card games?
____________

How many students chose board games?
____________

Which activity is the most favorite?

Answer:
Number of students chooses card games = 5
Number of students chooses board games =6
The most favorite activity is Board games as it chosen by 6 number of students .
Explanation:
Number of students chooses card games = 5 (as bar is marked up to 5)
Number of students chooses board games =6 (as bar is marked up to 6)
Number of students chooses puzzles = 2 (as bar is marked up to 2)
Compared to card games and puzzles , the board games are chosen by more students that is 6 number of students.
So , The most favorite activity is Board games

Question 3.
DIG DEEPER!
Order the activities in Exercise 2 from the most favorite to the least favorite.

_____________, _____________, _____________
Answer:
Board games (6) , Card games (5) and Puzzles (2).

Think and Grow: Modeling Real Life

Is the number of students who chose firefighter greater than, less than, or equal to the number of students who chose doctor?
greater than         less than             equal to
Answer:
Number of students chooses firefighter are greater than number of students chooses than doctor .
Explanation:
Number of students chooses firefighter = 5 (bar is marked up to 5)
Number of students chooses Police Officer = 7 (bar is marked up to 7)
Number of students chooses Doctor =4 (bar is marked up to 4)
Compare the students of firefighter and Doctor = 5 > 4
So Number of students chooses firefighter are greater than number of students who chooses doctor .

Show and Grow

Question 4.

Is the number of students who chose bike greater than, less than, or equal to the number of students who chose kite?
greater than         less than             equal to
Answer:
Number of students chooses bike are equal to the number of students who chooses kite.
Explanation:
Number of students chooses bike = 6
Number of students chooses kite = 6
Both have same number of students.
So Number of students chooses bike are equal to the number of students who chooses kite = 6

Read and Interpret Bar Graphs Practice 11.3

Question 1.

How many students chose reading? _____________
How many students chose kickball? _____________
Which activity is the least favorite?
Answer:
Number of students chooses Reading = 3
Number of students chooses Computer = 5
Least Favorite activity is Reading
Explanation:
Number of students chooses Reading = 3 (the bar is marked up to 3)
Number of students chooses Computer = 5 (the bar is marked up to 5)
Number of students chooses Kickball = 6 (the bar is marked up to 6)
Among three activities the Reading is chosen by only 3 students .
Compared to other two activities it is less chosen by  the students .

Question 2.
Writing
How do you know which category has the most when looking at a bar graph?

___________________________________________

___________________________________________

___________________________________________

___________________________________________
Answer:
The category which has the most is Kick ball as it is marked up to 6 bars.
longer the bar marking the most favorite is the activity .

Question 3.
Modeling Real Life
Use the bar graph.

Is the number of pairs of shorts greater than, less than, or equal to the number of shirts?
greater than         less than             equal to
Answer:
Number of pairs of shorts is lesser than the number of the shirts.
Explanation:
Number of Shirts = 5 (as the bar is marked up to 5 )
Number of Shorts = 4 (as the bar is marked up to 4 )
Number of Shirts are greater than Number of shirts = 5 > 4.
So, Number of pairs of shorts is lesser than the number of the shirts.

Review & Refresh

Question 4.
9 + 1 + 7 = ____________
Answer:
9+ 1 + 7 = 17

Question 5.
6 + 3 + 6 = ___________
Answer:
6 + 3 + 6 =15

Lesson 11.4 Represent Data

Explore and Grow

Use your color tiles to complete the tally chart and the picture graph.

Each ○ = 1 color tile.
Answer:

Number of Red Tiles = 4
Number of Blue Tiles = 6
Number of Yellow Tiles = 2
Bar chart – A bar graph can be defined as a chart or a graphical representation of data, quantities or numbers using bars or strips.
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.

Show and Grow

Question 1.
Complete the bar graph.

Answer:

Explanation:
We should complete the Bar graph using Tally graph
In tally graph it represent the numbers students who chooses the 3 different colors .
The number of students who chooses Blue color = 6 ( group of 5 + 1 )
The number of students who chooses pink color = 5 (group of 5 )
The number of students who chooses Yellow color = 2
The same is represented in the Bar chart representing the bars with respective colors and marking the respective number of students as per the color .

Apply and Grow: Practice

Question 2.
Complete the picture graph.


Answer:

Explanation:
We should complete the Picture graph using Tally graph
In tally graph it represent the numbers students who chooses the 3 different Farm Animals .
The number of students who chooses Pig = 4
The number of students who chooses Cow = 6 ( group of 5 + 1 )
The number of students who chooses Horse = 5 ( group of 5 )
The same is represented in the Picture chart representing the Each   = 1 student with respective Farm Animals and marking the respective number of students in the picture graph

Question 3.
Complete the bar graph.

Answer:

Explanation:
We should complete the Bar graph using Tally graph
In tally graph it represent the numbers students who chooses the 3 different Sports .
The number of students who chooses Swimming = 4
The number of students who chooses Karate = 2
The number of students who chooses Soccer = 5 (group of 5 )
The same is represented in the Bar chart representing the bars with Sports and marking the bars with respective number of students with different colors .

Think and Grow: Modeling Real Life

You ask 10 students whether they are right-handed or left-handed. 2 are left-handed. The rest are right-handed. Complete the picture graph.


Each = 1 student.
Answer:

Explanation:
Number of students = 10
Number of students left handed = 2
Number of students Right handed = 10 – 2 = 8
Represent Eight Students with Eight in the above figure .

Show and Grow

Question 4.
You ask 11 students whether they like the swings or the slide. 5 like the swings. The rest like the slide. Complete the bar graph.


Answer:

Explanation:
Number of students = 11
Number of students like swing = 5
Number of students like slide = 11 – 5 = 6
Mark the slide up to 6 with yellow color as bars.

Represent Data Practice 11.4

Question 1.
Complete the bar graph.


Answer:

Explanation:
We should complete the Bar graph using Tally graph
In tally graph it represent the numbers students who chooses the 3 different Winter Activities. .
The number of students who chooses Sledding = 6 (Group of 5 + 1)
The number of students who chooses Skating = 3
The number of students who chooses Snowman = 4
The same is represented in the Bar chart representing the bars  and marking the bars with respective number of students with different colors .

Question 2.
Complete the picture graph.

Each ○ = 1 balloon.
Answer:

Explanation:
We should complete the Picture graph using Tally graph
In tally graph it represent the numbers students who chooses the 2 different Balloons .
The number of students who chooses Blue balloon = 5 ( group of 5)
The number of students who chooses Red balloon = 2
The same is represented in the Picture chart representing the Each ○ = 1 balloon with respective Balloons color and marking the respective number of students in the picture graph

Question 3.
Modeling Real Life
You ask 8 students whether they buy or pack their lunches. 6 students buy. The rest pack. Complete the picture graph.


Each = 1 student.
Answer:

Explanation:
Total Number of students = 8
Number of students who buys lunch = 6
Number of students who packs their lunches = 8 – 6 = 2
Now mark 2 in the pack category as 2 students pack there lunches in the picture graph

Review & Refresh

Find the sum. Then change the order of the addends. Write the new equation.

Question 4.
2 + 6 = _____________
_____________ + _____________ = _____________
Answer:
2 + 6 = 8
6 + 2 = 8
Explanation:
Whatever may be the order of the addends the sum always will be the same .

Question 5.
_____________ = 8 + 1
_____________ = _____________ + _____________
Answer:
9 = 8 + 1
9 = 1 + 8
Explanation:
Whatever may be the order of the addends the sum always will be the same.

Lesson 11.5 Solve Problems Involving Data

Explore and Grow

Complete the bar graph to show 19 toys in all.

Write a question about your graph. Have your partner answer the question.
Answer:

Explanation:
Total Number of Toys = 19
Number of Stuffed animals = 6
Number of Cars = 8
Number of Dinosaurs = 5
The same is represented in the Bar chart representing the bars  and marking the bars with respective number of Toys with different colors .
My Partner answered the question with different numbers. but the overall number of toys = 19 .

Show and Grow

Question 1.

Each = 1 student.
How many more students like butterflies than birds? _________ students
How many students were asked? _________ students
Answer:
Number of students like bats = 4
Number of students like butterflies = 7
Number of students like birds = 6
Number of more students like butterflies than birds = 7 – 6 = 1 students
Number of students asked = total number of students
Total number of students = Number of students like( Bats + Butterflies + Birds ) = 4 + 7 + 6=17.
Therefore Number of students asked = 17.

Apply and Grow: Practice

Question 2.

Each = 1 student.
How many fewer students chose circle than square? _________ fewer students
How many students chose square or triangle?_________ students
Answer:
Number of students chooses square = 7
Number of students chooses Circle = 5
Number of students chooses Triangle = 7
Number of Fewer students chose circle than square = 7 – 5 = 2 students
Number of students chooses square = Number of students chooses Triangle = 7

Question 3.
DIG DEEPER!
You ask 9 students to name their favorite rainy-day activity. Complete the bar graph to show how many chose reading. Think: How do you know?

Answer:
Number of students asked favorite rainy-day activity = 9
Number of students likes Games = 3
Number of students likes Painting = 1
Number of students likes Reading = total number of students – games – painting =9 – 3 – 1
= 9 – 4 = 9 – 5
Number of students likes Reading = 5
Explanation:
Now the number of students like reading is marked with bars up to 5 with Yellow color as shown in the below figure .

Think and Grow: Modeling Real Life

Write and answer a question using the bar graph.

________________________________________

________________________________________

________________________________________
Answer:
How many more hits did Newton hit than Descartes? _________ More Hits
Answer:
Number of Hits by me = 4
Number of hits by Newton = 5
Number of hits by Descartes = 2
Number of more hits by Newton than Descartes = 5 – 2 = 3

Show and Grow

Question 4.
Write and answer a question using the tally chart.


________________________________________

________________________________________

________________________________________
Answer:
Who Laps more runs than me ? ________ runs.
Answer:
Number of lap runs by me = 2
Number of lap runs by Descartes = 5 ( group of 5)
Number of lap runs by Newton = 1.
Descartes lap runs more than me
Number of lap runs more than me = 5 – 2 = 3.
Therefore number of runs more than me by Descartes = 3

Solve Problems Involving Data Practice 11.5

Question 1.

How many more dogs are there than penguins? _________ more dogs
How many bears and dogs are there in all? _________ bears and dogs
Answer:
Number of Bears = 7
Number of Penguins = 2
Number of Dogs = 5
Number of dogs more than penguins = 5 – 2 = 3
3 more dogs are there than penguins
Number of Bears and Dogs = 7 + 5 = 12

Question 2.
DIG DEEPER!
You ask 19 students to name their favorite fruit. Complete the tally chart to show how many chose apples. Explain how you know.

________________________________________

________________________________________

________________________________________
Answer:
Total Number students = 19
Number of students like Banana = 5+2 = 7
Number of students like Orange = 2
Number of students like apple = 19 – 7 – 2 = 19 – 9 = 10
Explanation:
Now mark 10 apples in the above tally graph with 2 sets of group of 5.

Question 3.
Modeling Real Life
Write and answer a question using the bar graph.

________________________________________

________________________________________

________________________________________
Answer:
How many more students like potato than carrot ? _________ more Potatoes .
Explanation:
Number of students like carrots = 3
Number of Students like Potatoes = 6
Number of more students like potatoes than carrots = 6 – 3 = 3
Therefore 3 more students like potatoes than carrot .

Review & Refresh

Question 4.
51 + 40 = __________
Answer:

Question 5.
76 + 3 = __________
Answer:

Represent and Interpret Data Performance Task

Question 1.
Ask your classmates about their eye colors. Use your data to complete the tally chart.

Answer:

Total number of class mates = 15
Number of class mates with black eye color = 9
Number of class mates with brown eye color = 4
Number of class mates with blue eye color = 2
All the above data is marked in the tally graph as shown in above figure .

Question 2.
Use your tally chart to complete the bar graph.

Answer:

Question 3.
Describe two ways to tell how many students you asked.

________________________________________

________________________________________
Answer:
Number of students with black eyes = 9
Number of students with brown eyes = 4
Number of students with blue eyes = 2
The Total Number of students asked = Number of students with (black eyes + brown eyes + blue eyes)
= 9 + 4 = 2 = 15
By counting the number of bars will also say the total number of students .

Question 4.
Write and answer a question about your graphs.

________________________________________

________________________________________
Answer:
Is the number of Students with brown greater than, less than, or equal to the number of students with blue eyes?
greater than         less than             equal to
Explanation:
Number of students with brown eyes = 4
Number of students with blue eyes = 2
Therefore Number of students with brown eyes are greater than number of students with blue eyes.

Represent and Interpret Data Chapter Practice

Sort and Organize Data Homework & Practice 11.1

Complete the tally chart.

Question 1.

Answer:

Explanation:
The above chart is represented in tally chart of Number of Cars
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.
Number of red cars = 4 (represented with four vertical lines)
Number of white cars = 3 (represented with three vertical lines)
Number of blue cars = 5 (represented with four vertical lines and the fifth number is represented by a diagonal line across the previous four)

Question 2.

Answer:

Explanation:
Explanation:
The above chart is represented in tally chart of Number of pets
Tally chart – Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.
Number of Cats = 4 (represented with four vertical lines)
Number of Dogs = 2 (represented with two vertical lines)
Number of Fishes = 8 (represented with four vertical lines and the fifth number is represented by a diagonal line across the previous four and three vertical lines)

Read and Interpret Picture Graphs Homework & Practice 11.2

Question 3.

Each = 1 student.
How many students chose science? ____________
Which subject is the least favorite?
Answer:
Numbers of Students Who likes Art = 5
Number of students who likes Math = 6
Number of students who likes Science = 4
Among the three subjects the less favorite subject is Science .
As it has less number of students .

Read and Interpret Bar Graphs Homework & Practice 11.3

Question 4.

How many students chose turtle? __________
Which is the most favorite sea creature?
Answer:
Number of students choose turtle = 5
Number of students choose jellyfish = 2
Number of students choose Shark = 6
Among the three sea creature shark was chosen by more number of student compared with other two .
Therefore Most Favorite sea creature is Shark .

Represent Data Homework & Practice 11.4

Question 5.
Complete the bar graph.

Answer:

Explanation:
We should complete the Bar graph using Tally graph
In tally graph it represent the numbers Beads of 3 different colors.
The number of Beads of Blue color = 5 ( group of 5)
The number of Beads of Red color = 2
The number of Beads of  Yellow color = 4
The same is represented in the Bar chart representing the bars with respective colors and marking the respective number of Beads as per the color .

Question 6.
Modeling Real Life
You ask 13 students whether they like volleyball or basketball. 7 like volleyball. The rest like basketball. Complete the picture graph.

Each = 1 student.
Answer:
Total Number of Students = 13
Number of Students who likes Volley ball = 7
Number of students who likes Basketball = 13 – 7 = 6
Now Number of students who likes basketball is represented with 7 in the above figure.

Solve Problems Involving Data Homework & Practice 11.5

Question 7.

How many fewer students chose green than purple? ____________ fewer students
How many students were asked? ____________ students
Answer:
Number of Students who like purple = 5 + 4 =9
Number of Students who likes Green = 5
Number of Students who likes Orange = 2
Number of Fewer Students choose Green than purple = 9 – 5 = 4
Number of Students were asked =Numbers of Students who likes (purple + green +orange )
= 9 + 5 + 2 = 16
Therefore Number of Students were asked = 16

Question 8.
Modeling Real Life
Write and answer a question using the bar graph.

________________________________________

________________________________________
Answer:
How many students were asked? ____________ students
Answer:
Number of Students who like Computer = 4
Number of Students who likes Stuffed Animals = 3
Number of Students who likes Train = 6
Number of Students were asked =Numbers of Students who likes (Computer + Stuffed Animals + Train )
= 4 + 3 + 6 = 13
Therefore Number of Students were asked = 13

Represent and Interpret Data Cumulative Practice

Question 1.
Match each number on the left with a number that is 10 more.

Answer:

Question 2.
Complete.

56 + 6 = __________
Answer:
56 + 6 = 62
60 + 2 = 62

Question 3.
Order from shortest to longest.

____________, ____________, ____________
Answer:
Yellow , Blue , Red
Explanation:
Red is the longest line
Blue is second longest line
Yellow is third line which is less than both

Question 4.
Shade the circle next to the number that tells how many horns there are.

○ 3
○ 10
○ 6
○ 19
Answer:
Number of horns = 5 + 5 = 10

Question 5.
Shade the circle next to the sum.
12 + 5 = ____________
○ 15
○ 17
○ 16
○ 7
Answer:
12+5=17

Question 6.
There are 85 pages in a book. You read 10 of them. How many pages are left?

○ 95
○ 85
○ 75
○ 80
Answer:

Explanation:
Total Number of pages in a book = 85
Number of pages read by me = 10
Remaining number pages left to read = 85 – 10 = 75.

Question 7.
Is each sentence true?
52 is greater than 36.       Yes         No
100 < 90                          Yes         No
75 is less than 57.            Yes         No
89 > 81                            Yes         No
Answer:

Question 8.
You collect 22 cans for a food drive. Your friend collects 36. How many cans do you and your friend collect in all?

______________ cans
Answer:
Total Number of Cans collected by me = 22
Total Number of cans collected by my friend = 36
Total Number of cans collected by me and my friend = 22 + 36 = 58

Question 9.
Measure.

about ___________ color tiles
Answer:

we need to know the measure of the given figure
From the above figure it is clearly marked that it measures 13 cms long .

Question 10.
Shade the circles next to the choices that match the model.

○ 50 – 30
○ 5 tens – 2 tens
○ 50 – 20
○ 3 tens – 2 tens
Answer:

Explanation:
We notice in the given figure we have 5 tens in that 2 tens were crossed that means 2 tens were subtracted so remaining number of tens = 5 tens – 2 tens .

Question 11.

How many students chose ham? ___________

Which sandwich is the least favorite?

Answer:
As per the given bar graph we observe
Number of students choose ham  = 2
Numbers of students choose turkey = 4
Number of students choose Cheese = 4
Number of students choose turkey = Number of students choose Cheese = 4
So only ham is left with 2 less than turkey and cheese
Therefore ham sandwich is the least favorite

Question 12.
Use each card once to write an addition equation.

___________ + ___________ = ___________
Answer:
2 + 3 =5
3 + 2 =5
Explanation:
Whatever may be the order of the addends the sum always will be the same .

Conclusion:

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Lesson: 1 Points, Lines and Rays

• Lesson 13.1 Points, Lines and Rays
• Points, Lines and Rays Homework & Practice 13.1

Lesson: 2 Identify and Draw Angles

• Lesson 13.2 Identify and Draw Angles
• Identify and Draw Angles Homework & Practice 13.2

Lesson: 3 Identify Parallel and Perpendicular Lines

• Lesson 13.3 Identify Parallel and Perpendicular Lines
• Identify Parallel and Perpendicular Lines Homework & Practice 13.3

Lesson: 4 Understand Degrees

• Lesson 13.4 Understand Degrees
• Understand Degrees Homework & Practice 13.4

Lesson: 5 Find Angle Measures

• Lesson 13.5 Find Angle Measures
• Find Angle Measures Homework & Practice 13.5

Lesson: 6 Measure and Draw Angles

• Lesson 13.6 Measure and Draw Angles
• Measure and Draw Angles Homework & Practice 13.6

Lesson: 7 Add Angle Measures

• Lesson 13.7 Add Angle Measures
• Add Angle Measures Homework & Practice 13.7

Lesson: 8 Find Unknown Angle Measures

• Lesson 13.8 Find Unknown Angle Measures
• Find Unknown Angle Measures Homework & Practice 13.8

Performance Task

• Identify and Draw Lines and Angles Performance Task 13
• Identify and Draw Lines and Angles Activity
• Identify and Draw Lines and Angles Chapter Practice 13

Lesson 13.1 Points, Lines and Rays

Explore and Grow

Use a straightedge to connect the dots A through Z. Describe the picture you make. How many points do you connect? How many line segments do you make?

Answer:
Points connected are 25.
Line segments used are 25.

Structure
Draw your own connect-the-dots picture on another sheet of paper. Have your partner use a straightedge to connect the dots to make your picture. How many points did your partner connect? How many line segments did your partner make?
Answer:
Yes, he used line segments to connect the dots. He connected 20 dots and 19 line segments.

