Prasanna

Engage NY Eureka Math 1st Grade Module 1 Lesson 9 Answer Key

Eureka Math Grade 1 Module 1 Lesson 9 Problem Set Answer Key

Question 1.

Make a number bond to match the story.

Answer:

Question 2.

Make a number bond to match the story.

Answer:

Question 3.

Altogether, there are ____ flags.
Make a number bond to match the story.

Answer:

Question 4.

Altogether, there are ____ flowers.
Make a number bond to match the story.

Answer:

Eureka Math Grade 1 Module 1 Lesson 9 Exit Ticket Answer Key

Draw a picture and write a number sentence to match the story.

Ben has 3 red balls and gets 5 green balls. How many balls does he have now?

Answer:

Eureka Math Grade 1 Module 1 Lesson 9 Homework Answer Key

Question 1.
Use the picture to tell a math story.

Write a number sentence to tell the story.

Answer:

Write a number bond to match your story.

There are __ sharks.

Answer:

There are 8 sharks.

Question 2.
Use the picture to tell a math story.

Write a number bond to match your story.

Answer:

Write a number sentence to tell the story.

There are _______ students.

Answer:

There are 7 students.

Draw a picture to match the story.

Question 3.
Jim has 4 big dogs and 3 small dogs. How many dogs does Jim have?

Jim has ________ dogs.

Answer:

Jim has 7 dogs.

Question 4.
Liv plays at the park. She plays with 3 girls and 6 boys. How many kids does she play with at the park?

Liv plays with _______ kids.

Answer:

Liv plays with 9 kids.

Eureka Math Grade 1 Module 1 Lesson 9 Fluency Template Answer Key

Do as many as you can in 90 seconds. Write the number of bonds you finished here:

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Engage NY Eureka Math 1st Grade Module 1 Lesson 12 Answer Key

Eureka Math Grade 1 Module 1 Lesson 12 Problem Set Answer Key

Fill in the missing numbers.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

_______ balls = _______ balls + _______ balls
Bob had _______ balls at the park.

Answer:
As per the given data
6 balls = 2 balls + 4 balls
Bob had 4 balls at the park.

Question 5.

_______ apples + _______ apples = _______ apples
Mom gave me _______ apples.

Answer:
As per given data
3 apples + 7 apples = 10 apples
Mom gave me 10 apples.

Eureka Math Grade 1 Module 1 Lesson 12 Exit Ticket Answer Key

Draw a picture, and count on to solve the math story.

Write a number sentence to match your picture.

John caught _________ fish.

Answer:

John caught 7 fish.

Eureka Math Grade 1 Module 1 Lesson 12 Homework Answer Key

Use your 5-group cards to count on to find the missing number in the number sentences.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Use your 5-group cards to count on and solve the math stories. Use the boxes to show your 5-group cards.

Question 4.
Jack reads 4 books on Monday. He reads some more on Tuesday. He reads 7 books total. How many books does Jack read on Tuesday?

Jack reads __ books on Tuesday.

Answer:

Jack reads 3 books on Tuesday.

Question 5.
Kate has 1 sister and some brothers. She has 7 brothers and sisters in all. How many brothers does Kate have?

Kate has __ brothers

Answer:

Kate has 6 brothers

Question 6.
There are 6 dogs in the park and some cats. There are 9 dogs and cats in the park altogether. How many cats are in the park?

There are __ cats total.

Answer:

There are 3 cats total.

Engage NY Eureka Math 1st Grade Module 1 Lesson 10 Answer Key

Eureka Math Grade 1 Module 1 Lesson 10 Problem Set Answer Key

Question 1.
Use the picture to write the number sentence and the number bond.

______ little turtles + ______ big turtles = ______ turtles

Answer:

4 little turtles + 3 big turtles = 7 turtles

Question 2.

_____ dogs that are awake + ______ sleeping dogs = ______ dogs

Answer:

5 dogs that are awake + 4 sleeping dogs = 9 dogs

Question 3.

______ pigs + ______ pigs in mud = ______ pigs

Answer:

5 pigs + 2 pigs in mud = 7 pigs

Question 4.
Draw a line from the picture to the matching 5-group cards.

Answer:

Eureka Math Grade 1 Module 1 Lesson 10 Exit Ticket Answer Key

Question 1.
Draw to show the story. There are 3 large balls and 4 small balls.

How many balls are there? There are ______ balls.

Answer:

There are 7 balls.

Question 2.
Circle the set of tiles that match your picture.

Answer:
the set of tiles that match our picture is second one.

Eureka Math Grade 1 Module 1 Lesson 10 Homework Answer Key

Question 1.
Use your 5-group cards to solve.

Answer:

Draw the other 5-group card to show what you did.

Answer:

Question 2.
Use your 5-group cards to solve.

Answer:

Draw the other 5-group card to show what you did.

Answer:

Question 3.
There are 4 tall boys and 5 short boys. Draw to show how many boys there are in all.
There are ______ boys in all.
Write a number sentence to show what you did.

Answer:

Write a number bond to match the story.

Answer:

There are 9 boys in all.

Question 4.
There are 3 girls and 5 boys. Draw to show how many children there are altogether.
There are ______ children altogether.
Write a number sentence to show what you did.

Answer:

Write a number bond to match the story.

Answer:

There are 8 children altogether.

Eureka Math Grade 1 Module 1 Lesson 10 Fluency Template Answer Key

Target Practice
Choose a target number between 6 and 10 and write it in the middle of the circle on the top of the page. Roll a die. Write the number rolled in the circle at the end one of the arrows. Then, make a bull’s-eye by writing the number needed to make your target in the other circle.

Answer:

Engage NY Eureka Math 1st Grade Module 1 Lesson 7 Answer Key

Eureka Math Grade 1 Module 1 Lesson 7 Problem Set Answer Key

Circle the part. Count on to show 9 with the picture and number bond. Write the expressions.

Question 1.
Circle 7. How many more does 7 need to make 9?

Answer:

Question 2.
Circle 4. How many more does 4 need to make 9?

Answer:

Question 3.
Circle 3. How many more does 3 need to make 9?

Answer:

Question 4.
Draw a line to show partners of 9.

Answer:

Question 5.
Write a number bond for each partner of 9. Use the partners above for help.

Answer:

Eureka Math Grade 1 Module 1 Lesson 7 Exit Ticket Answer Key

Question 1.
Circle the pairs of numbers that make 9.

Answer:

Question 2.
Complete the number bonds to show 2 different ways to make 9.
a.

Answer:

b.

Answer:

Eureka Math Grade 1 Module 1 Lesson 7 Homework Answer Key

Ways to Make 9
Use the bookshelf picture to help you write the expressions and number bonds to show all of the different ways to make 9.

Answer:

Eureka Math Grade 1 Module 1 Lesson 6 Fluency Template 1 Answer Key

Shake Those Disks!—8

Answer:

Eureka Math Grade 1 Module 1 Lesson 6 Fluency Template 2 Answer Key

Do as many as you can in 90 seconds. Write the number of bonds you finished here:

Question 1.

Answer:

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Engage NY Eureka Math 1st Grade Module 1 Lesson 2 Answer Key

Eureka Math Grade 1 Module 1 Lesson 2 Problem Set Answer Key

Circle 2 parts you see. Make a number bond to match.

Question 1.

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Question 9.
How many pieces of fruit do you see? Write at least 2 different number bonds to show different ways to break apart the total.

Answer:

Eureka Math Grade 1 Module 1 Lesson 2 Exit Ticket Answer Key

Circle 2 parts you see. Make a number bond to match.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Eureka Math Grade 1 Module 1 Lesson 2 Homework Answer Key

Circle 2 parts you see. Make a number bond to match.

