Unit 4 Plan - Grade 3

Title	Assessment
Lesson 1 How Many Groups?	How Many Bags? Lin has 30 apples to share with her friends. She is putting them in bags, with 6 apples in each bag. How many bags does she need? Explain or show your reasoning. Show Solution She needs 5 bags. Sample response: When I put the 30 objects into groups of 6, there are e 5 groups.
Lesson 2 How Many in Each Group?	Apples in Bags Lin has 30 apples. She makes 6 bags with the same number of apples in each bag to give to her friends. How many apples are in each bag? Explain or show your reasoning. Show Solution Each bag has 5 apples. Sample response: If I put the 30 apples into 6 groups one by one, there will be 5 apples in each group. 6 groups of 5 is 30.
Lesson 3 Division Situation Drawings	Party Favors Clare has 48 markers. She puts 8 markers into each goodie bag for her birthday party. How many bags will she use? Which drawing matches the situation? Explain your reasoning. A B Show Solution B. Sample response: Both drawings show 48 markers, but only Drawing B shows 8 markers in each bag. After the 48 markers are put into groups of 8, there will be 6 bags.
Lesson 4 Interpret Division Expressions	Han’s Tops Han has 14 tops. He shares the tops equally between 2 boxes. How many tops will be in each box? Select all the ways that we could represent the situation. A. B. C. $\displaystyle{14 \div 2}$ D. $\displaystyle{14 \div 7}$ Show Solution A, C
Lesson 5 Write Division Expressions	Ant Legs Twenty-four legs belong to 4 ants. All ants have the same number of legs. Write a division expression to represent this situation. How many legs does each ant have? Explain or show your reasoning. Show Solution $24 \div 4$ 6 legs. Sample response: Students draw 4 groups of 6.
Section A Check Section A Checkpoint	Problem 1 There are 35 flowers in the garden. There are 7 flowers in each row. Make a drawing to represent the situation. How many rows of flowers are there? Show Solution Sample response: 5 rows Problem 2 Noah has 36 books. There are 4 shelves on his bookshelf. He puts the same number of books on each shelf. Write a division expression to represent the situation. How many books are on each shelf? Explain or show your reasoning. Show Solution $36 \div 4$ 9 books. Sample response:

Lesson 6 Division as an Unknown Factor	Boxed Muffins There are 30 muffins for the bake sale. Each box has 6 muffins. How many boxes are there? Tyler wrote two equations for this problem. $\underline{\hspace{1 cm}} \times 6 = 30$ $30 \div 6 = \underline{\hspace{1 cm}}$ He says the same number goes in each blank even though one equation is a multiplication equation and the other equation is a division equation. Is he correct? Explain or show your reasoning. Show Solution Yes. Sample response: Five goes in both blanks because it is the number of boxes, we just write it in different places for multiplication equations and division equations.
Lesson 7 Relate Multiplication and Division	Sharing Roses Clare has 14 roses. She wants to give each of her teachers 2 roses. How many teachers can she give roses to? Write a multiplication equation and a division equation to represent the situation. Use symbols for the unknown and explain your reasoning. Show Solution Sample response: ${?} \times 2 = 14$ and $14\div2={?}$ I know she has 14 roses and wants to put them in groups of 2. The question is asking me how many groups there will be, which is how many teachers will get roses and is represented by the ?. Note: It is most important that students accurately explain that the size of the groups is known, but not the number of groups. They may reverse the factors in the multiplication equation.
Lesson 8 Relate Quotients to Familiar Products	Multiplication and Division Facts Think about the multiplication facts that you know. How have they changed since the beginning of the year? Show Solution Sample responses: I used to only know the 5s and 10s, but now I’ve used those facts to learn more. I only knew a few at the beginning of the year, but now I know a lot more.
Lesson 9 Patterns in the Multiplication Table	Find the Unknown Product What number should replace the question mark? Explain or show your reasoning. Show Solution 32. Sample responses: The table shows that $4 \times 8$ is 32, and I know that $8 \times 4$ has the same value as $4 \times 8$ , so it is also 32. I know that $4 \times 4$ or 4 groups of 4 is 16. I added another 16 to get $8 \times 4$ , and $16 + 16 = 32$ .
Lesson 10 Explore Multiplication Strategies with Rectangles	Mark or Shade Parts to Find Area Here is a rectangle whose area can be found by multiplying $6 \times 7$ . Mark or shade the rectangle to show that we can write $2 \times (3 \times 7)$ or $(6 \times 5) + (6 \times 2)$ to find its area. What is the value of $6 \times 7$ ? Explain or show your reasoning. Show Solution Sample responses: 42. Sample response: I know that $6 \times 5$ is 30 and $6 \times 2$ is 12, and $30 + 12 = 42$ .
Lesson 11 Multiplication Strategies on Ungridded Rectangles	Expressions for a Rectangle Mark or shade this rectangle to show a strategy for finding its area. Write one or more expressions that represent how you find the area. Show Solution Sample response: $(6 \times 5) + (6 \times 4)$
Section B Check Section B Checkpoint	Problem 1 There are 24 students in the choir. They are standing in 3 equal rows. How many students are in each row? Select all equations that represent this situation. A. $3 \times 12 = {?}$ B. $3 \times {?} = 24$ C. $24 \times 3 = {?}$ D. ${?} \div 24 = 3$ E. $24 \div 3 = {?}$ Show Solution B, E Problem 2 Han knows $4 \times 5 = 20$ and $4 \times 3 = 12$ . Mark or shade the diagram to show how Han can use these facts to find the value of $4 \times 8$ . Explain your reasoning. Show Solution Sample response: The shaded part is $4 \times 5$ or 20 and the unshaded part is $4 \times 3$ , or 12, so the total number of small squares is $20 + 12$ or 32. It's also $4 \times 8$ . Problem 3 Find the value of each product. $5 \times 3=\underline{\hspace{1 cm}}$ $6 \times 3=(5\times3)+\underline{\hspace{1 cm}}$ $6 \times 6=(6\times3)\times\underline{\hspace{1 cm}}$ Show Solution 15 3 or $1\times3$ 2