Think and Grow: Points, Lines, Line Segments, and Rays

Example
Draw and label \(\overline{L M}\)
\(\overline{L M}\) is a ___
Another name for \(\overline{L M}\) is ___
Answer:
Line segments are represented by a single overbar with no arrowheads over the letters representing the two endpoints.
The line segment Represented as \(\overline{L M}\)

Example
Draw and label \(\overrightarrow{S T}\)
\(\overrightarrow{S T}\) is a ___

Answer:
\(\overrightarrow{S T}\)

Ray \(\overrightarrow{S T}\)

Show and Grow

Question 1.
Name the figure shown. Write how to say the name.

Answer:
It is a line segment vu. Line segments are represented by a single overbar with no arrowheads over the letters representing the two endpoints.
It is represented as \(\overline{V U}\)

Question 2.
Draw and label two points P and Q on the line shown.

Answer:

Question 3.

Answer:

Apply and Grow: Practice

Name the figure shown. Write how to say the name.

Question 4.

Answer:
It is called as point B.
A point in geometry is a location. It has no size i.e. no width, no length and no depth. A point is shown by a dot and named in capital letter.

Question 5.

Answer:
It is called as \(\overrightarrow{C D}\). The symbol of a ray is →.

Question 6.

Draw and label the figure.
Answer:

Question 7.
\(\overline{G H}\)
Answer:
\(\overline{G H}\) means a line segment. It is said as line segment GH.

Question 8.

Answer:
It is a ray. It is said as ray

Question 9.
\(\overrightarrow{L M}\)
Answer:
It means a ray. It is said as ray LM.

Use the figure.

Question 10.
Name a ray.
Answer:
\(\overrightarrow{A D}\).

Question 11.
Name a point that lies on two lines.
Answer:  E .

Question 12.
Name two different line segments.
Answer: DE and EF.
\(\overline{D E}\) and \(\overline{E F}\)

Question 13.
Logic
Your friend says he can draw two line segments between two points, and may be even more. His drawing is shown. Explain why this is not possible.

Answer:
Only one line can be drawn passing through any two points but a number of lines can be drawn through a point.

Think and Grow: Modeling Real Life

Example
There are direct ferry routes between each pair of cities on the map. Draw line segments to represent all of the possible ferry routes. How many ferry routes did you draw in all?

Start at Poole. Draw a line segment from Poole to each of the other cities. Repeat this process until a route is shown between each city.
You draw __ ferry routes in all.
Answer:
3 Possible routes.

Show and Grow

Question 14.
There are direct flights between each pair of cities on the map. Draw line segments to represent all of the possible flight routes. How many flights routes did you draw in all?

Answer:
Total 10 routes were found.

Question 15.
Which road signs contain a figure that looks like a ray?

Answer:
One way road sign look like a ray.

Question 16.
Which letters in the banner can be made by drawing line segments? Explain.
,
Answer:
Letters – W,E,L,M AND E.

Points, Lines and Rays Homework & Practice 13.1

Name the figure shown. Write how to say the name.

Question 1.

Answer:
It is said as Line segment EF and represented as \(\overline{E F}\).

Question 2.

Answer:
It is said as ray GH and represented as \(\overrightarrow{G H}\).

Question 3.

Answer:
It is said as line JK and represented as

Draw and label the figure.

Question 4.
two points L and M on the line shown

Answer:

Question 5.
\(\overrightarrow{N O}\)
Answer:

It is represented as \(\overrightarrow{N O}\).

Question 6.

Answer:

Use the figure.

Question 7.
Name a line segment.
___CE____

Question 8.
Name two different rays.
Answer:
\(\overrightarrow{C D}\) and \(\overrightarrow{E F}\).

Question 9.
Name two different lines
Answer
\(\overline{D B}\)and \(\overline{A E}\).

Question 10.
Writing
Explain the difference between a line and a line segment.

Line-segment

1. It has two end points.

2. The length of a line-segment is definite. So, it can be measured.

3. The symbol of a line-segment is _____

Line

1. There are no end points in a line.

2. There are no end points. So, length of a line cannot be measured.

3. The symbol of a line is ↔

Question 11.
Structure
Name the figure in as many ways as possible.

Answer:
\(\overline{X Y}\),\(\overline{Y Z}\) and \(\overline{X Z}\).
\(\overrightarrow{Y Z }\)
LINE – XZ

Question 12.
Structure
Draw and label a figure that has four points, two rays, and one line segment.
Answer:

\(\overrightarrow{R S }\) and \(\overrightarrow{Q S}\).
\(\overline{P S}\)

DIG DEEPER!
Write whether the statement is true or false. If false, explain.

Question 13.
A line segment is part of a line. _______
Answer: Yes

Question 14.
A ray is part of a line segment. ____
Answer:
No
Explanation:
Line-segment- It has two end points. But where as Ray has a starting point but no other end point.

Question 15.
There are an infinite number of points on a line. ___
Answer: Yes

Question 16.
Modeling Real Life
There are direct helicopter flights between each pair of resorts on the map. Draw line segments to represent all of the possible flight routes. How many flight routes did you draw in all?

Answer:
Total possible flight routes are 6 routes.

Question 17.
Modeling Real Life
Which road signs contain a figure that looks like it is made of only line segments?

Answer:
Road signs – +,T and Y are made of line segments.

Review & Refresh

Compare

Question 18.

Answer:
0.15 < 0.16.

Question 19.

Answer:
2.4 < 2.42

Question 20.

Answer:
6.90 = 6.9

Lesson 13.2 Identify and Draw Angles

Explore and Grow

Draw the hands of the clock to represent the given time.

For each clock, describe the angle that is formed by the minute hand and the hour hand.
Answer:

Reasoning
Explain how line segments, rays, and angles can be related.

Think and Grow: Angles

Angles can be either right, straight, acute, or obtuse.

Example

Write three names for the angle and classify it.
Three names for the angle are
___, ____ and ____.
The angle opens ___ a right angle and less than a straight line.
So, it is an __ angle.
Answer:
Three names for the angle are actue, obtuse and right angles.
The angle opens more than a right angle and less than a straight line.
So, it is an obtuse angle.

Show and Grow

write a name for the angle and classify it.

Question 1.

Answer:
It is a right angle called as ∠P.

Question 2.

Answer:
It is a straight angle. It can be represented as ∠XYZ, ∠ZYX.

Apply and Grow: Practice

Write a name for the angle and classify it.

Question 4.

Answer:
It is a obtuse angle. It is represented as ∠Q.

Question 5.

Answer:
It is a actue angle. It is represented as ∠MNO or ∠ONM.

Question 6.

Answer:
It is a straight angle. It can be represented as ∠RST, ∠TSR.

Draw and label the angle.

Question 7.
∠XYZ is right

Question 8.
∠JKL is straight.
Answer:

Use the figure. Use three letters to name each angle.

Question 9.
Name an acute angle.
Answer:
∠CFD

Question 10.
Name two different obtuse angles.
Answer:
∠CFG and ∠ACF.

Question 11.
Name two different straight angles.
Answer:
∠BDF and ∠CDE.

Question 12.
Name three different right angles.
Answer:
∠CFD , ∠CFG and ∠BDF.

Question 13.
Structure
Draw to complete each angle.

Answer:

Think and Grow: Modeling Real Life

Example
Which angle of the skateboard ramp is acute?
You need to find an angle that is open less than a right angle.

Angle A opens __more than __ a right angle and less than a straight line.
Angle B _is equal__ a right angle.
Angle C opens _less than__ a right angle.
Angle _∠C__ is an acute angle.

Show and Grow

Question 14.
Use three letters to name an angle of the wind turbine that is obtuse.

Answer:
∠VTU.

Question 15.
Trace and label two right angles, two obtuse angles, and two acute angles in the painting.

Answer:

Question 16.
DIG DEEPER!
How many different angles are in the window? Name all of the different angles.

Answer:
Right angles – ∠AFC , ∠BFD , ∠CFE
Obtuse angles – ∠AFD and ∠BFE.
Acute angles – ∠AFB, ∠BFC , ∠CFD and ∠DFE.
Straight angles – ∠AFE.

Identify and Draw Angles Homework & Practice 13.2

Write a name for the angle and classify it.

Question 1.

Answer:
∠O is straight angle.

Question 2.

Answer:
∠TUV is a right angle as TU is perpendicular to UV .

Question 3.
∠
Answer:
∠XYZ is a obtuse angle as, we can see clearly angle formed is more than 90 degrees.

Draw and label the angle.

Question 4.
∠ABC is obtuse.
Answer:

Question 5.
∠MNO is acute.
Answer:

Use the figure. Use three letters to name each angle.

Question 6.
Name an acute angle.
Answer: ∠BFC

Question 7.
Name a straight angle.
Answer: ∠DEF

Question 8.
Name two different right angles.
Answer: ∠DEA and ∠DEG.

Question 9.
Name three different obtuse angles
Answer: ∠EFJ and ∠EFC.

Question 10.
YOU BE THE TEACHER

Answer:
The above figure contains ∠JKL a angle.

Question 11.
DIG DEEPER!
Can you make a straight angle using an acute angle and an obtuse angle that share a common ray? Draw a picture to support your answer.
Answer:
Yes
Explanation:
The total sum of a straight angle =180.
As per the figure,
The Obtuse angle = 120 degrees.
The acute angle = 60 degrees.
Therefore The straight angle = Obtuse angle + Acute angle.
= 120 + 60
= 180 degrees.

Question 12.
Structure
Write a capital letter that has more than two right angles.
Answer: B

Question 13.
Modeling Real Life
Use three letters to name the angles of the flag of the Czech Republic that are obtuse.

Answer:
∠AFC and ∠EFC are obtuse angles.

Question 14.
Modeling Real Life
Horses see an object with binocular both eyes at the same time using vision. Classify the angle that describes the horse’s binocular vision.

Answer:
The angle that formed in binocular vision is Acute angle.

Review & Refresh

Question 15.
Write 1\(\frac{7}{12}\) as a fraction.
Answer:

(1 x 12 ) + 7 =19

Question 16.
Write \(\frac{9}{6}\) as a mixed number.
Answer:

Lesson 13.3 Identify Parallel and Perpendicular Lines

Explore and Grow

Use a straightedge to draw and label a figure for each description. If a figure cannot be drawn, explain why.

Answer:

Reasoning
Find the figure that shows two lines that cross once. How many angles are formed by two lines? Name and classify the angles of the figure above.
Answer:
Four angles are formed – ∠FOJ , ∠FOH ,∠GOJ and ∠GOH.

Think and Grow: Parallel and Perpendicular Lines

You can describe a pair of lines as intersecting, parallel, or perpendicular.

Example
Draw and label the lines with the given description.


Answer:

Show and Grow

Draw and label the lines with the given description.

Question 1.

Answer:

Question 2.

Answer:

Apply and Grow: Practice

Draw and label the lines with the given description.

Question 3.

Answer:

Question 4.

Answer:

Use the figure.

Question 5.
Name a pair of lines that appear to be parallel.
Answer:
AC ll DF.

Question 6.
Name two lines that are perpendicular.
Answer:
BE ⊥ DF and DE ⊥ EB.

Question 7.
Name two intersecting lines.
Answer:
DE and EB
CB and BE

Question 8.
Reasoning
All perpendicular lines are also intersecting lines. Are all intersecting lines perpendicular? Explain.
Answer:
Perpendicular Lines means which bisect the lines at right angles .But where as the intersecting lines meet at one point but doesnot form right angles.

Question 9.

Think and Grow: Modeling Real Life

Example
Which street appears to be parallel to 2nd Street?
Look for a street that will not intersect with 2nd street.
___ Street appears to be parallel to 2nd Street.

Answer:
3rd street.

Show and Grow

Question 10.
Which trail appears to be parallel to Fox Trail?

Answer:
Wolf Run Trail

Question 11.
Which trail appears to be perpendicular to Fox Trail?
Answer:
Oak Trail.

Question 12.
Trace and label a pair of line segments that appear to be parallel and a pair of line segments that appear to be perpendicular.

Answer:

Question 13.
DIG DEEPER!
Design three paths for a park. Two of the paths are perpendicular. Label these paths as Path 1 and Path 2. The third path intersects both perpendicular paths at exactly one point. Label this path as Path 3.
Answer:

Identify Parallel and Perpendicular Lines Homework & Practice 13.3

Example

Draw and label the lines with the given description.

Question 1.

Answer:

Question 2.

Answer:

Use the figure.

Question 3.
Name a pair of lines that appear to be parallel.
Answer:
AG ll CJ

Question 4.
Name two lines that are perpendicular.
Answer:
BE ⊥ DF
HE ⊥ DF

Question 5.
Name two intersecting lines.
Answer:
CJ and DF .

Question 6.
Structure
Name two line segments that appear to be parallel. Then name two line segments that appear to be perpendicular.

Answer:
AB ll DC and AD⊥ DC .

Question 7.
Reasoning
Can two lines that share a point be parallel? Explain.
Answer:
Two Lines can be parallel but a point cannot be a parallel.
Explanation:
Parallel lines are co planar lines that do not intersect. In two dimensions, parallel lines have the same slope . We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line. y=2x+3 .

Question 8.
DIG DEEPER!
l
Answer:
No, It cannot be an acute angle. Because it is a right angle.
Explanation:
As line SW is perpendicular to line UV and line SW is parallel to line TX then from figure it is clear that line TX will be perpendicular to line UV.

Question 9.

Modeling Real Life
Which street appears to be parallel to Park Avenue?
Answer:
Peach Street.

Question 10.
Modeling Real Life
Which street appears to be perpendicular to Peach Street?
Answer:
Lake Road

Question 11.
Modeling Real Life
Trace and label a pair of line segments that appear to be parallel and a pair of line segments that appear to be perpendicular.

Answer:

Review & Refresh

Find the equivalent amount of time.

Question 12.
20 min = ___ sec
Answer:
1min = 60sec
20 mins = 20 x 60
= 1200 sec.

Question 13.
6 yr = ___ wk
Answer:
1 year = 52 weeks.
6 years = 6 x 52
= 312 weeks

Lesson 13.4 Understand Degrees

Explore and Grow

Find the elapsed time for each set of clocks. Describe, in your own words, the turn that the minute hand makes.

Answer:
Elapsed time is the time or difference between a beginning time and an ending time.

Reasoning
Explain how elapsed time shown by an analog clock relates to angles formed in a circle.
Answer:
On a clock, we can see different kinds of angles based on its amplitude; void, acute, straight, obtuse, flat angles—even a full angle.

Think and Grow: Degrees

Angles are measured in units called degrees. Think of dividing a circle into 360 equal parts. An angle that turns through \(\frac{1}{360}\) of a circle measures 1°, and is called a“one-degree angle.” A full turn through the entire circle is 360°.

Example
Find the measure of the angle.

An angle that turns \(\frac{1}{360}\) of a circle measures _1__ degrees.
An angle that turns through \(\frac{20}{360}\) of a circle measures _20__ degrees.
So, the measure of the angle is _20 degrees__.

Example
Find the measure of a right angle.

Answer:
22.5 degrees.

Show and Grow

Find the measure of the angle.

Question 1.

Answer:
60 degrees.

Question 2.

Answer:
45 degrees.

Apply and Grow: Practice

Find the measure of the angle.

Question 3.

Answer:
85 degrees

Question 4.

Answer:
120 degrees.

Question 5.

Answer:
45 degrees.

Question 6.

Answer:
(1/9) x (—/—) = —–/360
=40 degrees.

Question 7.

Answer:
(1/2) x (—/—) = —–/360
=180 degrees.

Question 8.

Answer:
(1/5) x (—/—) = —–/360
=360/5=72 degrees.

Question 9.
A circle is divided into 8 equal parts. What is the measure of the angle that turns through 2 parts?
Answer:
Number of parts =8
Total sum of angle in circle = 360.
Measure of 1/8 part of angle formed = 360/8 =45 degree.
Therefore measure of angle that turns through 2 parts = 2 x 45 =90 degrees.

Question 10.
A circle is divided into 4 equal parts. What is the measure of the angle that turns through 3 parts?
Answer:
Number of parts =4
Total sum of angle in circle = 360.
Measure of 1/4 part of angle formed = 360/4 =90 degree.
Therefore measure of angle that turns through 3 parts = 3 x 45 =135 degrees.

Classify the angle as right, straight, acute or obtuse.

Question 11.
30°
Answer:
Acute angle
An acute angle lies between 0 degree and 90 degrees, or in other words; an acute angle is one that is less than 90 degrees.

Question 12.
120°
Answer:
Obtuse angle
It is the angle which lies between 90 degrees and 180 degrees or in other words; an obtuse angle is greater than 90 degrees and less than 180 degrees.

Question 13.
90°
Answer:
Right angle
A right angle is always equal to 90 degrees.

Question 14.
180°
Answer:
Straight angle
A straight angle is 180 degrees. It is just a straight angle because the angle between its arms is 180 degrees.

Reflex Angle

Question 15.
YOU BE THE TEACHER
Both circles are divided into sixths. Your friend says the measure of Angle D is greater than the measure of Angle C. Is your friend correct? Explain.

Answer:
No
Explanation:
Both the angles are divided into 6 equal parts irrespective of size of the circle. Both the angles C and D will be equal. As the sum of the circles is 360 degrees for all circles ,when divided equally the angles will be equal.

Question 16.
Reasoning
Does each figure show the same angle? If not, which two angles are shown? Explain your reasoning.

Answer:
Both the Angles are equal.

Think and Grow: Modeling Real Life

Example
Spokes divide the Ferris wheel into 20 equal parts. What is the angle measure of 1 part?
Write a fraction that represents 1 part.
Because the Ferris wheel has 20 equal parts,


Answer:

Show and Grow

Question 17.
The game spinner is divided into10 equal parts. What is the angle measure of 1 part?

Answer:
Number of parts divided=10
Total sum of angle in circle = 360.
Measure of 1/10 part of angle formed = 360/10 =36 degree.

Question 18.
DIG DEEPER!
A circular quesadilla is cut into 8 equal pieces. Five pieces are eaten. What is the angle measure formed by the remaining pieces?

Answer:
Total Number of parts divided = 8.
Total sum of angle = 360 degrees.
Angle of each part = 360/8 degrees = 45 degrees.
Number of parts eaten = 5
Angle of 5 parts = 5 x 45 degrees = 225 degrees.
Angle formed by remaining parts = 360- 225 degrees =135 degrees
or
Number of remaining parts =3
Angle of remaining parts = 3 x 45 degrees. = 135 degrees.

Question 19.
DIG DEEPER!
When a light wave hits an object, the object reflects a colored light at an angle to your eye. The color of the reflected light is the color you see. What fraction of a circle is shown by the angle? Explain.

Answer:
Reflected angle = 30 degrees.
Total sum of angle = 360 degrees.
Fraction angle reflected in circle = 30 / 360 degrees = 1 /12 fraction.

Understand Degrees Homework & Practice 13.4

Find the measure of each angle

Question 1.

Answer:
50 degrees

Question 2.

Answer:
(1/3) x (—/—) = —–/360
= 360/3 = 120 degrees.

Question 3.

Answer:
(1/12) x (—/—) = —–/360
= 360/12 = 30 degrees.

Question 4.

Answer:
(1/10) x (—/—) = —–/360
=360/10 = 36 degrees.

Question 5.

Answer:
(1/6) x (—/—) = —–/360
= 360/6 = 60 degrees.

Question 6.
A circle is divided into 5 equal parts. What is the measure of the angle that turns through 2 parts?
Answer:
Number of parts =5
Total sum of angle in circle = 360.
Measure of 1/5 part of angle formed = 360/5 =72 degree.
Therefore measure of angle that turns through 2 parts = 2 x 72 =144 degrees.

Question 7.
A circle is divided into 10 equal parts. What is the measure of the angle that turns through 3 parts?
Answer:
Number of parts =10
Total sum of angle in circle = 360.
Measure of 1/10 part of angle formed = 360/10 =36 degree.
Therefore measure of angle that turns through 3 parts = 3 x 36 =108 degrees.

Classify the angle as right, straight, acute, obtuse

Question 8.
90°
Answer:
Right angle
A right angle is always equal to 90 degrees.

Question 9.
45°
Answer:
Acute angle
An acute angle lies between 0 degree and 90 degrees, or in other words; an acute angle is one that is less than 90 degrees.