Question 1.

Answer:

Question 2.

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Question 8.

Answer:

How many animals do you see? Write at least 2 different number bonds to show different ways to break apart the total.

Question 9.

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Question 10.

Answer:

Eureka Math Grade 1 Module 1 Lesson 2 Fluency Template Answer Key

Number Bond Dash!

Do as many as you can in 90 seconds. Write the number of bonds you finished here:

Question 1.

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Engage NY Eureka Math 1st Grade Module 1 Lesson 6 Answer Key

Eureka Math Grade 1 Module 1 Lesson 6 Problem Set Answer Key

Circle the part. Count on to show 8 with the picture and number bond. Write the expressions.

Question 1.
Circle 6. How many more does 6 need to make 8?

Answer: 2
Adding 6 with 2 makes 8
6+2=8

Question 2.
Circle 5. How many more does 5 need to make 8?

Answer: 3
Add 3 to 5 to make it 8
5+3=8

Question 3.
Circle 4. How many more does 4 need to make 8?

Answer: 4
Add another 4 to make it 8
4+4=8

Question 4.
These number bonds are in an order starting with the biggest part first. Write to show which number bonds are missing.

Answer:

Question 5.
Use the expression to write a number bond and draw a picture that makes 8.

Answer: 8
By adding 3 with 5 we get 8
3+5=8

Question 6.
Use the expression to write a number bond and draw a picture that makes 8.

Answer: 8
Addition of 8 with 0 will give answer as 8
8+0=8

Eureka Math Grade 1 Module 1 Lesson 6 Exit Ticket Answer Key

Fill in the missing part of the number bond, and count on to find the total. Then, write 2 addition sentences for each number bond.

Question 1.

Answer: 8
There are 5 carrots in plate and 3 carrots are aside
adding 5 with 3 we get
5+3=8

Question 2.

Answer: 6
The are four strawberryies in the basket and two fallen from the basket
add 4 with 2 we get six
4+2=6

Eureka Math Grade 1 Module 1 Lesson 6 Homework Answer Key

Question 1.
Match the dots to show different ways to make 8. Then, draw a number bond for each pair.

Answer: There are 3 different ways to make 8 using the givien dots
adding of 5 and 3
5+3=8
adding of 2 and 6
2+6=8
adding of 7 and 1
7+1=8

Question 2.
Show 2 ways to make 8. Use the number bonds above for help.

Answer: Adding of 3 and 5
3+5=8
adding of 4 and 4
4+4=8

Question 3.
Fill in the missing number in the number bond. Write 2 addition sentences for the number bond you made. Notice where the equal sign is to make your sentence true.

Answer: There are 8 dots in the box
The numer bond formed is by using 8 and 0
Adding 8 woth 0 we get 8
8+0=8

Question 4.
These number bonds are in an order starting with the smallest part first. Write to show which number bonds are missing.

Answer:

Question 5.
Use the expression to write a number bond and draw a picture that makes 8.

Answer: 8
add 2 with 6
2+6=8

Question 6.
Use the expression to write a number bond and draw a picture that makes 8.

Answer: 8
Addition of 0 and 8 gives 8
0+8=8

Eureka Math Grade 1 Module 1 Lesson 6 Fluency Template Answer Key

Do as many as you can in 90 seconds. Write the number of bonds you finished here:

Question 1.

Answer: 1
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 2.

Answer: 0
The number bond can be formed by using 7 and 0
add 7 with 0 to get 7
7+0=7

Question 3.

Answer: 1
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 4.

Answer: 2
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 5.

Answer:1
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 6.

Answer:0
The number bond can be formed by using 7 and 0
add 7 with 0 to get 7
7+0=7

Question 7.

Answer:1
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 8.

Answer:2
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 9.

Answer:3
The number bond can be formed by using 3 and 4
add 3 with 4 to get 7
3+4=7

Question 10.

Answer:4
The number bond can be formed by using 3 and 4
add 3 with 4 to get 7
3+4=7

Question 11.

Answer:3
The number bond can be formed by using 3 and 4
add 3 with 4 to get 7
3+4=7

Question 12.

Answer:4
The number bond can be formed by using 3 and 4
add 3 with 4 to get 7
3+4=7

Question 13.

Answer:5
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 14.

Answer:2
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 15.

Answer:5
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 16.

Answer:1
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 17.

Answer:6
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 18.

Answer:7
The number bond can be formed by using 7 and 0
add 7 with 0 to get 7
7+0=7

Question 19.

Answer:5
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 20.

Answer:2
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 21.

Answer:6
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Question 22.

Answer:2
The number bond can be formed by using 5 and 2
add 5 with 2 to get 7
5+2=7

Question 23.

Answer:4
The number bond can be formed by using 3 and 4
add 3 with 4 to get 7
3+4=7

Question 24.

Answer:7
The number bond can be formed by using 7 and 0
add 7 with 0 to get 7
7+0=7

Question 25.

Answer: 1
The number bond can be formed by using 6 and 1
add 6 with 1 to get 7
6+1=7

Engage NY Eureka Math 1st Grade Module 1 Lesson 5 Answer Key

Eureka Math Grade 1 Module 1 Lesson 5 Problem Set Answer Key

Ways to Make 7. Use the classroom picture to help you write the expressions and number bonds to show all of the different ways to make 7.

Answer:

Eureka Math Grade 1 Module 1 Lesson 5 Exit Ticket Answer Key

Color in two dice that make 7 together. Then, fill in the number bond and number sentences to match the dice you colored.

Answer:

Eureka Math Grade 1 Module 1 Lesson 5 Homework Answer Key

Question 1.
Match the dice to show different ways to make 7. Then, draw a number bond for each pair of dice.

Answer:

Question 2.
Make 2 number sentences. Use the number bonds above for help.

Answer:

Question 3.
Fill in the missing number in the number bond. Then, write addition number sentences for the number bond you made.

Answer:

Question 4.
Color the dominoes that make 7.

Answer:

Question 5.
Complete the number bonds for the dominoes you colored.

Answer:

Eureka Math Grade 1 Module 1 Lesson 5 Fluency Template 1 Answer Key

Shake Those Disks!—6

Answer:

Eureka Math Grade 1 Module 1 Lesson 5 Fluency Template 2 Answer Key

Do as many as you can in 90 seconds. Write the number of bonds you finished here:

Question 1.

Answer:

Question 2.

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Engage NY Eureka Math 1st Grade Module 1 Lesson 4 Answer Key

Eureka Math Grade 1 Module 1 Lesson 4 Problem Set Answer Key

A
*Write the number that is 1 more.

Answer:

B
*Write the number that is 1 more.

Answer:

Ways to Make 6.
Use the apple picture to help you write all of the different ways to make 6.

Answer:

Eureka Math Grade 1 Module 1 Lesson 4 Exit Ticket Answer Key

Show different ways to make 6. In each set, shade some circles and leave the others blank.

Answer:

Eureka Math Grade 1 Module 1 Lesson 4 Homework Answer Key

Today, we learned the different combinations that make 6. For homework, cut out the flashcards below, and write the number sentences that you learned today on the back. Keep these flashcards in the place where you do your homework to practice ways to make 6 until you know them really well! As we continue to learn different ways to make 7, 8, 9, and 10 in the upcoming days, continue to make new flashcards.
*Note to families: Be sure students make each of the combinations that make 6. The flashcards can look something like this:

Answer:
For different ways to make 7, 8, 9, and 10

Engage NY Eureka Math 1st Grade Module 1 Lesson 3 Answer Key

Eureka Math Grade 1 Module 1 Lesson 3 Problem Set Answer Key

Draw one more in the 5-group. In the box, write the numbers to describe the new picture.

