EM2_G3_M1_Apply_23B_976487_Updated 04.23

MATH Conceptual Understanding of Multiplication

Dear Family,

Your student is making sense of multiplication by connecting it to addition. Instead of repeatedly adding the same number, they recognize that multiplying can be more efficient. They create representations of multiplication in equal groups or arrays by using cubes or drawing pictures. Then they write multiplication equations to match. For now, the factors are limited to 2, 3, 4, 5, and 10 as your student builds their understanding of multiplication.

Number in each group: 3

Key Terms and Symbols factor multiplication

multiplication symbol × multiply product

Number of groups: 4

At-Home Activities

How Can You Make Equal Groups?

Gather groups of everyday objects from around your home such as toy cars, crackers, or beads. Together with your student, arrange the objects into equal groups or arrays. Ask them to write or say a multiplication equation to represent the groups of objects. Encourage skip-counting to figure out the product.

Equal Groups and Arrays at the Grocery Store

Look for items packaged in equal groups and arrays, such as eggs, hamburger buns, or toilet paper. Discuss with your student the number of groups and the number in each group for each situation. Then have them use multiplication to find the total in each package.

Draw an array to show 4 rows of 3.

1. Count the pencils.

10

10

How many pencils are there in total? 32

I see each box holds 10 pencils. I count by tens. Then I count on 2 more.

2. Group the strawberries to help you count. Circle strawberries to show your groups.

a. How many strawberries are there in total? 35

b. Describe another way you can group the strawberries. The strawberries can be circled in 7 groups of 5.

I can circle groups of 10 I know 3 tens is 30 and there are 5 more.

30 + 5 = 35

I can also circle groups of 5

5 10 15 20 25 30 35 I skip-count by fives until all the groups have been counted.

REMEMBER

quarter to 5

I know that quarters are 4 equal parts of a whole. Quarter to is when the minute hand is three quarters of the way around the clock. At quarter to, the minute hand points at 9.

Quarter to

Quarter past

At quarter to 5, the hour hand is almost to the 5.

3. Draw the missing hand on the clock to show the time.

Name

1. Count the crayons.

How many crayons are there in total?

2. Group the dots to help you count. Circle dots to show your groups.

a. How many dots are there in total?

b. Describe another way you can group the dots.

REMEMBER

3. Draw the missing hand on the clock to show the time.

quarter past 9

Name

1. Use the equal groups for parts (a) and (b). 3 , 6 , 9 , 12 , 15

a. Skip-count by 3

If I need practice skip-counting by 3, I can whisper-count by ones and say every third number aloud. For example, I whisper “ 1 , 2 ” and say “3” aloud.

I whisper “4, 5” and say “6” aloud.

I write each number that I say aloud.

b. Fill in the blanks to show the total number of apples.

3 + 3 + 3 + 3 + 3 = 15

5 groups of three is 15 .

5 threes is 15 .

5 × 3 = 15

The multiplication symbol (×) is used to show multiplication. 5 × 3 = 15

Multiplication is another way to represent repeated addition when the groups are the same size. Instead of adding lots of numbers, we can multiply

× 3 = 15

REMEMBER

2. Read

David has 37 dollars.

Carla has 2 ten-dollar bills, 3 five-dollar bills, and 1 one-dollar bill. Who has more money?

Draw

I read the problem. I read again. As I reread, I think about what I can draw. I draw rectangles to represent each type of bill and label their values.

Then I add the values of the bills to find how much money Carla has.

I am trying to find who has more money. I know David has 37 dollars and Carla has 36 dollars.

Sample:

Write $20 + $15 + $1 = $36

David has more money than Carla. 37 dollars is more than 36 dollars.

Name

1. Use the equal groups for parts (a) and (b).

a. Skip-count by 5. , , ,

b. Fill in the blanks to show the total number of fingers.

five

2. Fill in the blanks to match the picture.

three

REMEMBER

3. Read

Eva has 57 dollars.

Luke has 1 twenty-dollar bill, 2 ten-dollar bills, 1 five-dollar bill, and 5 one-dollar bills.

Who has more money?

Draw

1. Use the picture for parts (a) and (b).

5 , 10 , 15 , 20 , 25 , 30

a. Skip-count by 5

b. Fill in the blanks to match the picture.

6 groups of 5 is 30 .

6 fives is 30

6 × 5 = 30

The product is 30 .

I can multiply the number in each group by the number of groups.

In multiplication, the total is called the product.

6 × 5 = 30

2. Use the array for parts (a)–(c).

a. Skip-count by 10 down the side of the array.

b. Fill in the blanks to match the array.

7 tens is 70 .

7 × 10 = 70

c. Circle the product in the equation.

I record my skip-count next to each row of the array.

The product is 70 because it is the total in the multiplication problem.

REMEMBER

Add. Show how you know.

3. 338 + 196 =  534 Sample: 338 + 196

I can make this an easier problem. I see 196 needs 4 more to make the next hundred, which is 200. I know I can get the 4 from 338. I decompose 338 into 334 and 4 338 334 4

I add the 4 to 196 to make 200 . + 4 196 200 334 + 200 is an easier problem for me than 338 + 196 Now I add 334 to 200. + 4 196 200 534 + 334

Name

1. Use the picture for parts (a) and (b). , ,

a. Skip-count by 10.

b. Fill in the blanks to match the picture. groups of is . tens is . × = The product is .

2. Use the array for parts (a)–(c).

a. Skip-count by 5 down the side of the array.

b. Fill in the blanks to match the array. fives is . × =

c. Circle the product in the equation.

REMEMBER

Add. Show how you know.

3. 148 +  297 =

Name

1. Use the equal groups for parts (a)–(c).

a. How many groups of crabs are there? 6 groups

b. How many crabs are in each group? 4 crabs are in each group.

c. Complete the multiplication equation.

6 × 4 = 24

Number of groups

Number in each group Product

I can multiply the number in each group by the number of groups.

In a multiplication equation, the two numbers we multiply together are called factors

6 × 4 = 24

2. Use the array for parts (a)–(c).

a. How many rows of crabs are there?

6 rows of crabs

b. How many crabs are in each row?

4 crabs are in each row.

c. Complete the equation.

6 × 4 = 24

Number of rows

Number in each row Product

I notice the total number of crabs is the same as in problem 1 , but now the crabs are organized in an array.

REMEMBER

Use compensation to subtract. Draw a tape diagram if needed.

3. 276 97 = 279 100 = 179

Sample:

I notice that 97 is close to the benchmark number 100. I can use the compensation strategy to subtract.

I add 3 to 97 to make 100. Then I add 3 to 276 to make 279

279 100 is an easier problem for me than 276 97.

I can subtract 100 from 279 to get 179.

279 100 = 179

?

The compensation strategy is useful when one number is close to a benchmark number.

Name

1. Use the equal groups for parts (a)–(c).

a. How many groups of ducks are there? groups

b. How many ducks are in each group? ducks are in each group.

c. Complete the equation.