Lesson 12 Multiply Multiples of 10	What’s the Value? Find the value of $6 \times 40$ . Explain or show your reasoning. Show Solution 240. Sample response: I decomposed 40 into $4 \times 10$ , then multiplied $6 \times 4$ to get 24. Twenty-four tens is 240.
Lesson 13 Solve Problems with Equal Groups	Buckets of Sunflowers There were 6 buckets of sunflowers at the farmers market. Each bucket had 11 sunflowers. How many sunflowers were in the buckets? Show your thinking using objects, a drawing, or a diagram. Show Solution 66 sunflowers. Sample response: Students use base-ten blocks to make 6 groups of 11.
Lesson 14 Ways to Represent Multiplication of Teen Numbers	Multiply and Explain Find the value of $5 \times 15$ and explain how it’s represented in the diagram. Show Solution 75. Sample response: We can see 15 broken down into 10 and 5. We can see $5 \times 10$ in the large part of the rectangle and $5 \times 5$ in the smaller part. If we add those parts of the rectangle, we get the product of $5 \times 15$ , which is 75.
Lesson 15 Equal Groups, Greater Numbers	Find the Area A rectangle is 6 feet by 15 feet. What is the area of the rectangle? Explain or show your reasoning. Show Solution 90 square feet. Sample response: $6 \times 10 = 60$ , $6 \times 5 = 30$ , and $60 + 30 = 90$ .
Lesson 16 Multiply Numbers Greater than 20	Multiply Numbers Greater than 20 What’s the value of $4 \times 24$ ? Explain or show your reasoning. Show Solution 96. Sample response: $4 \times 20 = 80$ , $4 \times 4 = 16$ , and $80 + 16 = 96$ .
Lesson 17 Use the 4 Operations to Solve Problems	Andre’s Balloons Andre has 125 balloons. He and 4 friends hung up some of the balloons for a party at school. Now there are 80 balloons left. Each person hung up the same number of balloons. How many balloons did each person hang up? Write an equation with a letter for the unknown quantity to represent the situation. Solve the problem. Explain or show your reasoning. Show Solution Sample response: $(125-80) \div 5 = {b}$ 9 balloons. Sample response: I subtracted $125-80$ to see how many balloons Andre and his friends hung up and got 45. Then I divided 45 by 5 to see how many balloons each person hung up and got 9.
Section C Check Section C Checkpoint	Problem 1 Find the value of $7 \times 60$ . Explain or show your reasoning. Show Solution 420. Sample response: 60 is 6 tens and $7 \times 6$ is 42 so $7 \times 60$ is 42 tens, and that's 420. Problem 2 Explain or show how each diagram represents $4 \times 13$ . Show Solution Sample responses: There are 4 rows or groups of squares and there are 13 in each row so altogether there are $4 \times 13$ squares. The diagram shows that I can add the products $4 \times 10$ and $4 \times 3$ to find the value of $4 \times 13$ . Problem 3 Andre’s book has 192 pages. He reads 15 pages each day for 5 days. How many pages does he still have to read to finish the book? Write an equation to represent the situation. Use a letter for the unknown quantity. Solve the problem. Explain or show your reasoning. Show Solution Sample response: $192 - (5 \times 15) = p$ . $p$ is the number of pages Andre still needs to read. 117 pages. Sample response: $5 \times 10 = 50$ , $5 \times 5 = 25$ , so $5 \times 15 = 75$ . $192-70 = 122$ and $122 - 5 = 117$ , so $192-75=117$ . There are 117 pages left to read.