Question 1.

1 more than 7 is __.
7 + 1 = ___

Answer:

1 more than 7 is 8
7 + 1 = 8

Question 2.

1 more than 9 is __.
9 + 1 = ___

Answer:

1 more than 9 is 10
9 + 1 = 10

Question 3.

1 more than 6 is __.
6 + 1 = ___

Answer:

1 more than 6 is 7
6 + 1 = 7

Answer: the numbers to describe the new picture above

Question 4.

1 more than 5 is __.
5 + 1 = ___

Answer:

1 more than 5 is 6
5 + 1 = 6

Question 5.

1 more than 8 is __.
8 + 1 = ___
Answer:

1 more than 8 is 9
8 + 1 = 9

Question 6.

__ more than 7.
__ = 7 + 1

Answer:

1 more than 7.
8 = 7 + 1

Question 7.

__ is more than 6.
__ = 6 + 1

Answer:

7 is more than 6.
7 = 6 + 1

Question 8.

__ is more than 5.
__ = 5 + 1

Answer:

1 is more than 5.
6 = 5 + 1

Question 9.
Imagine adding 1 more backpack to the picture. Then, write the numbers to match how many backpacks there will be.

1 more than 7 is __.
__ + 1 = ___

Answer:

1 more than 7 is 8.
7 + 1 = 8

Eureka Math Grade 1 Module 1 Lesson 3 Exit Ticket Answer Key

How many objects do you see? Draw one more. How many objects are there now?

Question 1.

__ is more than 9.
9 + 1 = __

Answer:

1 is more than 9.
9 + 1 = 10

Question 2.

1 more than 6 is __.
__ + 1 = ___

Answer:

1 more than 6 is 7.
6 + 1 = 7

Eureka Math Grade 1 Module 1 Lesson 3 Homework Answer Key

How many objects do you see? Draw one more. How many objects are there now?

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Question 5.
Imagine adding 1 more pencil to the picture.
Then, write the numbers to match how many pencils there will be.

Answer:

Question 6.
Imagine adding 1 more flower to the picture.
Then, write the numbers to match how many flowers there will be.

Answer:

Engage NY Eureka Math 1st Grade Module 1 Lesson 1 Answer Key

Eureka Math Grade 1 Module 1 Lesson 1 Sprint Answer Key

* Write the number of dots. Find 1 or 2 groups that make finding the total number of dots easier!

Answer:

B
* Write the number of dots. Find 1 or 2 groups that make finding the total number of dots easier!

Answer:

Eureka Math Grade 1 Module 1 Lesson 1 Problem Set Answer Key

Circle 5, and then make a number bond.

Question 1.

Answer:

Explanation:
A number bond is a simple addition of two numbers that add up to give the sum.
5 and 3 are the parts of the number.
The result 8 is the whole.

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Put nail polish on the number of fingernails shown from left to right. Then, fill in the parts. Make the number of fingernails on one hand a part.

Question 5.

Answer:

Question 6.

Answer:

Make a number bond that shows 5 as one part.

Make a number bond for the pictures that shows 5 as one part.

Question 7.

Question 8.

Answer:

Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Eureka Math Grade 1 Module 1 Lesson 1 Exit Ticket Answer Key

Question 1.

Answer:

Question 2.

Answer:

Eureka Math Grade 1 Module 1 Lesson 1 Homework Answer Key

Circle 5, and then make a number bond.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

Make a number bond that shows 5 as one part.

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

Make a number bond for the dominoes.

Question 9.

Answer:

Question 10.

Question 11.

Answer:

Question 12.

Answer:

Circle 5 and count. Then, make a number bond.

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Engage NY Eureka Math Grade 6 Module 5 Lesson 6 Answer Key

Eureka Math Grade 6 Module 5 Lesson 6 Exploratory Challenge Answer Key

Exploratory Challenge 1: Classroom Wall Paint

Question 1.
The custodians are considering painting our classroom next summer. In order to know how much paint they must buy, the custodians need to know the total surface area of the walls. Why do you think they need to know this, and how can we find the information?
Answer:
All classroom walls are different. Taking overall measurements and then subtracting windows, doors, or other areas will give a good approximation.

Question 2.
Make a prediction of how many square feet of painted surface there are on one wall in the room. If the floor has square tiles, these can be used as a guide.

Estimate the dimensions and the area. Predict the area before you measure. My prediction: _____ ft².

a. Measure and sketch one classroom wall. Include measurements of windows, doors, or anything else that would not be painted.

Answer:
Student responses will depend on the teacher’s choice of wall.

b. Work with your partners and your sketch of the wall to determine the area that needs paint. Show your sketch and calculations below; clearly mark your measurements and area calculations.
Answer:

c. A gallon of paint covers about 350 ft2. Write an expression that shows the total area of the wall. Evaluate it to find how much paint is needed to paint the wall.
Answer:
Answers will vary based on the size of the wall. Fractional answers are to be expected.

d. How many gallons of paint would need to be purchased to paint the wall?
Answer:
Answers will vary based on the size of the wall. The answer from part (d) should be on exact quantity because gallons of paint are discrete units. Fractional answers from part (c) must be rounded up to the nearest whole gallon.

Exploratory Challenge 2:

Answer:

Eureka Math Grade 6 Module 5 Lesson 6 Problem Set Answer Key

Question 1.
Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and 16 ft. wide. The window, mirror, and fireplace are not to be painted or papered. The window measures 18 in. wide and 14 ft. high. The fireplace is 5 ft. wide and 3 ft. high, while the mirror above the fireplace is 4 ft. wide and 2 ft. high. (Note: this drawing is not to scale.)

a. How many square feet of wallpaper are needed to cover the wall?
Answer:
Total wall area = 8 ft.× 16 ft. = 128 ft²
Window area = 14 ft.× 1.5 ft. = 21 ft²
Fireplace area= 3 ft.× 51t.= 15 ft²
Mirrorarea= 4 ft.× 2 ft.= 8 ft²
Net wall area to be covered 128 ft² – (21 ft² + 15 ft² + 8 ft²) = 84 ft²

b. The wallpaper is sold in rolls that are 18 in. wide and 33 ft. long. Rolls of solid color wallpaper will be used, so patterns do not have to match up.

i. What is the area of one roll of wallpaper?
Answer:
Area of one roll of wallpaper: 33 ft. × 1.5 ft. = 49.5 ft²

ii. How many rolls would be needed to cover the wall?
Answer:
84 ft² ÷ 49.5 ft² ≈ 1.7; therefore, 2 rolls would need to be purchased.

c. This week, the rolls of wallpaper are on sale for $11. 99/roll. Find the cost of covering the wall with wallpaper.
Answer:
We need two rolls of wallpaper to cover the wall, which will cost $11.99 × 2 = $23.98.

d. A gallon of special textured paint covers 200 ft² and is on sale for $22.99/gallon. The wall needs to be painted twice (the wall needs two coats of paint). Find the cost of using paint to cover the wall.
Answer:
Total wall area = 8 ft. × 16 ft. = 128 ft²
Windowarea = 14 ft. × 1.5 ft.= 21 ft²
Fireplace area = 3 ft.× 5 ft. = 15 ft²
Mirror area = 4 ft. × 2 ft. = 8 ft²
Net wall area to be covered 128 ft² – (21 ft² + 15 ft² + 8 ft²) = 84 ft²
If the wall needs to be painted twice, we need to point a total area of 84 ft² × 2 = 168 ft². One gallon is enough paint for this wall, so the cost will be $22. 99.