Question 10.
160°
Answer:
Obtuse angle
It is the angle which lies between 90 degrees and 180 degrees or in other words; an obtuse angle is greater than 90 degrees and less than 180 degrees.

Question 11.
60°
Answer:
Acute angle
An acute angle lies between 0 degree and 90 degrees, or in other words; an acute angle is one that is less than 90 degrees.

Question 12.
Which One Doesn’t Belong? Which angle measure does not belong with the other three?

Answer:
1/8 of a circle

Question 13.
DIG DEEPER!
Your friend uses the equation to find an angle a measure. Explain what the letters a and b represent.
360° ÷ a = b
Answer:
Where a is the Number of parts where circle is divided.
b is the angle of 1 part.

Question 14.
Modeling Real Life
The steering wheel is divided into 3 equal parts. Find the angle measure of 1 part.

Answer:
Number of parts =3
The total sum of angle in circle = 360.
The measure of 1/3 part of the angle formed = 360/3 =120 degrees.

Question 15.
DIG DEEPER!
You and your friend take pie-shaped pieces from a circular quiche. Your friend takes \(\frac{2}{8}\) of the quiche. You take a piece with an angle measure of 72°. Who takes a larger piece? Explain.
Answer:
It Is given that pie taken your friend is 2/8 So it is clear that quinche is divided into 8 parts.
Number of parts =8
Total sum of angle in circle = 360.
Measure of 1/8 part of angle formed = 360/8 =45 degree.
Piece taken by friend is 2/8 = 2 x 45 = 90 degrees.
Piece taken by you measures 72 degrees.
Therefore Your Friend takes larger piece.

Review & Refresh

Multiply

Question 16.

Answer:
=7 x (7/2)
=1/2 = 0.5

Question 17.

Answer:
= 10 x (53/6)
=88.33

Question 18.

Answer:
=4 x (51/8)
=51/2
=25.5

Lesson 13.5 Find Angle Measures

Explore and Grow

How many triangular pattern blocks can you put together around one vertex?

Answer: 2
How can you determine the measure of each angle in a triangular pattern block?
Answer:
If we add all three angles in any triangle we get 180 degrees.
So, the measure of (angle A + angle B + angle C) = 180 degrees.

Repeated Reasoning
Find all of the angle measures of the other pattern blocks. Organize your results in the table.

Answer:

Think and Grow: Find Angle Measures

Example
Use the pattern block to find the measure of the angle.

Each angle of the pattern block has a measure of _60__.
The angle is equal to _60 degrees__ of the angles of the pattern block.
So, the measure of the angle is __60 degrees_.

Example
Use the pattern block to find the measure of the angle.
Each acute angle of the pattern block has a measure of _30__.
The angle is equal to _30__ of the acute angles of the pattern block.

So, the measure of the angle is _150 degrees__.

Show and Grow

Use pattern blocks to find the measure of the angle.

Question 1.

Answer:

Question 2.

Answer:

Question 3.
Use pattern blocks to find how many 60° angles are in a straight angle.

Answer:

Total 3 triangles are used.

Apply and Grow: Practice

Use pattern blocks to find the measure of the angle.

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Question 9.

Answer:

Question 10.
How many 90° angles are in a straight angle? Explain.
Answer: 2
A straight has 180 degree as its sum of angle.
One right angle = 90 degrees.
=90 x2 =180.
So if we have 2 right angles the its sum will be equal to 180 degrees.

Question 11.
How many 30° angles are in a 150° angle? Explain.
Answer:
=150/30=5 times.

Question 12.
Structure
Use two different pattern blocks to form an obtuse angle. Find the angle measure. Draw a model to support your Answer.

Question 13.
DIG DEEPER!
Find the measure of the smaller angle formed by the clock hands. Then explain how you could find the measure of the larger angle.

Answer:
The angle formed at 3 clock = 90°.
The sum of angles=360°
The larger angle = 360° – 90°=270°

Think and Grow: Modeling Real Life

Example
A circular compass is divided into 8 equal sections. What is the measure of each angle formed at the center of the compass?

A full turn through a circle is 360°. So, divide 360° by 8.

Each angle formed at the center of the compass is __45°_.

Show and Grow

Question 14.
You have a circular craft table. You divide the table into 3 equal sections. What is the measure of each angle formed at the center of the table?
Answer:
Number of sections =3
The total sum of angle in circle = 360°.
The measure of 1/3 part of the angle formed at the center of the table = 360°/3 =120°

Question 15.
A chef has a wheel of cheese that is cut into6 equal pieces. The chef uses 2 pieces. What is the angle measure formed by the missing pieces?

Answer:
Number of parts =6
Total sum of angle in circle = 360°.
Measure of 1/6 part of angle formed= 360°/6 =60°
Chef uses 2 peices
Angle formed by used peices = 2 x 60° =120°
Therefore, the angle measure formed by the missing pieces = 120°

Question 16.What is the angle measure formed by the remaining slices?

Answer:
Number of parts =5
Total sum of angle in circle = 360°.
Measure of 1/5 part of angle formed= 360°/5 =72°
used peices = 2
Angle formed by Remaining peices = 3 x 72° =216°
Therefore, the angle measure formed by the remaining pieces = 216°

Question 17.
DIG DEEPER!
You make a tile pattern for a border on a wall. Each tile is the same size and shape as a pattern block. Draw two ways you can arrange 1 triangle tile and 1 hexagon tile to create a straight angle.
Answer:

Find Angle Measures Homework & Practice 13.5

Use pattern blocks to find the measure of the angle.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer: The angle formed is 80°. It cannot be represented by pattern blocks.

Question 7.
How many 30° angles are in a right angle? Explain.
Answer:
Right angle =90°
How many 30° angles we have in right angle = 90°/30°=3

Question 8.
Structure
Draw to show how you can use three different pattern blocks to form a straight angle.
Answer:

Question 9.
YOU BE THE TEACHER
Your friend says the measure of the angle shown is 120°. Is your friend correct? Explain.

Answer:
No, As the angle is 130°.

Question 10.
DIG DEEPER!
The hands of a clock form a straight angle. What time could it be? Explain.
Answer:
The time as per mage is 6 o clock.
Explanation:

• One hand is very thin and moves very fast. It’s called the seconds hand. Every time it moves, a second has gone by.
• Another hand is thick and long like the seconds hand. It’s called the minutes hand. Every time it moves one little tick, a minute has gone by. Every 60 times it moves a whole step, an hour has gone by.
• The last hand is thick, too, but smaller than the minutes hand. It’s called the hours hand. Every time it moves one big tick, an hour has gone by. Every 24 times it moves a whole step, a day has gone by

Question 11.
Modeling Real Life
The scale is divided into 5 equal sections by each whole kilogram measurement. What is the measure of each angle formed at the center of the scale? What is the mass of the bananas?

Answer:
The whole Kilogram is divided into 5 parts
1kg = 1000 grams
=1000 grams / 5
=200 grams.
As per the image the weight of banans showing mark on one.
one unit = 200 grams.
Therefor, weight of bananas = 200 grams.

Question 12.
DIG DEEPER!
The gasoline tank gauge is divided into 4 equal sections. What are the measures of the angles formed at the starting point of the red arrow?

Answer:
The gasoline is in a shape of semi circle.
Sum of the angles = 180°
Number of sections divided = 4 parts. (equal).
Angle of each section : 180° /4 = 45° .
Therefore the measures of the angles formed at the starting point of the red arrow = 45° .

Review & Refresh

Find the area of the rectangle.

Question 13.

Answer:
Area of Rectangle = length X breadth.
AREA = 19 m x 16 m = 304 sq m.

Question 14.

Answer:
Area of Rectangle = length X breadth.
AREA = 28 in x 15 in =420 sq in.

Lesson 13.6 Measure and Draw Angles

Explore and Grow

Find the measure of each angle. Then classify it.

Answer:

Construct Arguments
Does the angle shown have a measure of 90°? Explain.

Answer:
The intersecting line form right angle =90 degrees
The angle marked = ?
The total angle = 360 degrees.
The marked angle= 360 – 90 = 270 degrees.

Think and Grow: Measure and Draw Angles

Example
A protractor is a tool for measuring and drawing angles.

Find the measure of ∠STU. Then classify it.
Step 1: Place the center of the protractor on the vertex of the angle.

Step 2: Align one side of the angle, \(\overrightarrow{T U}\), with 0° mark on the inner scale of the protractor.
Step 3: Find where the other side of the angle, \(\overrightarrow{T S}\), passes through the inner scale.
So, the measure of ∠STU is ___. It is an ___ angle.

Example
Draw ∠ABC that measures 65°.
Step 1: Place the center of the protractor on point. Align \(\overrightarrow{B C}\) with the 0° mark on the inner scale of the protractor.
Step 2: Use the same scale to draw a point at 65°. Label the point A.
Step 3: Use the protractor to draw \(\overrightarrow{B A}\).

Answer:

Show and Grow

Question 1.
Find the measure of ∠DEF. Then classify it.

Answer:

Question 2.
Use a protractor to draw ∠XYZ that measures 110°.

Answer:

Apply and Grow: Practice

Find the measure of the angle. Then classify it.

Question 3.

Answer:

Question 4.

Answer:

Use a protractor to draw the angle.

Question 5.
25°
Answer:

Question 6.
160°

Answer:

Question 7.
180°
Answer:

Question 8.
48°
Answer:

Question 9.
Writing
Why does one side of the angle you are measuring have to be lined up with the straight side of the protractor?
Answer:
We see two sets of degrees along the edge: an inner and outer scale. Both scales go from 0 to 180, but they run in opposite directions. If the angle opens to the right side of the protractor, use the inner scale. If the angle opens to the left of the protractor, use the outer scale.
To mark 0° on the inner scale of the protractor. So that we can next mark the angle we want to measure.

Question 10.
Precision
Newton says the measure of ∠ABC is 130°. Explain what he did wrong.

Answer:
The ∠ABC is 50 degrees not 130 degrees .
To measure an angle ABC, we place the mid point of the protractor on the vertex B of the angle. The base AB arm falls along with the base line of the protractor as shown in the figure above
The angle is measured on the protractor counting from 0 up to the point where the arm BC lies. In the above figure ∠ABC = 50°.

Think and Grow: Modeling Real Life

Example
A contractor builds two roofs. How much greater is the angle measure of Roof A than the angle measure of Roof B?

Use a protractor to measure the angle of each roof.
The angle measure of Roof A is _50°_ and the angle measure of Roof B is _40°__.
Subtract the angle measure of Roof B from the angle measure of Roof A.
_50°__ − _40°__ = _10°__
The angle measure of Roof A is _10°__ greater than the angle measure of Roof B.

Show and Grow0

Question 11.
An inspector compares two ramps. How much greater is the angle measure of Ramp B than the angle measure of Ramp A?

Answer:

Ramp A angle is 10 degrees and Ramp B angle is 20 degrees
Ramp B angle is 10 degrees greater.

Question 12.
DIG DEEPER!
On a trail map, two straight trails intersect. One of the angles formed by the intersection is 70. What are the other three angle measures?
Answer:
A trail is formed with 4 angles.
Sum of the angles in trial = 360°.
if one angle =70°
Sum of other 3 angles = 360° – 70° = 290 °.

Measure and Draw Angles Homework & Practice 13.6

Find the measure of the angle. Then classify it.

Question 1.

Answer:

Question 2.

Answer:

Use a protractor to draw the angle.

Question 3.
40°
Answer:

Question 4.
125°
Answer:

Question 5.
Reasoning
Measure the angles of each quadrilateral. What do you notice about the sum of the angle measures of each quadrilateral?

Answer:
The angles of the square are 90° each .
The angles of Quadilateral are two angles are 90°.
And other angles are 50°.
For every quadrilateral, the sum of the interior angles will always be 360°.

Question 6.
Precision
Use a protractor to draw a triangle with the angle measures of 0°. Describe your drawing.
Answer:

Question 7.
DIG DEEPER!
Use a protractor to draw a triangle with the angle measures of 90°, 35°, and 55°.
Answer:

Question 8.
Modeling Real Life
A snowboarder compares 2 mountain trails. How much greater is the angle measure of Trail B than the angle measure of Trail A?

Answer:
The angle is 5° greater.

Question 9.
DIG DEEPER!
On a map, there is a Y-intersection where one straight road branches off into two straight roads. One of the angles formed by the intersection measures 45°. Give two possible measures for the other angles formed by the intersection.
Answer:

Review & Refresh

Find the equivalent length

Question 10.
5 km = ___ m.
Answer:
1km = 1000m
5 km = 5 x 1000 m = 5000m

Question 11.
7 m = ___ mm.
Answer:
1m = 1000mm
7 m = 7 x 1000 mm = 7000mm

Lesson 13.7 Add Angle Measures

Explore and Grow

Use a protractor to draw ∠PQR that measures 70°.
Draw another angle that measures 30° and shares side \(\overrightarrow{\mathrm{Q} R}\). Label your angle. How many angles are in your figure? What do you notice about their measures?

Make a copy of ∠PQR. Draw and label a different angle that measures 30° and shares \(\overrightarrow{\mathrm{Q} R}\). How many angles are in your figure? What do you notice about their measures?

Construct Arguments
What conclusions can you make from your figures above?
Answer:
The Above triangle formed is a scalene triangle- has no equal side.

Think and Grow: Add Angle Measures

When an angle is decomposed into parts that do not overlap, the angle measure of the whole equals the sum of the angle measures of the parts.
Two angles are adjacent when they share a common side and a common vertex, but no other points in common. When two or more adjacent angles form a larger angle, the sum of the measures of the smaller angles is equal to the measure of the larger angle.

Example
Find the measure of ∠WXY.
∠WXY and ∠ZXY are adjacent. The measure of ∠WXZ is equal to the sum of the measures of and ∠ZXY. Complete the equation.
_41°__ + __32°_ = _73°__

So, the measure of ∠WXY is _73°__.

Show and Grow

Question 1.
Complete the equation to find the ∠PQR.

Answer:
∠PQR = ∠PQS +∠SQR
= 43° + 77° =120°

Question 2.
Use a protractor to find the measure of each angle in the circle. Use the angle measures to complete the equation.

Answer:

Apply and Grow: Practice

Write an equation to find the measure of the angle.

Question 3.

Answer:
∠QRS= ∠QRT +∠TRS
= 62° + 19° =81°

Question 4.

Answer:
∠ABC = ∠ABD +∠DBC
= 66° + 37° =103°

Question 5.

Answer:
∠MNO = ∠MNQ +∠QNP +∠PNO
= 45° + 87° +22°
=154° .

Question 6.

∠VWX = ∠VWZ +∠ZWY +∠YWX
= 36° + 38° +73°
=147° .

Use a protractor to find the measure of each angle in the circle. Use the angle measures to write an equation.

Question 7.

Answer:
∠M= ∠LMO +∠OMN +∠LMN
= 100° + 80° +180°
=360°
° .

Question 8.

Answer:
∠W= ∠SWT +∠TWU +∠UWV +∠VWS
= 120° + 60° + 90° + 90°
=360°

Question 9.
Number Sense
The sum of seven adjacent angle measures that share a vertex is 154°. Each angle has the same measure. What is the measure of each angle?
Answer:
The sum of seven equal angles = 154°.
Measure of each angle = 154°/7 = 22°.

Question 10

DIG DEEPER!
∠PRS is adjacent to ∠QRS in Exercise 3. The measure of ∠PRS is 9°. Find the measure of ∠QRP. Classify angle ∠QRP.
Answer:
∠QRP = 9°
Two angles are adjacent when they share a common side and a common vertex, but no other points in common. When two or more adjacent angles form a larger angle, the sum of the measures of the smaller angles is equal to the measure of the larger angle.

Think and Grow : Modeling Real Life

Example
A store installs 3 security cameras on the same light post. Each camera has a viewing angle of 28°. The viewing angles of the cameras are adjacent. What is the total viewing angle of the cameras?
Add the viewing angle measures of the cameras.
28° + 28° + 28° = _84°__

The total viewing angle of the cameras is __84°_

Show and Grow

Question 11.
A landscaper installs 3 sprinklers in 1 location in the grass. Each sprinkler has a spraying angle of 90°. The spraying angles of the sprinklers are adjacent. What is the total spraying angle of the sprinklers?

Answer:
As 3 sprinklers are adjacent all the 3 angles are equal.
Each angle of the sprinkler = 90°
Total spraying angle of the sprinklers= 3 X 90° = 270°

Question 12.
DIG DEEPER!
You use 4 rhombus tiles and 4 trapezoid tiles to make the pattern for a mosaic. Each tile is the same size and shape as a pattern block. What is the measure ∠NUQ?

Answer:
As we know th pattern blocks of trapezoid have 60° and rhombus have 30°.
Each tile is the same size and shape as a pattern block
∠NUQ= 30° + 60°+ 60° =150°

Question 13.
DIG DEEPER!
You make the pattern for a quilt. Each rhombus is the same size and shape. Name all of the 60° angles in the pattern.

Answer:
All 60° angles in the pattern = ∠AHC +∠BHD +∠CHE+∠DHF +∠EHG.

Add Angle Measures Homework & Practice 13.7

Write an equation to find the measure of the angle.

Question 1.

Answer:
∠EFG= ∠EFH +∠HFG
= 27° + 44°
=71°

Question 2.

Answer:
∠JKL= ∠JKM +∠MKL
= 53° + 85°
=138°

Question 3.

Answer:
∠PQR= ∠PQT +∠TQS +∠SQR
= 68° + 47° +54°
=316°

Question 4.

Answer:
∠VWX= ∠VWZ +∠ZWY +∠YWX
= 19° + 42° +35°
=96°

Use a protractor to find the measure of each angle in the circle. Use the angle measures to write an equation.

Question 5.

Answer:

∠D= ∠CDB +∠BDA +∠ADC
= 120° + 60° +180°
=360°

Question 6.

Answer:
∠N= ∠JNM +∠MNL +∠LNK + ∠KNJ
= 150° + 30°+90° + 90°
=360°

Question 7.
Open-Ended
Is it possible for the sum of two acute adjacent angle measures to be greater than the measure of a right angle? If so, draw a sketch to support your answer.
Answer:
Here ∠ABC and ∠CBD are both acute angles.
∠ABD= ∠ABC +∠CBD
= 60°+60°
=120°
sum of two acute adjacent angle=120° is more than 90° .

Question 8.
DIG DEEPER!
Use a protractor to measure the angle. Then decompose the angle into 2 parts so that one part is 25° greater than the other. What is the measure of each part?

Answer:
The measure of given angle = 120°
The given angle is divided into two parts one angle is 25° greater than other.
The measure each part = a + ( a + 25°) = 120°
120° – 25° =2a
105° = 2a
a=55.5°
a + 25° = 77.5°

Question 9.
Modeling Real Life
A carpenter glues 3 identical pieces of wood next to each other to make the table shown. The 30° angles of the pieces of wood are adjacent. What is the total angle of the table formed by the pieces of wood?

Answer:
Angle of each wood piece = 30°
As all angles are adjacent so angle of other wood pieces will be same.
so all 3 angles = 30° each.
Total angles = 3 x 30° = 90° .

Question 10.
DIG DEEPER!
You use 3 triangle pattern blocks and 3 rhombus pattern blocks to make the pattern for an art project. What is the measure of ∠ADE?

Answer:
The pattern block angle of triangle = 60°
The pattern block angle of Rhombus = 60°
∠ADE = ∠ADB + ∠BDE. = 60°+60° =120°

Review & Refresh

Compare

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Lesson 13.8 Find Unknown Angle Measures

Explore and Grow

Draw and label ∠EDF where point F is between the rays of ∠CDE. Explain how you can find the measure of ∠CDF.

Answer:
∠CDE=∠CDF + ∠EDF
= 45 + 45 =90°  (USING PROTACTOR).

Explanation:

Draw and label ∠LMP. Explain how you can find the measure of ∠NMP.

Answer:

Reasoning
Draw in your figure above. Explain how you can find all of the angle measures in your figure. What do you notice?
Answer:
is a which bisect the LN. so angles are divided into 2 parts equally. Using protractor we can find the measure of the angles.
This are complementary angles.

Think and Grow: Find Unknown Angle Measures

Example
Find the measure of ∠DEG.
∠DEG and ∠GEF are complementary. The sum of their measures is 90.°
Step 1: Write an equation to find the measure of ∠DEG.