Lesson 18 Greater Numbers in Equal Groups	Recess Teams At recess, 42 students played a game. There were 3 teams with the same number of students on each team. How many students were on each team? Show your thinking using diagrams, symbols, or other representations. Show Solution 14 students. Any strategy is acceptable at this point in the unit. Sample responses: Students draw 42 things and circle 3 equal groups of 14. Students draw base-ten diagrams and put 1 ten and 4 ones into each group. Students write a series of multiplication equations with 3 as a factor and build up to 42.
Lesson 19 Ways to Divide Greater Numbers	Find the Value Find the value of $51 \div 3$ . Use base-ten blocks if they are helpful. Explain or show your reasoning. Show Solution 17. Sample responses: Students represent 51 with base-ten blocks and make 3 equal groups, decomposing tens as needed. Students make a drawing that shows 51 dots or shapes placed into 3 groups or a drawing that shows 51 dots or shapes placed into groups of 3.
Lesson 20 Strategies for Dividing	One More Division Find the value of $96 \div 6$ . Explain or show your reasoning. Show Solution 16. Sample responses: Students make a drawing of 6 groups with 1 ten and 6 ones in each group. I know that $10\times6$ is 60 and $6\times6$ is 36, and $60 + 36 = 96$ . $10 + 6=16$ .
Lesson 21 Solve Problems Using the Four Operations	Apples at the Farm Stand A booth at the apple orchard has 225 apples. 165 apples are not in baskets. The rest of the apples are in 6 baskets with the same number of apples in each basket. How many apples are in each basket? Write an equation to represent this situation. Use a letter for the unknown quantity. Solve the problem. Explain or show your reasoning. Show Solution Sample responses: $165 + (6 \times n) = 225$ or $225 - 165 = (6 \times n)$ or $(225 - 165) \div 6 = n$ 10 apples. Sample response: I subtracted 165 from 225 to find out how many apples were in baskets. It was 60 apples. I know that $6 \times 10$ is 60, so there would be 10 apples in each basket.
Lesson 22 School Community Garden	No cool-down
Section D Check Section D Checkpoint	Problem 1 Find the value of each quotient. Explain or show your reasoning. $60\div 4$ $96 \div 6$ Show Solution 15. Sample response: $10 \times 4 = 40$ , $5 \times 4 =20$ , $40 + 20 = 60$ , and $10 + 5 = 15$ . 16. Sample response: $10 \times 6 = 60$ , $6 \times 6 = 36$ , $60 + 36 = 96$ , and $10 + 6 = 16$ . Problem 2 Noah has 117 building blocks. He builds a shape with 25 blocks. Then he puts the rest of the blocks in 4 bins, with the same number of blocks in each bin. How many blocks are in each bin? Explain or show your reasoning. Show Solution 23 blocks. Sample response: $117 - 25 = 92$ , $92 \div 4 = 23$ .

Lesson 1

How Many Groups?

How Many Bags?

Lin has 30 apples to share with her friends. She is putting them in bags, with 6 apples in each bag. How many bags does she need? Explain or show your reasoning.

Show Solution

She needs 5 bags. Sample response: When I put the 30 objects into groups of 6, there are e 5 groups.

