Name Topic 1 Understand Multiplication and Division...

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NameHome-School Connection

Topic 1Understand Multiplication and Division of Whole NumbersTopic 1 Standards 3.OA.A.1, 3.OA.A.2, 3.OA.A.3, 3.OA.B.5

See the front of the Student’s Edition for complete standards.

Dear Family,

Your child is learning how to multiply. Help him or her think of multiplication as joining equal groups. For example, 5 × 2 is 5 groups of 2. So, 5 × 2 = 10.

Your child is also learning how to divide. Help him or her think of division as sharing equally. For example, 42 , 7 can be thought of as 42 crayons and 7 boxes. Each box has an equal number of crayons. There are 6 crayons in each box.

Do the activities below with your child to help him or her learn multiplication and division concepts and facts.

Multiplication Stories

Give your child a multiplication fact, such as 4 × 3. Have your child tell you a multiplication story for that fact. Sample story: Jake has 4 bags of apples. There are 3 apples in each bag. How many apples does Jake have in all? Repeat the activity with a different multiplication problem.

Division Stories

Give your child a division fact, such as 32 , 8. Have your child tell you a division story for that fact. Sample story: Sally has 32 pictures. She puts an equal number of pictures on 8 pages. How many pictures does Sally put on each page? Repeat the activity with a different division problem.

Observe Your ChildFocus on Mathematical Practice 8 Look for and express regularity in repeated reasoning.

Help your child become proficient with Mathematical Practice 8. Ask your child to explain the relationship of the factors in multiplication to the number of equal groups and the number in each group.


NombreDe la escuela al hogar

(en español)Tema 1

Multiplicación y división de números enterosEstándares del Tema 1 3.OA.A.1, 3.OA.A.2, 3.OA.A.3, 3.OA.B.5

Los estándares completos se encuentran en las páginas preliminares del Libro del estudiante.

Estimada familia:

Su niño(a) está aprendiendo a multiplicar. Ayúdelo a pensar en la multiplicación como la unión de grupos iguales. Por ejemplo, 5 × 2 es 5 grupos de 2. Por tanto, 5 × 2 = 10.

Su niño(a) también está aprendiendo a dividir. Ayúdelo(a) a pensar en la división como repartir equitativamente. Por ejemplo, 42 , 7 se puede pensar como 42 crayones y 7 cajas. Cada caja tiene la misma cantidad de crayones. Hay 6 crayones en cada caja.

Haga con su niño(a) las actividades de abajo para ayudarlo(a) a aprender los conceptos y las operaciones de multiplicación y división.

Cuentos sobre multiplicación

Dé a su niño(a) un problema de multiplicación, como 4 × 3. Pida a su niño(a) que le cuente un cuento sobre multiplicación para esa ecuación. Ejemplo de cuento: Jake tiene 4 bolsas de manzanas. Hay 3 manzanas en cada bolsa. ¿Cuántas manzanas tiene Jake en total? Repita la actividad con un problema de multiplicación diferente.

Cuentos sobre división

Dé a su niño(a) un problema de división, como 32 , 8. Pida a su niño(a) que le cuente un cuento sobre división para esa ecuación. Ejemplo de cuento: Sally tiene 32 fotos. Pone la misma cantidad de fotos en 8 páginas. ¿Cuántas fotos puso Sally en cada página? Repita la actividad con un problema de división diferente.

Observe a su niño(a)Enfoque en la Práctica matemática 8 Buscar y expresar uniformidad en los razonamientos repetidos.

Ayude a su niño(a) a adquirir competencia en la Práctica matemática 8. Pida a su niño(a) que explique la relación de los factores de multiplicación con el número de grupos iguales y el número en cada grupo.

Vocabulary


Name Reteach to Build Understanding

1-1

1. Equal groups are groups of objects that contain the same number of items.

There are 2 equal groups of counters.

2. Multiplication is an operation that gives the total number when you join equal groups.

2 × = 6

3. There are boxes.

Each box has toys.

4. Write an addition equation to represent the total number of toys in the boxes.

+ + =

5. Write a multiplication equation to represent the total number of toys in the boxes.

× =

6. Write an addition equation and a multiplication equation to represent the total number.

Addition equation:

Multiplication equation:

On the Back!

7. Use the picture to describe the equal groups. Write an addition sentence and a multiplication sentence.

?

4 4 4 4 4

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Share your thinking while you work.

PartnerTalk

Toss and Talk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3Center Game ★

Play again!

If you have more time

How to Win

You win if you are the first to get four connected rectangles, like:

Toss Explain how to find the total.Find the total.

2 2 times 3

3 5 × 2

4 5 groups of 3

5 8 × 3

6 6 times 3

7 9 groups of 3

8

9 7 groups of 3

10

11 6 times 5

12 1 × 3

Get Started or

Get 10 squares in one color and 10 in another color. Get two number cubes. Take turns with another player or team. Talk about math as you play!

At Your Turn

Toss two number cubes. Add the dots. Find your toss below.Follow the directions. Explain your thinking. Cover the answer. If the answer is taken, lose your turn. Have fun!