Answer:

Show and Grow

Question 1.
Write and solve an equation to find the measure of ∠NLM.

Answer:
Supplementary angles form a straight line and have a sum of 180 degrees.
∠NLM=180°- ∠KLN
= 180° – 62° = 118°

Apply and Grow: Practice

Write and solve an equation to find the measure of the angle.

Question 2.

Answer:
Complementary angles form a right angle (L shape) and have a sum of 90 degrees.
∠MKL=90°- ∠MKJ
= 90° – 45° = 45°

Question 3.

Answer:
Supplementary angles form a straight line and have a sum of 180 degrees.
∠MNP=180°- ∠PNO
= 180° – 22° = 158°

Question 4.

Answer:
∠TRU= ∠SRQ -∠SRT -∠URQ
= 90° – 30° – 40°
=20°

Question 5.

Answer:
∠YWZ= ∠XWV -∠VWZ -∠YWX
= 180° – 31°-111°
=38°

Question 6.
Find the measures of ∠AEB, ∠AED, and ∠DEC.

∠AEB= ∠AEC -∠BEC
= 180° – 67° = 113°
∠DEC= ∠DEB -∠BEC
= 180° – 67° = 113°
∠AED= ∠AEC -∠DEC
= 180° – 113° = 67°

Question 7.
DIG DEEPER!
Write and solve equations to find the measure of ∠KMJ.

Answer:
∠KME= ∠KMG -∠GME
= 180° – 124° = 56°
∠KMJ= ∠JME -∠KME
= 90° – 56° = 34°

Question 8.
Writing
Define complementary angles and supplementary angles in your own words.
Answer:
Complementary angles form a right angle (L shape) and have a sum of 90 degrees.
Supplementary angles form a straight line and have a sum of 180 degrees.

Think and Grow: Modeling Real Life

Example
The foul lines on a baseball field are perpendicular. A baseball player hits a ball as shown. What is the measure of the angle between the path of the ball and the 1st base foul line?

Think: What do you know? What do you need to find? How will you solve?
The 3rd base foul line and 1st base foul line are perpendicular.
So, the measure of the angle between the foul lines is _90° __.
Write an equation to find the measure of the angle between the path of the ball and the 1st base foul line.

Show and Grow

Question 9.
Runway 1 and Runway 2 are perpendicular. What is the measure of the missing angle between Runway 1 and Runway 3?

Answer:
Angle between Runway 1 and Runway 3= 90 – Angle between Runway 2 and Runway 3.
=90 – 58 =32°

Question 10.
DIG DEEPER!
What is the measure of the missing g angle between View Street and Elm Street?

Answer:
Angle between View Street and Elm Street=360 – Angle between IIIstreet and view street – Angle between elm street and IIIstreet.
=360- 90 -152
=118°

Find Unknown Angle Measures Homework & Practice 13.8

Write and solve an equation to find the measure of the angle.

Question 1.
∠JKM

Answer:
∠JKM= ∠JKL -∠MKL
= 90° – 9° = 81°

Question 2.
∠PNM

∠PNM= ∠MNO -∠PNO
= 180° – 145° = 35°

Question 3.
∠QRU

Answer:
∠QRU= ∠QRS -∠URT-∠TRS
= 90°-28° – 13°
=49°

Question 4.
∠ZWV

Answer:
∠ZWV= ∠VWX -∠ZWY-∠YWX
= 180°- 32° – 24°
=124°

Question 5.
Reasoning
∠ABC and ∠CBD are adjacent. ∠ABC is a right angle.
∠CBD is acute.

Answer:
∠ABD=∠ABC-∠CBD
= 90 – 35 = 65°

Question 6.
Structure
Which equations can you use to find the measure of angle ∠MKJ?

Answer:
180 – 57 = x

Question 7.
Open-Ended
An acute angle and an obtuse angle are adjacent and supplementary. What might the measures of each angle be?
Answer:

Question 8.
Modeling Real Life
Newton bounces a ball off of a wall to Descartes. \(\overline{A D}\)⊥\(\overline{D B}\). The measures of ∠ADC and ∠BDE are equivalent. Find the measures of ∠ADC and ∠BDE.

Answer:
∠ADC and ∠BDE. are equal
∠CDE= ∠ADC + ∠BDE – ∠BDA.
180 = a + a – ∠BDA.
∠BDA.=180 -2a

Question 9.
Modeling Real Life
Owls see an object with both eyes at the same time using binocular vision. What angle measure describes the owl’s binocular vision? Explain.

Answer:
left monocular + Binocular vision = 180
Binocular vision = 180 – 110=70 degrees.

Review & Refresh

Write the fraction as a money amount and as a decimal

Question 10.
\(\frac{49}{100}\)
Answer:
0.49

Question 11.
\(\frac{25}{100}\)
Answer:
0.25

Question 12.
\(\frac{7}{100}\)
Answer:
0.07

Identify and Draw Lines and Angles Performance Task 13

A rural town is expanding and needs to plan the construction of new roads.

Question 1.
What is another name for Main Street?

Answer:
Line AC.

Question 2.
Use the directions to complete the map.
a. Draw and label it with a street name of your choice.
b. The library will be at point E on and on the other side of Main Street as the school. Plot and label the library E at point E.
c. Draw a new road through point E that is perpendicular to Main Street. Label it with a street name of your choice.

Question 3.
City planners want to construct a new residential neighborhood southeast of the town hall.
a. The measure of ∠ABD is \(\frac{1}{6}\) of 360°. What is the measure of the angle?
Answer:
∠ABD=(1/6) x 360 =60 degree.
b. Classify ∠DBC. What is its measure?
Answer:
∠DBC=180 -∠ABD = 180-60 = 120 degrees.
c. Draw a road from point B to the new neighborhood. The road divides ∠DBC exactly in half.
Answer:

Question 4.
Is the distance between the supermarket and the police station more than or less than a mile? Explain.
Answer:
Distance between the supermarket and the police station= AB + BC
= (1/4) + (5/8).
=(2+5)/8
=7/8.=0.8 mile
which is less than 1 mile.

Identify and Draw Lines and Angles Activity

Geometry Dots

Directions:

1. Players take turns connecting two dots, each using a different color.
2. On your turn, connect two dots, vertically or horizontally. If you close a square around an angle, find the measure of the angle inside the square. If you do not close a square, your turn is over.
3. Continue playing until you find all of the angle measures.
4. The player that finds the most angle measures wins!

Answer:

Identify and Draw Lines and Angles Chapter Practice 13

13.1 Points, Lines and Rays

Name the figure. Write how to say the name.

Question 1.

Answer:
It is a point said as Point F

Question 2.

Answer:

It is said as line GH. and represented as GH with overhead arrow.

Question 3.

Answer:
It is a ray JK .It is represented with Over head arrow to left.

Draw and label the figure.

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Use the figure

Question 7.
Name a line segment.
Answer: CE

Question 8.
Name two different rays.
Answer: CA and  CB.

13.2 Identify and Draw Angles

Question 9.
Write a name for the angle and classify it.

Answer:
∠SRQ. It is a obtuse angle.

Question 10.
∠TUV is a right angle. Draw and label the angle.
Answer:

13.3 Identify Parallel and Perpendicular Lines

Draw and label the lines with the given description.

Question 11.

Answer:

Question 12.

Answer:

13.4 Understand Degrees

Find the measure of each angle.

Question 13.

Answer:
115°

Question 14.

Answer:
=(1/5) x(—–/—–)= —-/360.
=72°/360°

Question 15.

Answer:
=1/4 x 360
=90°

Question 16.
A circle is divided into 12 equal parts. What is the measure of the angle that turns through 2 parts?
Answer:
Number parts divided = 12
Total sum of the angles = 360°
Angle of 1 part = 360°/12. = 30°.
The measure of the angle that turns through 2 parts = 2 x 30°. = 60°.

Question 17.
Which one Doesn’t Belong? Which angle measure does not belong with the other three?

Answer:
1/6 of a circle = 360/6 = 60°.
60/360 of a circle = 1/6.
60°
1/8 of a circle = 360°/8=45°
Therefore 1/8 of a circle is different.

13.5 Find Angle Measures

Use pattern blocks to find the measure of the angle.

Question 18.

Answer:

Question 19.

Answer:

Question 20.

Answer:

Question 21.

Answer:

13.6 Measure and Draw Angles

Question 22.
Find the measure of the angle. Then classify it.

Question 23.
Use a protractor to draw a 45° angle.
Answer:

Modeling Real Life
On a map, two straight railroad tracks intersect. One of the angles formed by the intersection is 30°. What are the three other angle measures?

13.7 Add Angle Measures

Question 25.
Write an equation to find the measure ∠EFG.

Answer:
∠EFG = ∠EFH+∠HFG.
=37° + 48° = 85°.

Question 26.
Use a protractor to find the measure of each angle in the circle. Use the angle measures to write an equation.

Answer:

13.8 Find Unknown Angle Measures

Write and solve an equation to find the measure of the angle.

Question 27.

Answer:
Complementary angles =90°.
∠ABD = ∠ABC-∠DBC.
=90°-27° = 63°.

Question 28.

Answer:
Supplementary angle =180°
∠HFG = ∠EFG-∠EFH.
=180° + 42° = 38°.

Question 29.

Answer:
Complementary angles =90°.
∠MKL = ∠LKJ-∠MKN-∠NKJ.
=90°-45°-22°= 23°.

Question 30.

Answer:
Supplementary angles =180°.
∠SPR = ∠OPQ-∠OPS-∠RPQ.
=180°-25°-52°= 103°.

Conclusion: 

The solutions provided in the Big Ideas Math Answers Grade 4 Chapter 13 Identify and Draw Lines and Angles are prepared by the subject experts. So Download Bigideas Math Answers Grade 4 Chapter 13 Identify and Draw Lines and Angles for free and start practicing the problems. Also, bookmark our page to get the Solution Key of Big Ideas Math Grade 4 Chapters.

Avail free Big Ideas Math Grade 2 Chapter 9 Add Numbers within 1,000 Answer Key PDF on this page. This handy Big Ideas Math Answers Grade 2 9th Chapter Add Numbers within 1,000 contains solutions for each and every question in the textbook. Students can download BIM Book Grade 2 Chapter 9 Add Numbers within 1,000 Answers PDF and prepare well for the test.

Big Ideas Math Book 2nd Grade Answer Key Chapter 9 Add Numbers within 1,000

Practicing Big Ideas Math Grade 2 Book Chapter 9 Add Numbers within 1,000 will help the students who want to score good marks in the examination. We advise you to refer the different topics such as Add 10 and 100, Use a Number Line to Add Hundreds and Tens, Use a Number Line to Add Three-Digit Numbers, Use Compensation to Add Three-Digit Numbers, Use Partial Sums to Add Three-Digit Numbers, Use Models to Add Three-Digit Numbers, Add Three-Digit Numbers, and so on.

By learning all those lessons, students can know various methods of adding numbers below 1000. Students have to work hard right from the beginning days of their school to be strong in the basics of math. Solve all the questions and verify whether your method of solving and the solution is correct or not by checking Big Ideas Math Book Answers Grade 2 Chapter 9 Add Numbers within 1,000. Tap on the link given below to learn that particular concept.

Vocabulary

• Add Numbers within 1,000 Vocabulary

Lesson 1 Add 10 and 100

• Lesson 9.1 Add 10 and 100
• Add 10 and 100 Homework & Practice 9.1

Lesson 2 Use a Number Line to Add Hundreds and Tens

• Lesson 9.2 Use a Number Line to Add Hundreds and Tens
• Use a Number Line to Add Hundreds and Tens Homework & Practice 9.2

Lesson 3 Use a Number Line to Add Three-Digit Numbers

• Lesson 9.3 Use a Number Line to Add Three-Digit Numbers
• Use a Number Line to Add Three-Digit Numbers Homework & Practice 9.3

Lesson 4 Use Compensation to Add Three-Digit Numbers

• Lesson 9.4 Use Compensation to Add Three-Digit Numbers
• Use Compensation to Add Three-Digit Numbers Homework & Practice 9.4

Lesson 5 Use Partial Sums to Add Three-Digit Numbers

• Lesson 9.5 Use Partial Sums to Add Three-Digit Numbers
• Use Partial Sums to Add Three-Digit Numbers Homework & Practice 9.5

Lesson 6 Use Models to Add Three-Digit Numbers

• Lesson 9.6 Use Models to Add Three-Digit Numbers
• Use Models to Add Three-Digit Numbers Homework & Practice 9.6

Lesson 7 Add Three-Digit Numbers

• Lesson 9.7 Add Three-Digit Numbers
• Add Three-Digit Numbers Homework & Practice 9.7

Lesson 8 Add Up to 4 Two-Digit Numbers

• Lesson 9.8 Add Up to 4 Two-Digit Numbers
• Add Up to 4 Two-Digit Numbers Homework & Practice 9.8

Lesson 9 Explain Addition Strategies

• Lesson 9.9 Explain Addition Strategies
• Explain Addition Strategies Homework & Practice 9.9

Performance task 

• Add Numbers within 1,000 Performance Task
• Add Numbers within 1,000 Activity

Add Numbers within 1,000 Vocabulary

Organize It
Use the review words to complete the graphic organizer.

Answer:

Define It

Answer:

Lesson 9.1 Add 10 and 100

Explore and Grow

Model 231. Make a quick sketch of your model.

231

Model 10 more than 231. Make a quick sketch of your model.
231 + 10 = _____

Model 100 more than 231. Make a quick sketch of your model.
231 + 100 = _____
Answer:
Model 10 more than 231. Sketch of it:

231 + 10 = 241.

231 + 100 = 331. Sketch of it:

231 + 100 = 331.

Model 100 more than 231.

Show and Grow

Question 1.
317 + 10 = _____
317 + 100 = _____
Answer:
317 + 10 = 327.
317 +100 = 417.

Explanation:

Question 2.
168 + 10 = _____
168 + 100 = _____
Answer:
168 + 10 = 178.
168 + 100 = 268.

Explanation:

.

Question 3.
223 + 10 = _____
223 + 100 = _____
Answer:
223 + 10 = 233.
223 + 100 = 323.

Explanation:

Question 4.
490 + 10 = ____
490 + 100 = _____

Answer:
490 + 10 = 500.
490 + 100 = 590.

Explanation:

Apply and Grow: Practice

Question 5.
731 + 10 = _____
Answer:
731 + 10 = 741

Explanation:

Question 6.
674 + 100 = _____
Answer:
674 + 100 = 774.

Explanation:

Question 7.
620 + 10 = ____
Answer:
620 + 10 = 630.

Explanation:

Question 8.
713 + 10 = ____
Answer:
713 + 10 = 723.

Explanation:

Question 9.
564 + 100 = _____
Answer:
564 + 100 = 664.

Explanation:

Question 10.
349 + 10 = _____
Answer:
349 + 10 = 359.

Explanation:

Question 11.
456 + 100 = ____
Answer:
456 + 100 = 556.

Explanation:

Question 12.
802 + 100 = _____
Answer:
802 + 100 = 902.

Explanation:

Question 13.
192 + 10 = ____
Answer:
192 + 10 = 202.

Explanation:

Question 14.
900 + 100 = ____
Answer:
900 + 100 = 1000.

Explanation:

Question 15.
349 + ____ = 449
Answer:
349 + 100 = 449.

Explanation:
349 + ??? = 449.
449 – 349 =???
100 = ???
Hence, 349 + 100 = 449.

Question 16.
____ + 10 = 791
Answer:
781 + 10 = 791.

Explanation:
??? + 10 = 791
791-10 = ???
781 = ???
Hence, 781 + 10 = 791.

Question 17.
Number Sense
Use each number once to complete the equations.

____ + 10 = ____
_____ + _____ = 512
Answer:
312 + 10 = 322
412 + 10 = 422
100 + 10 = 110
322 + 10 = 332
412 + 100 = 512

Think and Grow: Modeling Real Life

You and a friend play skee ball. Your score is 290. Your friend’s score is 220. On the last roll, you score 10 more and your friend scores 100 more. Who wins?
Addition equations:

You Friend
Answer:
GIVEN:
My score = 290
Friends score = 220
In the last roll,10 runs more my score
=> 290+ 10 = 300.
In the last roll,100 runs more my friend score
=> 220 + 100 = 320.
DIFFERENCE:
My friends score – My score=
320 – 300 = 20 runs.
COMPARE:

Hence, my friend wins the match by 20 runs.

Show and Grow

Question 18.
You and a friend play a card game. Your score is 420. Your friend’s score is 530. In the last round, you score 100 more and your friend scores 10 more. Who wins?

You Friend
Answer:
GIVEN:
My score = 420
Friends score = 530
In the last round ,100 runs more my score
=> 420+ 100 = 520.
In the last roll,10 runs more my friend score
=> 530 + 10 = 540.
DIFFERENCE:
My friends score – My score=
540 – 520 = 20 .
COMPARE:

Hence, my friend wins the match by 20.

Question 19.
You spin the wheel and score 100 points. Your friend scores 335. On the last spin, you score275 more and your friend scores 10 more. Who wins?

You Friend
Answer:
GIVEN:
My score = 100 points
Friends score = 335 points
In the last spin ,275 runs more my score
=> 100+ 275 = 375 points.
In the last spin,10 runs more my friend score
=> 335 + 10 = 345 points.
DIFFERENCE:
My  score – My  friends score=
375 – 345 = 30 points.
COMPARE:

Hence, I win the match by 30points.

Add 10 and 100 Homework & Practice 9.1

Question 1.
850 + 100 = _____
Answer:
850 +100 =950.

Question 2.
625 + 10 = ____
Answer:
625 + 10 = 635.

Question 3.
704 + 10 = ____
Answer:
704 + 10 = 714.

Question 4.
294 + 100 = ____
Answer:
294 + 100 = 394.

Question 5.
556 + 100 = ____
Answer:
556 + 100 = 656.

Question 6.
471 + 100 = _____
Answer:
471 + 100 =571.

Question 7.
308 + 100 = ____
Answer:
308 + 100 =408.

Question 8.
149 + 10 = _____
Answer:
149 + 10 =159.

Question 9.
690 + 10 = ____
Answer:
690 + 10 =700.

Question 10.
990 + 10 = _____
Answer:
990 + 10 =1000.

Question 11.
621 + ____ = 631
Answer:
621 + 10 = 631.

Question 12.
____ + 100 = 613
Answer:
513 + 100 = 613.

Question 13.
YOU BE THE TEACHER
Your friend says that 847 + 10 = 947. Is your friend correct? Explain.
_____________________________
_____________________________
Answer:
Your friend says that 847 + 10 = 947.
847 + 10 = 857.
Hence, my Friend is not correct because the total is 857 not 947.

Question 14.
Modeling Real Life
You pick 220 blueberries. Your friend picks 200. You pick 10 more and your friend picks 100 more. Who picks more blueberries?

You Friend
Answer:
GIVEN:
Number of blueberries I picked up  = 220
Number of blueberries my friend picked up = 200
10 more Blueberries I picked up later
Total number of blueberries I has => 220 + 10 = 230.
100 more Blueberries my Friend picked up later
Total number of blueberries my friends has=>200 + 100 =300.
DIFFERENCE:
Total number of blueberries my friends has  – Total number of blueberries I have
=>300 – 230
=> 70.
COMPARE:

Hence, my friend wins because he has 70 blueberries more than me.

Question 15.
Modeling Real Life
You download 100 songs. Your friend downloads 125. Then you download 145 more and your friend downloads 10 more. Who downloads more songs?
You Friend
Answer:
GIVEN:
Number of songs I downloaded = 100
Number of songs my friend downloaded = 125
Number of songs I downloaded more = 145
Total number of songs I downloaded = 100 + 145 = 245.
Number of songs my friend downloaded more = 10
Total number of songs my friend downloaded = 125 + 10 = 135.
DIFFERENCE:
Total number of songs I downloaded – Total number of songs my friend downloaded
= 245 – 135
= 110.
Hence, I downloaded 110 songs more than my friend.

Review & Refresh

Question 16.

Answer:
DIFFERENCE:
56 – 8 = 48.

Question 17.

Answer:
DIFFERENCE:
73 – 5 = 68.

Question 18.

Answer:
DIFFERENCE:
41 – 26 = 15.

Lesson 9.2 Use a Number Line to Add Hundreds and Tens

Explore and Grow

Show how to skip count by tens five times on the number line.

