splash screen chapter 4 multiplication concepts and facts click the mouse or press the space bar to...

Chapter 4Multiplication Concepts and Facts

Click the mouse or press the space bar to continue.

Chapter 4Multiplication Concepts and Facts

Click the mouse or press the space bar to continue.

Lesson 4-1 Multiplication as Repeated Addition

Lesson 4-2 Arrays and Multiplication

Lesson 4-3 Multiply by 2


Lesson 4-5 Problem-Solving Skill: Extra or Missing Information



Lesson 4-8 Problem-Solving Investigation: Choose a Strategy

Lesson 4-9 Multiply by 0 and 1

44Multiplication Concepts and Facts

Five-Minute Check (over Chapter 3)

Main Idea and Vocabulary

California Standards

Example 1: Real-World Example


4-14-1 Multiplication as Repeated Addition

(over Chapter 3)

A. +

B. –

Use + or – to make the number sentence true.

125 75 = 250 – 50


(over Chapter 3)


300 – 10 = 250 40

A. +

B. –


(over Chapter 3)


562 – 42 > 512 30

A. –

B. +


(over Chapter 3)


600 50 < 400 + 240

A. +

B. –



• I will relate multiplication and addition.

• multiply

• factor

• product


Standard 3NS2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.

Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

Find how many are in 7 equal groups of 3.

For Alejo’s party, his mother made 7 cupcakes. There were 3 walnuts on top of each cupcake. How many walnuts were there in all?



One Way: Counters

There are 7 groups. There are 3 counters in each group. This is a total of 21 counters.


Another Way: Repeated Addition

Write an addition sentence to show equal groups.

3 + 3 + 3 + 3 + 3 + 3 + 3 = 21

Answer: So, 7 equal groups of 3 are 21. There were 21 walnuts in all.


A. 24

B. 18

C. 10

D. 16

Jamie made ants on a log for a snack. She had 6 pieces of celery and put 4 raisins on each piece. How many raisins in all?

Mongo drew 6 pentagons. A pentagon has 5 sides. How many sides did he draw?


Find how many are in 6 equal groups of 5.


One Way: Repeated Addition

5 + 5 + 5 + 5 + 5 + 5 = 30


Another Way: Multiplication Sentence

× =

number of pentagons (groups)

6factor

number ofof sides

5factor

total

30product

Answer: So, there is a total of 30 sides.


Pam drew 5 octagons. An octagon has 8 sides. How many sides did she draw?

A. 35 sides

B. 45 sides

C. 40 sides

D. 13 sides

Five-Minute Check (over Lesson 4-1)



Key Concept: Commutative Property

Example 1: Use an Array

Example 2: Use an Array


4-24-2 Arrays and Multiplication

(over Lesson 4-1)

A. 10

B. 25

C. 20

D. 15

Multiply. Use repeated addition.

5 × 3


(over Lesson 4-1)

A. 15

B. 10

C. 25

D. 30


3 × 5


(over Lesson 4-1)

A. 16

B. 24

C. 10

D. 12


4 × 6


(over Lesson 4-1)

A. 24

B. 10

C. 12

D. 26


6 × 4


(over Lesson 4-1)

A. 8

B. 12

C. 16

D. 1


4 × 4



• I will use arrays to multiply.

• array

• Commutative Property of Multiplication


Standard 3AF1.5 Recognize and use the Commutative and Associative Properties of Multiplication (e.g., if 5 × 7 = 35, then what is 7 × 5? and if 5 × 7 × 3 = 105, then what is 7 × 3 × 5?).


Sue’s mom made cereal bars for her class. She arranged them in 3 rows of 7. How many cereal bars did she make?

To find the total number of cereal bars, you can use addition or multiplication.

One Way: Add Another Way: Multiply

7 + 7 + 7 = 21

3 × 7 = 21

Answer: So, 3 equal groups of 7 cereal bars is 21 in all.


A. 12

B. 24

C. 36

D. 32

Jenny’s sister made brownies for her scout troop. She arranged them in 4 rows of 8. How many brownies did she make?

Donato bought a carton of eggs that had 3 rows of 6 eggs. How many eggs were in the carton?