Number of groups

Number in each group

2. Use the array for parts (a)–(c).

a. How many rows of ducks are there? rows of ducks

b. How many ducks are in each row? ducks are in each row.

c. Complete the equation.

Number of rows

Number in each row

REMEMBER

Use compensation to subtract. Draw a tape diagram if needed.

3. 922 198 = =

Name

Use the Read–Draw–Write process to solve each problem.

1. Jayla has 3 buckets of toy cars. There are 5 toy cars in each bucket. How many toy cars does Jayla have?

3 × 5 = 15

Jayla has 15 toy cars.

I read the problem. I read again. As I reread, I think about what I can draw. I draw 3 circles to represent the 3 buckets.

I draw 5 small circles in each bucket to represent the 5 toy cars.

I see 3 groups of 5

2. Ray organizes his coins into 5 rows. Each row has 6 coins.

How many coins does Ray have?

5 × 6 = 30

Ray has 30 coins.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw circles to show 5 rows with 6 coins in each row.

6 coins in each row

5 rows

I can use my drawing to write a multiplication equation.

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. Shen and Oka are counting their stickers. Shen has 18 fewer stickers than Oka. Oka has 49 stickers.

a. How many stickers does Shen have?

b. How many stickers do Shen and Oka have in total?

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram with one tape to show the number of Oka’s stickers.

Sample: 49 − 18 = 31

Shen has 31 stickers. 31 + 49 = 80

They have 80 stickers in total.

I know Shen has 18 fewer stickers than Oka. I draw a shorter tape to show Shen’s stickers and label the 18 fewer stickers. 18 S

? 49

I can subtract 18 from 49 to find the number of Shen’s stickers.

S

To find the total number of stickers, I can add 31 and 49

Name

Use the Read–Draw–Write process to solve each problem.

1. Mia sells 4 bags of lemons. There are 6 lemons in each bag. How many lemons does Mia sell? Mia sells lemons.

2. There are 5 rows of chairs in the room. Each row has 10 chairs. How many chairs are in the room?

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. Adam and Ivan find acorns.

Adam finds 19 fewer acorns than Ivan. Ivan finds 34 acorns.

a. How many acorns does Adam find?

b. How many acorns do Adam and Ivan find in total?

FAMILY MATH Conceptual Understanding of Division

Dear Family,

Your student is exploring how multiplication connects to division. They represent real-world division situations with equal-groups models, arrays, and equations using the division symbol. Sometimes the total and the number of groups are known, and sometimes the total and the number in each group are known.

Share 10 crackers.

2 equal groups of 5 crackers

5 equal groups of 2 crackers

÷2054=

totalnumber in each row

Key Terms and Symbols divide division division symbol ÷

Mia puts 10 pencils into equal groups. She puts 2 pencils in each group. How many equal groups of pencils are there?

There are 5 equal groups.

number of rows

At-Home Activity

Everyday Division

Look for opportunities to practice division situations at home.

• While making snacks, invite your student to help share the food equally among those sharing the snack. For example, ask, “If we have 15 apple slices to share equally among 3 people, how many apple slices will each person get?”

• While playing with toy cars or building blocks, invite your student to make an array with the objects to match a division equation. For example, write 15 ÷ 3 = 5.  Together with your student, arrange 15 blocks into an array with 3 rows. Then have them explain where they see each part of the division equation in the array.

Name

Use the pictures to help you fill in the blanks.

1. There are 12 carrots in equal groups.

a. The total number is 12 .

b. The number in each group is 4 .

c. The number of equal groups is 3 .

I know there is a total of 12 carrots. I can draw circles to show the equal groups.

1 2 3

There are 3 equal groups. There are 4 carrots in each group.

2. There are 18 flowers.

a. Circle groups of 6 flowers.

b. There are 3 groups of 6

c. Circle two correct statements.

3 is the number of equal groups.

6 is the number of equal groups.

I count 6 flowers and circle them.

3 is the number in each group.

6 is the number in each group.

I continue to count and circle groups of 6 until all the flowers are circled.

6 is the number in each group.

2 3

1 4 5 6

I see that I have 3 groups.

1 2 3

So, 3 is the number of groups.

3. Circle the best unit and tool to use to measure the length of the alarm clock.

10:00

foot yard

12-inch ruler inch tile

I know I can measure inches with inch tiles, feet with a 12-inch ruler, and yards with a yardstick.

I can use benchmarks to help me determine which unit to measure with.

I know a paper clip is about 1 inch, a math book is about 1 foot, and a table is about 1 yard.

The alarm clock is smaller than a table and a math book, but it is larger than a paper clip. I can measure with inches.

I can measure the length of the alarm clock with any of the tools, but I will use inch tiles.

Name

Use the pictures to help you fill in the blanks.

1. There are 10 flowers in equal groups.

a. The total number is .

b. The number in each group is .

c. The number of equal groups is

2. There are 15 clovers.

a. Circle groups of 5 clovers.

b. There are groups of 5.

c. Circle two correct statements.

3 is the number in each group.

5 is the number in each group.

3 is the number of equal groups.

5 is the number of equal groups.

3. Circle the best unit and tool to use to measure the length of the bus.

Name

1. There are 18 pears.

They are in 3 equal groups.

How many pears are in each group?

a. What are you trying to find? Circle it. the number in each group the number of groups

b. Draw to show the pears equally shared in 3 groups.

c. Fill in the blanks to match your drawing.

The total is 18

The number in each group is 6 .

The number of groups is 3 .

There are 18 pears in 3 equal groups.

My drawing shows there are 6 pears in each group.

I draw 3 circles to represent the 3 groups. I show how to equally share the 18 pears by first drawing one dot in each group.

I keep drawing one dot in each group until I have equally shared 18 dots.

Another way to think about an equal-sharing problem is to use the word divide.

A problem that includes sharing equally is called a division problem.

REMEMBER

Use the Read–Draw–Write process to solve the problem.

2. Jayla throws a football 39 yards.

Deepa throws a football 12 fewer yards than Jayla.

How many total yards are the two footballs thrown?

Sample:

39 − 12 = 27

27 + 39 = 66

The two footballs are thrown 66 yards in total.

I read the problem. I read again.

As I reread, I think about what I can draw. I draw a tape diagram with two tapes.

I draw one tape to represent how far Jayla throws her football. I know Deepa throws her football 12 fewer yards than Jayla, so I draw a shorter tape to represent how far Deepa throws.

Jayla Deepa

?

39 yd 12 yd

I label the difference between the two tapes, which is 12 yards. I need to find how many total yards the footballs are thrown. I draw arms and a question mark to represent the unknown, the total of the two tapes.

I see that I need to add the distance Jayla throws and the distance Deepa throws to find the unknown.

When I look at the tape diagram, I see another unknown. I need to find how far Deepa throws her football before I can find the total.