154 + _____ = ____
Answer:

ADDITION:
154 + 5(10)
=154 + 50
= 204.
Hence, 154 + 50 = 204.

Show how to skip count by hundreds five times on the number line.
1Q
154 + _____ = _____
Answer:

ADDITION:
154 + 5(100)
=154 + 500
= 654.
Hence, 154 + 500 = 654.

Show and Grow

Question 1.
380 + 340 = ____

Answer:

ADDITION:
380+ 3(100) +40
= 380 + 300 +40
=680 + 40
= 720.
Hence, 380 + 340 = 720.

Question 2.
462 + 270 = _____

Answer:

ADDITION:
462 +2(100) + 70
=462 + 200 + 70
= 662 + 70
=732.
Hence, 462 + 270 = 732.

Apply and Grow: Practice

Question 3.
550 + 210 = _____

Answer:

ADDITION:
550 + 2(100) + 10
= 550 + 200 + 10
= 750 + 10
= 760.
Hence, 550 + 210 = 760.

Question 4.
725 + 160 = ____

Answer:

ADDITION:
725 + 100 + 60
=825 + 60
=885.
Hence, 725 + 160 = 885.

Question 5.
469 + 350 = ____

Answer:

ADDITION:
469 + 3( 100) + 50
= 469 + 300 +50
=769 + 50
=819.
Hence, 469 + 350 = 819.

Question 6.
Reasoning
Complete the number line and the equation.

____ + ____ = _____
Answer:

ADDITION:
720 + 100 + 100
=820 + 100
=920.
SUBTRACTION:
960 -920 = 40
Hence, 720 + 100 +100 +40 =960.

Think and Grow: Modeling Real Life

A post office has 330 large envelopes and some small envelopes. There are560 envelopes in all. How many small envelopes are there?
Addition equation:
Model:

______ small envelopes
Answer:
GIVEN:
Number of large envelopes post office has = 330
Total number of envelopes post office has = 560
Number of small envelopes post office has = ???
=> Total number of envelopes post office has  – Number of large envelopes post office has
=> 560 – 330 = 230.

Hence, Number of small envelopes post office has = 230.

Show and Grow

Question 7.
A postal carrier delivers 280 letters and some post cards. She delivers 390 pieces of mail in all. How many postcards does she deliver?

_____ postcards
Answer:
GIVEN:
Number of letters delivered by postal carrier = 280
Total Number of pieces mails delivered by the postal carrier = 390
Number of postcards delivered by the postal carrier = ???
=>Total Number of pieces mails delivered by the postal carrier  –  Number of letters delivered by postal carrier
=>  390 – 280 = 110.
Hence, the number of postcards delivered by the postal carrier = 110.

Question 8.
There are some children and 180 adults on a subway. There are 300 passengers in all. How many children are there?

_____ children
Answer:
GIVEN:
Number of adults on the subway = 180
Total number of passengers on the subway = 300
Number of children on the subway = ???
=> Total number of passengers on the subway – Number of adults on the subway
=> 300 – 180
=> 120.
Hence, the Number of children on the subway = 120.

Use a Number Line to Add Hundreds and Tens Homework & Practice 9.2

Question 1.
150 + 610 = _____

Answer:

ADDITION:
150 + 6(100) + 10
=> 150 +600 + 10
=> 750 +10
=>760.
Hence, 150 + 610 = 760.

Question 2.
291 + 450 = ____

Answer:

ADDITION:
291 + 4(100) + 5(10)
=> 291 + 400 +50
=> 691 + 50
=> 741.
Hence, 291 + 450 = 741.

Question 3.
553 + 250 = _____

Answer:

ADDITION:
553 +2(100) +5(10)
=>553 + 200 + 50
=>753 + 50
=>803.
Hence, 553 + 250 = 803.

Question 4.
Number Sense
Write the equation shown by the number line.

____ + ____ = ______
Answer:
ADDITION:
430 + 100  +100  +100 + 10 + 10
=>530 +100+ 100 + 10 + 10
=> 630 + 100 + 10 + 10
=> 730 +  10 + 10
=> 740 + 10
=> 750.
Hence, 430 + 100  +100  +100 + 10 + 10 = 750.

Question 5.
Modeling Real Life
A carpenter has 320 nails and some screws. There are 470 nails and screws in all. How many screws are there?

______ screws
Answer:
GIVEN:
Number of nails a carpenter has = 320
Total number of nails and screws a carpenter has = 470
Number of screws a carpenter has = ??
SUBTRACTION:
Number of screws a carpenter has = Total number of nails and screws a carpenter has – Number of nails a carpenter has
= 470 – 320
=150.
Hence, Number of screws a carpenter has = 150.

Question 6.
Modeling Real Life
A concession stand sells some drinks and 260 hot dogs. There were 400 drinks and hot dogs sold in all. How many drinks were sold?
______ drinks
Answer:
GIVEN:
Number of hot dogs a concession stand sells = 260
Total number of drink a concession stand sold = 400
Number of drinks sold = ??
SUBTRACTION:
Number of drinks sold = Total number of drink a concession stand sold – Number of hot dogs a concession stand sells
= 400 – 260
= 140.
Hence, Number of drinks sold = 140.

Review & Refresh

Question 7.
Show 416 two ways.

Answer:
ONE WAY: TABLE WAY

ADDITION:
=> 4(100) + 1(10)  + 6(1)
=> 400 + 10 + 6
=> 410 + 6
=>416.
OTHER WAY: NUMBER LINE WAY

ADDITION:
0+4(100) +1(10) + 6(1)
= 0 + 400 + 10 + 6
= 400 + 10 + 6
= 410 + 6
= 416.

Lesson 9.3 Use a Number Line to Add Three-Digit Numbers

Explore and Grow

Use each sum as the missing addend in the next equation.
425 + 200 = ____

How does this help you find 425 + 222?
___________________
____________________
Answer:
GIVEN:
To Find 425 + 222 = ???
ADDITION:
425 + 200 = 625.

625 + 20 = 645.

645 + 2 = 647.

Hence, 425 + 222 = 647.

Show and Grow

Question 1.
371 + 145 = ______

Answer:

ADDITION:
371 + 100 +45
= 471 + 45
= 516.
Hence, 371 + 145 = 516.

Question 2.
419 + 237 = ______

Answer:

ADDITION:
419 + 100 + 100 + 37
=519 + 100 + 37
=619 +37
= 656.
Hence, 419 + 237 = 656.

Apply and Grow: Practice

Question 3.
524 + 312 = _____

Answer:

ADDITION:
524 + 100 + 100 + 100 +12
= 624 + 100 + 100 +12
= 724 + 100 +12
= 824 + 12
= 836.
Hence, 524 + 312 = 836.

Question 4.
645 + 108 = ____

Answer:

ADDITION:
645 + 100 + 8
= 745 + 8
= 753.
Hence, 645 + 108 = 753.

Question 5.
836 + 74 = ____

Answer:

ADDITION:
836 + 74
= 910.
Hence, 836 + 74 = 910.

Question 6.
Number Sense
Write the equation shown by the number line.

_____ + ______ = ______
Answer:
EQUATION:
326+ 200 + 50 + 2
= 526 +  50 + 2
= 576 + 2
=578.
Hence, 326+ 200 + 50 + 2 = 578.

Think and Grow: Modeling Real Life

There are 289 boys and 323 girls running in a race. How many runners are there in all?
Addition equation:
Model:

_____ runners
Answer:
Number of boys running in the race = 289
Number of girls running in the race = 323
Total Number of runners in all = ???
ADDITION:
Total Number of runners in all = Number of boys running in the race – Number of girls running in the race
= 289 + 323
= 612.

Hence, Total Number of runners in all = 612.

Show and Grow

Question 7.
A textbook has 478 pages in Volume 1 and443 pages in Volume 2. How many pages are there in all?

_____ pages
Answer:
Total number of pages in the text book = 921.
Number of pages in Volume 1 in the text book = 478
Number of pages in Volume 2 in the text book = 443
Total number of pages in the text book = ???
ADDITION:
Total number of pages in the text book = Number of pages in Volume 1 in the text book + Number of pages in Volume 2 in the text book
= 478 + 443
= 921.
Hence, the total number of pages in the text book = 921.

Question 8.
DIG DEEPER!
The pictures show your fitness tracker before and after you take a walk. How many steps did you take on your walk?

_____ steps

Answer:
Total number of steps taken in the walk = 1027.

Explanation:
GIVEN:
Number of steps took after = 132
Number of steps took after = 895
Total number of steps taken in the walk = ???
ADDITION:
Total number of steps taken in the walk = Number of steps took after + Number of steps took after
= 132 + 895
= 1027.
Hence, Total number of steps taken in the walk = 1027.

Use a Number Line to Add Three-Digit Numbers Homework & Practice 9.3

Question 1.
291 + 407 = _____

Answer:
291 + 407 = 698.

Explanation:

ADDITION:
291 + 100 +100 + 100 + 100 + 7
= 391 + 100 + 100 + 100 + 7
= 491 + 100 + 100 + 7
= 591 + 100 + 7
= 691 + 7
= 698.
Hence, 291 + 407 =698.

Question 2.
752 + 138 = ____

Answer:
752 + 138 = 890.

Explanation:

ADDITION:
752 + 100 + 38
= 852 + 38
= 890.
Hence, 752 + 138 = 890.

Question 3.
372 + 319 =_____
 
Answer:
372 + 319 = 691.

Explanation:

ADDITION:
372 + 100 + 100 + 100 + 19
= 472 + 100 + 100 + 19
= 572 + 100 + 19
= 672 + 19
= 691.
Hence, 372 + 319 = 691.

Question 4.
Structure
Use the number lines to show 257 + 321 two ways.

257 + 321 = _____
Answer:
257 + 321 = 578.

Explanation:
ONE WAY: NUMBERLINE REPRESENTATION

OTHER WAY: EQUATION WAY REPRESENTATION:
257 + 100 + 100 + 100 + 21
= 357 + 100 + 100 + 21
= 457+ 100 + 21
= 557 + 21
= 578.
Hence, 257 + 321 = 578.

Question 5.
Modeling Real Life
A florist has 416 daisies and152 roses. How many flowers are there in all?

______ flowers
Answer:
Total number of flowers a florist has = 568.

GIVEN:
Number of daisies a florist has = 416
Number of roses a florist has = 152
Total number of flowers a florist has = ???

Explanation:
ADDITION:
Total number of flowers a florist has = Number of daisies a florist has
Number of roses a florist has
= 416 + 152
= 568.
Hence, Total number of flowers a florist has = 568.

Question 6.
DIG DEEPER!
A school has 872 students.139 students are in the second grade. How many students are not in second grade?
______ students
Answer:
Number of students not in second grade = 733.

GIVEN:
Total number of students present in school =872
Number of students in second grade = 139
Number of students not in second grade = ???

Explanation:
SUBTRACTION:
Number of students not in second grade = Total number of students present in school – Number of students in second grade
= 872 – 139
= 733.
Hence, Number of students not in second grade = 733.

Review & Refresh

Draw more lines to show fourths.
Question 7.

Answer:

Explanation:
1/4 of the figure is shaded.

Question 8.

Answer:

Explanation:
3/4 of the figure is shaded.

Lesson 9.4 Use Compensation to Add Three-Digit Numbers

Explore and Grow

Add to the model to make 300. Make a quick sketch of your work.

Answer:
What number did you add to make 300? _____
How can this help you find 296 + 124?
____________________
____________________

GIVEN:
In the figure given, the number count is 296.
given number = 300
what should be added to 296 to make 300?
SUBTRACTION:
300 – 296 = 4.

Hence, 4 should b added to 296 to make it 300.

This help in the calculating the sum easily .
296 + 124 = 420.

Show and Grow

Question 1.
Use compensation to add.

Answer:
GIVEN:
294 + 148 =??
Add 6 to 294.
subtract 6 from 148.
294 + 148
+6        -6
300 + 142 = 442.
Hence, 294 + 148 = 442.

Apply and Grow: Practice

Use compensation to add.
Question 2.

Answer:
GIVEN:
628 + 206 = ???
Add 2 to 628
Subtract 2 from 206.
628  +  206
+  2        – 2
630  +   204 = 834.
Hence, 628 + 206 = 834.

Question 3.

Answer:
703 + 145 =???
Add 5 to 145.
Subtract 5 from 703.
703 + 145
–  5     + 5
698 +  150 = 848.
Hence, 703 + 145 = 848.

Question 4.
490 + 367 = ?

____ + ____ = _____
Answer:
490 + 367 =??
Add 3 to 367.
Subtract 3 from 490.
490  +  367
–  3       + 3
487  +  370 = 857.
Hence, 490 + 367 = 857.

Question 5.
172 + 520 = ?

_____ + _____ = ______
Answer:
172 + 520 =???
Add 8 to 172.
Subtract 8 from 520.
172   +    520
+ 8         –   8
180   +    512 =  692.
Hence, 172 + 520 = 692.

Question 6.
614 + 275 = ______
Answer:
614  + 275 =???
Add 6 to 614.
Subtract 6 from 275.
614    +   275
+6           –  6
620    +   269 = 889.
Hence,  614 + 275 =889.

Question 7.
308 + 549 = _____
Answer:
308 + 549 = ???
Add 2 to 308.
Subtract 2 from 549.
308   +    549
+2            – 2
310   +    547 = 857.
Hence, 308 + 549 = 857.

Question 8.
Reasoning
Show two different ways to use compensation to find 406 + 113.

Answer:
ONE WAY:
406 + 113 = ??
Add 4 to 406.
Subtract 4 from 113.
406     +    113
+ 4            –  4
410     +    109 = 519.

OTHER WAY:
406 + 113 = ???
Add 7 to 113.
Subtract 7 from 406.
406     +    113
–  7            + 7
399   +      120 = 519.
Hence, 399 + 120 = 519.

Think and Grow: Modeling Real Life

You want to raise $500 in 2 days. Do you reach your goal?
Addition equation:

Yes     No
Answer:
GIVEN:
You want to raise $500 in 2 days.
Amount raised in day 1 = $283
Amount raised in day 2 = $205
ADDITION:
Total amount raised in day 1 and day 2 = $283 + $205 = $ 488.
SUBTRACTION:
Amount to be raised in two days = $500
Difference in amount = Amount to be raised in two days – Total amount raised in day 1 and day 2
= $500 – $488
= $2.
Hence, more $2 required to reach the goal.

Show and Grow

Question 9.
A museum wants a weekend total of 700 guests. Does the museum reach the goal?

Yes No
Answer:
GIVEN:
Total guests in the museum = 700
Number of guests on Saturday = 338
Number of guests on Sunday = 389
ADDITION
Total number of guests on Saturday and Sunday = 338 + 389 = 727
SUBTRACTION:
Difference in the guests total = Total number of guests on Saturday and Sunday – Total guests in the museum
= 727 – 700 = 27.
Hence, the museum reaches the goal by 27 guests more.

Question 10.
DIG DEEPER!
You want to score 400 in 3 bowling games. What score do you need in the third game to reach your goal?

Answer:
Score to be needed  in 3 bowling games = 400
Score in game 1 = 107
Score in game 2 = 144
ADDITION:
Total score in game 1 and game 2 = 107 + 144 = 251.
SUBTRACTION:
Score needed in the third game to reach your goal = score to be needed  in 3 bowling games – Total score in game 1 and game 2
= 400 – 251
= 149.
Hence, Score needed in the third game to reach your goal = 149.

Use Compensation to Add Three-Digit Numbers Homework & Practice 9.4

Use compensation to add.
Question 1.

Answer:
393 + 122 = ???
Add 7 to 393.
Subtract 7 from 122.
393   +   122
+7          –  7
400    +  115 = 515.
Hence, 393 + 122 = 515.

Question 2.

Answer:
GIVEN:
106 + 614 =???
Add 4 to 106.
Subtract 4 from 614.
106     +    614
+4              – 4
110     +    610 = 720.
Hence, 106 + 614 = 720.

Question 3.
237 + 315 = ?

_____ + _____ = ______
Answer:
GIVEN:
237 + 315 = ???
Add 3 to 237
Subtract 3 from 315
237   +   315
+ 3          –  3
240   +   312 = 552.
Hence, 237 + 315 = 552.

Question 4.
285 + 320 = ?

_____ + _____ = _____
Answer:
GIVEN:
285  +  320 ==?
Add 5 to 285
Subtract 5 from 320
285   +  320
+ 5         – 5
290   +  315 = 605.
Hence, 285 + 320 = 605.

Question 5.
YOU BE THE TEACHER
Your friend uses compensation to find 550 + 298. Is your friend correct? Explain.

Answer:
GIVEN:
550 + 298 = 852
550   +  298
Add 2 to 298
Subtract 2 from 550
550   +   298
– 2         +  2
552   +   300 = 852.
Hence, my friend compensation is correct because 550 + 298 = 852.

Question 6.
Modeling Real Life
Newton wants to read 571 pages in two weeks. He reads 321 pages in the first week and196 pages in the second week. Does he reach his goal?

Yes No
Answer:
GIVEN:
Total number pages newton wants to read in two weeks = 571
Number of pages he read in first week = 321
Number of pages he read in second week = 196
Did he reach his goal ??
ADDITION:
Total number of pages he read in first week and second week = 321 + 196 = 517
SUBTRACTION:
Number of pages left for reading by newton =  Total number pages newton wants to read in two weeks – Total number of pages he read in first week and second week
= 571 – 517
= 54.
Hence ,No Newton did not reach his goal because he read only 517 pages out of 571 pages.

Question 7.
DIG DEEPER!
You need 850 points to get to level 4 in a video game. How many points do you need in level 3to reach your goal?

______ points
Answer:
GIVEN:
Total points to go into level 4 in a video game = 850
Scored points in level 1 = 348
Scored points in level 2 = 297
Needed points in level 3 =???
ADDITION:
Total points scored in both level 1 and level 2 in a video game = 348 +297 = 645.
SUBTRACTION:
Needed points in level 3 = Total points to go into level 4 in a video game – Total points scored in both level 1 and level 2 in a video game
= 850 – 645
= 205.
Hence, Needed points in level 3 = 205.

Review & Refresh

Question 8.

Answer:
SUBTRACTION:
95 – 38 = 57.
Hence, difference of 95 – 38 = 57.

Question 9.

Answer:
SUBTRACTION:
82 – 40 = 42.
Hence, difference of 82 – 40 = 42.

Question 10.

Answer:
SUBTRACTION:
59 -21 =38.
Hence, difference of 59 -21 = 38.

Lesson 9.5 Use Partial Sums to Add Three-Digit Numbers

Explore and Grow

Model each number. Make quick sketches of your models. Then solve.

_____ + ____ = _____
324 + 215 = _____
Answer:

Hence, 324 + 215 = 539.

Show and Grow

Question 1.

Answer:

236 + 359 = ???
236 + 359 = 695.
Hence,  Sum of 236 + 359 = 695.

Question 2.

Answer:

582 + 173 =???
582 + 173 = 755.
Hence, Sum of 582 + 173 = 755.

Question 3.

Answer:

364 + 432 = ???
364 + 432 = 796.
Hence, Sum of 364 + 432 = 796.

Question 4.

Answer:

454  + 488 = ???
454  + 488 = 942.
Hence, Sum of 454  + 488 = 942.

Question 5.

Answer:

145 + 341 = ???
145 + 341 = 486.
Hence, Sum of 145 + 341 = 486.

Question 6.

Answer:

576 + 248 = ???
576 + 248 = 824.
Hence, Sum of 576 + 248 = 824.

Apply and Grow: Practice

Question 7.

Answer:

217 + 435 =???
217 + 435 = 652.
Hence, Sum of  217 + 435 = 652.

Question 8.

Answer:

532 + 129 = ???
532 + 129 = 661.
Hence, sum of 532 + 129 = 661.

Question 9.

Answer:

651 + 237 = ???
651 + 237 = 888.
Hence, Sum of 651 + 237 = 888.

Question 10.

Answer:

779 + 130 = ???
779 + 130 = 909.
Hence, Sum of 779 + 130 = 909.

Question 11.

Answer:

362 + 217 = ???
362 + 217 = 579.
Hence, Sum of 362 + 217 = 579.

Question 12.

Answer:

806 + 115 = ???
806 + 115 = 921.
Hence, Sum of 806 + 115 = 921.