Lesson 2

How Many in Each Group?

Apples in Bags

Lin has 30 apples. She makes 6 bags with the same number of apples in each bag to give to her friends. How many apples are in each bag? Explain or show your reasoning.

Show Solution

Each bag has 5 apples. Sample response: If I put the 30 apples into 6 groups one by one, there will be 5 apples in each group. 6 groups of 5 is 30.

equal sized groups. 30 objects in groups of 5

Lesson 3

Division Situation Drawings

Party Favors

Clare has 48 markers. She puts 8 markers into each goodie bag for her birthday party. How many bags will she use?

Which drawing matches the situation? Explain your reasoning.

Show Solution

B. Sample response: Both drawings show 48 markers, but only Drawing B shows 8 markers in each bag. After the 48 markers are put into groups of 8, there will be 6 bags.

Lesson 4

Interpret Division Expressions

Han’s Tops

Han has 14 tops. He shares the tops equally between 2 boxes. How many tops will be in each box?

Select all the ways that we could represent the situation.

A.

B.

C.

$\displaystyle{14 \div 2}$

D.

$\displaystyle{14 \div 7}$

Show Solution

A, C

Lesson 5

Write Division Expressions

Ant Legs

Twenty-four legs belong to 4 ants. All ants have the same number of legs.

Write a division expression to represent this situation.
How many legs does each ant have? Explain or show your reasoning.

Show Solution

$24 \div 4$
6 legs. Sample response: Students draw 4 groups of 6.

Section A Check

Section A Checkpoint

Problem 1

There are 35 flowers in the garden. There are 7 flowers in each row.

Make a drawing to represent the situation.
How many rows of flowers are there?

Show Solution

Sample response:
5 rows

Problem 2

Noah has 36 books. There are 4 shelves on his bookshelf. He puts the same number of books on each shelf.

Write a division expression to represent the situation.
How many books are on each shelf? Explain or show your reasoning.

Show Solution

$36 \div 4$
9 books. Sample response:

Lesson 6

Division as an Unknown Factor

Boxed Muffins

There are 30 muffins for the bake sale. Each box has 6 muffins. How many boxes are there?

Tyler wrote two equations for this problem.

$\underline{\hspace{1 cm}} \times 6 = 30$

$30 \div 6 = \underline{\hspace{1 cm}}$

He says the same number goes in each blank even though one equation is a multiplication equation and the other equation is a division equation. Is he correct? Explain or show your reasoning.

Show Solution

Yes. Sample response: Five goes in both blanks because it is the number of boxes, we just write it in different places for multiplication equations and division equations.

Lesson 7

Relate Multiplication and Division

Sharing Roses

Clare has 14 roses. She wants to give each of her teachers 2 roses. How many teachers can she give roses to?

Write a multiplication equation and a division equation to represent the situation. Use symbols for the unknown and explain your reasoning.

Show Solution

Sample response:

${?} \times 2 = 14$ and $14\div2={?}$

I know she has 14 roses and wants to put them in groups of 2. The question is asking me how many groups there will be, which is how many teachers will get roses and is represented by the ?.

Note: It is most important that students accurately explain that the size of the groups is known, but not the number of groups. They may reverse the factors in the multiplication equation.

Lesson 8

Relate Quotients to Familiar Products

Multiplication and Division Facts

Think about the multiplication facts that you know. How have they changed since the beginning of the year?

Show Solution

Sample responses: I used to only know the 5s and 10s, but now I’ve used those facts to learn more. I only knew a few at the beginning of the year, but now I know a lot more.

Lesson 9

Patterns in the Multiplication Table

Find the Unknown Product

What number should replace the question mark? Explain or show your reasoning.

Multiplication table with missing products.

Show Solution

32. Sample responses: The table shows that $4 \times 8$ is 32, and I know that $8 \times 4$ has the same value as $4 \times 8$ , so it is also 32. I know that $4 \times 4$ or 4 groups of 4 is 16. I added another 16 to get $8 \times 4$ , and $16 + 16 = 32$ .

Lesson 10

Explore Multiplication Strategies with Rectangles

Mark or Shade Parts to Find Area

Here is a rectangle whose area can be found by multiplying $6 \times 7$ .