The tape diagram shows me that I can subtract 12 from 39 to find Deepa’s distance. Now I can add to find the total.

Name

1. There are 20 plums.

They are in 4 equal groups.

How many are in each group?

a. What are you trying to find? Circle it. the number in each group the number of groups

b. Draw to show the plums equally shared in 4 groups.

c. Fill in the blanks to match your drawing.

The total is .

The number in each group is

The number of groups is .

2. There are 15 sticks.

a. Draw to show the sticks divided into 3 equal groups.

b. How many sticks are in each group?

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. The length of Pablo’s hallway rug is 91 centimeters. His bathroom rug is 60 centimeters shorter than the hallway rug. What is the total length of Pablo’s hallway rug and bathroom rug?

Name

Fill in the blanks to match the array.

1. There are 15 soccer balls in equal rows.

a. The number in each row is 3 .

b. The number of rows is 5 .

c. 15 total ÷ 3 = 5

number in each row number of rows

I know a row is a horizontal group. I see there are 3 balls in each row.

I can count the number of rows. There are 5 rows.

Now I can write a division equation with the division symbol. 15 ÷ 3 = 5

2. Liz puts 18 trophies on 3 shelves. She puts an equal number of trophies on each shelf. How many trophies does Liz put on each shelf?

a. Draw an array to represent the problem.

I can draw 3 lines to represent the shelves. I draw circles to represent the trophies.

b. Write a division equation to represent the problem.

18 ÷ 3 = 6

c Liz puts 6 trophies on each shelf.

I put one circle in each row. That’s 3

I write a division equation. I see that the 18 trophies are divided into 3 equal groups.

18 ÷ 3

I can see each group has 6 trophies.

18 ÷ 3 = 6

So, Liz puts 6 trophies on each shelf.

I keep putting circles in each row, one at a time, until I reach 18

3, 6, 9, 12, 15, 18

I can skip-count by 3 up to 18

REMEMBER

Complete each statement and write a related repeated addition equation.

3. Circle rows.

2 rows of 6 is 12 . 6 + 6 = 12

A row is a horizontal group. I circle all the acorns in each row.

Circle columns.

There are 2 rows. I count 6 acorns in each row.

I can repeatedly add the number in each row to show there are 12 acorns in all.

6 columns of 2 is 12 .

A column is a vertical group. I circle all the acorns in each column. 2 2 2 2 2 2

There are 6 columns. I count 2 acorns in each column.

I can repeatedly add the number in each column to show there are 12 acorns in all.

2 rows of 6 and 6 columns of 2 have the same total, which is 12

Name

Fill in the blanks to match the array.

1. There are 12 keys in equal rows.

a. The number in each row is

b. The number of rows is .

c. ÷ =

total number in each row number of rows

2. Carla hangs 10 pictures on the wall.

She hangs the pictures in 2 equal rows.

How many pictures does Carla put in each row?

a. Draw an array to represent the problem.

b. Write a division equation to represent the problem.

c. Carla puts pictures in each row.

REMEMBER

Complete each statement and write a related repeated addition equation.

3. Circle rows.

Circle columns.

4 rows of is .

5 columns of is

Name

Use the Read–Draw–Write process to solve each problem.

1. David puts 24 jars in a box. He puts the jars in 3 equal rows. How many jars does he put in each row?

24 ÷ 3 = 8

David puts 8 jars in each row.

I read the problem. I read again. As I reread, I think about what I can draw. I draw 3 lines to represent the 3 rows. I put one circle on each line. That is 3 circles.

I keep putting circles on each line until I reach 24 3, 6, 9, 12, 18, 15, 24 21,

Now that 24 jars are in 3 equal rows, I can see how many jars are in each row.

2. Oka puts 36 party favors into bags. She puts 4 party favors in each bag. How many bags does Oka use?

36 ÷ 4 = 9 Oka uses 9 party bags.

I read the problem. I read again. As I reread, I think about what I can draw. Because each bag holds 4 party favors, I draw groups of 4 until I get to the total, which is 36.

I circle each group of 4 and count the number of groups to find how many bags Oka uses.

I see from my drawing that there are 9 equal groups.

REMEMBER

Add. Show how you know.

3. 34 + 16 = 50

I can break apart addends and add like units. I decompose, or break apart, 34 into 30 and 4.

16 into

I add the ones: 4 +

Then I add the tens and ones together: 40 + 10 = 50.

Name

Use the Read–Draw–Write process to solve each problem.

1. Pablo and Casey play a game with 20 cards. They put the cards in 4 equal rows.

How many cards are in each row?

2. A farmer puts 15 pigs into pens. He puts 3 pigs in each pen.

How many pens does the farmer use?

REMEMBER

Add. Show how you know.

3. 22 + 68 =

FAMILY MATH Properties of Multiplication

Dear Family,

Your student is exploring strategies to multiply with large factors. They learn that they can rotate an array and skip-count either by rows or columns and the total stays the same. Another strategy involves breaking the array into two smaller, simpler multiplication problems and then adding the totals.

Key Terms and Symbols

break apart and distribute strategy commutative property of multiplication parentheses ( ) rotate

Rotating an array helps to show that the order of the factors can change without changing the product. This is called the commutative property of multiplication.

At-Home Activity

Tile Multiplication

When the factors are large or unfamiliar, breaking the array apart into smaller and more familiar multiplication facts can make the total easier to find. Students call this the break apart and distribute strategy.

If you have a wall or floor with square tiles, use chalk, masking tape, or another similar material to draw an outline around an array of tiles. With your student, discuss different strategies for counting the total number of tiles inside the array. Write down or say the multiplication equations to match. Then look at the array from another angle to notice other ways to count the tiles. Consider splitting the original array into smaller arrays to notice more strategies for finding the total number of tiles.

Instead of tiles, you could draw an array of squares outside with sidewalk chalk or create an array with square sticky notes to complete the activity.

Name

Fill in the blanks to match each array.

4 × 2 = 8

I see 4 rows of 2 bows, which is 8 bows total.

I know that 4 must be the unknown factor in the equation.

I see 2 rows of 4 bows, which is also 8 bows total.

I know that 2 must be the unknown factor in the equation.

There are 2 rows with 8  balls in each row.

I see there are 16 balls in all.

2 × 8 = 16

16

I can turn, or rotate, the array to show 8 rows with 2 balls in each row. The product, 16, stays the same. 8 ×

1.

2.

3. 2 × 8 = 16 8 × 2 =

2 × 4 = 8

4. a. Draw an array to show 2 × 5.

I can draw an array that has 2 rows with 5 objects in each row.

b. Explain how the array also shows 5 × 2

The array also shows 5 × 2 because when I rotate it, there are 5 rows of 2. I did not add or take away any shapes in the array. The product, or total, stayed the same.

I know that my array can be rotated to show 5 rows of 2

I notice both arrays have 10 circles.

I can change the order of the factors and have the same product.