To find the total number in the array of eggs, you can write a multiplication sentence.

Answer: So, 3 rows of 6 eggs is 18 eggs.


3 × 6 = 18


A. 7 pieces

B. 12 pieces

C. 14 pieces

D. 15 pieces

Anne Marie bought a box of chocolates. They were in 3 rows of 4. How many pieces of chocolate were in the box?

In The Jam Shop, Mrs. Hessle arranged jars of jam in 8 rows with 4 jars in each row. She then decided she could display more jars of jam if she arranged 4 rows with 8 in each row. Was Mrs. Hessle correct? Explain.



rows

8 ×

number in each row

4 =

total

32


rows

4 ×

number in each row

8 =

total

32

Answer: Both arrangements show 32 jars of jam. Mrs. Hessle was not correct.


In the candle shop, Mr. Montoya arranged the candles in 7 rows with 3 jars in each row. Choose another way he could display them to show the same amount of candles.

A. 2 rows of 12 jars

B. 4 rows of 5 jars

C. 3 rows of 7 jars

D. 5 rows of 5 jars


Main Idea


Example 1: Multiply by 2

Example 2: Use Skip Counting

4-34-3 Multiply by 2

(over Lesson 4-2)

A. 6

B. 4

C. 12

D. 2

ALGEBRA Use the Commutative Property of Multiplication to find the missing number.

6 × 2 = 122 × = 12


A. 3

B. 4

C. 21

D. 7

ALGEBRA Use the Commutative Property ofMultiplication to find the missing number.

3 × 7 = 21 × 3 = 21

(over Lesson 4-2)


A. 4

B. 5

C. 20

D. 9

ALGEBRA Use the Commutative Property ofMultiplication to find the missing number.

4 × 5 = 205 × 4 =

(over Lesson 4-2)



• I will multiply by 2.

The students in Ms. Dennis’s class work in 2 groups of 6. How many students are there in all?

You need to find 2 groups of 6 or 2 × 6.


One Way: Draw a Picture


Draw 2 groups of 6.

6 + 6 or 12

Another Way: Use an Array


Show an array with 2 rows and 6 columns.

2 rows of 6 = 6 + 6 or 12

Answer: So there are 2 × 6 or 12 students in all.


A. 20 players

B. 22 players

C. 24 players

D. 30 players

There were 2 teams of 10 players in the soccer finals. How many players were there in all?

Mr. Murphy drove 2 miles round trip to work every day. How many miles did he drive in a five-day work week?

There are 5 days. Each day he drives 2 miles. To find how many miles he drives altogether, find 2 × 5.


Count 2 jumps of 5.


Answer: So, Mr. Murphy drives 2 × 5, or 10 miles in a work week.


A. 2 miles

B. 3 miles

C. 4 miles

D. 6 miles

Mrs. Ankrum drove 2 miles round trip to work every day. How many miles did she drive in a 3-day work week?


Main Idea



Example 2: Use a Number Sentence

Example 3: Double a Known Fact


(over Lesson 4-3)

A. 10

B. 20

C. 7

D. 12

Multiply 2 × 5.


A. 16

B. 10

C. 18

D. 6

Multiply 8 × 2.

(over Lesson 4-3)


A. 16

B. 5

C. 14

D. 12

Multiply 2 × 7.

(over Lesson 4-3)


A. 11

B. 13

C. 18

D. 20

Multiply 9 × 2.

(over Lesson 4-3)


There were 6 cars in the parking lot. How many tires were on the 6 cars?




One Way: Repeated Addition

Use repeated addition to find 6 × 4.

4 + 4 + 4 + 4 + 4 + 4 = 24


Another Way: Skip Count

Count 6 jumps of 4.

Answer: So, there are 6 × 4 or 24 wheels in all.

6 jumps of 4 is 24.


A. 49 tires

B. 28 tires

C. 30 tires

D. 35 tires

There were 7 minivans in the school parking lot. How many tires were on the 7 minivans?

There are 4 tomatoes on each tomato plant in Chee’s garden. There are 7 plants. How many tomatoes are there in all?

Answer: So, there are 28 tomatoes.