Question 13.

Answer:

448 + 312 = ???
448 + 312 = 760.
Hence, Sum of 448 + 312 = 760.

Question 14.

Answer:

581 + 243 = ???
581 + 243 = 824.
Hence, Sum of 581 + 243 = 824.

Question 15.
Which One Doesn’t Belong?
Which expression does not belong with the other three?
200 + 300 + 50 + 20 + 5 + 6
581
500 + 70 + 11
500 + 80 + 5 + 6
Answer:
Expression 1:
200 + 300 + 50 + 20 + 5 + 6
=500 + 50 + 20 + 5 + 6
= 550 + 20 + 5 + 6
= 570 + 5 + 6
= 575 + 6
= 581.
Expression 2:
581
Expression 3:
500 + 70 + 11
= 570 + 11
= 581.
Expression 4:
500 + 80 + 5 + 6
=580 + 5 +6
= 585 + 6
= 591.
Hence, Expression 4 does not belong with the other three Expressions because the number given is not matching other three answers..

Think and Grow: Modeling Real Life

A video rental store has 348 fewer video games than movies. There are 116 video games. How many movies are there?
Model:

_____ movies
Answer:
GIVEN:
Number of video games a video rental store has= 116
Let the number of movies be X
Difference of video games and movies = 348
EQUATION:
X – 116 = 348
=> X = 348 + 116
=> X = 464.

Hence, the number of movies rental store has = 464.

Show and Grow

Question 16.
A library has 477 fewer magazines than books. There are 243 magazines. How many books are there?

____ books
Answer:
GIVEN:
Let the number of books = X
Number of magazines = 243
Difference of books and magazines = 477
EQUATION:
=> X – 243 = 477
=> X = 477 +243
=> X = 720
Hence, total number of books in the library = 720.

Question 17.
A clothing store has some shirts on hangers. There are 214 shirts on shelves. The store has 356 shirts in all. How many shirts are on hangers?

_____ shirts
Answer:
Number of shirts in all clothing store has = 356
Number of shirts on shelves = 214
Number of shirts on hangers = ???
SUBTRACTION:
Number of shirts on hangers = Number of shirts in all clothing store has – Number of shirts on shelves
= 356 -214 = 142.
Hence, Number of shirts on hangers = 142.

Use Partial Sums to Add Three-Digit Numbers Homework & Practice 9.5

Question 1.

Answer:

ADDITION:
442 + 215 = 657.
Hence, Sum of 442 + 215 = 657.

Question 2.

Answer:

ADDITION:
336 +465 = 801.
Hence, Sum of 336 +465 = 801.

Question 3.

Answer:

ADDITION:
451 + 401 = 852.
Hence, Sum of 451 + 401 = 852.

Question 4.

Answer:

ADDITION:
371 +248 = 619.
Hence, Sum of 371 +248 = 619.

Question 5.

Answer:

ADDITION:
672 + 283 = 955.
Hence, Sum of 672 + 283 = 955.

Question 6.

Answer:

ADDITION:
527 + 106 = 633.
Hence, Sum of 527 + 106 = 633.

Question 7.
DIG DEEPER!
Find the missing digits. Then find the sum.

Answer:
GIVEN:
Hundreds = 7
Tens = 0
Ones = 8
EXPLANATION:
— 4  5
+ 3 —  3
= 7  0  8
4 + 6 = 10
1 + 3 + 3 =7
MISSING NUMBERS ARE :
Hundreds place = 3
tens place = 6
ADDITION: 345 + 363 = 708.
Hence, missing numbers are 3 and 6.

Question 8.
Modeling Real Life
There are 180 fewer muffins than rolls. There are 425 muffins. How many rolls are there?
______ rolls
Answer:
Total number of muffins = 425
Let the number of rolls be X
Difference  in the muffins and rolls = 180
EQUATION:
X – 180 = 425
=> X = 425 – 180
=> X = 245
Hence, the number of rolls = 245.

Question 9.
Modeling Real Life
A truck driver drives 672 miles on Monday. He drives some more miles on Tuesday. He drives 954 miles in all. How many miles did he drive on Tuesday?
_____ miles
Answer:
GIVEN:
Number of miles driver drove on Monday = 672
Number of miles driver drove in all = 954
Number of miles driver drove on Tuesday = ???
SUBTRACTION:
Number of miles driver drove on Tuesday = Number of miles driver drove in all – Number of miles driver drove on Monday
= 954 – 672
= 282.
Hence, Number of miles driver drove on Tuesday = 282.

Review & Refresh

Question 10.
Circle the closed shapes with only 3 vertices.

Answer:

Hence, shapes having only 3 vertices are circled.

Lesson 9.6 Use Models to Add Three-Digit Numbers

Explore and Grow

Model to solve. Make a quick sketch of your model.

Answer:
GIVEN:
327 + 458 =???
ADDITION:

327 + 458 = 785.
Hence, Sum of 327 + 458 = 785.

Show and Grow

Question 1.
383 + 255 = ?

Answer:
GIVEN:
383 + 255 = ???
ADDITION:

383 + 255 = 638.
Hence, Sum of 383 + 255 = 638.

Apply and Grow: Practice

Question 2.
238 + 354 = ?

Answer:
GIVEN:
238 + 354 = ???
ADDITION:

238 + 354 = 592.
Hence, Sum of 238 + 354 = 592.

Question 3.
692 + 147 = ?

Answer:
GIVEN:
692 + 147 = ???
ADDITION:

692 + 147 =  839
Hence, sum of 692 + 147 = 839.

Question 4.
553 + 250 = ?

Answer:
GIVEN:
553 + 250 = ???
ADDITION:

553 + 250 =  803.
Hence, Sum of 553 + 250 =  803.

Think and Grow: Modeling Real Life

Your school wants to collect 750 canned goods. Your school collects 432 cans of soup and386 cans of vegetables. Does your school reach the goal? Explain.
Models:

Yes No
____________________
____________________
Answer:
Number of canned goods school wants to collect   = 750
Number of cans of soup school collected =  432
Number of cans of vegetables school collected = 386
ADDITION:
Total number of cans of soup and cans of vegetables school collected
= 432 + 386 = 818.

SUBTRACTION:
Number of canned goods school wants to collect  –  Total number of cans of soup and cans of vegetables school collected
= 818 – 750
= 68.
Yes, school reached its goal by 68 more than its wanted goods.

Show and Grow

Question 5.
A charity needs 600 volunteers. 328 people sign up on Saturday and 219 people sign up on Sunday. Are there enough volunteers? Explain.

Yes No
______________________
______________________
Answer:
GIVEN:
Total number of volunteers in a charity = 600
Number of people signed up on Saturday = 328
Number of people signed up on Sunday = 219
ADDITION:
Total number of people signed up on  Saturday and Sunday = 328 + 219 = 547.
NO, there are not enough volunteers because:
SUBTRACTION:
Total number of volunteers in a charity – Total number of people signed up on  Saturday and Sunday
= 600 – 547
= 53.
Hence, no there are not enough because 53 more people are required to sign up into the charity.

Use Models to Add Three-Digit Numbers Homework & Practice 9.6

Question 1.
614 + 250 = ?

Answer:
GIVEN:
614 + 250 = ???
ADDITION:

614 + 250 = 864.
Hence, 614 + 250 = 864.

Question 2.
192 + 717 = ?

Answer:
GIVEN:
192 + 717 = ???
ADDITION:

192 + 717 = ???
Hence, Sum of 192 + 717 = 909.

Question 3.
Open-Ended
Complete the addition problem so that you need to regroup to add.

Answer:
GIVEN:
235 + 32? = ???
ADDITION:

253 + 325 = 578.
REGROUPING OF NUMBERS:
Add 7 to 235.
Subtract 7 from 325.
253    +     325
+  7           –   7
260    +     318 = 578.
Hence, Sum of 253 + 325 = 578.

Question 4.
Modeling Real Life
The cafeteria needs 700 trays. They have 312 brown trays and 342 orange trays. Does the cafeteria have enough trays? Explain.
Yes No
_____________________________
_____________________________
Answer:
GIVEN:
Total number of trays cafeteria needs = 700
Number of brown trays cafeteria has = 312
Number of  orange trays cafeteria has = 342
ADDITION:
Total  number of brown and orange trays cafeteria has = 312 + 342 = 654
SUBTRACTION:
Total number of trays cafeteria needs – Total  number of brown and orange trays cafeteria has
= 700 – 654
= 46.
Hence, there are no enough trays in the cafeteria.46 more trays the cafeteria needs.

Review & Refresh

Draw to show the time.
Question 5.

Answer:

Question 6.

Answer:

Lesson 9.7 Add Three-Digit Numbers

Explore and Grow

Find each sum.

Answer:
GIVEN:
445 + 254 = ???
253 + 318 = ???
627 + 194 =???
ADDITION:

445 + 254 = 699
253 + 318 =  571
627 + 194 = 821
Hence, Sum of 445 + 254 = 699
253 + 318 =  571
627 + 194 = 821.

Compare the problems. How are they the same? How are they different?
_________________________
_________________________
Answer:
They are same with the process of adding and they are different in the results.

Show and Grow

Question 1.

Answer:
GIVEN:
184+438 = ???
ADDITION:

Hence, sum of 184+438 = 622.

Question 2.

Answer:
GIVEN:
227 + 267 = ???
ADDITION:

Hence, Sum of 227 + 267 = 494.

Question 3.

Answer:
GIVEN:
421 + 354 = ???
ADDITION:

Hence, Sum of 421 + 354 = 775.

Question 4.

Answer:
GIVEN:
279 + 514 = ???
ADDITION:

Hence, Sum of 279 + 514 = 793.

Question 5.

Answer:
GIVEN:
313 + 288 = ???
ADDITION:

Hence, Sum of 313 + 288 = 601.

Question 6.

Answer:
GIVEN:
396 + 156 = ???
ADDITION:

Hence, Sum of 396 + 156 = 552.

Question 7.

Answer:
GIVEN:
659 + 258 = ???
ADDITION:

Hence, Sum of 659 + 258 = 917.

Question 8.

Answer:
GIVEN:
463 + 485 = ???
ADDITION:

Hence, Sum of 463 + 485 = 948.

Question 9.

Answer:
GIVEN:
298 + 378 = ???
ADDITION:

Hence, Sum of 298 + 378 = 676.

Apply and Grow: Practice

Question 10.

Answer:
GIVEN:
245 + 605 = ???
ADDITION:

245 + 605 = 810
Hence, Sum of 245 + 605 = 810.

Question 11.

Answer:
GIVEN:
450 + 291 = ???
ADDITION:

450 + 291 = 741.
Hence, Sum of 450 + 291 = 741.

Question 12.

Answer:
GIVEN:
198 + 527 = ???
ADDITION:

198 + 527 = 725.
Hence, Sum of 198 + 527 = 725.

Question 13.

Answer:
GIVEN:
742 + 116 = ???
ADDITION:

742 + 116 = 858.
Hence, Sum of 742 + 116 = 858.

Question 14.

Answer:
GIVEN:
537 + 176 = ???
ADDITION:

537 + 176 = 713.
Hence, Sum of 537 + 176 = 713.

Question 15.

Answer:
GIVEN:
382 + 351 = ???
ADDITION:

382 + 351 = 733.
Hence, Sum of 382 + 351 = 733.

Question 16.

Answer:
GIVEN:
463 + 194 = ???
ADDITION:

463 + 194 = 657.
Hence, Sum of 463 + 194 = 657.

Question 17.

Answer:
GIVEN:
186 + 567 = ???
ADDITION:

186 + 567 = 753.
Hence, Sum of 186 + 567 = 753.

Question 18.

Answer:
GIVEN:
623 + 298 = ???
ADDITION:

623 + 298 = 921.
Hence, Sum of 623 + 298 = 921.

Question 19.
DIG DEEPER!
Find the missing digits

Answer:
GIVEN:
462 + ___43 = 705.
SUBTRACTION:
=> 705 – 462 = 243.

1___7 + 115 = 252.
SUBTRACTION:
=> 252 – 115 = 137.

395 + 14___ = 540.
SUBTRACTION:
=> 540 – 395 = 145.

Hence, Sum of  462 + 343 = 705.
147 + 115 = 252.
395 + 145 = 540.

Think and Grow: Modeling Real Life

A puzzle has 540 pieces. You put 254 pieces together. Your friend puts 286 pieces together. Did you and your friend use all of the pieces?

Addition equation:
Yes         No
Answer:
Total number of pieces the puzzles has = 540
Number of pieces kept together by me = 254
Number of pieces kept together by my Friend = 286
ADDITION:
Total number of pieces kept together = Number of pieces kept together by me + Number of pieces kept together by my Friend
= 254 + 286
= 540.
Hence, my friend and me used all the pieces of puzzle.
Yes ,its a addition equation.

Show and Grow

Question 20.
A sticker book has 800 stickers. You use 413 of them. Your friend uses 377. Did you and your friend use all of the stickers?

Yes No
Answer:
Total number of stickers a sticker book has = 800
Number of stickers used by me =413
Number of stickers used by my Friend = 377
ADDITION:
Total number of stickers used = Total number of stickers used by me and my Friend
= 413 + 377 = 790.
Number of stickers remaining = Total number of stickers a sticker book has – Total number of stickers used by me and my Friend
= 800 -790
= 10.
Number of stickers remaining = 10.
Hence, NO we did not use all stickers. There are 10 more stickers to be used.

Question 21.
A bus has 850 miles to travel. How many miles does the bus have left to travel?

______ miles
Answer:
Total number of miles the bus travels = 850
Number of miles bus travelled on day 1 = 423
Number of miles bus travelled on day 2 = 417
ADDITION:
Number of miles bus travelled on day 1 and day 2 = 423 + 417 = 840.
DIFFERENCE:
Number of miles left out for the bus to travel =Total number of miles the bus travels – Number of miles bus travelled on day 1 and day 2
= 850 – 840
= 10.
Hence, Number of miles left out for the bus to travel =10.

Add Three-Digit Numbers Homework & Practice 9.7

Question 1.

Answer:
GIVEN:
341 + 278 = ???
ADDITION:

Hence, Sum of 341 + 278 = 619.

Question 2.

Answer:
GIVEN:
705 + 126 = ???
ADDITION:

Hence, Sum of 705 + 126 = 831.

Question 3.

Answer:
GIVEN:
582 + 249 = ???
ADDITION:

Hence, Sum of  582 + 249 = 831.

Question 4.

Answer:
GIVEN:
573 + 338 = ???
ADDITION:

Hence, Sum of 573 + 338 = 911.

Question 5.

Answer:
GIVEN:
264 + 310 = ???
ADDITION:

Hence, Sum of 264 + 310 = = 574.

Question 6.

Answer:
GIVEN:
516 + 156 = ???
ADDITION:

Hence, Sum of 516 + 156 = 672.

Question 7.

Answer:
GIVEN:
490 + 137 = ???
ADDITION:

Hence, Sum of 490 + 137 = 627.

Question 8.

Answer:
GIVEN:
625 + 297 = ???
ADDITION:

Hence, Sum of 625 + 297 = = 922.

Question 9.

Answer:
GIVEN:
364 + 386 = ???
ADDITION:

Hence, Sum of 364 + 386 = 750.

Question 10.
Open-Ended
Complete the addition problem so that you do not need to regroup to add.

Answer:
GIVEN:
256 + 3____3 = ???

Missing number = 4
ADDITION:
256 + 343 = 599.
Hence, Sum of 256 + 343 = 599.

Question 11.
Modeling Real Life
The art room has 645 markers. One class is using 312 markers. Another class is using 209. Are both classes using all the markers?

Yes No
Answer:
GIVEN:
Number of Markers art room has = 645
Number of markers one class using = 312
Number of markers another class using = 209
ADDITION:
Total Number of markers used by one class and another class = 312 + 209 = 521
SUBTRACTION:
Number of markers unused = Number of Markers art room has – Total Number of markers used by one class and another class
= 645 – 521
= 124.
Hence, Number of markers unused = 124.
NO, all markers are not used.

Question 12.
Modeling Real Life
340 water balloons need to be filled. You fill 122 and your friend fills 145. How many more water balloons need to be filled?

____ water balloons
Answer:
GIVEN:
Number of balloons needed to be filled = 340
Number of balloons filled by me = 122
Number of balloons filled by my friend = 145
ADDITION:
Total Number of balloons filled by me and my friend = 122 + 145 =  267.
SUBTRACTION:
Number of balloons more to be filled = Number of balloons needed to be filled – Total Number of balloons filled by me and my friend
= 340 – 267
= 73.
Hence, Number of balloons more to be filled = 73.

Review & Refresh

Use place value to find the missing numbers.
Question 13.
324, 325, ____, 327, _____, _____, ______
Answer:
GIVEN:
324, 325, ____, 327, _____, _____, ______
SUBTRACTION:
=> 325 – 324 = 1  (PLACE VALUE)
ADDITION:
325 + 1 = 326
327 + 1 = 328
328 + 1 = 329
329 + 1 = 330
Hence, the missing number sequence =324, 325, 326, 327, 328, 329, 330.

Question 14.
463, 473, ____, 493, ____, _____, ______
Answer:
GIVEN:
463, 473, ____, 493, ____, _____, ______
SUBTRACTION:
=> 473- 463 = 10(PLACE VALUE)
ADDITION:
463 + 10 = 473
473 + 10 = 483
483 + 10 = 493
493 + 10 = 503
503 + 10 = 513
513 + 10 = 523
Hence, the missing number sequence = 463, 473, 483, 493, 503, 513, 523.

Lesson 9.8 Add Up to 4 Two-Digit Numbers

Explore and Grow

Use any strategy to solve.
Newton has 19 red balloons, 23 green balloons,31 yellow balloons, and 17 blue balloons. How many balloons does he have in all?
_____ balloons
Answer:
GIVEN:
Number of red balloons Newton has = 19
Number of green balloons Newton has = 23
Number of yellow balloons Newton has = 31
Number of blue balloons Newton has = 17
ADDITION:
Total number of balloons Newton has = Number of red balloons Newton has + Number of green balloons Newton has + Number of yellow balloons Newton has  + Number of blue balloons Newton has
= 19 + 23 + 31 + 17
= 42 + 31 + 17
= 73 + 17
= 90.
Hence, Total number of balloons Newton has = 90.

Compare your strategy to your partner’s strategy. How are your strategies the same? How are they different?
______________________
_______________________
Answer:
Strategy of mine and my friends are different yet the process to calculate the sum of the numbers is same.

Show and Grow

Question 1.

Answer:
GIVEN:
26 + 88 + 32 = ???
ADDITION:
26 + 88 + 32
= 114 + 32
= 146.
Hence, Sum of 26 + 88 + 32 = 146.

Question 2.

Answer:
GIVEN:
60 + 15 + 55 = ???
ADDITION:
60 + 15 + 55
= 75 + 55
= 130.
Hence, Sum of 60 + 15 + 55 = 130.

Question 3.

Answer:
GIVEN:
77 + 96 +24 = ???
ADDITION:
77 + 96 +24
= 173 + 24
= 197.
Hence, Sum of 77 + 96 +24 = 197.

Question 4.

Answer:
GIVEN:
57 + 13 + 33+ 48 = ???
ADDITION:
57 + 13 + 33+ 48
= 70 + 33+ 48
= 103 + 48
= 151.
Hence, Sum of 57 + 13 + 33+ 48 = 151.

Question 5.

Answer:
GIVEN:
89 + 62 +10 + 51 = ???
ADDITION:
89 + 62 +10 + 51
= 151 + 10 + 51
= 161 + 51
= 212.
Hence, Sum of 89 + 62 +10 + 51 = 212.

Question 6.

Answer:
GIVEN:
95 + 71 + 46 + 53 = ???
ADDITION:
95 + 71 + 46 + 53
= 166 + 46 + 53
= 212 + 53
= 265.
Hence, Sum of 95 + 71 + 46 + 53 = 265.

Apply and Grow: Practice

Question 7.

Answer:
GIVEN:
17 + 84 + 23 = ???
ADDITION:
17 + 84 + 23
= 101 + 23
= 124.
Hence, Sum of 17 + 84 + 23 = 124.

Question 8.

Answer:
GIVEN:
21 + 42 + 39 = ???
ADDITION:
21 + 42 + 39
= 63 + 39
= 102.
Hence, Sum of 21 + 42 + 39 = 102.

Question 9.

Answer:
GIVEN:
92 + 58 + 19 = ???
ADDITION:
92 + 58 + 19
= 150 + 19
= 169.
Hence, Sum of 92 + 58 + 19 = 169.

Question 10.

Answer:
GIVEN:
58 + 12 + 6 + 24 = ???
ADDITION:
58 + 12 + 6 + 24
= 70 + 6 + 24
= 76 + 24
= 100.
Hence, Sum of 58 + 12 + 6 + 24 = 100.

Question 11.

Answer:
GIVEN:
42 + 26 + 33 + 14 = ???
ADDITION:
42 + 26 + 33 + 14
= 68 + 33 + 14
= 101 + 14
= 115.
Hence, Sum of 42 + 26 + 33 + 14 = 115.

Question 12.

Answer:
GIVEN:
13 + 52 + 37 + 48 = ???
ADDITION:
13 + 52 + 37 + 48
= 65 + 37 + 48
= 102 + 48
= 150.
Hence, Sum of 13 + 52 + 37 + 48 = 150.

Question 13.

Answer:
GIVEN:
64 + 20 + 35 + 56 = ???
ADDITION:
64 + 20 + 35 + 56
= 84 + 35 + 56
=  119 + 56
= 175.
Hence, Sum of 64 + 20 + 35 + 56 = 175.

Question 14.

Answer:
GIVEN:
36 + 92 + 40 + 15 = ???
ADDITION:
36 + 92 + 40 + 15
= 128 + 40 + 15
= 168 + 15
= 183.
Hence, Sum of 36 + 92 + 40 + 15 = 183.

Question 15.

Answer:
GIVEN:
19 +  3 + 47 + 25 = ???
ADDITION:
19 +  3 + 47 + 25
= 22 + 47 + 25
= 69 + 25
= 94.
Hence, Sum of  19 + 3 + 47 + 25 = 94.

Question 16.
Number Sense
Solve. Which two digits in the ones place did you add first? Explain.
7 + 15 + 36 + 25 = _______
______________________
______________________
Answer:
GIVEN:
7 + 15 + 36 + 25 = ???
The two digits in ones place added first are 5 number.
= 15 + 25 + 36 + 7
= 40 + 36 + 7
= 76 + 7
= 83.
Hence, Sum of 7 + 15 + 36 + 25  = 83.

Think and Grow: Modeling Real Life

How many seeds does your class plant in all?

Addition problem:
_____ seeds
Answer:
GIVEN:
Number of Sunflower plant seeds = 81
Number of Marigold plant seeds = 92
Number of Pumpkin plant seeds = 83
Number of Tomato plant seeds = 78
ADDITION:
Total number of plants seeds = Number of Sunflower plant seeds + Number of Marigold plant seeds + Number of Pumpkin plant seeds + Number of Tomato plant seeds
= 81 + 92 + 83 + 78
= 173 + 83 + 78
= 256 + 78
= 334.
Hence, the total number of plants seeds = 334.

Show and Grow

Question 17.
How many fish are there in all?

Answer:
GIVEN:
Number of Angelfish = 43
Number of Rainbow fish = 37
Number of Swordtail = 29
Number of Tetra = 59
Total Number of all fishes = Number of Angelfish + Number of Rainbow fish + Number of Swordtail + Number of Tetra
= 43 + 37 + 29 + 59
= 80 + 29 + 59
= 109 + 59
= 168.
Hence, Total Number of all fishes = 168.

Question 18.
DIG DEEPER!
You need 100 craft sticks for a project. You have a 24-pack, a 32-pack, and a 36-pack. How many more craft sticks do you need?
______ more craft sticks
Answer:
GIVEN:
Number of craft sticks needed for a project = 100
Number of packs in first pack = 24
Number of packs in second pack = 32
Number of packs in third pack = 36
ADDITION:
Total number of packs in all three packs = Number of packs in first pack + Number of packs in second pack + Number of packs in third pack = 24 + 32 + 36 = 92.
SUBTRACTION:
Number of stickers needed = Number of craft sticks needed for a project – Total number of packs in all three packs
= 100 – 92
=8.
Hence, Number of stickers needed = 8.

Add Up to 4 Two-Digit Numbers Homework & Practice 9.8

Question 1.

Answer:
GIVEN:
43 + 62 + 18 =???
ADDITION:
43 + 62 + 18
=105 + 18
= 123.
Hence, Sum of 43 + 62 + 18 = 123.

Question 2.

Answer:
GIVEN:
74 + 30 +69 = ???
ADDITION:
74 + 30 +69
= 104 + 69
= 173.
Hence, Sum of 74 + 30 +69 = 173.

Question 3.

Answer:
GIVEN:
34 + 57 + 27 = ???
ADDITION:
34 + 57 + 27
= 91 + 27
= 118.
Hence, Sum of 34 + 57 + 27 = 118.

Question 4.

Answer:
GIVEN:
51 + 16 + 6 + 24 = ???
ADDITION:
51 + 16 + 6 + 24
= 67 + 6 + 24
= 73 + 24
= 97.
Hence, Sum of 51 + 16 + 6 + 24 = 97.

Question 5.

Answer:
GIVEN:
84 + 62 + 10 + 31 = ???
ADDITION:
84 + 62 + 10 + 31
= 146 + 10 + 31
= 156 + 31
= 187.
Hence, Sum of 84 + 62 + 10 + 31 = 187.

Question 6.

Answer:
GIVEN:
66 + 49 + 34 +21 = ???
ADDITION:
66 + 49 + 34 +21
= 115 + 34 + 21
= 149 + 21
= 170.
Hence, Sum of 66 + 49 + 34 +21 = 170.

Question 7.

Answer:
GIVEN:
50 + 26 + 45 + 44 = ???
ADDITION:
50 + 26 + 45 + 44
= 76 + 45 + 44
= 121 + 44
= 165.
Hence, Sum of 50 + 26 + 45 + 44 = 165.

Question 8.

Answer:
GIVEN:
73 + 14 + 26 + 27 = ???
ADDITION:
73 + 14 + 26 + 27
= 87 + 26 + 27
= 113 + 27
= 140.
Hence, Sum of 73 + 14 + 26 + 27 = 140.

Question 9.

Answer:
GIVEN:
65 + 8 + 32 + 71 = ???
ADDITION:
65 + 8 + 32 + 71
= 73 + 32 + 71
= 105 + 71
= 176.
Hence, Sum of 65 + 8 + 32 + 71 = 176.

Question 10.
Number Sense
Find the missing number.

Answer:
GIVEN:
38 + 41 + ____ + 52 = 159.
Let the missing number be X.
ADDITION:
38 + 41 + X + 52 = 159
=> 79 + X + 52 = 159
=> X + 131 = 159
=> X = 159 – 131
=> X = 28.
EQUATION:
38 + 41 + 28 + 52 = 159.
Hence, missing number = 28.

Question 11.
Modeling Real Life
How many sandwiches are there in all?

______ sandwiches
Answer:
GIVEN:
Number of Turkey Sandwiches = 59
Number of Ham Sandwiches = 23
Number of Cheese Sandwiches = 35
Number of Peanut Butter Sandwiches = 45
ADDITION:
Total number of all sandwiches = Number of Turkey Sandwiches + Number of Ham Sandwiches + Number of Cheese Sandwiches + Number of Peanut Butter Sandwiches
= 59 + 23 +35 + 45
= 162.
Hence, the total number of all sandwiches = 162.

Question 12.
DIG DEEPER!
You need 210 votes to win a school election. You receive 67 votes from the first grade and 93 votes from the second grade. How many more votes do you need?
____ votes
Answer:
Number of votes required to win school election = 210
Number of votes received from first grade = 67
Number of votes received from second grade = 93
ADDITION:
Total number of votes received from first and second grade = 67 + 93 = 160
SUBTRACTION:
Number of votes required to win the election = Number of votes required to win school election – Total number of votes received from first and second grade
= 210 – 160 = 50.
Hence, Number of votes required to win the election =  50.

Review & Refresh

Write a number that makes the statement true.
Question 13.
865 < _____
Answer:
GIVEN:
865 < _____.
Hence, 865 < 900.

Question 14. _____ > 374
Answer:
GIVEN: _____ > 374
Hence,  415 > 374.

Question 15.
736 = ____
Answer:
GIVEN:
736 = _____
Hence, 736 = 736.

Question 16.
451 > _____
Answer:
GIVEN:
451 > ______
Hence, 451 > 389.

Lesson 9.9 Explain Addition Strategies

Explore and Grow

Use two different strategies to find 274 + 519.

Answer:
ONE WAY :COMPENSATION METHOD
274 + 519 = ???
Add 6 to 274.
Subtract 6 from 519.
274     +     519
+  6             –   6
280     +     513  = 793.
Hence, Sum of 274 + 519 = 793.
OTHER WAY: USE MODELS TO ADD

Hence, Sum of 274 + 519 = 793.
Explain why you chose one of your strategies.
_________________________
_________________________
Answer:
I choose COMPENSATION METHOD and USE MODELS TO ADD for adding numbers because its easy to understand and easy to calculate the addition also.

Show and Grow

Choose any strategy to solve. Explain how you solved.
Question 1.
379 + 240 = ____
___________________
____________________
Answer:
GIVEN:
379 + 240 = ???
ADDITION:

Hence, Sum of 379 + 240 = 619.

Apply and Grow: Practice

Choose any strategy to solve. Explain how you solved.
Question 2.
426 + 355 = _____
___________________
___________________
Answer:
GIVEN:
426 + 355 = ???

Hence, Sum of 426 + 355 = 781.

Question 3.
671 + 219 = _____
____________________
____________________
Answer:
GIVEN:
671 + 219 = ???
ADDITION:

Hence, Sum of 671 + 219 = 890.

Question 4.
YOU BE THE TEACHER
Your friend uses compensation to solve. Is your friend correct? Explain.

____________________
____________________
Answer:
GIVEN:
182 + 506 = 688
ADDITION:
182     +    506
+6               -6
188     +    500 = 688
Hence, my friend compensation is correct because sum of 182 + 506 = 688.

Think and Grow: Modeling Real Life

Choose any strategy to solve. Explain how you solved.
You have 567 pennies in a piggy bank and 428 in a jar. How many pennies do you have in all?

Addition equation:
______ pennies
_______________________
_______________________
Answer:
GIVEN:
Number of pennies in  piggy bank = 567
Number of pennies in a jar = 428
ADDITION:
Total number of pennies in piggy bank and a jar = Number of pennies in  piggy bank  + Number of pennies in a jar
= 567 + 428 =  995.
Hence, the total number of pennies in piggy bank and a jar = 995.

Show and Grow

Choose any strategy to solve. Explain how you solved.
Question 5.
A beekeeper has 494 worker bees and 376 drone bees. How many bees does he have in all?

______ bees
___________________
___________________
Answer:
GIVEN:
Number of worker bees a beekeeper has = 494
Number of drone bees a beekeeper has = 376
ADDITION:
Total number of worker bees and drone bees  a beekeeper has = 494 + 376 = 870
Hence, the total number of worker bees and drone bees a beekeeper has = 870.

Question 6.
There are 365 days in one year. How many days are there in two years?
______ days
______________________
______________________
Answer:
CONVERTION:
1 YEAR = 365 DAYS
2 YEARS =????
MULTIPLICATION:
=> 2 x 365 = 730 days.
Hence, Number of days in 2 years = 730.

Explain Addition Strategies Homework & Practice 9.9

Choose any strategy to solve. Explain how you solved.
Question 1.
656 + 181 = _____
_________________________
_________________________
Answer:
GIVEN:
656 + 181 = ???

Hence, Sum of 656 + 181 = 837.

Question 2.
567 + 348 = ______
______________________
______________________
Answer:

Hence, Sum of 567 + 348 =915.

Question 3.
DIG DEEPER!
Find the missing numbers.

Answer:
SUBTRACTION:
765 – 541 = 224
870 – 358 = 512
542 – 108 = 434

Hence, 541 + 224 = 765
358 + 512 = 870
108 + 434 = 542.

Choose any strategy to solve. Explain how you solved.
Question 4.
Modeling Real Life
A farmer has 415 tomato plants and 250 pepper plants. How many plants does he have in all?

_____ plants
___________________
___________________
Answer:
Number of tomatoes plants farmer has = 415
Number of pepper plants farmer has = 250
ADDITION:
Total number of tomatoes plants and pepper plants farmer has = 415 + 250 = 665
Hence , the total number of tomatoes plants and pepper plants farmer has = 665.

Question 5.
Modeling Real Life
You practice the trumpet for 45 minutes each day. How many minutes do you practice in 4 days?
______ minutes
_________________________
________________________
Answer:
GIVEN:
Practice time of the trumpet each day = 45 minutes
Practice time of the trumpet in 4 days= ???
MULTIPLICATION:
=> 4 x 45 = 180 minutes.
Hence, Practice time of the trumpet in 4 days=  180 minutes.

Review & Refresh

Question 6.
97 − 71 = _____
Answer:
GIVEN:
97 – 71 = ???
DIFFERENCE:
97 – 71 =26.
Hence, 97 – 71 =26.

Question 7.
56 − 14 = _____
Answer:
GIVEN:
56 – 14 = ???
DIFFERENCE:
56 – 14 = 42
Hence, 56 – 14 = 42.

Add Numbers within 1,000 Performance Task

A store has four different robot kits.

Question 1.
How many parts are there in the green, purple, and orange kits?
______ parts
Answer:
GIVEN:
FOUR different robot kits.
Number of robot parts in green kit = 280
Number of robot parts in purple kit = 157
Number of robot parts in orange kit = 360
ADDITION:
Total number of robot parts in green, purple, and orange kits = 280 + 157 + 360
= 437 + 360 = 797.
Hence, Total number of robot parts in green, purple, and orange kits = 797.

Question 2.
The orange kit has 183 fewer parts than the yellow kit. How many parts are in the yellow kit?
______ parts
Answer:
Let robot parts in yellow kit be X
Number of robot parts in orange kit = 183
Difference in Number of robot parts in orange and yellow kit = 360
= X – 183 = 360
=> X = 360 + 183
=> X = 543.
Hence, robot parts in yellow kit = 543.
Question 3.
Your friend wants to buy two kits so that he has700 parts. Which two kits should he buy?
_____ and ______
Answer:
GIVEN:
Your friend wants to buy two kits so that he has700 parts.
Number of robot parts in green kit = 280
Number of robot parts in purple kit = 157
Number of robot parts in orange kit = 360
Number of robot parts in yellow kit = 543
Check the sum of four kits robot parts to each other.
280 + 157 = 437                     157 + 280 = 437
280 + 360 = 640                     157 + 360 = 517
280 + 543 = 823                     157 + 543 = 700

360+ 280 = 640
360 + 157 = 517
360 + 543 = 903
Therefore, 157 + 543 = 700.
ADDITION:
Two kits that have to be purchased = Number of robot parts in purple kit +  Number of robot parts in yellow kit =157 + 543 = 700.
Hence, Two kits that have to be purchased =700.

Question 4.
a. You have some robot parts at home. You buy two purple kits and one orange kit. Now you have 774 parts. How many parts did you have to start?
_______ parts
Answer:
GIVEN:
Number of robot parts in purple kit = 157
Two purple kit  robot parts total = 2 x 157 = 314
Number of robot parts in orange kit = 360
Total parts in Two purple kit and orange kit = 314 + 360 = 674
Total number of robot parts had= 774
DIFFERENCE:
Number of robot parts required to start =  Total number of robot parts had – Total robot parts in Two purple kit and orange kit
= 774 – 674
= 100
Hence, Number of robot parts required to start are 100 more.

b. Your cousin has 450 robot parts at home. She buys a kit and now has 36 more parts than you. Which kit did she buy?
______ kit
Answer:
GIVEN:
Number of robot parts my cousin has = 450
Number of robot parts me having = 674
Number of robot parts she has more than me = 36
=> 674 + 36 = 710
Checking the sum of kits with my friends kit
=> 450 + 280 =730
450 + 157 = 607
450 + 360 = 810
450 + 543 = 993
CONDITION GIVEN:
She buys a kit and now has 36 more parts than you.
=> 450 + 280 = 730.
Hence, Kit my friend purchased is green kit.

Add Numbers within 1,000 Activity

Three in a Row: Three-Digit Addition
To Play: Players take turns. On your turn, spin both spinners. Add the two numbers and cover the sum. Continue playing until someone gets three in a row.

Add Numbers within 1,000 Chapter Practice

9.1 Add 10and 100

Question 1.
230 + 10 = _____
Answer:
GIVEN:
230 + 10 = ???
ADDITION:
230 + 10 = 240.
Hence, Sum of 230 + 10 = 240.

Question 2.
419 + 10 = _____
Answer:
GIVEN:
419 + 10 = ???
ADDITION:
419 + 10 = 429.
Hence, Sum of 419 + 10 = 429.

Question 3.
623 + 100 = _____
Answer:
GIVEN:
623 + 100 = ???
ADDITION:
623 + 100 = 723.
Hence, Sum of 623 + 100 = 723.

Question 4.
899 + 10 = _____
Answer:
GIVEN:
899 + 10 = ???
ADDITION:
899 + 10 = 999.
Hence, Sum of 899 + 10 = 999.

Question 5.
384 + 100 = _____
Answer:
GIVEN:
384 + 100 = ???
ADDITION:
384 + 100 = 484.
Hence, sum of 384 + 100 = 484.

Question 6.
167 + 100 = _____
Answer:
GIVEN:
167 + 100 = ???
ADDITION:
167 + 100 = 267.
Hence, sum of 167 + 100 = 267.

9.2 Use a Number Line to Add Hundreds and Tens

Question 7.
592 + 340 = _____

Answer:

ADDITION:
592 + 100 + 100 + 100 + 40
= 692 + 100 + 100 + 40
= 792 + 100 + 40
= 892 + 40
= 932.
Hence, Sum of 592 + 100 + 100 + 100 + 40 = 932.

Question 8.
Modeling Real Life
You have 170 football stickers and some baseball stickers. You have 360 stickers in all. How many baseball stickers do you have?

_______ baseball stickers
Answer:
GIVEN:
Total number of stickers in all = 360
Number of football stickers = 170
Number of baseball stickers = ???
SUBTRACTION:
Number of baseball stickers = Total number of stickers in all – Number of football stickers
= 360 – 170
= 130.
Hence, Number of baseball stickers = 130.

9.3 Use a Number Line to Add Three-Digit Numbers

Question 9.
365 + 342 = _____

Answer:

ADDITION:
365 +100 + 100 + 100 + 42
= 465 + 100 + 100 + 42
= 565 + 100 + 42
= 665 + 42
= 707.
Hence, 365 +100 + 100 + 100 + 42 = 707.

Question 10.
604 + 217 = ____

Answer:

ADDITION:
604 + 100 + 100 + 17
= 704 + 100 + 17
= 804 + 17
= 821.
Hence, Sum of 604 + 100 + 100 + 17 = 821.

9.4 Use Compensation to Add Three-Digit Numbers

Use Compensation to Add
Question 11.
205 + 631 = ?

_____ + ____ = _____
Answer:
205 + 631 = ???
Add 5 to 205.
Subtract 5 from 631.
205   +    631
+   5          –  5
210     +   626 = 836.
Hence, Sum of 205 + 631 = 836.

Question 12.
452 + 311 = ?

_____ + ____ = _____
Answer:
GIVEN:
452 + 311 = ???
Add 8 to 452.
Subtract 8 from 311.
452      +    311
+ 8             –   8
460      +    302 = 762.
Hence, Sum of 452 + 311 = 762.

Question 13.
YOU BE THE TEACHER
Newton uses compensation to find 198 + 267. Is he correct? Explain.

Answer:
GIVEN:
198 + 267 = ???
Add 2 to 198.
Subtract 2 from 267.
198    +    267
+ 2           –  2
200    +   265 = 465.
Hence, Newton compensation is not correct because the sum of 198 + 267 = 465 not 467.

9.5 Use Partial Sums to Add Three-Digit Numbers

Question 14.

Answer:
GIVEN: 264 + 483 =???
ADDITION:

Hence, Sum of 264 + 483 = 747.

Question 15.

Answer:
GIVEN:
807 + 123 = ??
ADDITION:

Hence, Sum of 807 + 123 = 933.

Question 16.

Answer:
GIVEN:
325 + 324 = ???
ADDITION:

Hence, Sum of 325 + 324 = 649.

Question 17.

Answer:
GIVEN:
640 + 293 = ???
ADDITION:

Hence, Sum of 640 + 293 = 933.

9.6 Use Models to Add Three-Digit Numbers

Question 18.
395 + 410 = ?

Answer:
GIVEN:
395 + 410 = ???

Hence, Sum of 395 + 410 = 805.

9.7 Add Three-Digit Numbers

Question 19.
Number Sense
Find the missing digits.

Answer:
GIVEN:

SUBTRACTION:
918 – 561 = 357.
379 – 264 = 115.
792 – 646 = 146.

ADDITION:
561 + 357 = 918.
115 + 264 = 379.
646 + 146 = 792.
Hence, the missing numbers are  357, 115 and 146.

9.8 Add Up to 4 Two-Digit Numbers

Question 20.

Answer:
GIVEN:
54 + 32 + 20 = ???
ADDITION:
54 + 32 + 20
= 86 + 20
= 106.
Hence, 54 +32 +20 = 106.

Question 21.

Answer:
GIVEN:
43 + 58 +17 = ???
ADDITION:
43 + 58 +17
= 101 + 17
=118.
Hence, 43 + 58 +17 = 118.

Question 22.

Answer:
GIVEN:
16 + 81 + 74 = ???
ADDITION:
16 + 81 + 74
= 97 + 74
= 151.
Hence, 16 +61 + 74 = 151.

Question 23.

Answer:
GIVEN:
92 + 52+ 38 +41 = ???
ADDITION:
92 + 52+ 38 +41
= 144 + 38 +41
= 182 + 41
= 223.
Hence, 92 + 52+ 38 +41 = 223.

Question 24.

Answer:
GIVEN:
90+ 5 +13 + 48 = ???
ADDITION:
66 + 44 +30 +9
= 95 + 13 + 48
= 108 + 48
= 156.
Hence, 90+ 5 +13 + 48 = 156.

Question 25.

Answer:
GIVEN:
66 + 44 +30 +9 = ???
ADDITION:
66 + 44 +30 +9
= 110+30 +9
= 140 + 9
= 149.
Hence, 66 + 44 +30 +9 = 149.

9.9 Explain Addition Strategies

Choose any strategy to solve. Explain how you solved.
Question 26.
538 + 176 = ______
________________________
_________________________
Answer:
EQUATION METHOD:
538 + 100 + 10 + 10 +10 + 10  + 10 + 10 + 10 + 6
=638 + 10 + 10 +10 + 10  + 10 + 10 + 10 + 6
= 648 + 10 +10 + 10  + 10 + 10 + 10 + 6
= 658 + 10 + 10  + 10 + 10 + 10 + 6
= 668 + 10  + 10 + 10 + 10 + 6
= 678 + 10 + 10 + 10 + 6
= 688 + 10 + 10 + 6
= 698 + 10 + 6
= 708 +6
= 714.

Conclusion:

We have given a detailed explanation for each and every topic discussed in Big Ideas Math Book Grade 2 Chapter 9 Add Numbers within 1,000 Solutions. We have also provided the exercise problems along with the answers to help in practising the Add Numbers within 1,000 chapter. Stay tuned to our website to get the answers for all chapters of grade 2.

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Big Ideas Math Book 1st Grade Answer Key Chapter 2 Fluency and Strategies within 10

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Vocabulary

• Fluency and Strategies within 10 Vocabulary

Lesson 1: Add 0

• Lesson 2.1 Add 0
• Add 0 Practice 2.1

Lesson 2 Subtract 0 and Subtract All

• Lesson 2.2 Subtract 0 and Subtract All
• Subtract 0 and Subtract All Practice 2.2

Lesson 3: Add and Subtract 1

• Lesson 2.3 Add and Subtract 1
• Add and Subtract 1 Practice 2.3

Lesson 4: Add Doubles from 1 to 5

• Lesson 2.4 Add Doubles from 1 to 5
• Add Doubles from 1 to 5 Practice 2.4

Lesson 5: Use Doubles

• Lesson 2.5 Use Doubles
• Use Doubles Practice 2.5

Lesson 6: Add in Any Order

• Lesson 2.6 Add in Any Order
• Add in Any Order Practice 2.6

Lesson 7: Count on to Add

• Lesson 2.7 Count on to Add
• Count on to Add Practice 2.7

Lesson 8: Count Back to Subtract

• Lesson 2.8 Count Back to Subtract
• Count Back to Subtract Practice 2.8

Lesson 9: Use Addition to Subtract

• Lesson 2.9 Use Addition to Subtract
• Use Addition to Subtract Practice 2.9

Performance Task

• Fluency and Strategies within 10 Performance Task
• Fluency and Strategies within 10 Chapter Practice

Fluency and Strategies within 10 Vocabulary

Organize It

Review words:
addend
sum
difference

Use the review words to complete the graphic organizer.

Question 1.

Answer:

Explanation:
A number that is added to another number is known as an addend.
In this case, 3 and 4 are the addends.
Sum is the result of adding two numbers.
So, 3 + 4 = 7
7 is the result that means sum.

Question 2.

Answer:

Define It

Use your vocabulary cards to match.

Answer:

Explanation:
A number line can be defined as a straight line with numbers placed at equal intervals or segments along its length. A number line can be extended infinitely in any direction and is usually represented horizontally.
Count on is nothing the count that goes forward.
Count back is nothing but count that goes backward.

Lesson 2.1 Add 0

Explore and Grow

Use linking cubes to model each story.

There are 6 ducks in the pond. 0 ducks join them. How many ducks are in the pond flow?

____ ducks

Answer:
Number of ducks in pond = 6
Number of ducks joined= 0
Total number of ducks= 6+0=6 Ducks

Answer:
Number of ducks in pond = 0
Number of ducks joined= 8
Total number of ducks= 0+8=8 ducks

Show and Grow

Use the picture to write an equation.

Question 1.

Answer:
4 + 0 = 4

Explanation:
By seeing the above picture we say that one of the addend is 4 and another addend is 0.
Now add both the numbers
4 + 0 = 4
Thus the result is 4.

Question 2.

Answer:
0 + 1=1
Explanation:
From the above figure we notice 0 and 1 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 1 = 1
Thus the result is 1.

Question 3.

Answer:
0 + 6 = 6
Explanation:
From the above figure we notice 0 and 6 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 6 = 6
Thus the result is 6

Question 4.

Answer:
8 + 0 = 8
Explanation:
From the above figure we notice 0 and 8 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
8 + 0 = 8
Thus the result is 8.

Apply and Grow: Practice

Use the picture to write an equation.

Question 5.

Answer:
7 + 0 = 7
Explanation:
From the above figure we notice 0 and 7 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
7 + 0= 7
Thus the result is 7.

Question 6.

Answer:
0 + 10 = 10
Explanation:
From the above figure we notice 0 and 10 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 10 = 10
Thus the result is 10.

Question 7.
9 + 0 = _____
Answer:
9 + 0 = 9
Explanation:
From the above figure we notice 0 and 9 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
9 + 0 = 9
Thus the result is 9.

Question 8.
0 + 8 = ______
Answer:
0 + 8 = 8
Explanation:
From the above figure we notice 0 and 8 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 8 = 8
Thus the result is 8.

DIG DEEPER!
Find each sum. Think: What do you notice?

Question 9.
3 + 0 = ______
0 + 3 = ______
Answer:
3 + 0 = 3
0 + 3 = 3
We notice that any number added with 0 will be the same number.

Question 10.
0 + 6 = ______
6 + 0 = ______
Answer:
0 + 6 = 6
6 + 0 = 6
We notice that any number added with 0 will be the same number.

Question 11.
MP Logic
There are 7 penguins in all. How many penguins are inside the igloo?

Answer:
Total Number of penguins = 7
Number of penguins outside = 7
Number of penguins inside = x
x + 7 = 7
x = 0

Think and Grow: Modeling Real Life

There are no students at a bus stop. Then 9 students arrive. How many students are at the bus stop now?

Model:

Addition equation:

_________ students
Answer:

0 + 9 = 9
Number of students at bus stop = 9 students
Explanation:
From the above figure we notice 0 and 9 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 9 = 9
Thus the result is 9.

Show and Grow

Question 12.
Your friend does not have any tokens. You give your friend 7 tokens. How many tokens does your friend have now?
Model:

Addition equation:

__________ tokens
Answer:

0 + 7 = 7
Number of tokens with my friend = 7 tokens
Explanation:
From the above figure we notice 0 and 7 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 7 = 7
Thus the result is 7.

Add 0 Practice 2.1

Use the picture to write an equation.

Question 1.

________ + 0 = _________
Answer:
9 + 0 = 9
Explanation:
From the above figure we notice 0 and 9 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
9 + 0 = 9
Thus the result is 9.

Question 2.

________ + 0 = _________
Answer:
0 + 3 = 3
Explanation:
From the above figure we notice 0 and 3 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 3 = 3
Thus the result is 3

Question 3.
10 + 0 = ________
Answer:
10 + 0 = 10
Explanation:
From the above figure we notice 0 and 10 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
10 + 0 = 10
Thus the result is 10.

Question 4.
0 + 5 = _______
Answer:
0 + 5 = 5
Explanation:
From the above figure we notice 0 and 5 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 5 = 5
Thus the result is 5.

Question 5.
0 + 6 = _______
Answer:
0 + 6 = 6
Explanation:
From the above figure we notice 0 and 6 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 6 = 6
Thus the result is 6.

Question 6.
0 + 0 = _______
Answer:
0 + 0 =0
Explanation:
From the above figure we notice 0 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 0 = 0
Thus the result is 0.

Question 7.
DIG DEEPER!
Find each sum. Think: What do you notice?
7 + 0 = ______
0 + 7 = ______
Answer:
7 + 0 = 7
0 + 7 = 7
Explanation:
From the above figure we notice 0 and 1 are addends . Adding 0 to any number gives the sum as the number itself. If the order of the addends changes, the sum stays the same.Now add both the numbers
0 + 1 = 1
Thus the result is 1.

Question 8.
MP Logic
There are 8 students in all. How many students are inside the museum?

Answer:
Number of students = 8
Number of students out side the museum= 8
Number of students inside the museum=  x
x + 8 = 8
x = 0
Number of students inside the museum = 0

Question 9.
Modeling Real Life
There are no seals on the shore. Then 10 seals swim to the shore. How many seals are on the shore now?

__________ seals
Answer:

0 + 10 = 10
Number of seals on the shore = 0 + 10 = 10 seals
Explanation:
From the above figure we notice 0 and 10 are addends . Adding 0 to any number gives the sum as the number itself. Now add both the numbers
0 + 10 = 10
Thus the result is 10.

Review & Refresh

Write the number of goldfish.

Question 10.

Answer:
1
Explanation:
As per above figure we notice only 1 goldfishes in the aquarium.

Question 11.

Answer:
3
Explanation:
As per above figure we notice 3 goldfishes in the aquarium.

Question 12.

Answer:
0
Explanation:
As per above figure we notice no goldfish in the aquarium.

Question 13.

Answer:
2
Explanation:
As per above figure we notice 2 goldfishes in the aquarium.

Lesson 2.2 Subtract 0 and Subtract All

Explore and Grow

Use linking cubes to model each story.

There are 5 beavers on the log. None of the beavers leave. How many beavers are left?

________ beavers
Answer:
Number of beavers = 5
Number of beavers leave= 0
Number of beavers Remaining = 5 – 0 = 5

There are 5 beavers on the log. All of the beavers leave. How many beavers are left?

_________ beavers

Answer:
Number of beavers = 5
Number of beavers left = 5
Number of beavers remaining =5 – 5 = 0

Show and Grow

Use the picture to write an equation.

Question 1.

_________ – 0 = ________
Answer:
2 – 0  = 2
Explanation:
From the above equation we notice 2 is minuend and 0 is subtrahend. Subtracting 0 from any number gives the number itself as the difference. Now subtract the 2 and 0
2 – 0 = 2
Thus the difference is 2

Question 2.

_________ – _________ = 0
Answer:
1 – 1 = 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 3.

_________ – 0 = _________
Answer:
4 – 0 = 4
Explanation:
From the above equation we notice 4 is minuend and 0 is subtrahend. Subtracting 0 from any number gives the number itself as the difference. Now subtract the 4 and 0
4 – 0 = 4
Thus the difference is 4

Question 4.

_________ – _________ = 0
Answer:
2 – 2 = 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Apply and Grow: Practice

Use the picture to write an equation.

Question 5.

_________ – 0 = _________

Answer:
8 – 0 = 8
Explanation:
From the above equation we notice 8 is minuend and 0 is subtrahend. Subtracting 0 from any number gives the number itself as the difference. Now subtract the 2 and 0
8 – 0 = 8
Thus the difference is 8

Question 6.

_________ – _________ = 0
Answer:
8 – 8 = 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 7.
5 – 5 = _______
Answer:
5 – 5 = 0

Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 8.
6 – 0 = ________
Answer:
6 – 0 = 6
Explanation:
From the above equation we notice 6 is minuend and 0 is subtrahend Subtracting 0 from any number gives the number itself as the difference. Now subtract the 6 and 0
6 – 0 = 6
Thus the difference is 6

Question 9.
9 – 0 = ________
Answer:
9 – 0 = 9
Explanation:
From the above equation we notice 9 is minuend and 0 is subtrahend Subtracting 0 from any number gives the number itself as the difference. Now subtract the 9 and 0
9 – 0 = 9
Thus the difference is 9

Question 10.
7 – 7 = ________
Answer:
7 – 7 = 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 11.
MP Structure
Complete the equation. Then use the words to complete the sentence.

Words:
difference
number
subtract

4 – ______ = 4
When you ______ 0 from a number,  the ______ is that ______ .
Answer:
4 – 0 = 4
When you subtract 0 from a number,  the number is that difference.

Think and Grow: Modeling Real Life

Your friend has 7 pennies. You have 7 fewer pennies than your friend. How many do you have?

Draw a picture:

Subtraction equation:

_________ pennies
Answer:

Number of pennies with my friend = 7
Number of pennies with me  = x
x = 7 – 7 (7 fewer than my friend )
x = 0
Number of pennies with me = 0

Show and Grow

Question 12.
You have 6 pieces of chalk. You give all of your chalk to your friend. How many pieces do you have left?
Draw a picture:

Subtraction equation:

_________ pieces of chalk
Answer:

Number of chalks with me = 6
Number of chalks given to my friend = 6
Number of chalks remaining with me = 6 – 6 = 0

Subtract 0 and Subtract All Practice 2.2

Use the picture to write an equation.

Question 1.

________ – 0 = ________
Answer:
5 – 0 = 5

Question 2.

________ – _______ = 0
Answer:
5 – 5 = 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 3.
3 – 3 = _______
Answer:
3 – 3 = 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 4.
1 – 0 = _________
Answer:
1 – 0 = 1

Question 5.
1 – 1= _________
Answer:
1 – 1= 0
Explanation:
When a number is subtracted from itself the difference is always equal to 0.
Thus the difference is 0

Question 6.
7 – 0 = _________
Answer:
7 – 0 = 7

Question 7.
MP Structure
Complete the equation. Then use the words to complete the sentence.

Words:
difference
number
subtract

9 – ______ = 0
When you ______ a ______ from itself, the ______________ is 0.

Answer:
9 – 9 = 0
When you subtract a number from itself, the difference is 0

Question 8.
Modeling Real Life You have 4 stuffed animals. You give all of them to your friend. How many stuffed animals do you have left?

________ stuffed animals

Answer:
Number of stuffed animals  with me = 4
Number of stuffed animals given to my friend= 4
Number of stuffed animals remaining = 4 – 4 = 0

Review & Refresh

Write the number of dots you see on each domino. Then write the numbers in order.

Question 9.

Answer:

Question 10.

Answer:

Lesson 2.3 Add and Subtract 1

Explore and Grow

Use linking cubes to model each story.

There are 7 kids on the bench. 1 kid joins them. How many kids are on the bench flow?
__________ kids

Answer:
Number of kids = 7
Number of kids joined = 1
Total number of kids = 7 + 1 = 8

There are 8 kids on the bench. 1 kid leaves. How many kids are left?
__________ kids

Answer:
Number of kids = 8
Number of kids left = 1
Total number of kids = 8 – 1 = 7

Show and Grow

Use the picture to write an equation.

Question 1.

___________ – __________ = ___________
Answer:
7 – 1 = 6
Explanation:
From the above figure, we notice six people are playing and one person is leaving . so we get equation as
6 + 1 = 7 .
In Total we notice 7 people in the picture .

Question 2.

___________ + __________ = ___________
Answer:
7 + 1 = 8
Explanation:
From the above figure, we notice 7 people are playing and 1 person is joining. so we get equation as
7 + 1 = 8 .
In Total we notice 8 people in the picture .

Apply and Grow: Practice

Use the picture to write an equation.

Question 3.

___________ + __________ = ___________
Answer:
9 + 1 = 10
Explanation:
From the above picture we notice 9 people in the pool and 1 person is joining the pool. so total number of people in pool is 9 + 1 = 10 .
Thus Total people in the pool are 10 people.

Question 4.

___________ + __________ = ___________
Answer:
8 + 1 = 9
Explanation:
From the above picture we notice 8 people in the pool and 1 person is leaving the pool. so total number of people in the picture is 8 + 1 = 9 .
Thus Total people are 9 people.

Question 5.
5 – 1 = ________
Answer:
5 – 1 = 4
Explanation:
From the above equation we notice 5 is minuend and 1 is subtrahend.
Now subtract
5 – 1 = 4
Thus the difference is 4

Question 6.
6 + 1 = ________
Answer:
6 + 1 = 7
Explanation:
From the above figure we notice 6 and 1 are addends .Now add both the numbers
6 + 1 = 7
Therefore the sum is 7.

Question 7.
8 + 1 = ________
Answer:
8 + 1 = 9
Explanation:
From the above figure we notice 8 and 1 are addends .Now add both the numbers
8 + 1 = 9
Therefore the sum is 9.

Question 8.
7 – 1 = ________
Answer:
7 – 1 = 6
Explanation:
From the above equation we notice 7 is minuend and 1 is subtrahend.
Now subtract
7 – 1 = 6
Thus the difference is 6

DIG DEEPER!
Circle the problem with the greater sum or difference.
Question 9.
2 – 1                2 + 1
Answer:

Explanation:
from above equations we get
2 – 1 = 1 as difference and
2 + 1 = 3 as sum
now compare difference and sum
1 < 3
Therefore , 3 is greater than 1

Question 10.
5 + 1              6 – 1
Answer:

Explanation:
from above equations we get
6 –  1 = 5 as difference and
5 + 1 = 6 as sum
now compare difference and sum
6 > 5
Therefore , 6 is greater than 5

Question 11.
YOU BE THE TEACHER
Circle to show who is correct. Show how you know?
Answer:

Explanation:
when a given number is increased by 1 then we get the next number of that number, Also, we know that a next number of a number is called successor.
From the number line we can notice when 3 is added with 1 we get 4 as sum which is next number of 3.

Think and Grow: Modeling Real Life

You have 9 action figures. Newton has 1 more than you. Descartes has 1 fewer than you. Who has more, Newton or Descartes?

Equations:            Newton            Descartes

Who has more    Newton           Descartes
Answer:
Number of action figures with me= 9
Number of action figures with Newton = 9 + 1 = 10
Number of action figures with Descartes = 9 – 1 = 8
Newton has 2 more action figures than Descartes.

Show and Grow

Question 12.
You have 5 video games. Newton has 1 fewer than you. Descartes has 1 more than you. Who has fewer, Newton or Descartes?
Equations:            Newton            Descartes

Who has fewer?    Newton           Descartes
Answer:
Number of video games with me = 5
Number of video games with Newton  = 5 – 1 = 4
Number of video games with Descartes = 5 + 1 = 6
Newton has 2 fewer than Descartes.

Add and Subtract 1 Practice 2.3

Use the picture to write an equation.

Question 1.

___________ + ___________ = ___________
Answer:
5 + 1 = 6
Explanation:
From the above equation we notice 5 and 1 are addends .when a given number is increased by 1 then we get the next number of that number as sum, next number of 5 is 6
Now add both the numbers
5 + 1 = 6
Therefore the sum is 6.