This is how to show the commutative property of multiplication.

5. Miss Diaz measures the heights of her flowers. Use the table to create a line plot.

I use the information given and the headings in the table to help me write the title.

I look at the table. The first column tells me the heights that I need to label on my line plot.

I use the heights to label each tick mark. I draw slashes to show that I am skipping all the numbers from zero to our first height measurement.

The second column tells me how many flowers of each height there are.

I use an X to represent 1 flower on my line plot.

I put 3 Xs above 31.

I put 2 Xs above 33. I put 3 Xs above 34. I put 5  Xs above 36. I put 4 Xs above 38

Name

Fill in the blanks to match each array. 1.

4. a. Draw an array to show 2 × 3.

b. Explain how the array also shows 3 × 2.

REMEMBER

5. Mia records the lengths of the fish she catches. Use the table to create a line plot. Length of Fish (inches)

Title:

Length (inches)

1. Skip-count by fours. 4

I can whisper-count by twos to help me count by fours. I can say every other skip-count of twos in a slightly louder voice to help me skip-count by fours.

Complete the equations. 2.

I can use my skip-count from problem 1 to help me find the unknown.

I see that 3 fours is 12 , so 3 × 4 = 12 .

I use the commutative property of multiplication to help me find the unknown factor in the last two equations.

5. Draw to show why the statement in the box is true. 4 ×

4,8,12,16,20,24,28

I can draw an array with 4 rows of 7 objects. I can also think of my array as 7 columns with 4 objects in each column.

It’s the same array.

I can think of the rows as the number of groups and skip-count by sevens. 7 14 21 28

Or, I can think of the columns as the number of groups and skip-count by fours.

4, 8, 12, 16, 20, 24, 28

Either way, the array has 28 circles. So, I know that 4 × 7 = 7 × 4.

REMEMBER

Use the line plot to answer each question.

I find the number of flowers that are shorter than 36 centimeters by counting all the Xs that are above the numbers less than 36.

I see 3 Xs above 34, 2 Xs above 33, and 3 Xs above 31 .

3 + 2 + 3 = 8

There are 8 flowers shorter than 36 centimeters.

6. How many flowers are shorter than 36 centimeters? 8 flowers

7. What is the least frequent height of Miss Diaz’s flowers? 33 inches

8. How many total flowers does Miss Diaz have? 17 flowers

I find the least frequent flower height by finding the height with the least number of Xs. I only see 2 Xs above 33. The least frequent flower height is 33 inches.

To find the total number of flowers, I count all the Xs that are in the line plot. There are 17  Xs. So, Miss Diaz has 17 flowers.

REMEMBER

Use the line plot to answer each question.

9. How many fish are longer than 7 inches?

10. What is the most frequent length of fish Mia catches?

11. How many total fish does Mia catch?

Fill in the blanks to describe each array.

1.

The number bond shows me that 5 fours and 4 fours make 9 fours.

I can rewrite the equation with parentheses, which are symbols we use in an expression to show groups. They help us know what to do first.

I see 5 × 4 = 20.

I can skip-count by fours to find 4 × 4 4, 8, 12 , 16 4 × 4 = 16

I add the totals, 20  and 16, to show that 9 × 4 = 36

I know how to multiply by 5, so I shade 5 fours. Now the large array is decomposed into two smaller arrays. It shows that 5 fours and 3 fours make 8 fours.

I see 5  threes and 1  three is 6  threes I use this to complete the first equation.

( 5 × 3) + ( 1 × 3) = 6 × 3

I know 5 × 3 = 15 and 1 × 3 = 3, so I complete the second equation.

15 + 3 = 18

I add the totals, 15 and 3, to show that 6 × 3 = 18

I use my array to complete the equations.

The shaded array, 5 fours, can be written as 5 × 4, which is 20

The unshaded array, 3 fours, can be written as 3 × 4, which is 12

I add the totals of the two smaller arrays to find the total number of squares in the larger array.

20 + 12 = 32

threes1 three

6 threes

3. Shade the array to show two parts. Then fill in the blanks to describe the array.

5  fours + 3 fours = 8 fours

REMEMBER

Use the Read–Draw–Write process to solve the problem.

4. There are 3 groups of bananas.

There are 5 bananas in each group.

How many bananas are there in all?

5 + 5 + 5 = 15

3 × 5 = 15

There are 15 bananas in all.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw 3 circles to represent the groups of bananas.

I draw 5 dots in each circle to represent the bananas in each group.

I write a repeated addition equation to show how many bananas there are in all.

Fill in the blanks to describe each array.

1. 2 fours

5 fours 7 fours

+ = 5 fours2 fours7 fours (5 × 4) 7 × 4 (2 × 4)+=

2.

5 twos3 twos = 8 twos (5 × 2)(3 × 2) = 8 × 2 + + = 16

+

3.

5 fours4 fours = 9 fours

= 36

+

= 9 × 4 ( × 4) ( × 4)

Shade each array to show two parts. Then fill in the blanks to describe each array.

4.

5.

Use the Read–Draw–Write process to solve the problem.

6. There are 4 flowers.

There are 6 petals on each flower.

How many petals are there in all?

1. Use the array to fill in the blanks.

a. Skip-count the rows by 3 and the columns by 10.

b. 10 rows of 3 is 30 .

10 threes is 30 . 10 × 3 = 30

c. 3 columns of 10 is 30 . 3 tens is 30 3 × 10 = 30

d. Complete the equation to show how 10 threes and 3 tens are related. 10 × 3 = 3 × 10

Because 10 rows of 3 and 3 columns of 10 both equal 30, I can say 10 × 3 = 3 × 10

Complete the equations.

2 × 3 = 6

I can use my skip-count from problem 1 to help me find the unknown. 6

I see 2 threes is 6, so 2 × 3 = 6

3

I use the commutative property of multiplication to complete

× 2 = 6

I use the commutative property of multiplication to help me find the unknown factor.

5. Draw to show why 3 × 6 = 6 × 3.

Sample: 12,15,18

3,6,9,

6 12 18

I can draw an array with 3 rows of 6 objects.

6 12 18

I can also think of my array as 6 columns with 3 objects in each column.

12, 15, 18 6, 9, 3,

My array shows 3 rows of 6 equals 18 and 6  columns of 3 equals 18.

So, 3 × 6 = 6 × 3.

REMEMBER

Make pairs. Then circle whether the total number is even or odd.

6.

even / odd

There are 2 snowflakes in a pair.

I circle 5 groups of 2 I have 1 extra snowflake. There are 11 snowflakes in all.

A number is even if each object has a partner. There is 1 snowflake that does not have a partner.

Numbers that are not even are called odd numbers 11 is an odd number.

Name

1. Use the array to fill in the blanks.

a. Skip-count the rows by 3 and the columns by 5.

b. 5 rows of 3 is . 5 threes is . × =

c. 3 columns of 5 is .

