Splash Screen Chapter 6 Division Concepts and Facts Click the mouse or press the space bar to...

Chapter 6Division Concepts and Facts

Click the mouse or press the space bar to continue.

Chapter 6Division Concepts and Facts

Click the mouse or press the space bar to continue.

http://ca.gr3math.com/

Lesson 6-1 Relate Division to Subtraction

Lesson 6-2 Relate Multiplication to Division

Lesson 6-3 Problem-Solving Strategy: Choose an Operation

Lesson 6-4 Divide by 2


Lesson 6-6 Problem-Solving Investigation: Choose a Strategy


Lesson 6-8 Division Properties

66Division Concepts and Facts



Five-Minute Check (over Chapter 5)

Main Idea and Vocabulary

California Standards

Example 1: Use Models to Divide

Example 2: Repeated Subtraction

6-16-1 Relate Division to Subtraction

Understand Division



• I will divide using subtraction.

• division

• divide



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

Preparation for Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.


Colm and his brothers have 24 shirts in their closet. They are sizes small, medium, or large. There is an equal number of each size. How many shirts of each size are there?




There are 8 counters in each group. So, 24 ÷ 3 = 8.

Answer: There are 8 shirts of each size.

Using counters, divide 24 counters equally into 3 groups until all the counters are gone.

8 8 8


A. 7 sweaters

B. 6 sweaters

C. 3 sweaters

D. 8 sweaters


Corbin and her sisters have 36 sweaters in their drawer. They are yellow, pink, green, red, blue, and purple. There is an equal number of each color. How many sweaters of each color are there?


Coach Green wants to put her 21 softball players into equal groups of 3. How many equal groups can she form?

Use repeated subtraction to find 21 ÷ 3.




One Way: Number Line

Start at 21. Count back by 3s until you reach 0. How many times did you subtract?



Another Way: Paper and Pencil

Subtract groups of 3 until you reach 0. How many groups did you subtract?

21– 318

18– 315

15– 312

12– 3

9

9– 3

6

6– 3

3

3– 3

0

Answer: So, 21 ÷ 3 = 7. Coach Green can form 7 equal groups.


A. 6 teams

B. 7 teams

C. 5 teams

D. 8 teams


A classroom game requires teams of 4 students. In a class of 24 students, how many teams will there be?


Five-Minute Check (over Lesson 6-1)

Main Idea and Vocabulary


Example 1: Relate Multiplication to Division

Example 2: Write a Fact Family

6-26-2 Relate Multiplication to Division

Relate Multiplication to Division



• I will divide using related multiplication facts.

• dividend

• divisor

• quotient

• fact family



Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.


Use the array of cherries to write related multiplication and division sentences.




One Way: Multiplication

numberof rows

factor2

numberin each row

factor4

numberin all

product8× =



Another Way: Division

÷ =

numberin all

dividend8

numberof rows

divisor2

number in each row

quotient4



Answer: The related multiplication and division sentences are 2 × 4 = 8 and 8 ÷ 2 = 4.


A. 4 ÷ 3 = 1, 3 × 4 = 12

B. 4 × 4 = 16, 3 ÷ 3 = 1

C. 3 × 4 = 12, 12 ÷ 4 = 3

D. 3 × 3 = 9, 9 ÷ 3 = 3


Use the array of stars to choose related multiplication and division facts.


Use the numbers 5, 6, and 30 to write the related multiplication and division sentences for this array.


5 × 6 = 30

6 × 5 = 30

30 ÷ 5 = 6

Answer:

Notice each fact uses the same three numbers.

30 ÷ 6 = 5


A. 6 × 9 = 54, 9 × 6 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9

B. 6 × 6 = 36, 9 × 9 = 81, 54 ÷ 9 = 6, 54 ÷ 6 = 9

C. 54 × 6 = 326, 54 × 9 = 546, 9 ÷ 3 = 3, 6 ÷ 3 = 2

D. 6 × 9 = 54, 6 × 9 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9


Use the numbers 6, 9, and 54 to choose the related multiplication and division sentences.