Mark or shade the rectangle to show that we can write $2 \times (3 \times 7)$ or $(6 \times 5) + (6 \times 2)$ to find its area.
What is the value of $6 \times 7$ ? Explain or show your reasoning.

<span>Diagram. Rectangle partitioned into 6 rows of 7 of the same size squares. Rectangle length, 7. Rectangle width, 6.</span>

Show Solution

Sample responses:
42. Sample response: I know that $6 \times 5$ is 30 and $6 \times 2$ is 12, and $30 + 12 = 42$ .

Lesson 11

Multiplication Strategies on Ungridded Rectangles

Expressions for a Rectangle

Mark or shade this rectangle to show a strategy for finding its area.
Write one or more expressions that represent how you find the area.

<p>Area diagram. Rectangle. Top measurement 9, left side measurement 6.</p>

Show Solution

Sample response:

$(6 \times 5) + (6 \times 4)$

Section B Check

Section B Checkpoint

Problem 1

There are 24 students in the choir. They are standing in 3 equal rows. How many students are in each row? Select all equations that represent this situation.

A.

3 \times 12 = {?}

B.

3 \times {?} = 24

C.

24 \times 3 = {?}

D.

{?} \div 24 = 3

E.

24 \div 3 = {?}

Show Solution

B, E

Problem 2

Han knows $4 \times 5 = 20$ and $4 \times 3 = 12$ .

Mark or shade the diagram to show how Han can use these facts to find the value of $4 \times 8$ . Explain your reasoning.

Show Solution

Sample response:

The shaded part is $4 \times 5$ or 20 and the unshaded part is $4 \times 3$ , or 12, so the total number of small squares is $20 + 12$ or 32. It's also $4 \times 8$ .

Problem 3

Find the value of each product.

$5 \times 3=\underline{\hspace{1 cm}}$
$6 \times 3=(5\times3)+\underline{\hspace{1 cm}}$
$6 \times 6=(6\times3)\times\underline{\hspace{1 cm}}$

Show Solution

15
3 or $1\times3$
2

Lesson 12

Multiply Multiples of 10

What’s the Value?

Find the value of $6 \times 40$ . Explain or show your reasoning.

Show Solution

240. Sample response: I decomposed 40 into

4 \times 10

, then multiplied

6 \times 4

to get 24. Twenty-four tens is 240.

Lesson 13

Solve Problems with Equal Groups

Buckets of Sunflowers

There were 6 buckets of sunflowers at the farmers market. Each bucket had 11 sunflowers. How many sunflowers were in the buckets? Show your thinking using objects, a drawing, or a diagram.

Show Solution

66 sunflowers. Sample response: Students use base-ten blocks to make 6 groups of 11.

Lesson 14

Ways to Represent Multiplication of Teen Numbers

Multiply and Explain

Find the value of $5 \times 15$ and explain how it’s represented in the diagram.

Show Solution

75. Sample response: We can see 15 broken down into 10 and 5. We can see $5 \times 10$ in the large part of the rectangle and $5 \times 5$ in the smaller part. If we add those parts of the rectangle, we get the product of $5 \times 15$ , which is 75.

Lesson 15

Equal Groups, Greater Numbers

Find the Area

A rectangle is 6 feet by 15 feet. What is the area of the rectangle? Explain or show your reasoning.

Show Solution

90 square feet. Sample response:

6 \times 10 = 60

,

6 \times 5 = 30

, and

60 + 30 = 90

.

Lesson 16

Multiply Numbers Greater than 20

What’s the value of $4 \times 24$ ? Explain or show your reasoning.

Show Solution

96. Sample response: $4 \times 20 = 80$ , $4 \times 4 = 16$ , and $80 + 16 = 96$ .

Lesson 17

Use the 4 Operations to Solve Problems

Andre’s Balloons

Andre has 125 balloons. He and 4 friends hung up some of the balloons for a party at school. Now there are 80 balloons left. Each person hung up the same number of balloons. How many balloons did each person hang up?

Write an equation with a letter for the unknown quantity to represent the situation.
Solve the problem. Explain or show your reasoning.

Show Solution

Sample response: $(125-80) \div 5 = {b}$
9 balloons. Sample response: I subtracted $125-80$ to see how many balloons Andre and his friends hung up and got 45. Then I divided 45 by 5 to see how many balloons each person hung up and got 9.