× =

number of groups

7

number ineach group

4

total

28


A. 15 cows

B. 16 cows

C. 20 cows

D. 25 cows

There are 5 cows in each field on Mario’s farm. There are 4 fields. How many cows in all?

Apples are packed in a box in 4 rows. Each row has 8 apples. How many apples are in the box?

You need to find 4 × 8.


4 is double of 2. So, 4 × 8 is double 2 × 8.


4 × 8 = 2 × 8 + 2 × 8

Answer: So, 4 × 8 = 32. There are 32 apples in the box.

16 + 16 = 32


A. 10 pineapples

B. 28 pineapples

C. 24 pineapples

D. 40 pineapples

Pineapples are packed in a carton in 4 rows. Each row has 6 pineapples. How many pineapples are in the carton?


Main Idea


Example 1: Problem-Solving Skill

4-54-5 Problem-Solving Skill: Extra or Missing Information

(over Lesson 4-4)

A. 9

B. 1

C. 19

D. 20

Multiply 4 × 5.


A. 32

B. 12

C. 24

D. 42

Multiply 8 × 4.

(over Lesson 4-4)


A. 24

B. 11

C. 21

D. 28

Multiply 7 × 4.

(over Lesson 4-4)


A. 10

B. 24

C. 12

D. 28

Multiply 4 × 6.

(over Lesson 4-4)



• I will decide if there is extra or missing information.


Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

My school’s hayride will start at 6:00 P.M. There are 4 wagons that hold 9 children each. Half of the children going are girls. What is the total number of children that can ride on the 4 wagons?


Understand

What facts do you know?

• The hayride starts at 6:00 P.M.

• There are 4 wagons that hold 9 children.

• Half of the children are girls.

What do you need to find?

• Find the number of children that can ride on the 4 wagons.


Plan

Decide what facts are important to solve the question.


• the number of wagons

• the number of children each wagon holds

Solve

To find the total number, multiply the number of wagons by the number of children each wagon holds.

Answer: So, 36 children can ride on the hay wagons.


4 × 9 = 36

4 × 9 =

Check

Look back at the problem. Since 9 + 9 + 9 + 9 = 36, you know the answer is correct.



Main Idea



Example 2: Skip Count



(over Lesson 4-5)

A. 15

B. 9

C. You need to know how tall Kari is.

D. 32

Solve. If there is missing information, tell whatfacts you need to solve the problem. Kari is 12 years old. Her brother is 3 years older and is 52 inches tall. How old is Kari’s brother?


A. $21

B. None

C. $3

D. You need to know how much money he gave to the clerk.

Solve. If there is missing information, tell whatfacts you need to solve the problem. Filipe spent $23 at the store. How much change did he receive?

(over Lesson 4-5)


A farmer has a pumpkin patch with 8 rows. Each row has 5 pumpkins. How many pumpkins does the farmer have?

You need to find 8 × 5.



One Way: Draw a Picture

Use repeated addition.5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40


Another Way: Use an Array

8 rows of 5 = 8 × 5 or 40

Answer: So, 8 × 5 = 40 pumpkins.


A. 28 curlers

B. 35 curlers

C. 40 curlers

D. 42 curlers

Laurie has a set of curlers that has 5 rows. Each row has 7 curlers. How many curlers does Laurie have?

There are 4 bracelets with 5 beads on each bracelet. How many beads in all?



Answer: So, 4 × 5 = 20 beads.


A. 25 charms

B. 16 charms

C. 24 charms

D. 11 charms

There are 3 necklaces with 8 charms on each necklace. How many charms in all?


Lila has 9 nickels. How much money does she have?

You know that a nickel is 5¢. Use a multiplication sentence to find 9 × 5¢.

Answer: So, Lila has 45¢.

× =

number of groups

9

number ineach group

5¢

× =9 5¢ 45¢


A. 45 cents

B. 40 cents

C. 38 cents

D. 58 cents

Joy has 8 nickels. How much money does she have?


Main Idea


Example 1: Skip Count

Example 2: Double a Known Fact



(over Lesson 4-6)

A. 14

B. 24

C. 45

D. 4

Multiply 5 × 9.