3 fives is . × =

d. Complete the equation to show how 5 threes and 3 fives are related.

11. Draw to show why 4 × 3 = 3 × 4.

REMEMBER

Make pairs. Then circle whether the total number is even or odd.

12.

even / odd

Name

Fill in the blanks to describe the array.

1.

6 threes

6 threes = 5 threes + 1 three

6 × 3 = (5 × 3) + (1 × 3)

18 = 15 + 3

5 threes

1 three

The number bond shows that 6 threes can be decomposed into 5 threes and 1 three.

I can skip-count by threes to find 5 × 3

3, 6, 9, 12 , 15 5 × 3 = 15

I see from my skip-count that 1 × 3 = 3.

I can add the totals, 15 and 3, to show that 6 × 3 = 18.

This is called the break apart and distribute strategy.

2. Show two different ways to make 8 threes. Shade the arrays and complete the equations.

Sample:

8 threes = 5  threes +  3 threes

8 × 3 = ( 5 × 3) + ( 3 × 3) 24 = 15 + 9

8 threes = 4  threes + 4  threes

8 × 3 = ( 4 × 3) + ( 4 × 3) 24 = 12 + 12

I know how to multiply by 5, so I shade 5 threes. Now the array shows that 5 threes and 3 threes makes 8 threes.

I use the array to complete the equations. The shaded array of 5 threes can be written as 5 × 3, or 15.

The unshaded array of 3 threes can be written as 3 × 3, or 9.

I add the totals of the two smaller arrays to find the total number of squares in the larger array.

15 + 9 = 24

So, 8 × 3 = 24

I can also show 4 threes and 4 threes because that way I only have to find 4 × 3 = 12 I know 12 + 12 = 24.

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. There are 4 bags of limes. There are 5 limes in each bag.

How many limes are there in all?

5 + 5 + 5 + 5 = 20

There are 20 limes in all.

I read the problem. I read again. As I reread, I think about what I can draw. I draw 4 circles to represent the bags of limes.

I draw 5 dots in each circle to represent the number of limes in each bag.

I write a repeated addition equation to show how many limes there are in total.

Name

Fill in the blanks to describe the array.

1. 2 threes

5 threes

7 threes

7 threes = 5 threes + 2 threes

7 × 3 = (5 × 3) + (2 × 3)

21 = +

2. Show two different ways to make 7 threes. Shade the arrays and complete the equations.

a.

7 threes =  threes +  threes

7 × 3 = ( × 3) + ( × 3)

7 × 3 = +

7 × 3 =

b.

7 threes =  threes +  threes

7 × 3 = ( × 3) + ( × 3)

7 × 3 = +

7 × 3 =

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. There are 7 friends.

Each friend eats 3 jelly beans. How many jelly beans do they eat in all?

Two Interpretations of Division

Dear Family,

Your student continues to deepen their understanding of equal groups. They relate finding an unknown factor in multiplication to finding the quotient, the answer in a division problem. Drawing equal groups and arrays helps to represent the situation when finding either the size of each group or the number of groups. Tape diagrams can also help to identify what is known and what is unknown.

Eva puts flowers into vases. She has 8 flowers. She puts 2 flowers in each vase. How many vases have flowers?

Key Term quotient

12 apples are placed equally into 3 bags. How many apples are in each bag?

???

12 ÷ 3 = 12

equal groups modelarray model

The unknown in both equations is the number of groups.

12 apples are placed equally into bags. There are 3 apples in each bag. How many bags of apples are there?

3

This tape diagram shows that the total and number of groups are known, but the size of each group is unknown. 12

3 × = 12

This tape diagram shows that the total and the size of each group are known, but the number of groups is unknown.

8 ÷ 2 = 4 4 × 2 = 8

4 vases have flowers. 4 vases have flowers.

At-Home Activity

Two Types of Everyday Division

Look for opportunities to discuss different types of division in everyday life.

• Count the total number of socks in a drawer and ask your student how many pairs there are when there are 2 socks in each pair. Discuss why 2 is the size of the group in this situation.

• Select 9 shirts. Ask your student how many should go in each pile if you want to make 3 equal piles. Discuss why 3 is the number of groups in this situation.

Ask your student, “What equation can help you solve the problem?” For example, if there are 8 socks total and 2 socks in each pair, the division equation is 8 ÷ 2 = and the unknown factor equation is × 2 = 8.

Name

1. Oka sorts 15 toy cars into bins. Each bin holds 5 cars.

How many bins does Oka use?

a. Circle groups of 5 to show the cars in each bin.

There are many ways to make groups of 5

This is another way I can circle equal groups.

b. Complete the equations and statement.

3 × 5 = 15 15 ÷ 5 = 3

Oka uses 3 bins.

I know there are 5 cars in each group.

I need to find the number of groups Oka uses. There are 3 fives in 15, so 3 is the number of groups in both equations.

c. What do the unknowns in the equations represent? Circle the correct answer. the number of groups the size of each group

2. James gives 18 stickers to his friends. He gives 3 stickers to each friend.

How many friends get stickers?

a. Draw a picture to represent the problem.

Sample: 18

333 3 3 3

b. Complete the equations to find the unknown.

× 3 = 18 6

18 ÷ 3 = 6

c. Complete the solution statement. 6 friends get stickers.

3

I draw a tape diagram to represent the problem. I know the total is 18 and the size of each group is 3 18

I think about how many threes are in 18 to find the number of groups. I keep drawing groups of 3 until I get to 18

I know there are 6 threes in 18, so 6 is the number of groups.

When we divide, we call the answer the quotient

Once I find the quotient, 6, I can complete the solution statement.

REMEMBER

Add. Show how you know.

3. 31 + 23 + 19 + 14 = 87

Sample:

I can add like units to find the sum.

I decompose each number into tens and ones.

I add the ones.

I add the tens and ones.

Name

1. Amy has 12 pens. She gives 2 pens to each friend.

How many friends get pens?

a. Circle groups of 2 to show the pens each friend gets.

b. Complete the equations and statement.

× 2 = 12 12 ÷ 2 = friends get pens.

c. What do the unknowns in the equations represent? Circle the correct answer. the number of groups the size of each group

2. David puts 20 grapes into bowls. He puts 5 grapes in each bowl.

How many bowls does he use?

a. Draw a picture to represent the problem.

b. Complete the equations to find the unknown.

× 5 = 20

20 ÷ 5 =

c. Complete the solution statement.

David uses bowls.

REMEMBER

Add. Show how you know.

3. 21 + 16 + 33 + 12 =

4. 14 + 27 + 22 + 15 =

Name

1. Divide 12 birds into groups of 4.

How many groups of 4 are there?

× 4 = 12 3

I circle groups of 4 birds until all 12 birds are circled.

I see there are 3 groups of four.

12 ÷ 4 = 3

There are 3 groups of 4.

To help me solve, I can relate the situation to an unknown factor problem and think about how many fours are in 12

Use the Read–Draw–Write process to solve the problem.