Section C Check

Section C Checkpoint

Problem 1

Find the value of $7 \times 60$ . Explain or show your reasoning.

Show Solution

420. Sample response: 60 is 6 tens and $7 \times 6$ is 42 so $7 \times 60$ is 42 tens, and that's 420.

Problem 2

Explain or show how each diagram represents $4 \times 13$ .

Show Solution

Sample responses:

There are 4 rows or groups of squares and there are 13 in each row so altogether there are $4 \times 13$ squares.
The diagram shows that I can add the products $4 \times 10$ and $4 \times 3$ to find the value of $4 \times 13$ .

Problem 3

Andre’s book has 192 pages. He reads 15 pages each day for 5 days. How many pages does he still have to read to finish the book?

Write an equation to represent the situation. Use a letter for the unknown quantity.
Solve the problem. Explain or show your reasoning.

Show Solution

Sample response: $192 - (5 \times 15) = p$ . $p$ is the number of pages Andre still needs to read.
117 pages. Sample response: $5 \times 10 = 50$ , $5 \times 5 = 25$ , so $5 \times 15 = 75$ . $192-70 = 122$ and $122 - 5 = 117$ , so $192-75=117$ . There are 117 pages left to read.

Lesson 18

Greater Numbers in Equal Groups

Recess Teams

At recess, 42 students played a game. There were 3 teams with the same number of students on each team. How many students were on each team?

Show your thinking using diagrams, symbols, or other representations.

Show Solution

14 students. Any strategy is acceptable at this point in the unit. Sample responses:

Students draw 42 things and circle 3 equal groups of 14.
Students draw base-ten diagrams and put 1 ten and 4 ones into each group.
Students write a series of multiplication equations with 3 as a factor and build up to 42.

Lesson 19

Ways to Divide Greater Numbers

Find the Value

Find the value of $51 \div 3$ . Use base-ten blocks if they are helpful. Explain or show your reasoning.

Show Solution

17. Sample responses: Students represent 51 with base-ten blocks and make 3 equal groups, decomposing tens as needed. Students make a drawing that shows 51 dots or shapes placed into 3 groups or a drawing that shows 51 dots or shapes placed into groups of 3.

Lesson 20

Strategies for Dividing

One More Division

Find the value of $96 \div 6$ . Explain or show your reasoning.

Show Solution

16. Sample responses:

Students make a drawing of 6 groups with 1 ten and 6 ones in each group.
I know that $10\times6$ is 60 and $6\times6$ is 36, and $60 + 36 = 96$ . $10 + 6=16$ .

Lesson 21

Solve Problems Using the Four Operations

Apples at the Farm Stand

A booth at the apple orchard has 225 apples. 165 apples are not in baskets. The rest of the apples are in 6 baskets with the same number of apples in each basket. How many apples are in each basket?

Write an equation to represent this situation. Use a letter for the unknown quantity.
Solve the problem. Explain or show your reasoning.

Show Solution

Sample responses: $165 + (6 \times n) = 225$ or $225 - 165 = (6 \times n)$ or $(225 - 165) \div 6 = n$
10 apples. Sample response: I subtracted 165 from 225 to find out how many apples were in baskets. It was 60 apples. I know that $6 \times 10$ is 60, so there would be 10 apples in each basket.

Lesson 22

School Community Garden

No cool-down

Section D Check

Section D Checkpoint

Problem 1

Find the value of each quotient. Explain or show your reasoning.

$60\div 4$
$96 \div 6$

Show Solution

15. Sample response: $10 \times 4 = 40$ , $5 \times 4 =20$ , $40 + 20 = 60$ , and $10 + 5 = 15$ .
16. Sample response: $10 \times 6 = 60$ , $6 \times 6 = 36$ , $60 + 36 = 96$ , and $10 + 6 = 16$ .

Problem 2

Noah has 117 building blocks. He builds a shape with 25 blocks. Then he puts the rest of the blocks in 4 bins, with the same number of blocks in each bin.

How many blocks are in each bin? Explain or show your reasoning.

Show Solution

23 blocks. Sample response: $117 - 25 = 92$ , $92 \div 4 = 23$ .

Unit 4 Relating Multiplication To Division — Unit Plan