(over Lesson 4-6)

A. 2

B. 13

C. 15

D. 8

Multiply 3 × 5.


(over Lesson 4-6)

A. 30

B. 11

C. 13

D. 9

Multiply 6 × 5.


(over Lesson 4-6)

A. 40

B. 13

C. 44

D. 38

Multiply 5 × 8.


Yago and his two sisters made their hand prints on a poster. How many fingers were on the poster?


Find 3 × 10.

Count 3 jumps of 10.

Answer: So, 3 × 10 = 30 fingers.


A. 20 toes

B. 30 toes

C. 10 toes

D. 15 toes

Joe and his friend made their footprints on the sidewalk. How many toes were on the sidewalk?

Roberto found 7 dimes in his pocket. How much money did he find?

You need to find 7 × 10¢.


10 is the double of 5. So, 7 × 10¢ is double 7 × 5¢.

7 × 10¢ = 7 × 5¢ + 7 × 5¢


= 35¢ + 35¢

= 70¢

Answer: So, 7 × 10¢ = 70¢.


A. 8 cents

B. 80 cents

C. 800 cents

D. 18 cents

Gus found a bag with 8 dimes in it. How much money did he find?

Pam sold 5 tickets for the school play. Each ticket cost $10. How much money did Pam receive for the tickets?


To solve the problem, you need to multiply 5 by $10.

5 × $10 = $50

Answer: So, Pam received $50 for the tickets.

5 × $10 =


The model shows that 5 × 10 = 50.

Check


A. $16

B. $50

C. $60

D. $40

Conchita bought 6 boxes of clay from the art supply store for $10 each. How much money did she spend?


Main Idea


Example 1: Problem-Solving Investigation

4-84-8 Problem-Solving Investigation: Choose a Strategy

(over Lesson 4-7)

A. 13

B. 30

C. 7

D. 300

Multiply 3 × 10.


(over Lesson 4-7)

A. 18

B. 80

C. 2

D. 88

Multiply 8 × 10.


(over Lesson 4-7)

A. 0

B. 10

C. 100

D. 1

Multiply 10 × 0.


(over Lesson 4-7)

A. 20

B. 12

C. 10

D. 200

Multiply 10 × 2.


(over Lesson 4-7)

A. 9

B. 19

C. 0

D. 90

Multiply 9 × 10.



• I will choose the best strategy to solve a problem.


Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

DENZELL: Our third grade class will make 6 holiday baskets to give away. We will fill each basket with 7 food items.

YOUR MISSION: Find out how many items are needed to fill the food baskets.


Understand

What facts do you know?

• You know the class will make 6 baskets.

• You also know they will fill each one with 7 items.

What do you need to find?

• You need to find out the total number of food items needed.


Plan

You can use the draw a picture strategy to solve this math problem.


Solve


Draw a picture to represent the situation.

The picture shows that 6 × 7 = 42.

Answer: So, the third grade class needs 42 food items to fill the baskets.


Check

Look back at the problem. Check by using repeated addition. 7 + 7 + 7 + 7 + 7 + 7 = 42. So you know the answer is correct and reasonable.




Key Concept: Multiplication Properties

Example 1: Use Properties to Multiply

4-94-9 Multiplying by 0 and 1

(over Lesson 4-8)

Use any strategy to solve. Marion bought 4 lbs of apples at $2 a pound, 2 lbs of tomatoes at $3 a pound, and lettuce at $1.50. How much change did she receive from a $20 bill?

A. $0.50

B. $1.00

C. $4.00

D. $4.50



• I will multiply by 0 and 1.

• Zero Property of Multiplication

• Identity Property of Multiplication


Standard 3NS2.6 Understand the special properties of 0 and 1 in multiplication and division.

8 × 1 = 8

Find 8 × 1. Tell what property you used.


Answer: The product is 8. Identity Property of Multiplication.


A. 9; Identity Property of Multiplication

B. 10; Associative Property

C. 10; Identity Property of Multiplication

D. 9; Associative Property

Find 9 × 1. Which property did you use?

splash screen chapter 4 multiplication concepts and facts click the mouse or press the space bar to...

Documents