Question 2.
A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If each tile has a length of 36 in. and a width of 24 in., how many tiles are needed to cover the classroom floor?
Answer:
Area of the classroom: 30 ft. × 20 ft. = 600 ft²
Area of each tile 3 ft. × 2 ft. = 6 ft²
Area of the classroom \(\frac{\text { Area of the classroom }}{\text { Area of each tile }}=\frac{600 \mathrm{ft}^{2}}{6 \mathrm{ft}^{2}}\) = 100

100 tiles are needed to cover the classroom floor. Allow for students who say that if the tiles are 3 ft. × 2 ft., and they orient them in a way that corresponds to the 30 ft. × 20 ft. room, then they will have ten rows of ten tiles giving them 100 tiles.

Using this method, the students do not need to calculate the areas and divide. Orienting the
tiles the other way, students could say that they will need 105 tiles as they will need 6\(\frac{2}{3}\) rows of 15 tiles, and since \(\frac{2}{3}\) of a tile cannot be purchased, they will need 7 rows of 15 tiles.

Question 3.
Challenge: Assume that the tiles from Problem 2 are unavailable. Another design is available, but the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered?
Answer:
Solutions will vary. An even number of tiles fit on the 30 foot length of the room (20 tiles), but the width requires 13\(\frac{1}{3}\) tiles. This accounts for a 20 tile by 13 tile array. 20 × 13 = 260. 260 tiles need to be ordered.

The remaining area is 30 ft. × 0.5 ft. (20 × \(\frac{1}{3}\)) Since 20 of the \(\frac{1}{3}\) tiles are needed, 7 additional tiles must be cut to form \(\frac{21}{3}\). 20 of these will be used with \(\frac{1 {3}\) of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles.

Question 4.
A rectangular flower bed measures 10 m by 6 m. It has a path 2 m wide around it. Find the area of the path.

Answer:
Total Area = 14 m × 10 m = 140 m²
Flower bed area = 10 m × 6 m = 60 m²
Area of path: 140 m² – 60 m² = 80 m²

Question 5.
A diagram of Tracy’s deck is shown below, shaded blue. He wants to cover the missing portion of his deck with soil in order to grow a garden.

a. Find the area of the missing portion of the deck. Write the expression and evaluate it.

Answer:
Students should use one of two methods to find the area: finding the dimensions of the garden area (interior rectangle, 6 m????× 2 m or finding the total area minus the sum of the four wooden areas, shown below.

6 m × 2 m = 12 m²
8 × 6 – 7 × 3 – 5 × 1 – 8 × 1 – 2 × 1 = 12 (All linear units are in meters; area is in square metres.)

b. Find the area of the missing portion of the deck using a different method. Write the expression and evaluate it.
Answer:
Students should choose whichever method was not used in part (a).

c. Write two equivalent expressions that could be used to determine the area of the missing portion of the deck.
Answer:
8 × 6 – 7 × 3 – 5 × 1 – 8 × 1 – 2 × 1
6 × 2

d. Explain how each expression demonstrates a different understanding of the diagram.
Answer:
One expression shows the dimensions of the garden area (interior rectangle, 6 m × 2 m), and one shows finding the total area minus the sum of the four wooden areas.

Question 6.
The entire large rectangle below has an area of 3\(\frac{1}{2}\) ft². If the dimensions of the white rectangle are as shown below, write and solve an equation to find the area, A, of the shaded region.

Answer:

Eureka Math Grade 6 Module 5 Lesson 6 Exit Ticket Answer Key

Question 1.
Find the area of the deck around this pool. The deck is the white area in the diagram.

Answer:
Area of Walkway and Pool:
A = bh
A = 90 m × 25 m
A = 2,250 m²

Area of Pool:
A = bh
A = 50 m × 15 m
A = 750 m²

Area of Walkway:
2,250 m² – 750 m² = 1,500 m²

Engage NY Eureka Math Grade 6 Module 5 Lesson 5 Answer Key

Eureka Math Grade 6 Module 5 Lesson 5 Exercise Answer Key

Opening Exercise:

Here is an aerial view of a woodlot.

Question 1.
If AB = 10 units, FE = 8 units, AF = 6 units, and DE = 7 units, find the lengths of the other two sides.
DC =
BC =
Answer:
DC = 2 units
BC = 13 units

Question 2.
If DC = 10 units, FE = 30 units, AF = 28 units, and BC = 54 units, find the lengths of the other two sides.
AB =
DE =
Answer:
AB = 40 units
DE = 26 units

Eureka Math Grade 6 Module 5 Lesson 5 Example Answer Key

Example 1: Decomposing Polygons into Rectangles

The Intermediate School is producing a play that needs a special stage built. A diagram of the stage is shown below (not to scale).

Question a.
On the first diagram, divide the stage into three rectangles using two horizontal lines. Find the dimensions of these rectangles, and calculate the area of each. Then, find the total area of the stage.
Answer:
Dimensions: 2 m by 4m, 2 m by 4 m, and 7 m by 5 m
Area: 2 m × 4m = 8 m², 2 m × 4 m = 8 m², 7 m × 5 m = 35 m²
Total: 8 m² + 8 m² + 35 m² = 51 m²

Question b.
On the second diagram, divide the stage into three rectangles using two vertical lines. Find the dimensions of these rectangles, and calculate the area of each. Then, find the total area of the stage.
Answer:
Dimensions: 2 m by 9 m, 2 m by 9 m, and 3 m by 5 m
Area: 2 m × 9 m = 18 m × 2 m × 9 m = 18 m², 3 m × 5m = 15 m²
Total: 51 m²

Question c.
On the third diagram, divide the stage into three rectangles using one horizontal line and one vertical line. Find the dimensions of these rectangles, and calculate the area of each. Then, find the total area of the stage.

Answer:
Dimensions: 2 m by 9 m, 2 m by 4 m, and 5 m by 5 m
Area: 2 m × 9 m = 18 m², 2 m × 4 m = 8 m², 5 m × 5 m = 25 m²
Total: 51 m²

Question d.
Think of this as a large rectangle with a piece removed.

i. What are the dimensions of the large rectangle and the small rectangle?
Answer:
Dimensions: 9 m by 7 m and 3 m by 4 m

ii. What are the areas of the two rectangles?
Answer:
Area: 9 m × 7 m = 63 m², 3 m × 4 m = 12 m²

iii. What operation Is needed to find the area of the original figure?
Answer:
Subtraction

iv. What is the difference in area between the two rectangles?
Answer:
63 m² – 12 m² = 51 m²

v. What do you notice about your answers to (a), (b), (c), and (d)? 7 m
Answer:
The area is the same.

vi. Why do you think this is true?
Answer:
No matter how we decompose the figure, the total area is the sum of its ports. Even if we take the area around the figure and subtract the part that is not included, the area of the figure remains the same, 51 m².

Area of Rectangle 1: b . h
2m . 4m = 8m²
Area of Rectangle 2: b . h
2 m 4m = 8 m²
Area of Rectangle 3: b . h
7m 5m 35 m²
Area of Polygon: 8m² + 8m² + 35 m² = 51 m²

Area of Rectangle 1: b . h
9m . 2m = 18 m²
Area of Rectangle 2: b . h
9m . 2m =18 m²
Area of Rectangle 3: b . h
3m . 5m = 15 m²
Area of Polygon: 18 m² + 18 m² + 15 m² = 51 m²

Area of Rectangle: b . h
9m . 7 m = 63 m²
Area of Missing Rectangle 2: b . h
3m . 4m = 12 m²
Area of Polygon: 63 m² – 12 m² = 51 m²

Example 2: Decomposing Polygons into Rectangles and Triangles

Parallelogram ABCD is part of a large solar power collector. The base measures 6 m and the height is 4 m.

