Tag: Eureka Math Grade 3 Module 1

Engage NY Eureka Math 3rd Grade Module 1 Lesson 7 Answer Key

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 7 Problem Set Answer Key

Question 1.
a. Draw an array that shows 6 rows of 2.
b. Write a multiplication sentence where the first factor represents the number of rows.
________ × ________ = ________

Answer:
a.

Explanation:
Drawn an array that shows 6 rows of 2 as 6 × 2 as shown above in the picture.

b. Multiplication sentence where the first factor represents the number of rows as 6 × 2 = 12.

Explanation:
Wrote a multiplication sentence where the first factor represents the number of rows as 6 × 2 = 12.

Question 2.
a. Draw an array that shows 2 rows of 6.
b. Write a multiplication sentence where the first factor represents the number of rows.
____2____ × ____6____ = ___12_____

Answer:
a.

Explanation:
Drawn an array that shows 2 rows of 6 as 2 × 6 as shown above in the picture.

b. Multiplication sentence where the first factor represents the number of rows as 2 × 6 = 12.

Explanation:
Wrote a multiplication sentence where the first factor represents the number of rows as 2 × 6 = 12.

Question 3.
a. Turn your paper to look at the arrays in Problems 1 and 2 in different ways. What is the same and what is different about them?
b. Why are the factors in your multiplication sentences in a different order?

Answer:

a. Same is the result because both have the same value as 12, Different is number of rows and number of columns are not the same,

Explanation:
Turned my paper to look at the arrays in Problems 1 and 2 in different ways.
Is the same because both got same results as 12 and different about them is in problems 1 and 2 the number of rows and number of columns are not the same as one is 6 rows × 2 columns  and in other it is  2 rows × 6 columns.

b. The factors in my multiplication sentences are in a different order because first we are taking 6 rows × 2 columns and in other it is  2 rows × 6 columns.

Explanation:
The factors in my multiplication sentences are in a different order because first we are taking 6 rows X 2 columns  and in other it is  2 rows × 6 columns,
So, rows and columns differ in the both.

Question 4.
Write a multiplication sentence for each expression.
You might skip-count to find the totals.

Explanation:
Wrote a multiplication sentence for each expression as shown above, might have skipped-count to find the totals.

Question 5.
Write and solve multiplication sentences where the second factor represents the size of the row.

Explanation:
Wrote and solved multiplication sentences where the second factor represents the size of the row as
2 × 4 = 8 and 4 × 2= 8.

Question 6.
Ms. Nenadal writes 2 × 7 = 7 × 2 on the board.
Do you agree or disagree? Draw arrays to help explain your thinking.

Answer:
Yes, I agree Ms. Nenadal writings as 2 × 7 = 7 × 2,

Explanation:
Given Ms. Nenadal writes 2 × 7 = 7 × 2 on the board,
Yes, I agree because 2 × 7 = 14 and 7 × 2 = 14,
Drawn arrays to help and explained my thinking as shown above.

Question 7.
Find the missing factor to make each equation true.

Explanation:
Found the missing factor to make each equations true as below
5 × 2 = 2 × 5,
As each equation is true, so the missing factor in 2 X ___ is 5 as LHS is equal to RHS, So 5 X 2 = 2 X 5.

2 × 8 = 8 × 2,
As each equation is true, so the missing factor in ___ X 8 is 2 as LHS is equal to RHS, So 2 X 8 = 8 X 2.

2 × 10 = 10 × 2,
As each equation is true, so the missing factor in ___ X 2  is 10 as LHS is equal to RHS, So 2 X 10 = 10 X 2.

2 × 9 = 9 × 2,
As each equation is true, so the missing factor in 2 × ___ is 9 as LHS is equal to RHS, So 2 × 9 = 9 × 2.

Question 8.
Jada gets 2 new packs of erasers. Each pack has 6 erasers in it.
a. Draw an array to show how many erasers Jada has altogether.
b. Write and solve a multiplication sentence to describe the array.
c. Use the commutative property to write and solve a different multiplication sentence for the array.

Answer:

a.