6 9 24 12

18 15 21 3

24 27 30 10

12 21 18 27

1•1


PartnerTalk

Toss and Talk

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3Center Game ★★

Play again!


How to Win


Toss Match each product with its factors. Explain how to find a match.

2 The product is 6.

3 The product is 30.

4 The product is 9.









Get Started or


At Your Turn


8 times 3 7 groups of 6 3 × 7 6 × 5

3 × 9 3 groups of 3 6 times 3 6 times 7

3 × 8 2 × 3 5 groups of 3 3 × 6

7 groups of 3 2 times 5 9 groups of 3 1 × 3

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Vocabulary

0 1 2 3 4 5 6 8 10 12 147 9 11 13 15

0 1 2 3 4 5 6 7 8 9 10 11 141312 15 16 17 18 19 20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15



1-2

1. A number line is a line divided into equal units and numbered in order. You can show skip counting on a number line.

Each arrow represents one jump.

How many jumps are represented on the number line?

The number line models skip counting by .

2. Kathy puts 2 plums in each of 5 lunch bags. How many plums does Kathy use?

Number of jumps: 5 Number in each jump:

5 × = Kathy uses plums.

3. Emilio has 4 stacks of pennies. Each stack has 4 pennies. How many pennies does Emilio have? Use the number line to solve.

Number of jumps: Number in each jump:

× = Emilio has pennies.

On the Back!

4. Rory gives 3 strawberries to each of 6 friends. How many strawberries does he give away? Use a number line to solve.

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Name Math and Science Activity1-2

Butterflies in Flight

Did You Know? Monarch butterflies fly south for the winter. In the fall, daylight becomes shorter in northern parts of Canada and the United States. That is when the butterflies fly to warmer climates. Many monarchs fly to the forests of Mexico and form large groups.

El Rosario Butterfly Sanctuary in Mexico is a winter home for monarchs. While visiting the sanctuary, Ana saw 3 butterflies on each of 5 leaves.

➊ Draw a picture to model the total number of butterflies Ana saw.

➋ Use the number line to show the total number of butterflies Ana saw.

➌ Write a multiplication equation to show the butterflies Ana saw.

➍ Extension Ana saw 2 monarch butterflies on each of 3 leaves. Each monarch butterfly has 2 wings. How many wings did Ana see? Show how to find the answer using the number lines below.

Fall Journey of Monarch Butterflies

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

Total butterflies

1 2 3 4 5 6 7 8 9 10 0

Total wings

1 2 3 4 5 6 7 8 9 10 11 12

1•2Math and Science Activity

Vocabulary



1-3

1. An array shows objects in equal rows and columns. The triangles are in an array.

There are rows in this array.

There are triangles in each row.

2. The stickers are in an array.

There are rows.

There are stickers in each row.

3. Use addition to find the total number of stickers in the array.

3 + 3 + 3 + 3 + 3 + 3 =

4. Multiplication can also be used to find the total number of stickers in the array. Multiply the number of rows by the number of stickers in each row.

6 × 3 =

5. Write an addition equation and a multiplication equation for the array of cans.

Addition equation:

Multiplication equation:

On the Back!

6. Write this addition problem on the back: 4 + 4 + 4 + 4 + 4. Draw an array and write a multiplication equation for the array.

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PartnerTalk

2 3 4 5 6

Teamwork


Get Started Get 40 squares.Put in a bag.

Repeat for Each Round

Pick a tile. Fill the tile space on the right.Display that many squares in one row.Ask your partner to: a. Pick another tile and fill the first tile space.

b. Display your row that number of times.

times

Build your array here.

How many squares do you have in all?


Put the tiles back in the bag.Make a new array every time you choose two tiles.

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PartnerTalk

2 3 4 5 6 7 8 9

2 3 4 5 6

Teamwork


Get Started or

Get one paper clip, 40 squares, and .

Repeat for Each Round

Choose a number. Mark it with a paper clip.Build an array with that number of squares.Ask your partner to display tiles in the tile spaces below to show what you did.


Choose two tiles from or . Fill both spaces.Make an array. What do you have to do to your array if you change the order of the numbers?

Choose a number.

40 2415

35 3016

12 2818

21 1420

Build an array with that number of squares.

times

1•3

Vocabulary

Array A Array B



1-4

1. The Commutative (Order) Property of Multiplication states that numbers can be multiplied in any order and the product is the same.

Write the multiplication equation represented by each array.

Array A:

Array B:

2. Look at the top array of muffins. Complete the sentences.

The muffins are in rows.

There are muffins in each row.

3. Complete the multiplication equation to find the total number of muffins in the top array.

5 × =

4. Look at the bottom array of muffins. Complete the sentences.

The muffins are in rows.

There are muffins in each row.

5. Complete the multiplication equation to find the total number of muffins in the bottom array.

3 × =

On the Back!

6. Draw an array to show 7 × 4 and an array to show 4 × 7. Write each multiplication equation.

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Vocabulary



1-5

1. Division is an operation that tells how many equal groups there are or how many are in each group.

There are 18 counters. They have been put into 3 equal groups. How many counters are in each group?

The counters have been put into equal groups.

There are counters in each group.

So, 18 , 3 = .