Question a.
Draw a diagonal from A to C. Find the area of both triangles ABC and ACD.
Answer:

Triangle ABC
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) (6 m) (4 m)
A = 12 m².

Triangle ACD
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) (6m)(4m)
A = 12 m²

Question b.
Find the area of both triangles ABD and BCD. Then find the area of the trapezoid.
Answer:

Triangle ABD
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) (8m)(5m)
A = 20 m²

Triangle BCD
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) (4 m) (5 m)
A = 10 m²

A = 20 m² + 10 m² = 30 m²

Question c.
How else could we find this area?
Answer:
We could consider the rectangle that surrounds the trapezoid. Find the area of that rectangle, and then subtract the area of both right triangles.

Area of Rectangle;
A = bh
A = (8 m) (5 m)
A = 40 m²

Triangle 1
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) (3 m) (5 m)
A = 7.5 m²

Triangle 2
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) (1 m) (5 m)
A = 2.5 m²

A = 40 m² – 7.5 m² – 2.5 m² = 30 m² (or)

A = 40 m² – (7.5 m² + 2.5 m²) = 30 m²

Eureka Math Grade 6 Module 5 Lesson 5 Problem Set Answer Key

Question 1.
If AB = 20 units, FE = 12 units, AF = 9 units, and DE = 12 units, find the length of the other two sides. Then, find the area of the irregular polygon.

Answer:
CD = 8 units, BC = 21 units, Area = 276 square units.

Question 2.
If DC = 1.9 cm, FE = 5.6 cm, AF = 4.8 cm, and BC = 10.9 cm, find the length of the other two sides. Then, find the area of the irregular polygon.

Answer:
AB = 7.5 cm, DE = 6.1 cm, Area = 47.59 cm²

Question 3.
Determine the area of the trapezoid below. The trapezoid is not drawn to scale.

Answer:
Area of Triangle 1
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) × 22 m × 13 m
A = 198 m²

Area of Triangle 2
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) × 3 m × 18 m
A = 27 m²

Area of Trapezoid = Area of Triangle 1 + Area of Triangle 2
Area = 198 m² + 27 m² = 225 m²

Question 4.
Determine the area of the shaded isosceles trapezoid below. The image is not drawn to scale.

Answer:
Area of Rectangle
A = bh
A = 18 m × 12 m
A = 216 m²

Area of Triangles 1 and 2
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) × 7.5 m × 12 m
A = 45 m²

Area of Trapezoid = Area of Rectangle – Area of Triangle 1 – Area of Triangle 2
A = 216 m² – 45 m² – 45 m² = 126 m²

Question 5.
Here is a sketch of a wall that needs to be painted:

a. The windows and door will not be painted. Calculate the area of the wall that will be painted.
Answer:
Whole wall: 12 ft. × 8 ft. = 96 ft²
Window: 2 ft. × 2 ft. = 4 ft²
There are two identical windows, 4 ft² × 2 = 8 ft²
Door: 6 ft. × 3 ft. = 18 ft²
96 ft² – 8 ft² – 18 ft² = 70 ft²

b. If a quart of Extra-Thick Gooey Sparkle paint covers 30 ft². how many quarts must be purchased for the painting job?
Answer:
70 ÷ 30 = 2\(\frac{1}{3}\)
Therefore, 3 quarts must be purchased.

Question 6.
The figure below shows a floor plan of a new apartment. New carpeting has been ordered, which will cover the living room and bedroom but not the kitchen or bathroom. Determine the carpeted area by composing or decomposing in two different ways, and then explain why they are equivalent.

Answer:
Answers will vary. Sample student responses are shown.
Bedroom: 15 ft. × 25 ft. = 375 ft²
Living room: 35 ft. × 20 ft. = 700 ft²
Sum of bedroom and living room: 375 ft² + 700 ft² = 1,075 ft²

Alternatively, the whole apartment is 45 ft. × 35 ft. = 1,575 ft²
Subtracting the kitchen and bath (300 ft² and 200 ft²) still gives 1,075 ft².
The two areas are equivalent because they both represent the area of the living room and bedroom.

Eureka Math Grade 6 Module 5 Lesson 5 Exit Ticket Answer Key

Question 1.
Find the missing dimensions of the figure below, and then find the area. The figure is not drawn to scale.

Answer:
The solution can be any of these below.

Question 2.
Find the area of the parallelogram below by decomposing it into two triangles. The figure is not drawn to scale.

Answer:
Area of Triangle 1
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) × 8 mi.× 10 mi.
A = 40 mi²

Area of Triangle 2
A = \(\frac{1}{2}\) bh
A = \(\frac{1}{2}\) × 8 mi. × 10 mi.
A = 40 mi²

Area of Parallelogram = Area of Triangle 1 + Area of Triangle 2
A = 40 mi² + 40 mi² = 80 mi²
The area of the parallelogram is 80 mi².

Engage NY Eureka Math Grade 6 Module 5 Lesson 4 Answer Key

Eureka Math Grade 6 Module 5 Lesson 4 Exercise Answer Key

Opening Exercise:

Draw and label the altitude of each triangle below.

Question a.

Answer:

Question b.

Answer:

Question c.

Answer:

Exploratory Challenge/Exercises 1 – 5:

Question 1.
Use rectangle X and the triangle with the altitude inside (triangle X) to show that the area formula for the triangle is A = \(\frac{1}{2}\) × base × height.

a. Step One: Find the area of rectangle X.
Answer:
A = 3 in. × 2.5 in. = 7.5 in²

b. Step Two: What is half the area of rectangle X?
Answer:
Half of the area of the rectangle is 7.5 in² ÷ 2= 3.75 in²

c. Step Three: Prove, by decomposing triangle X, that it is the same as half of rectangle X. Please glue your decomposed triangle onto a separate sheet of paper. Glue it into rectangle X. What conclusions can you make about the triangle’s area compared to the rectangle’s area?
Answer:
Because the triangle fits inside half of the rectangle, we know the triangle’s area is half of the rectangle’s area.

Question 2.
Use rectangle Y and the triangle with a side that ¡s the altitude (triangle Y) to show the area formula for the triangle is A = \(\frac{1}{2}\) × base × height.

a. Step One: Find the area of rectangle Y.
Answer:
A = 3 in. × 3 in. = 9 in²

b. Step Two: What is half the area of rectangle Y?
Answer:
Half the area of the rectangle is 9 in² ÷ 2 = 4.5 in².

c. Step Three: Prove, by decomposing triangle Y, that it is the same as half of rectangle Y. Please glue your decomposed triangle onto a separate sheet of paper. Glue it into rectangle Y. What conclusions can you make about the triangle’s area compared to the rectangle’s area?
Answer:
The right triangle also fits in exactly half of the rectangle, so the triangle’s area is • Students may struggle once again half the size of the rectangle’s area. with this step since they have yet to see an obtuse

Question 3.
Use rectangle Z and the triangle with the altitude outside (triangle Z) to show that the area angle. formula for the triangle is A = \(\frac{1}{2}\) × base × height.

a. Step One: Find the area of rectangle Z.
Answer:
A= 3 in. × 2.5 in.=7.5 in²

b. Step Two: What is half the area of rectangle Z?
Answer:
Half of the area of the rectangle is 7.5 in² ÷2 = 3.75 in².

c. Step Three: Prove, by decomposing triangle Z, that it is the same as half of rectangle Z. Please glue your decomposed triangle onto a separate sheet of paper. Glue it into rectangle Z. What conclusions can you make about the triangle’s area compared to the rectangle’s area?
Answer:
Similar to the other two triangles, when the altitude is outside the triangle, the area of the triangle is exactly half of the area of the rectangle.