2. Friends sort 24 note cards into piles. Each pile has 4 note cards. How many piles of note cards do the friends make?

24 ÷ 4 = 6

The friends make 6 piles of note cards. I read the problem. I read again.

As I reread, I think about what I can draw. I draw a tape diagram to show that the total is 24 and the size of each group is 4. The unknown is the number of groups. 24

4

I find the number of groups by asking myself how many fours are in 24 I skip-count by fours until I get to 24

4, 8, 12 , 16, 20, 24

I complete the tape diagram to show there are 6 fours in 24. 24

REMEMBER

Subtract. Use addition to check your work.

I see that 295 is close to the benchmark number 300 So, I decompose

I check my answer by using addition and an open number line.

I need to check whether 416 + 295 = 711

I start at 416 and add 300 to get 716. Then I subtract 5 to get 711

I know my answer is correct because 416 + 295 = 711

Name

1. 15 butterflies are divided into groups of 5

2. Divide 20 fish into groups of 10

How many groups of 5 are there?

How many tens are in 20?

× 5 = 15

15 ÷ 5 =

There are groups of 5

20 ÷ 10 =

Use the Read–Draw–Write process to solve the problem.

3. Pablo sorts 36 rocks into piles. Each pile has 4 rocks.

How many piles of rocks does he make?

× 10 = 20

REMEMBER

Subtract. Use addition to check your work.

4. 528 – 392 =

Name

1. 18 flowers are divided into 2 equal groups.

I see that there are 9 flowers in each group.

I know 2 × 9 = 18. I can use the multiplication fact to help me find 18 ÷ 2 =

How many flowers are in each group?

= 18 2 × 9

18 ÷ 2 = 9

There are 9 flowers in each group.

2. 15 bears are divided into 3 equal rows.

I can count the bears to find the total.

I see the total, 15, is divided into 3 equal rows.

There are 5 bears in each row.

= 15 × 53

How many bears are in each row?

15 ÷ 3 = 5

There are 5 bears in each row.

Use the Read–Draw–Write process to solve the problem.

3. 21 napkins are shared equally between 3 tables.

How many napkins are on each table?

21 ÷ 3 = 7

There are 7 napkins on each table.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram that has a total of 21 to represent the 21 napkins. I partition the tape diagram into 3 equal parts to represent the 3 tables, or groups.

To find the unknown, I divide 21 equally into 3 groups. I draw 1 dot in each group. That’s a total of 3 napkins. I draw another dot in each group and skip-count by threes until I get to 21

I see there are 7 dots in each group, and I counted by threes 7 times.

REMEMBER

Use the Read–Draw–Write process to solve the problem.

4. Deepa makes 42 hats. She makes 17 more hats than Eva. How many hats does Eva make?

42 17 = 25

Eva makes 25 hats.

I read the problem. I read again. As I reread, I think about what I can draw. I draw a tape and label it as 42 to represent the number of hats Deepa makes.

D 42

I know Deepa makes 17 more hats than Eva. I draw a shorter tape to represent the number of hats Eva makes. I label the difference 17.

17

E ?

D 42

I can subtract 17 from 42 to find the number of hats Eva makes. I use compensation to subtract the arrow way.

42 22 25 - 20 + 3

Name

1. 12 ladybugs are divided into 3 equal groups.

2. fish are divided into equal rows.

How many ladybugs are in each group?

How many fish are in each row?

= 12 3 × = 20 ×

12 ÷ 3 =

There are ladybugs in each group.

Use the Read–Draw–Write process to solve the problem.

3. 18 flowers are shared equally among 3 vases.

How many flowers are in each vase?

20 ÷ =

There are fish in each row.

REMEMBER

Use the Read–Draw–Write process to solve the problem.

4. Casey practices the piano for 62 minutes. She practices the piano 16 minutes more than Gabe. How many minutes does Gabe practice the piano?

Name

1. 4 friends equally share 36 jelly beans. How many jelly beans will each friend get?

a. Circle the tape diagram that represents the problem.

I know the total number of jelly beans, 36, and the number of groups, 4.

The tape diagram on the left represents the problem because it shows 36 partitioned into 4 equal parts (friends). The number in each group is unknown.

The tape diagram on the right represents a problem with a total of 36 and 4 in each group. The number of groups is unknown.

b. Complete the equation and statement.

36 ÷ 4 = 9

Each friend gets 9 jelly beans.

Because I know the total is 36 and the number of groups is 4, I can think: 4 groups of what number is 36? I can divide to find the unknown.

Use the Read–Draw–Write process to solve each problem.

2. Mia divides 55 crackers equally onto 5 trays. How many crackers are on each tray?

55 ÷ 5 = 11

There are 11 crackers on each tray.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram that has a total of 55 to represent the 55 crackers.

I partition the tape diagram into 5 equal parts to represent the 5 trays.

The unknown is the size of each group.

To help me solve, I can think: 5 groups of what number is 55?

I know 5 × 11 = 55, so I complete the tape diagram to show 5 groups of 11

55 11 11 11 11 11 55

3. Mr. Lopez has 40 paintbrushes for art class. He puts all of them on tables. Each table gets 5 paintbrushes. How many tables get paintbrushes?

40 ÷ 5 = 8 8 tables get paintbrushes.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram that has a total of 40

I know the size of the group is 5. The unknown is the number of groups.

To help me solve, I think about how many fives are in 40 I know 8 × 5 = 40, so I complete the tape diagram to show 8 groups of 5.

REMEMBER

Subtract. Show how you know.

4. 92 – 68 = 24

I notice that 68 is close to 70. I choose to use compensation to subtract. I show my thinking on an open number line.

I start at 92 and subtract 70.

But I need to subtract 68, not 70. So, I add back 2 .

70

Name

1. 15 rings are sorted into 3 equal groups. How many rings are in each group?

a. Circle the tape diagram that represents the problem.

b. Complete the equation and statement.

15 ÷ 3 =

There are rings in each group.

Use the Read–Draw–Write process to solve each problem.

2. 5 friends equally share 35 glow sticks.

How many glow sticks does each friend get?

3. The store has 70 books on shelves. There are 10 books on each shelf.

How many shelves have books?

REMEMBER

Subtract. Show how you know.

4. 64 37 =

FAMILY MATH Application of Multiplication and Division Concepts

Dear Family,

Your student is using the familiar break apart and distribute strategy to solve more challenging problems, including two-step word problems. They explore different ways of breaking apart problems into smaller or familiar parts. These parts can be simpler to work with and result in the same answer. In multiplication, breaking apart a factor into smaller parts to make simpler problems uses the associative and distributive properties. However, your student does not name these properties until grade 4. Instead, they use arrays and write equations to describe the strategies.