Jada has 12 erasers altogether,

Explanation:
Given Jada gets 2 new packs of erasers. Each pack has 6 erasers in it.
So, drawn an array to show 2 × 6 = 12 number of erasers
Jada has altogether.

b. Multiplication sentence is 2 × 6 = 12, the array has 12 erasers.

Explanation:
Wrote and solved a multiplication sentence as 2 × 6 = 12 erasers, describing the array as 2 packs in rows and 6 erasers in columns, So 2 packs X 6 erasers = 12 erasers.

c.  Commutative property for multiplication sentence for the array is 2 × 6 = 6 × 2 = 12.

Explanation:
Used the commutative property to write and solve a different multiplication sentence for the array as 2 × 6 = 6 x 2 = 12 erasers.

Eureka Math Grade 3 Module 1 Lesson 7 Exit Ticket Answer Key

Do you agree or disagree with the statement in the box?
Draw arrays and use skip-counting to explain your thinking.

Answer:
Yes, I agree with the statement in the box as 2 x 5 = 5 X 2,

Explanation:
Yes, I agree or disagree with the statement in the box as 2 × 5 = 10 = 5 × 10,
Drawn arrays and used skip-counting as 2 × 5 = 10 = 5 × 10.

Eureka Math Grade 3 Module 1 Lesson 7 Homework Answer Key

Question 1.
a. Draw an array that shows 7 rows of 2.
b. Write a multiplication sentence where the first factor represents the number of rows.
____7____ × ___2____ = ____14____

Explanation:
Drawn an array that shows 7 rows of 2 as 7 × 2 as shown above in the picture.

b. Multiplication sentence where the first factor represents the number of rows as 7 × 2 = 14.

Explanation:
Wrote a multiplication sentence where the first factor represents the number of rows as 7 × 2 = 14.

Question 2.
a. Draw an array that shows 2 rows of 7.
b. Write a multiplication sentence where the first factor represents the number of rows.
____2____ × ___7_____ = ___14____

Explanation:
Drawn an array that shows 2 rows of 7 as 2 × 7 as shown above in the picture.

b. Multiplication sentence where the first factor represents the number of rows as 2 × 7 = 14.

Explanation:
Wrote a multiplication sentence where the first factor represents the number of rows as 2 × 7 = 14.

Question 3.
a. Turn your paper to look at the arrays in Problems 1 and 2 in different ways. What is the same and what is different about them?
b. Why are the factors in your multiplication sentences in a different order?

a. Same is the result because both have the same value as 14,
Different is number of rows and number of columns are not the same,

Explanation:
Turned my paper to look at the arrays in Problems 1 and 2 in different ways.
Is the same because both got same results as 14 and different about them is in problems 1 and 2 the number of rows and number of columns are not the same as one is 7 rows × 2 columns  and in other it is  2 rows × 7 columns.

b. The factors in my multiplication sentences are in a different order because first we are taking 7 rows × 2 columns and in other it is  2 rows × 7 columns.

Explanation:
The factors in my multiplication sentences are in a different order because first we are taking 7 rows X 2 columns  and in other it is  2 rows × 7 columns,
So, rows and columns differ in the both.

Question 4.
Write a multiplication sentence to match the number of groups.
Skip-count to find the totals. The first one is done for you.


Explanation:
Wrote a multiplication sentence to match the number of groups as shown above, might have skipped-count to find the totals.

Question 5.
Write and solve multiplication sentences where the second factor represents the size of the row.


Explanation:
Wrote and solved multiplication sentences where the second factor represents the size of the row as
2 × 6 = 12 and 6 × 2= 12.

Question 6.
Angel writes 2 × 8 = 8 × 2 in his notebook.
Do you agree or disagree? Draw arrays to help explain your thinking.

Explanation:
Given Angel writes 2 × 8 = 8 × 2 in his notebook,
Yes, I agree because 2 × 8 = 16 and 8 x 2 = 16,
Drawn arrays to help and explained my thinking as shown above.

Question 7.
Find the missing factor to make each equation true.


Explanation:
Found the missing factor to make each equations true as below
2 × 6 = 6 × 2,
As each equation is true, so the missing factor in 6 × ___ is 2 as LHS is equal to RHS, So 2 × 6 = 6 × 2.

7 × 2 = 2 × 7,
As each equation is true, so the missing factor in ___ × 2 is 7 as LHS is equal to RHS, So 7 × 2 = 2 × 7.

9 × 2 = 2 × 9,
As each equation is true, so the missing factor in ___ × 9 is 2 as LHS is equal to RHS, So 9 × 2 = 2 × 9.

2 × 10 = 10 × 2,
As each equation is true, so the missing factor in 2 × ___ is 10 as LHS is equal to RHS, So 2 × 10 = 10 × 2.

Question 8.
Tamia buys 2 bags of candy.
Each bag has 7 pieces of candy in it.
a. Draw an array to show how many pieces of candy Tamia has altogether.
b. Write and solve a multiplication sentence to describe the array.
c. Use the commutative property to write and solve a different multiplication sentence for the array.

a.

Tamia has 14 candy’s altogether,

Explanation:
Given Tamia buys 2 bags of candy. Each bag has 7 pieces of candy in it.
So, drawn an array to show 2 × 7 = 14 number of candy’s Tamia has altogether.

b. Multiplication sentence is 2 × 7 = 14, the array has 14 candy’s.

Explanation:
Wrote and solved a multiplication sentence as 2 × 7 = 14 candy’s, describing the array as 2 bags in rows and 7 candy’s in columns, So 2 bags X 7 candy’s = 14 candy’s.

c.  Commutative property for multiplication sentence for the array is 2 × 7 = 7 × 2 = 14.

Explanation:
Used the commutative property to write and solve a different multiplication sentence for the array as 2 × 7 = 7 x 2 = 14 candy’s.

Engage NY Eureka Math 3rd Grade Module 1 Lesson 6 Answer Key

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 6 Problem Set Answer Key

Question 1.
Rick puts 15 tennis balls into cans. Each can holds 3 balls.
Circle groups of 3 to show the balls in each can.

Rick needs ____5___ cans.
___5___ × 3 = 15
15 ÷ 3 = __5____

Answer:
Rick needs 5 cans,

Explanation:
Given Rick puts 15 tennis balls into cans and each can holds 3 balls. Circled groups of 3 to show the balls in each can.
Rick needs 15 ÷ 3 = 5, 5 × 3 = 15,
Therefore Rick needs 5 cans.

Question 2.
Rick uses 15 tennis balls to make 5 equal groups.
Draw to show how many tennis balls are in each group.
There are ____3___ tennis balls in each group.
5 × __3____ = 15
15 ÷ 5 = ___3___

Answer:
There are 3 tennis balls in each group.

Explanation:
Given Rick uses 15 tennis balls to make 5 equal groups.
Drawn circles to show 3 number of tennis balls are in each group as 15 ÷ 5 = 3, 5 × 3 = 15,
Therefore, there are 3 tennis balls in each group.

Question 3.
Use an array to model Problem 1.
a. ___5___ × 3 = 15
15 ÷ 3 = ___5___
The number in the blanks represents
_____5 groups___________________.

Explanation:
Used an array to model Problem 1 as
5 × 3 = 15 or 15 ÷ 3 = 5,
The number in the blanks represents groups as
5 groups of balls.

b. 5 × __3____ = 15
15 ÷ 5 = __3____
The number in the blanks represents
____________3 balls in each group________.

Answer:
The number in the blanks represents 3 balls in each group,

Explanation:
Rick uses 15 tennis balls to make 5 equal groups,
15 ÷ 5 = 3 or 5 × 3= 15, The number in the blanks
represents 3 balls in each group.

Question 4.
Deena makes 21 jars of tomato sauce. She puts 7 jars in
each box to sell at the market. How many boxes does Deena need?
21 ÷ 7 = __3____
___3___ × 7 = 21
What is the meaning of the unknown factor and quotient?
_________3______________

Answer:
Deena needs 3 boxes,

Explanation:
Given Deena makes 21 jars of tomato sauce and she puts 7 jars in each box to sell at the market.
So number of boxes Deena needs are 21 ÷ 7 = 3, (3 × 7 = 21)
Therefore, Deena needs 3 boxes.

Question 5.
The teacher gives the equation 4 × __3__ = 12. Charlie finds the answer by writing and solving 12 ÷ 4 = __3__.
Explain why Charlie’s method works.

Answer:
Charlie method is 12 ÷ 4 = 3,

Explanation:
Given The teacher gives the equation 4 × ____ = 12.
Charlie finds the answer by writing and solving as
12 ÷ 4 = 3,
because multiplication and division are closely related,
given that division is the inverse operation of multiplication.
When we divide, we look to separate into equal groups,
while multiplication involves joining equal groups.
If we divide this product by one of the factors,
we get the other factor as a result. So Charlie uses division method to solve missing factor in the given equation as 3. So the equation is 4 X 3 = 12.

Question 6.
The blanks in Problem 5 represent the size of the groups.
Draw an array to represent the equations.

Explanation:
Drawn an array that represents the equations as  4 × 3 = 12.

Eureka Math Grade 3 Module 1 Lesson 6 Exit Ticket Answer Key

Cesar arranges 12 notecards into rows of 6 for his presentation.
Draw an array to represent the problem.
12 ÷ 6 = ___2_____
____2____ × 6 = 12
What do the unknown factor and quotient represent?
___2 notecards in each row____

Explanation:
Given Cesar arranges 12 notecards into rows of 6 for his presentation.
Drawn an array to represent the problem as 12 ÷ 6 = 2, 2 × 6 = 12, means 6 rows  and 2 columns as shown above, The unknown factor and quotient 2
represents 2 notecards in each row.

Eureka Math Grade 3 Module 1 Lesson 6 Homework Answer Key

Question 1.
Mr. Hannigan puts 12 pencils into boxes. Each box holds 4 pencils.
Circle groups of 4 to show the pencils in each box.

Mr. Hannigan needs ___3____ boxes.
___3___ × 4 = 12
12 ÷ 4 = __3____

Mr. Hannigan needs 3 boxes,

Explanation:
Given Mr. Hannigan puts 12 pencils into boxes.
Each box holds 4 pencils.
Circled groups of 4 to show the pencils in each box as shown above, So Mr. Hannigan needs 12 ÷ 4 = 3 boxes,
( 3 x 4 = 12).

Question 2.
Mr. Hannigan places 12 pencils into 3 equal groups.
Draw to show how many pencils are in each group.
There are ___4____ pencils in each group.
3 × ___4___ = 12
12 ÷ 3 = ___4___

There are 4 pencils in each group,

Explanation:
Given Mr. Hannigan places 12 pencils into 3 equal groups,
Drawn to show 4 number of pencils are in each group as 12 ÷ 3 = 4, 3 × 4 = 12, Therefore 4 pencils are there in each group.

Question 3.
Use an array to model Problem 1.
a. ___3___ × 4 = 12
12 ÷ 4 = ___3___
The number in the blanks represents
___________3 groups______________.
a.

The number in the blanks represents 3 groups,

Explanation:
Used an array to model Problem 1 as 3 x 4 = 12, or 12 ÷ 4 = 3, therefore the number in the blanks represents 3 groups.

b. 3 × ___4___ = 12
12 ÷ 3 = __4____
The number in the blanks represents
___________4 pencils in each group_____________.

Answer:

The number in the blanks represents 4 pencils in each group,

Explanation:
Given Mr. Hannigan places 12 pencils into 3 equal groups.
12 ÷ 3 = 4 or 3 × 4= 12, The number in the blanks represents 4 pencils in each group.

Question 4.
Judy washes 24 dishes. She then dries and stacks the dishes equally into 4 piles. How many dishes are in each pile?
24 ÷ 4 = ___6____
4 × ___6_____ = 24
What is the meaning of the unknown factor and quotient?
__________6 dishes are in each pile____________________

Answer:
There are 6 dishes in each pile,

Explanation:
Given Judy washes 24 dishes and she then dries and stacks the dishes equally into 4 piles.
So number of dishes in each pile are 24 ÷ 4 = 6, or 4 × 6 = 24, The meaning of the unknown factor and quotient is 6 dishes are there in each pile.

Question 5.
Nate solves the equation _____ × 5 = 15 by writing and solving 15 ÷ 5 = ____. Explain why Nate’s method works.

Answer:
Nate solves the equation as 3 × 5 = 15,

Explanation:
Given Nate solves the equation _____ × 5 = 15 by writing and solving as 15 ÷ 5 = 3, Nate’s method is correct because in the given equation ___ X 5 = 15 , we bring 5 to the other side it becomes as
15 ÷ 5 = 3 now we check as 3 × 5 it becomes 15 only.
So Nate’s method work.

Question 6.
The blanks in Problem 5 represent the number of groups.
Draw an array to represent the equations.

Explanation:
Drawn an array to represent the equations as
3 × 5 = 15 or 15 ÷ 5 = 3 as shown in the picture above.

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

Eureka Math Grade 3 Module 1 Answer Key

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

Question 1.
Fill in the blanks to make true statements.

a. 3 groups of five = ___15______
3 fives = ____15_____
3 × 5 = ___15______

3 groups of five = 15,
3 fives = 15,
3 × 5 = 15,

Explanation:
Given expressions as
3 groups of five means 3 × 5 = 15,
3 fives = 3 × 5 = 15 and
3 × 5 = 15 as 3 is multiplied by 5 we get 15.

b. 3 + 3 + 3 + 3 + 3 = __15___
5 groups of three = ___15______
5 × 3 = ____15_____

3 + 3 + 3 + 3 + 3 = 15,
5 groups of three = 15,
5 × 3 = 15,

Explanation:
Given expressions as
3 + 3 + 3 + 3 + 3 = 15 as 3 is added 5 times,
5 groups of three = 15 means 5  × 3 = 15,
5 × 3 = 15 as 5 is multiplied by 3 we get 15.

c. 6 + 6 + 6 + 6 = ___24________
____4___ groups of six = ___24_______
4 × __6____ = ____24______

6 + 6 + 6 + 6 = 24,
4 groups of six = 24,
4 × 6 = 24,

Explanation:
Given expressions as
6 + 6 + 6 + 6 = 24 as 6 is added 4 times,
4 groups of six = 24 means 4  × 6 = 24,
4 × 6 = 24 as 4 is multiplied by 6 we get 24.

d. 4 +__4__ + __4__ + __4__ + _4___ + __4__ = ___24______
6 groups of ____4____ = ____24_______
6 × __4____ = ____24______

4 + 4 + 4 + 4 + 4 + 4 = 24,
6 groups of 4 = 24,
6 × 4 = 24,

Explanation:
Given expressions as
4 + ___ + ___ +___ +___ +___ =  means by seeing the picture
4 is added 6 times as 4 + 4 + 4 + 4 + 4 + 4 we get 24,
6 groups of ______ =  means again by seeing the picture
6 × 4 we get 24, So 6 groups of 4 = 24,
6 × 4 = 24 as 6 is multiplied by 4 we get 24.

Question 2.
The picture below shows 2 groups of apples. Does the picture show 2 × 3? Explain why or why not.

No, the picture does not show 2 × 3,

Explanation:
Given the picture below shows 2 groups of apples but in the 2 groups the number of apples are not the same as in group -1 we have 3 apples, group 2 we have 2 apples in total there are 5 apples and 2 × 3 = 6 whose value is not same as shown in the picture.
So, the picture does not show 2 × 3.

Question 3.
Draw a picture to show 2 × 3 = 6.

Explanation:
Drawn a picture above to show 2 × 3 = 6 .

Question 4.
Caroline, Brian, and Marta share a box of chocolates. They each get the same amount. Circle the chocolates below to show 3 groups of 4. Then, write a repeated addition sentence and a multiplication sentence to represent the picture.

Addition sentence is 4 + 4 + 4 = 12,
Multiplication sentence is 3 × 4 = 12,

Explanation:
Given Caroline, Brian, and Marta share a box of chocolates and they each get the same amount as 12 ÷ 3 = 4 each.
Circled the chocolates above to show 3 groups of 4 and wrote a repeated addition sentence as  4 + 4 + 4 = 12 and a multiplication sentence to represent the picture as 3 × 4 = 12.

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

Question 1.
The picture below shows 4 groups of 2 slices of watermelon.
Fill in the blanks to make true repeated addition and multiplication sentences that represent the picture.

True repeated addition is 2 + 2 + 2 + 2 = 8,
Multiplication sentences is 4 X 2 = 8.

Explanation:
Given the picture above shows 4 groups of 2 slices of watermelon.
Filled in the blanks to make true repeated addition as 2 + 2 + 2 + 2 = 8 and multiplication sentences that represent the picture as 4 X 2 = 8.

Question 2.
Draw a picture to show 3 + 3 + 3 = 9. Then, write a multiplication sentence to represent the picture.

Addition sentence is  3 + 3 + 3 = 9,
Multiplication sentences is 3 X 3 = 9.

Explanation:
Drawn a picture above as  3 groups of 3 birds  to show 3 + 3 + 3 = 9 and writing a multiplication sentence to represent the picture as 3 X 3 = 9 birds in total.

Eureka Math Grade 3 Module 1 Lesson 1 Homework Answer Key

Question 1.
Fill in the blanks to make true statements.

a. 4 groups of five = ____20_____
4 fives = ___20______
4 × 5 = ____20_____

4 groups of five = 20,
4 fives = 20,
4 × 5 = 20,

Explanation:
Given expressions as
4 groups of five means 4 × 5 = 20,
4 fives = 4 × 5 = 20 and
4 × 5 = 20 as 4 is multiplied by 5 we get 20.

b. 5 groups of four = _________
5 fours = _________
5 × 4 = _________

5 groups of four = 20,
5 fours = 20,
5 × 4 = 20,

Explanation:
Given expressions as
5 groups of four means 5 × 4 = 20,
5 fours = 5 x 4 = 20 and
5 × 4 = 20 as 5 is multiplied by 4 we get 20.

c. 6 + 6 + 6 = ___18________
____3___ groups of six = ____18______
3 × __6____ = ____18______

6 + 6 + 6  = 18,
3 groups of 6 = 18,
3 × 6 = 18,

Explanation:
Given expressions as 6 + 6 + 6 = 18 as
6 is added 3 times we get 18,
_____ groups of six =  means again by seeing the picture
3 groups of 6 =  3 × 6 we get 18, So 3 groups of 6 = 18,
3 × 6 = 18 as 3 is multiplied by 6 we get 18.

d. 3 + __3__ + __3__ + __3__ + __3__ + __3__ = ___18____
6 groups of ____3____ = _____18______
6 × __3__ = ____18______

3 + 3 + 3 + 3 + 3 + 3 = 18,
6 groups of 3 = 18,
6 × 3 = 18,

Explanation:
Given expressions as
3 + ___ + ___ +___ +___ +___ =  means by seeing the picture
3 is added 6 times as 3 + 3 + 3 + 3 + 3 + 3 we get 18,
6 groups of ______ =  means again by seeing the picture
6 × 3 we get 18, So 6 groups of 3 = 18,
6 × 3 = 18 as 6 is multiplied by 3 we get 18.

Question 2.
The picture below shows 3 groups of hot dogs. Does the picture show 3 × 3? Explain why or why not.

Yes, the picture shows 3 × 3,

Explanation:
Given the picture below shows 3 groups of hot dogs,
In the 3 groups the number of hot dogs are the same as 3, So in total we have 3 X 3 = 9 hotdogs in the picture which matches with the given equation as 3 × 3 whose value is also same 9, So, the picture shows 3 × 3.

Question 3.
Draw a picture to show 4 × 2 = 8,

Explanation:
Drawn picture of flowers as shown above to show 4 × 2 = 8.

Question 4.
Circle the pencils below to show 3 groups of 6. Write a repeated addition and a multiplication sentence to represent the picture.


Repeated addition sentence is 6 + 6 + 6 = 18,
Multiplication sentence is 3 X 6 = 18,

Explanation:
Circled the pencils above to show 3 groups of 6.
Wrote a repeated addition as 6 + 6 + 6 = 18 and a multiplication sentence as 3 X 6 = 18 to represent the picture.