Question 4.
When finding the area of a triangle, does it matter where the altitude is located?
Answer:
It does not matter where the altitude is located. To find the area of a triangle, the formula is always
A = \(\frac{1}{2}\) × base × height.

Question 5.
How can you determine which part of the triangle is the base and which is the height?
Answer:
The base and the height of any triangle form a right angle because the altitude is always perpendicular to the base.

Exercises 6 – 8:

Calculate the area of each triangle. Figures are not drawn to scale.

Question 6.

Answer:
A = \(\frac{1}{2}\) × (24 in.) (8 in.) = 96 in²

Question 7.

Answer:

Question 8.
Draw three triangles (acute, right, and obtuse) that have the same area. Explain how you know they have the same area.
Answer:
Answers will vary.

Eureka Math Grade 6 Module 5 Lesson 4 Problem Set Answer Key

Calculate the area of each figure below. Figures are not drawn to scale.

Question 1.

Answer:
A = \(\frac{1}{2}\) (21 in.) (8 in.) = 84 in²

Question 2.

Answer:
A = \(\frac{1}{2}\) (72 m) (21 m) = 756 m²

Question 3.

Answer:
A = \(\frac{1}{2}\) (75.8 km) (29.2 km) = 1,106.68 km²

Question 4.

Answer:
A = \(\frac{1}{2}\) (5 m) (12 m) = 30 m²
A = \(\frac{1}{2}\) (7 m) (29 m) = 101.5 m²
A = (12 m) (19 m) = 228 m²
A = 30 m² + 30 m² + 101.5 m² + 228 m²
A = 389.5 m²

Question 5.
The Andersons are going on a long sailing trip during the summer. However, one of the sails on their sailboat ripped, and they have to replace it. The sail is pictured below. If the sailboat sails are on sale for $2 per square foot, how much will the new sail cost?

Answer:
A = \(\frac{1}{2}\) bh
= \(\frac{1}{2}\) (8 ft.) (12 ft.)
= 48 ft²
\(\frac{2 \text { dollars }}{\mathrm{ft}^{2}}\) × 48 ft² = 96 dollars(or $96)
The cost of the new sail is $96.

Question 6.
Darnell and Donovan are both trying to calculate the area of an obtuse triangle. Examine their calculations below.

Which student calculated the area correctly? Explain why the other student is not correct.
Answer:
Donovan calculated the area correctly. Although Darnell did use the altitude of the triangle, he used the length between the altitude and the base rather than the length of the actual base.

Question 7.
Russell calculated the area of the triangle below. His work is shown.

A = \(\frac{1}{2}\) bh
A = 150.5 cm²
Although Russell was told his work is correct, he had a hard time explaining why it is correct. Help Russell explain why his calculations are correct.
Answer:
The formula for the area of triangle is A = bit. Russell followed this formula because 7 cm is the height of the triangle, and 43 cm is the base of the triangle.

Question 8.
The larger triangle below has a base of 10.14 m; the gray triangle has an area of 40.325 m².

a. Determine the area of the larger triangle if it has a height of 12.2 m.
Answer:
A = \(\frac{1}{2}\) (10.14 m) (12.2 m)
= 61.854 m²

b. Let A be the area of the unshaded (white) triangle in square meters. Write and solve an equation to determine the value of A, using the areas of the larger triangle and the gray triangle.
Answer:
40.325m² + A = 61.854m²
40.325m² + A – 40.325 m² = 61.854 m² – 40.325 m²
A = 21.529 m²

Eureka Math Grade 6 Module 5 Lesson 4 Exit Ticket Answer Key

Find the area of each triangle. Figures are not drawn to scale.

Question 1.

Answer:
A = \(\frac{1}{2}\) (12.6 cm) (16.8 cm) = 105.84 cm²

Question 2.

Answer:
A = \(\frac{1}{2}\) (28 in.) (15 in.) = 210 in²

Question 3.

Answer:
A = \(\frac{1}{2}\) (12 ft.) (21 ft.) = 126 ft²

Engage NY Eureka Math Grade 6 Module 5 Lesson 3 Answer Key

Eureka Math Grade 6 Module 5 Lesson 3 Exercise Answer Key

Exercises:

Question 1.
Work with a partner on the exercises below. Determine if the area formula A = \(\frac{1}{2}\) bh is always correct. You may use a calculator, but be sure to record your work on your paper as well. Figures are not drawn to scale.

Answer:

Question 2.
Can we use the formula A = \(\frac{1}{2}\) × base × height to calculate the area of triangles that are not right triangles? Explain your thinking.
Answer:
Yes, the formula A = \(\frac{1}{2}\) × base × height can be used for more than just right triangles. We just need to be able to determine the height when it is not necessarily the length of one of the sides.

Question 3.
Examine the given triangle and expression.
\(\frac{1}{2}\) (11 ft.) (4ft.)
Explain what each part of the expression represents according to the triangle.
Answer:
11 ft. represents the base of the triangle because 8 ft. + 3 ft. = 11 ft.
4 ft. represents the altitude of the triangle because this length is perpendicular to the base.

Question 4.
Joe found the area of a triangle by writing A = \(\frac{1}{2}\) (11 in.)(4 in.), while Kaitlyn found the area by writing A = \(\frac{1}{2}\) (3 in.)(4 in.) + \(\frac{1}{2}\) (8 in.)(4 in.). Explain how each student approached the problem.
Answer:
Joe combined the two bases of the triangle first and then calculated the area of the entire triangle, whereas Kaitlyn calculated the area of two smaller right triangles and then added these areas together.

Question 5.
The triangle below has an area of 4.76 sq. in. If the base is 3.4 in., let h be the height in inches.

a. Explain how the equation 4.76 in² = (3.4 in. )h represents the situation.
Answer:
The equation shows the area, 4. 76 in², is one-half the base, 3.4 in times the height, in inches, h.

b. Solve the equation.
Answer:
4.76 in² = \(\frac{1}{2}\) (3.4 in.)h
4.76 in² = (1.7 in.)h
4.76 in² + 1.7 in. = (1.7 in.)h + 1.7 in.
2.8 in. = h

Eureka Math Grade 6 Module 5 Lesson 3 Problem Set Answer Key

Calculate the area of each shape below. Figures are not drawn to scale.

Question 1.

Answer:
A = \(\frac{1}{2}\) (3.3 in.)(4.4 in.) = 7.26 in²
A = \(\frac{1}{2}\) (6. 1 in.)(4.4 in.) 13.42 in²
A = 7.26 in² + 13.42 in² = 20.68 in²
or
A = \(\frac{1}{2}\) (9.4 in. )(4. 4 in.) = 20.68 in²

Question 2.

Answer:
A = \(\frac{1}{2}\) (8m)(14m)= 56m²
A = \(\frac{1}{2}\) (16m)(14m)= 112m²
A = 56m² ÷ 112 m² = 168m²
or
A = \(\frac{1}{2}\) (24 m)(14 m) = 168m²

Question 3.

Answer:
A = \(\frac{1}{2}\) (5 ft) (12 ft) = 30 ft²
A = (12 ft.)(12 ft.) = 144 ft²
A = \(\frac{1}{2}\) (5 ft.)(12 ft.) = 30 ft²
A = 30ft² + 144ft² + 30ft² = 204 ft²

Question 4.