At-Home Activities

Fact Fluency Hide-and-Seek

9 fours = 10 fours − 1 four 9 × 4 = (10 × 4) − (1 × 4) 9 × 4 = 40 − 4 9 × 4 = 36

Hide known multiplication and division problems around your home using the factors 2, 3, 4, 5, and 10.

• Write multiplication and division problems on brightly colored paper. Examples of problems you could write for your student are 2 × 4 =

16 ÷ 2 =

5 × = 20, or × 3 = 15.

• Hide the facts in common places where your student can find them such as inside a cupboard or on the back of a door. Have your student solve each problem. Encourage your student to use a strategy, such as break apart and distribute, to solve more challenging problems.

• Consider asking your student to write similar problems for you to solve. Ask your student to check your work.

Problem Solving

• Look for opportunities to show how multiplying and dividing is used in daily life.

• “I am making our lunches for the week. I have 15 carrot sticks and I want to put 3 in each lunch. How many lunches can I make? What if I add 6 more carrot sticks?”

• “You get 32 pieces of candy at the Fall Carnival, but you are only allowed to eat 4 pieces each day. How many days will it take to eat all the candy?”

Name

Use the array to complete the equations.

1.

(5 × 3) = 15 (1 × 3) = 3

(5 × 3) = 15 (1 × 3) = 3

6 threes = 5 threes + 1 three

6 × 3 = ( 5 × 3) + ( 1 × 3)

6 × 3 = 15 + 3

6 × 3 = 18

The array shows 5 threes and 1 three. The shaded array, 5 threes, can be written as 5 × 3, or 15

The unshaded array, 1 three, can be written as 1 × 3, or 3

I add the totals of the two smaller arrays to find the total number of squares in the larger array.

I can also draw a number bond to represent how I broke apart 6 threes.

6 threes represents the total number of rows of three.

5 threes represents the number of shaded rows.

1 three represents the number of unshaded rows.

6 threes

5 threes

1 three

5 threes

1 three

Use the array to complete the equations.

9 fours = 10 fours 1 four

9 × 4 = (10 × 4) (1 × 4)

9 × 4 = 40 4

10 × 4 = 40

9 × 4 = 36

9 fours is 1 four less than 10 fours. So, I can think about 9 fours as 10 fours minus 1 four.

9 fours

10 fours

I know 10 fours is 40 and 1 four is 4

1 four

So, 9 × 4 is the same 40 4, which is 36

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. Mr. Davis has 41 tomatoes.

He uses some tomatoes to make sauce.

He has 19 tomatoes left.

How many tomatoes does Mr. Davis use?

Sample:

41 19 = 22

Mr. Davis uses 22 tomatoes.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram to represent the total number of tomatoes, 41

I know there are 19 tomatoes left, so I label one part as 19

41

Mr. Davis’s Sauce Left ? 19

I can subtract 19 from 41 to find the number of tomatoes Mr. Davis uses to make sauce.

Name

Use the array to complete the equations.

(5 × 4) = (3 × 4) =

8 fours = 5 fours + 3 fours

8 × 4 = (5 × 4) + (3 × 4)

8 × 4 = 20 +

8 × 4 =

1. Complete the number bond. Then, use it to complete the equations.

2.

7 fours

7 fours = 5 fours + fours

7 × 4 = (5 × 4) + ( × 4)

7 × 4 = 20 +

7 × 4 =

Use the array to complete the equations.

3.

5 fours 10 ×

9 fives = 10 fives − 1 f ive

9 × 5 = (10 × 5) (1 × 5)

9 × 5 = 50

9 × 5 =

REMEMBER

Use the Read–Draw–Write process to solve the problem.

4. There are 65 apples in a basket. Miss Diaz uses some apples to make pies. There are 27 apples left in the basket.

How many apples does Miss Diaz use to make pies?

Name

Complete the equations. Use each part of the array to help you divide.

1.

15 ÷ 3 = 2

21 ÷ 3 = 6 ÷ 3 =

5 7

There are 21 squares in the array. I can use the break apart and distribute strategy to find 21 ÷ 3

I can decompose the total into smaller parts. I know 5 threes is 15 and 2 threes is 6.

Divide by using the break apart and distribute strategy. Explain your thinking.

5 and 2 make 7. So, 21 ÷ 3 = 7 15

18 ÷ 3 = 5 + = 16 3

2. I broke apart 18 into 15 and 3 to make simpler problems.

15 ÷ 3 = 5 and 3 ÷ 3 = 1.

5 and 1 make 6. So, 18 ÷ 3 = 6

I know 3 is the unknown part of the number bond because 15 + 3 = 18. I divide each part of 18 by 3. 15 ÷ 3 = 5. 3 ÷ 3 = 1 .

Then I find the answer by adding the quotients, 5 and 1 .

REMEMBER

3. Write the name of the polygon.

I know that a polygon is a closed shape that has straight sides. A polygon has the same number of sides as the number of angles.

I can name a polygon by counting the number of sides.

hexagon quadrilateral triangle pentagon

quadrilateral pentagon hexagon triangle

A pentagon has 5 sides.

A hexagon has 6 sides.

A triangle has 3 sides.

A quadrilateral has 4 sides.

Name

Complete the equations. Use each part of the array to help you divide.

2. Use the arrays to help you complete the equations.

Divide by using the break apart and distribute strategy. Explain your thinking.

1.

3.

4.

5.

REMEMBER

6. Write the name of the polygon.

Name

Fill in the blanks to match the arrays.

1.

I see 3 arrays, so there are 3 groups.

Each array has 4 rows of 2 , which is represented as 4 × 2 .

I see 3 groups of 4 × 2 .

2. Draw a line to break apart the array into 2 equal groups. Fill in the blanks to match the array.

I see 2 groups of 4 × 5 .

2 × ( 4 × 5 )

I draw a line that breaks the array into 2 equal groups.

I could also draw a line to make 2 groups of 2 × 10

Each group has 4 rows of 5, which is represented as 4 × 5.

REMEMBER

3. Draw 2 different arrays. Write a related repeated addition equation to represent each array.

Sample: 14 square tiles

7 + 7 = 14 2

I have 14 square tiles.

I can make 2 rows with 7 square tiles in each row.

7 + 7 = 14

I can rotate the array to show 7 rows of 2 . 2 +

= 14

2 rows of 7 and 7 rows of 2 have the same total, 14

Name

Fill in the blanks to match the arrays.

1.

I see 3 groups of × .

3 × ( × )

I see groups of × . × ( × )

3. The array is broken apart into 2 equal groups. Fill in the blanks to match the array.

I see 2 groups of × .

2 × ( × )

4. Draw a line to break apart the array into 2 equal groups. Fill in the blanks to match the array.

I see 2 groups of × .

2.

REMEMBER

5. Draw 2 different arrays. Write a related repeated addition equation to represent each array.

15 square tiles

Name

Use the Read–Draw–Write process to solve each problem.

1. David buys 4 rose bushes and 1 bag of plant food. Each rose bush costs $6.

The bag of plant food costs $9

a. What is the total cost of the rose bushes?