2. There are 24 medals to give to 4 teams. Each team receives the same number of medals. How many medals does each team receive?

Use the bar diagram to solve.

medals

4 teams

? medals for each team

Total numberof medals

So, 24 , 4 = .

On the Back!

3. Mrs. Schultz has 36 drumsticks to give to 9 drummers. Each drummer will receive the same number of drumsticks. How many drumsticks will each drummer receive? Use the bar diagram to solve.

36

? ? ? ? ? ? ? ? ?

36 drumsticks

? drumsticks for each drummer

9 drummers

R 1•5


PartnerTalk

Toss and Talk


Play again!


How to Win


TossLook at the number of things in the large box. How many can you put in each small box if

you make equal groups?

2 15 stuffed animals?

3 36 toys?

4 10 shapes?

5 12 shells?

6 18 peaches?

7 16 miniature cars?

8 36 pens?

9 15 oranges?

10 12 eggs?

11 18 markers?

12 10 apples?

Get Started or


At Your Turn


3 5 4 3

4 2 6 2

6 4 5 4

3 3 2 9

1•5


PartnerTalk

Toss and Talk


Play again!


How to Win


Toss Explain how to solve by sharing equally. Use paper and a pencil to draw a picture.

2 16 apples, 4 bagsHow many apples in each bag?

3 10 oranges, 2 bagsHow many oranges in each bag?

418 points, 2 teams

How many points for each team if the teams are tied?

5 $15.00, 3 peopleHow many dollars for each person?

6 12 people, 2 carsHow many people in each car?

736 peaches, 4 basketsHow many peaches in

each basket?

8 16 chairs, 2 rowsHow many chairs in each row?

9 1 dozen eggs, 2 rowsHow many eggs in each row?

10 12 eggs, 4 omeletsHow many eggs in each omelet?

11 12 roses, 3 vasesHow many roses in each vase?

12 18 pictures, 6 pagesHow many pictures on each page?

Get Started or


At Your Turn


3 9 6 8

6 4 9 5

5 3 6 5

8 9 6 4

1•5

Vocabulary



1-6

1. When dividing, you can use repeated subtraction to find the number of equal groups when you know the number in each group.

Jason has 12 plums. He puts 3 plums in each bowl. How many bowls does Jason fill?

There are plums in each equal group.

2. Use repeated subtraction to find the number of bowls Jason fills.

12 - 3 = 9

9 - 3 =

6 - 3 =

3 - 3 =

Stop when you reach 0.

You subtract 3 times.

3. Write a division equation to represent the number of bowls Jason fills.

12 , 3 =

Jason can fill bowls with plums each.

4. Use repeated subtraction to find how many groups of 6 are in 24.

24 - 6 = 18

18 - 6 =

- =

- =

Stop when you reach .

There are groups of in 24.

On the Back!

5. Leah has 42 raisins. There are 6 raisins in each salad. How many salads are there? Find 42 , 6. Show the steps you used.

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Color Number of Fish

Gray 20

Orange 24

Orange/Black 32

Silver 15


Name Math and Science Activity1-6

Fish School

Did You Know? Some fish travel in large groups called schools. Fish form schools for protection from predators. They form schools because it makes it easier to find food. Schooling also increases the length of time a fish can swim. Some schools can contain as many as one million fish!

Darren volunteers at a pet store. He puts an equal number of fish in each tank.

➊ Darren puts all of the gray fish in 4 different tanks. Write subtraction equations to find how many fish Darren puts in each tank.

➋ Darren wrote these subtraction equations to find the number of silver fish to put in each tank. Write a division equation Darren could use to represent the same problem.

➌ Darren placed all of the orange/black fish in 8 different tanks. Draw a picture to represent how the fish were shared equally among the tanks.

➍ Extension Darren does not have enough tanks for each color of fish. He decides to combine the gray fish and the silver fish. There are an equal number of fish in each of 7 tanks. How many fish are in each tank? Show your answer using a division equation and subtraction equations.

15 - 3 = 1212 - 3 = 9 9 - 3 = 6 6 - 3 = 3 3 - 3 = 0

1•6Math and Science Activity

Vocabulary

Painters Rooms



1-7

1. Jonas has 20 trading cards that he shares equally among himself and three friends. You can use an array to find the number of cards each person gets.

Use counters to make an array to represent the trading cards.

Separate the array into equal groups to represent the number of equal shares.

There are counters in each equal share.

Each person gets trading cards.

2. Sometimes it is appropriate to use more than one tool to solve a problem.

Twelve painters are working in equal groups to paint the rooms of a hotel. There are 2 painters in each group. Each group must paint 3 rooms. How many rooms are being painted?

Let each square represent 1 painter. Draw 12 squares separated into groups of 2 to show the number of equal groups.

Let each circle represent 1 room. Draw 3 circles next to each group of 2 painters.

There are circles.

The painters painted rooms.

On the Back!

3. Freda saved $4 each week for 8 weeks to donate. She donates the same amount to 2 charities. How much will Freda donate to each charity? Choose a tool to solve the problem. Explain why you chose that tool. Solve the problem.

R 1•7

Name Topic 1 Understand Multiplication and Division...

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