Answer:
A = \(\frac{1}{2}\) (48 km) (7 km) = 168km²
A = (35 km)(48 km) = 1,680 km²
A = \(\frac{1}{2}\) (48 km) (7 km) = 168km²
A = 168 km² + 1,680 km² + 168 km² = 2,016km²

Question 5.
Immanuel is building a fence to make an enclosed play area for his dog. The enclosed area will be in the shape of a triangle with a base of 48 m and an altitude of 32 m. How much space does the dog have to play?
Answer:
A = \(\frac{1}{2}\) bh = \(\frac{1}{2}\) (48 m) (32 m) = 768 m²
The dog has 768 m² in which to play.

Question 6.
Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the comer and against two walls to form a triangle. Chauncey wants to buy a triangular shaped cover for the bench.
If the storage bench is 2\(\frac{1}{2}\) ft. along one wall and 4\(\frac{1}{4}\) ft. along the other wall, how big will the cover have to be to cover the entire bench?

Answer:
A = \(\frac{1}{2}\) (2\(\frac{1}{2}\) ft.) (4\(\frac{1}{4}\) ft.)

= \(\frac{1}{2}\) (\(\frac{5}{2}\) ft) (\(\frac{17}{4}\) ft.)

= \(\frac{85}{16}\)ft² = 5\(\frac{5}{16}\) ft²

Chauncey would have to buy a cover that has an area of 5\(\frac{5}{16}\) ft² to cover the entire scale. bench.

Question 7.
Examine the triangle to the right.

a. Write an expression to show how you would calculate the area.
Answer:
\(\frac{1}{2}\) (7 in.) (4 in.) + \(\frac{1}{2}\) (3 in.) (4in.) or \(\frac{1}{2}\) (10 in.) (4in.)

b. Identify each part of your expression as it relates to the triangle.
Answer:
If students wrote the first expression, then 7 in. and 3 in. represent the two parts of the base, and 4 in. is the height, or the altitude, of the triangle.

If students wrote the second expression, then 10 in. represents the base because 7 in. + 3 in. = 10 in., and 4 in. represents the height, or the altitude, of the triangle.

Question 8.
The floor of a triangular room has an area of 32\(\frac{1}{2}\) sq. m. If the triangle’s altitude is 7\(\frac{1}{2}\) m, write an equation to determine the length of the base, b, in meters. Then solve the equation.
Answer:

Therefore, the base is 8\(\frac{2}{3}\) m.

Eureka Math Grade 6 Module 5 Lesson 3 Exit Ticket Answer Key

Calculate the area of each triangle using two different methods. Figures are not drawn to scale.

Question 1.

Answer:
1
A = \(\frac{1}{2}\) (3ft.) (7 ft.)= 10.5 ft²
A = \(\frac{1}{2}\) (12 ft.) (7 ft.) = 42 ft²
A= 10.5 ft² + 42 ft² = 525 ft²
OR
A = \(\frac{1}{2}\) (15 ft.) (7 ft.) = 52.5 ft²

Question 2.

Answer:
A = \(\frac{1}{2}\) (9 in.)(18 in.) = 81 in²
A = \(\frac{1}{2}\) (32 in. )(18 in) = 288 in²
A = 81 in² + 288 in² = 369 in²
OR
A = \(\frac{1}{2}\) (41 in.)(18 in.)= 369 in²

Eureka Math Grade 6 Module 5 Lesson 3 Multiplication of Decimals Answer Key

Multiplication of Decimals – Round 1

Directions: Evaluate each expression.