6 × 4 = 24

The total cost of the rose bushes is $24.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram with 4 groups to represent the 4 rose bushes. I label each group with a 6 to show that each bush costs $6. 24

I can find the total cost of the rose bushes by multiplying 4 and 6

b. How much does David spend altogether? 24 + 9 = 33

David spends $33 altogether.

I draw a tape diagram to represent how much David spends altogether. 33 24 9

I add to find the total cost of the plant food and the rose bushes.

2. A gift shop divides 45 mugs equally onto 5 shelves.

a. How many mugs are on each shelf?

45 ÷ 5 = 9

There are 9 mugs on each shelf.

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw a tape diagram that has a total of 45 to represent the 45 mugs. I make 5 equal parts to represent the 5 shelves. 45

I know the total and the number of groups. I need to find the size of each group. I divide to find the number of mugs on each shelf.

b. What is the total number of mugs on 4 shelves?

4 × 9 = 36

The total number of mugs on 4 shelves is 36.

Now I know there are 9 mugs on each shelf. 45

9 9 9 9 9

I can use the same tape diagram to help me find how many mugs are on 4 shelves.

REMEMBER

3. Draw the array. Then fill in the blanks.

2 rows of seven

2 rows of seven is equal to 14

7 + 7 = 14

7 doubled is 14 .

Is 7 doubled even or not even? Even

I draw 1 row of 7. I double it by drawing 1 more row of 7

I now have 2 rows of 7 I know the sum of a doubles fact is even. 14 is even.

Name

Use the Read–Draw–Write process to solve each problem.

1. Amy buys 5 flashlights and 1 first aid kit.

Each flashlight costs $6

The first aid kit costs $12.

a. What is the total cost of the flashlights?

Flashlights

b. How much does Amy spend altogether?

2. A gardener spreads 24 seeds equally among 4 pots.

a. How many seeds are in each pot?

b. What is the total number of seeds in 3 pots?

REMEMBER

3. Draw the array. Then fill in the blanks.

2 columns of five

2 columns of five is equal to .

=

5 doubled is Is 5 doubled even or not even?

Name

Use the Read–Draw–Write process to solve each problem.

1. Robin earns $7 each week for walking his dog. He walks his dog for 4 weeks.

He gives $6 of his earnings to his younger brother.

a. How much money does Robin earn for walking his dog?

7 × 4 = 28

Robin earns $28 for walking his dog.

b. How much money does Robin have left after giving money to his brother?

28 6 = 22

Robin has $22 left.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram with 4 equal parts to represent the 4 weeks. I label each part 7 to represent how much money Robin earns each week.

The total is unknown. ?

7 7 7 7

I see 4 groups of 7. I can multiply 4 and 7 to find how much Robin earns for walking his dog.

I draw a tape diagram to represent the problem in part 1 (b).

I know one part is 6 and the total is 28. I need to find the unknown part. 28 6 22

To help me find how much money Robin has left, I can think: 6 and what number makes 28?

2. Eva buys 8 tickets for the school fair.

Each ticket costs $3.

She also spends $7 on food at the fair. How much money does Eva spend altogether?

3 × 8 = 24 24 + 7 = 31

Eva spends $31 altogether.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram to represent the 8 tickets by drawing 8 equal parts.

I know that each ticket costs $3. ?

My drawing shows that Eva spends $24 on tickets.

To find out how much Eva spends altogether, I can draw another tape diagram.

One part is the total she spends on tickets, 24, and the other part is 7, the amount she spends on food. ?

24 7

I can add the two parts to find the amount Eva spends altogether.

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. There are 4 ladybugs.

Each ladybug has 7 spots. How many spots are there in all?

Sample:

7 + 7 + 7 + 7 = 28

There are 28 spots in all.

I read the problem. I read again. As I reread, I think about what I can draw.

I draw a tape diagram with 4 equal parts to represent the 4 ladybugs.

I label each part 7 to represent the spots on each ladybug. The unknown is the total number of spots. I use a question mark to label the unknown.

I see 4 groups of 7

Name

Use the Read–Draw–Write process to solve each problem.

1. Pablo has 5 pages of trading cards in a book. Each page holds 9 cards.

a. How many trading cards does Pablo have?

b. Pablo gives 9 trading cards to his friends. How many does he have left?

2. Ray bakes 4 batches of blueberry muffins. Each batch has 10 blueberry muffins. He bakes an additional 6 apple muffins. How many muffins does he bake altogether?

REMEMBER

Use the Read–Draw–Write process to solve the problem.

3. Luke buys 2 packs of yogurt. Each pack has 8 yogurts. How many yogurts does Luke buy in all?

Acknowledgments

Kelly Alsup, Lisa Babcock, Cathy Caldwell, Mary Christensen-Cooper, Cheri DeBusk, Jill Diniz, Melissa Elias, Janice Fan, Scott Farrar, Krysta Gibbs, Julie Grove, Karen Hall, Eddie Hampton, Tiffany Hill, Robert Hollister, Rachel Hylton, Travis Jones, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Geoff Patterson, Victoria Peacock, Marlene Pineda, Elizabeth Re, Meri Robie-Craven, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Theresa Streeter, Mary Swanson, James Tanton, Julia Tessler, Saffron VanGalder, Jackie Wolford, Jim Wright, Jill Zintsmaster

Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

Credits

For a complete list of credits, visit http://eurmath.link/media-credits

MATH IS EVERYWHERE

Do you want to compare how fast you and your friends can run?

Or estimate how many bees are in a hive?

Or calculate your batting average?

Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars.

Fueled by your curiosity to understand the world, math will propel you down any path you choose.

Ready to get started? ISBN

Module 1

Multiplication and Division with Units of 2, 3, 4, 5, and 10

Module 2

Place Value Concepts Through Metric Measurement

Module 3

Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

Module 4

Multiplication and Area

Module 5

Fractions as Numbers

Module 6

Geometry, Measurement, and Data

What does this painting have to do with math?

Swiss-born artist Paul Klee was interested in using color to express emotion. Here he created a grid, or array, of 35 colorful squares arranged in 5 rows and 7 columns. We will learn how an array helps us understand a larger shape by looking at the smaller shapes inside. Learning more about arrays will help us notice patterns and structure—an important skill for multiplication and division.

On the cover

Farbtafel “qu 1,” 1930

Paul Klee, Swiss, 1879–1940

Pastel on paste paint on paper, mounted on cardboard

Kunstmuseum Basel, Basel, Switzerland

Paul Klee (1879–1940), Farbtafel “qu 1” (Colour Table “Qu 1” ), 1930, 71. Pastel on coloured paste on paper on cardboard, 37.3 x 46.8 cm. Kunstmuseum Basel, Kupferstichkabinett, Schenkung der KleeGesellschaft, Bern. © 2020 Artists Rights Society (ARS), New York.