Main Idea


Example 1: Problem-Solving Strategy

6-36-3 Problem-Solving Strategy: Choose an Operation



• I will choose an operation to use to solve a problem.



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


Lakita’s doctor saw patients for 5 hours today. During this time, the doctor saw 20 patients. How many patients did the doctor see each hour if she saw the same number?



Understand

What facts do you know?

• The doctor saw patients for 5 hours.

• She saw 20 patients in all.

What do you need to find?

• The number of patients the doctor saw each hour.



Plan

Think about what is happening. You have a group of 20 patients. You want to know how many patients the doctor saw each hour in the 5 hours. You should use division.




Solve

Divide 20 ÷ 5.

Answer: So, the doctor saw 4 patients each hour.

total number of patients

20 ÷

number of hours

5 =

number of patients

4


Check

You can use multiplication to check division.

Since 5 × 4 = 20, it makes sense that 4 patients would have been seen each hour.




Main Idea


Example 1: Make Equal Groups

6-46-4 Divide by 2


6-46-4 Divide by 2

• I will divide by 2.


6-46-4 Divide by 2




Arlo and his brother have 18 water toys in their pool. If they share the toys equally, how many will each child get?

6-46-4 Divide by 2

To share equally between 2 people means to divide by 2. You can write a related fact to find 18 ÷ 2 or 2 18.

2 × = 18


6-46-4 Divide by 2

Answer: So, 18 ÷ 2 = 9 or 2 18. Each person will get 9 toys.

9

The number line shows that 18 divided into groups of 2 is 9.

Check


A. 9 bracelets

B. 7 bracelets

C. 8 bracelets

D. 6 bracelets

6-46-4 Divide by 2

Tiffany and her cousin have 16 bracelets in the jewelry box. If they share them equally, how many will each child get?



Main Idea


Example 1: Real-World Example


6-56-5 Divide by 5


6-56-5 Divide by 5

• I will learn to divide by 5.


6-56-5 Divide by 5




Raul stacked 30 boxes on 5 empty shelves in a storage room. Each shelf had the same number of boxes on it. How many boxes were on each shelf?

You need to find 30 ÷ 5.

6-56-5 Divide by 5


6-56-5 Divide by 5

One Way: Use Models

There are 30 counters and 5 counters are in each group. There are 6 equal groups.


6-56-5 Divide by 5

30– 525

25– 520

20– 515

15– 510

10– 5

5

5– 5

0

Subtract groups of 5 until you reach 0. Count the number of groups you subtracted.

Another Way: Repeat Subtraction


6-56-5 Divide by 5

Answer: So, 30 ÷ 5 = 6 or 5 30. There are 6 boxes on each shelf.

6


A. 9 cans

B. 6 cans

C. 8 cans

D. 7 cans

6-56-5 Divide by 5

Tim put 32 cans on 4 shelves in a grocery store. Each shelf has the same number of cans on it. How many cans are on each shelf?


Niran has a scrapbook for his baseball cards. He has 25 cards. If 5 cards will fit on a page, how many pages can he fill?

Write a related multiplication fact to find 25 ÷ 5.

6-56-5 Divide by 5

25 ÷ 5 =

5 × 5 = 25

Answer: So, 25 ÷ 5 = 5 or 5 25. Niran can fill 5 pages.5

5 × = 25


6-56-5 Divide by 5

Check

25 divided into groups of 5 forms 5 groups. 5 groups of 5 = 25

The model show that 25 ÷ 5 = 5.


A. 7 pages

B. 8 pages

C. 9 pages

D. 10 pages

6-56-5 Divide by 5

Heather has a photo album for her vacation. She has 63 photos. If 6 photos fit on each page, how many pages can she fill?



Main Idea


Example 1: Problem-Solving Investigation

6-66-6 Problem-Solving Investigation: Choose a Strategy



• 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.


KINAH: I want to plant a vegetable garden. I have 6 tomato plants, 5 pepper plants, and 5 zucchini plants. I want to put the plants into 4 equal rows.

YOUR MISSION: Find how many plants should be planted in each row.



Understand

What facts do you know?

• Kinah has 6 tomato, 5 pepper, and 5 zucchini plants.

• She wants to plant them in 4 equal rows.

What do you need to find?

• Find how many plants to put in each row.



Plan

You need to look at how to arrange items. So, the draw a picture strategy is a good choice.



Solve

The picture shows 6 + 5 + 5 or 16 plants. There are 4 equal groups of 4 plants.


Since 16 ÷ 4 = 4, Kinah needs to plant 4 plants in each row.


Check

Look back at the problem. Since 4 × 4 = 16, you know that the answer is correct.




Main Idea



6-76-7 Divide by 10


6-76-7 Divide by 10

• I will learn to divide by 10.


6-76-7 Divide by 10



You need to find 80 ÷ 10.

Juanita arranged her 80 football cards into stacks of 10. How many stacks does she have?

6-76-7 Divide by 10


6-76-7 Divide by 10

One Way: Use Repeated Subtraction

80– 10

70

70– 10

60

60– 10

50

50– 10

40

40– 10

30

30– 10

20

20– 10

10

10– 10

0

Subtract groups of 10 until you reach 0. Count the number of groups you subtracted. You subtracted 10 groups eight times.


6-76-7 Divide by 10

Write a related multiplication fact to find 80 ÷ 10.You know that 10 × 8 = 80.

Another Way: Use a Related Fact

So, 80 ÷ 10 = 8 or 10 80.8

Answer: So, Juanita has 8 stacks.


6-76-7 Divide by 10

George put his 60 bananas into bunches of 10. How many bunches does he have?

A. 10 bunches

B. 8 bunches

C. 6 bunches

D. 5 bunches



Main Idea


Key Concept: Division Properties

6-86-8 Division Properties



• I will learn to use properties about using 1 and 0 in division.



Standard 3NS2.6 Understand the special properties of 0 and 1 in division. Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.




Five-Minute Checks

Math Tool Chest

Image Bank

Understand Division

Relate Multiplication to Division


To use the images that are on the following four slides in your own presentation:

1. Exit this presentation.

2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides.

3. Select an image, copy it, and paste it into your presentation.



Lesson 6-1 (over Chapter 5)

Lesson 6-2 (over Lesson 6-1)








(over Chapter 5)

One tricycle has 3 wheels. Two tricycles have6 wheels. How many wheels will there be on6 tricycles?

A. 16 wheels

B. 18 wheels

C. 9 wheels

D. 12 wheels


(over Lesson 6-1)

Divide. Use a number line or paper and pencil.

A. 3

B. 6

C. 2

D. 8

16 ÷ 8


(over Lesson 6-1)


A. 3

B. 6

C. 1

D. 9

9 ÷ 3


(over Lesson 6-1)


A. 10

B. 5

C. 7

D. 12

35 ÷ 7


(over Lesson 6-1)


A. 6

B. 7

C. 12

D. 14

24 ÷ 4


(over Lesson 6-2)

Write the fact family for the following set of numbers: 3, 8, 24.

A. 8 × 3 = 24, 3 × 8 = 24, 24 ÷ 8 = 3, 24 ÷ 3 = 8

B. 8 × 3 = 24, 8 × 4 = 32, 24 ÷ 3 = 8, 32 ÷ 4 = 8

C. 24 × 3 = 8, 24 × 8 = 3, 8 ÷ 3 = 24, 3 ÷ 8 = 24

D. 8 + 3 = 11, 3 + 8 = 11, 11 – 8 = 3, 11 – 3 = 8


(over Lesson 6-2)

Write the fact family for the following set of numbers: 1, 5, 5.

A. 5 × 1 = 5, 1 × 5 = 5, 5 ÷ 5 = 1, 1 ÷ 5 = 5

B. 5 × 1 = 5, 5 × 5 = 25, 5 ÷ 1 = 5, 25 ÷ 5 = 5

C. 1 × 5 = 5, 5 × 1 = 5, 5 ÷ 1 = 5, 5 ÷ 5 = 1

D. 5 × 1 = 1, 1 × 5 = 5, 5 ÷ 1 = 1, 5 ÷ 5 = 5


(over Lesson 6-3)

Solve. Gracia had 6 daises and 9 roses. How many flowers did Gracia have in all?

A. 15 flowers

B. 3 flowers

C. 13 flowers

D. 2 flowers


(over Lesson 6-3)

Solve. Brian had 6 pots each with 2 lilacs. How many lilacs did Brian have?

A. 10 lilacs

B. 12 lilacs

C. 9 lilacs

D. 4 lilacs


(over Lesson 6-4)

Divide. Write a related multiplication fact.

A. 9; 2 × 9 = 18

B. 2; 9 × 2 = 18

C. 18; 6 × 3 = 18

18 ÷ 2


(over Lesson 6-4)


A. 2; 2 × 3 = 6

B. 4; 2 × 4 = 8

C. 3; 2 × 3 = 6

6 ÷ 2


(over Lesson 6-4)


A. 6; 2 × 6 = 12

B. 6; 2 × 3 = 6

C. 10; 2 × 10 = 20

12 ÷ 2


(over Lesson 6-4)


16 ÷ 2

A. 4; 4 × 4 = 16

B. 8; 2 × 8 = 16

C. 32; 2 × 16 = 32


(over Lesson 6-4)


A. 10; 5 × 2 = 10

B. 5; 5 × 3 = 15

C. 5; 2 × 5 = 10

10 ÷ 2


(over Lesson 6-4)


8 ÷ 2

A. 4; 2 × 4 = 8

B. 6; 2 × 4 = 8

C. 3; 2 × 3 = 6


(over Lesson 6-4)


A. 9; 3 × 3 = 13

B. 7; 2 × 7 = 14

C. 12; 4 × 3 = 12

14 ÷ 2


(over Lesson 6-4)


A. 2; 2 × 2 = 4

B. 8; 2 × 4 = 8

C. 6; 3 × 4 = 12

4 ÷ 2


(over Lesson 6-5)


A. 5; 5 × 5 = 25

B. 10; 6 × 6 = 36

C. 15; 3 × 5 = 15

25 ÷ 5


(over Lesson 6-5)


A. 25; 5 × 5 = 25

B. 10; 10 × 5 = 50

C. 15; 3 × 5 = 15

50 ÷ 5


(over Lesson 6-5)


A. 10; 2 × 5 = 10

B. 5; 1 × 1 = 1

C. 1; 1 × 5 = 5

5 ÷ 5


(over Lesson 6-5)


A. 7; 5 × 7 = 35

B. 5; 5 × 6 = 30

C. 12; 3 × 4 = 12

35 ÷ 5


(over Lesson 6-6)

Three men are standing in line. Mr. Smith is 3 inches taller than Mr. Sanchez. Mr. Jones is 2 inches shorter than Mr. Smith. Which man is shortest?

A. Mr. Smith

B. Mr. Sanchez

C. Mr. Jones


(over Lesson 6-7)

Divide 70 ÷ 10.

A. 7

B. 10

C. 11

D. 70


(over Lesson 6-7)

Divide 30 ÷ 10.

A. 10

B. 13

C. 3

D. 11


(over Lesson 6-7)

Divide 50 ÷ 10.

A. 5

B. 10

C. 15

D. 20


(over Lesson 6-7)

Divide 20 ÷ 10.

A. 2

B. 10

C. 15

D. 20


(over Lesson 6-7)

Divide 90 ÷ 10.

A. 9

B. 15

C. 90

D. 100


(over Lesson 6-7)

Divide 100 ÷ 10.

A. 1

B. 100

C. 0

D. 10

This slide is intentionally blank.

Splash Screen Chapter 6 Division Concepts and Facts Click the mouse or press the space bar to...

Documents

Transcript of Splash Screen Chapter 6 Division Concepts and Facts Click the mouse or press the space bar to...