Question 1.
5 × 1 =
Answer:
5

Question 2.
5 × 0.1 =
Answer:
0.5

Question 3.
5 × 0.01 =
Answer:
0.05

Question 4.
5 × 0.001 =
Answer:
0.005

Question 5.
2 × 4 =
Answer:
8

Question 6.
0.2 × 4 =
Answer:
0.8

Question 7.
0.02 × 4 =
Answer:
0.08

Question 8.
0.002 × 4 =
Answer:
0.008

Question 9.
3 × 3 =
Answer:
9

Question 10.
3 × 0.3 =
Answer:
0.9

Question 11.
3 × 0.03 =
Answer:
0.09

Question 12.
0.1 × 0.8 =
Answer:
0.08

Question 13.
0.1 × 0.08 =
Answer:
0.008

Question 14.
0.01 × 0.8 =
Answer:
0.008

Question 15.
0.01 × 0.08 =
Answer:
0.0008

Question 16.
0.3 × 0.2 =
Answer:
0.6

Question 17.
0.03 × 0.2 =
Answer:
0.006

Question 18.
0.02 × 0.3 =
Answer:
0.006

Question 19.
0.02 × 0.03 =
Answer:
0.0006

Question 20.
0.2 × 0.2 =
Answer:
0.04

Question 21.
0.02 × 0.2 =
Answer:
0.004

Question 22.
0.2 × 0.02 =
Answer:
0.004

Question 23.
5 × 3 =
Answer:
15

Question 24.
5 × 0.3 =
Answer:
1.5

Question 25.
0.5 × 3 =
Answer:
1.5

Question 26.
0.3 × 0.5 =
Answer:
0.15

Question 27.
9 × 2 =
Answer:
18

Question 28.
0.2 × 9 =
Answer:
1.8

Question 29.
0.9 × 2 =
Answer:
1.8

Question 30.
0.2 × 0.9 =
Answer:
0.18

Question 31.
4 × 0.4 =
Answer:
1.6

Question 32.
0.4 × 0.4 =
Answer:
0.16

Question 33.
0.04 × 0.4 =
Answer:
0.016

Question 34.
0.8 × 0.6 =
Answer:
0.48

Question 35.
0.8 × 0.06 =
Answer:
0.048

Question 36.
0.006 × 0.8 =
Answer:
0.0048

Question 37.
0.006 × 0.08 =
Answer:
0.00048

Question 38.
0.7 × 0.9 =
Answer:
0.63

Question 39.
0.07 × 0.9 =
Answer:
0.063

Question 40.
0.9 × 0.007 =
Answer:
0.0063

Question 41.
0.09 × 0.007 =
Answer:
0.00063

Question 42.
1.2 × 0.7 =
Answer:
0.84

Question 43.
1.2 × 0.07 =
Answer:
0.084

Question 44.
0.007 × 0.12 =
Answer:
0.00084

Multiplication of Decimals – Round 1

Directions: Evaluate each expression

Question 1.
9 × 1 =
Answer:
9

Question 2.
0.9 × 1 =
Answer:
0.9

Question 3.
0.09 × 1 =
Answer:
0.09

Question 4.
0.009 × 1 =
Answer:
0.009

Question 5.
2 × 2 =
Answer:
4

Question 6.
2 × 0.2 =
Answer:
0.4

Question 7.
2 × 0.02 =
Answer:
0.04

Question 8.
2 × 0.002 =
Answer:
0.004

Question 9.
3 × 2 =
Answer:
6

Question 10.
0.3 × 2=
Answer:
0.6

Question 11.
2 × 0.03 =
Answer:
0.06

Question 12.
0.7 × 0.1 =
Answer:
0.07

Question 13.
0.07 × 0.1 =
Answer:
0.007

Question 14.
0.01 × 0.7 =
Answer:
0.007

Question 15.
0.01 × 0.07 =
Answer:
0.0007

Question 16.
0.2 × 0.4 =
Answer:
0.08

Question 17.
0.02 × 0.4 =
Answer:
0.008

Question 18.
0.4 × 0.02 =
Answer:
0.008

Question 19.
0.04 × 0.02 =
Answer:
0.0008

Question 20.
0.1 × 0.1 =
Answer:
0.01

Question 21.
0.01 × 0.1 =
Answer:
0.0001

Question 22.
0.1 × 0.01 =
Answer:
0.001

Question 23.
3 × 4 =
Answer:
12

Question 24.
3 × 0.4 =
Answer:
1.2

Question 25.
0.3 × 4 =
Answer:
1.2

Question 26.
0.4 × 0.3 =
Answer:
0.12

Question 27.
7 × 7 =
Answer:
49

Question 28.
7 × 0.7 =
Answer:
4.9

Question 29.
0.7 × 7 =
Answer:
4.9

Question 30.
0.7 × 0.7 =
Answer:
0.49

Question 31.
2 × 0.8 =
Answer:
1.6

Question 32.
0.2 × 0.8 =
Answer:
0.16

Question 33.
0.02 × 0.8 =
Answer:
0.016

Question 34.
0.6 × 0.5 =
Answer:
0.3

Question 35.
0.6 × 0.05 =
Answer:
0.03

Question 36.
0.005 × 0.6 =
Answer:
0.003

Question 37.
0.005 × 0.06 =
Answer:
0.0003

Question 38.
0.9 × 0.9 =
Answer:
0.81

Question 39.
0.09 × 0.9 =
Answer:
0.081

Question 40.
0.009 × 0.9 =
Answer:
0.0081

Question 41.
0.009 × 0.09 =
Answer:
0.00081

Question 42.
1.3 × 0.6 =
Answer:
0.78

Question 43.
1.3 × 0.06 =
Answer:
0.078

Question 44.
0.006 × 1.3 =
Answer:
0.0078

Engage NY Eureka Math 6th Grade Module 3 Lesson 2 Answer Key

Eureka Math Grade 6 Module 3 Lesson 2 Example Answer Key

Example 1:
Take It to the Bank
Read Example 1 silently. In the first column, write down any words and definitions you know. In the second column, write down any words you do not know.

For Tim’s 13th birthday, he received $150 in cash from his mom. His dad took him to the bank to open a savings account. Tim gave the cash to the banker to deposit into the account. The banker credited Tim’s new account $150 and gave Tim a receipt. One week later, Tim deposited another $25 that he had earned as allowance. The next month, Tim’s dad gave him permission to withdraw $35 to buy a new video game. Tim’s dad explained that the bank would charge a $5 fee for each withdrawal from the savings account and that each withdrawal and charge results in a debit to the account.

In the third column, write down any new words and definitions that you learn during the discussion.
Answer:

Example 2:
How Hot, How Cold?
Temperature is commonly measured using one of two scales, Celsius or Fahrenheit. In the United States, the Fahrenheit system continues to be the accepted standard for nonscientific use. All other countries have adopted Celsius as the primary scale in use. The thermometer shows how both scales are related.

a. The boiling point of water is 100°C. Where is loo degrees Celsius located on the thermometer to the right?
Answer:
It is not shown because the greatest temperature shown in Celsius is 50°C.

b. On a vertical number line, describe the position of the integer that represents 100°C.
Answer:
The integer is 100, and it would be located 100 units above zero on the Celsius side of the scale.

c. Write each temperature as an integer.
i. The temperature shown on the thermometer in degrees Fahrenheit:
Answer:
100

ii. The temperature shown on the thermometer in degrees Celsius:
Answer:
38

iii. The freezing point of water in degrees Celsius:
Answer:
0

d. If someone tells you your body temperature is 98. 6°, what scale is being used? How do you know?
Answer:
Since water boils at 100°C, they must be using the Fahrenheit scale.

e. Does the temperature 0 degrees mean the same thing on both scales?
Answer:
No. 0°C corresponds to 32°F, and 0°F corresponds to approximately – 18°C.

Eureka Math Grade 6 Module 3 Lesson 2 Exercise Answer Key

Exercise 1.
Read Example 1 again. With your partner, number the events in the story problem. Write the number above each sentence to show the order of the events.
For Tim’s 13” birthday, he received $150 in cash from his mom. His dad took him to the bank to open a savings account.

Tim gave the cash to the banker to deposit into the account. The banker credited Tim’s new account $150 and gave Tim

a receipt. One week later, Tim deposited another $25 that he had earned as allowance. The next month, Tim’s dad gave

him permission to withdraw $35 to buy a new video game. Tim’s dad explained that the bank would charge a $5 fee for

each withdrawal from the savings account and that each withdrawal and charge results in a debit to the account.
Answer:

Exercise 2.
Write each individual description below as an integer. Model the integer on the number line using an appropriate scale.

Answer:

Exercise 3.
Write each word under the appropriate column, “Positive Number” or “Negative Number.”
Gain Loss Deposit Credit Debit Charge Below Zero Withdraw Owe Receive
Answer:

Exercise 4.
Write an integer to represent each of the following situations:
a. A company loses $345, 000 in 2011.
Answer:
– 345, 000

b. You earned $25 for dog sitting.
Answer:
25

c. Jacob owes his dad $5.
Answer:
– 5

d. The temperature at the sun’s surface is about 5, 500°C
Answer:
5, 500

e. The temperature outside is 4 degrees below zero.
Answer:
– 4

f. A football player lost 10 yards when he was tackled.
Answer:
– 10

Exercise 5.
Describe a situation that can be modeled by the integer – 15. Explain what zero represents in the situation.
Answer:
Answers will vary. I owe my best friend $15. in this situation, 0 represents my owing nothing to my best friend.

Eureka Math Grade 6 Module 3 Lesson 2 Problem Set Answer Key

Question 1.
Express each situation as an integer in the space provided.
a. A gain of 56 points in a game
Answer:
56

b. A fee charged of $2
Answer:
– 2

c. A temperature of 32 degrees below zero
Answer:
– 32

d. A 56-yard loss in a football game
Answer:
– 56

e. The freezing point of water in degrees Celsius
Answer:
0

f. A $12,500 deposit
Answer:
12,500

For Problems 2 – 5, use the thermometer to the right.

Question 2.
Each sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation.
a. The temperature is – 1o degrees Fahrenheit below zero.
Answer:
Correct: The temperature is – 10°F.
OR
The temperature is 10 degrees below zero Fahrenheit.

b. The temperature is – 22 degrees Celsius below zero.
Answer:
Correct: The temperature is – 22°C.
OR
The temperature is 22 degrees below zero Celsius.

Question 3.
Mark the integer on the thermometer that corresponds to the temperature given.
a. 70°F
b. 12°C
c. 110°F
d. – 4°C
Answer:

Question 4.
The boiling point of water is 2 12°F. Can this thermometer be used to record the temperature of a boiling pot of water? Explain.
Answer:
No, it cannot because the highest temperature in Fahrenheit on this thermometer is 120°.

Question 5.
Kaylon shaded the thermometer to represent a temperature of 20 degrees below zero Celsius as shown in the diagram. Is she correct? Why or why not? If necessary, describe how you would fix Kaylon’s shading.
Answer:
She is incorrect because she shaded a temperature of – 20°F. I would fix this by marking a line segment at – 20°C and shade up to that line.

Eureka Math Grade 6 Module 3 Lesson 2 Exit Ticket Answer Key

Question 1.
Write a story problem that includes both integers – 8 and 12.
Answer:
Answers may vary. One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat.

Question 2.
What does zero represent in your story problem?
Answer:
Zero represents no change in the boxer’s weight.

Question 3.
Choose an appropriate scale to graph both integers on the vertical number line. Label the scale.
Answer:
I chose a scale of 1.

Question 4.
Graph both points on the vertical number line.
Answer: