Post on 28-Dec-2015
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.
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 6-5 Divide by 5
Lesson 6-6 Problem-Solving Investigation: Choose a Strategy
Lesson 6-7 Divide by 10
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
6-16-1 Relate Division to Subtraction
• I will divide using subtraction.
• division
• divide
6-16-1 Relate Division to Subtraction
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?
6-16-1 Relate Division to Subtraction
6-16-1 Relate Division to Subtraction
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
6-16-1 Relate Division to Subtraction
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.
6-16-1 Relate Division to Subtraction
6-16-1 Relate Division to Subtraction
One Way: Number Line
Start at 21. Count back by 3s until you reach 0. How many times did you subtract?
6-16-1 Relate Division to Subtraction
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
6-16-1 Relate Division to Subtraction
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
California Standards
Example 1: Relate Multiplication to Division
Example 2: Write a Fact Family
6-26-2 Relate Multiplication to Division
Relate Multiplication to Division
6-26-2 Relate Multiplication to Division
• I will divide using related multiplication facts.
• dividend
• divisor
• quotient
• fact family
6-26-2 Relate Multiplication to Division
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.
6-26-2 Relate Multiplication to Division
6-26-2 Relate Multiplication to Division
One Way: Multiplication
numberof rows
factor2
numberin each row
factor4
numberin all
product8× =
6-26-2 Relate Multiplication to Division
Another Way: Division
÷ =
numberin all
dividend8
numberof rows
divisor2
number in each row
quotient4
6-26-2 Relate Multiplication to Division
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
6-26-2 Relate Multiplication to Division
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.
6-26-2 Relate Multiplication to Division
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
6-26-2 Relate Multiplication to Division
Use the numbers 6, 9, and 54 to choose the related multiplication and division sentences.
Five-Minute Check (over Lesson 6-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
6-36-3 Problem-Solving Strategy: Choose an Operation
6-36-3 Problem-Solving Strategy: Choose an Operation
• I will choose an operation to use to solve a problem.
6-36-3 Problem-Solving Strategy: Choose an Operation
Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
6-36-3 Problem-Solving Strategy: Choose an Operation
Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.
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?
6-36-3 Problem-Solving Strategy: Choose an Operation
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.
6-36-3 Problem-Solving Strategy: Choose an Operation
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.
6-36-3 Problem-Solving Strategy: Choose an Operation
6-36-3 Problem-Solving Strategy: Choose an Operation
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.
6-36-3 Problem-Solving Strategy: Choose an Operation
Five-Minute Check (over Lesson 6-3)
Main Idea
California Standards
Example 1: Make Equal Groups
6-46-4 Divide by 2
6-46-4 Divide by 2
Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.
Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
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?
Five-Minute Check (over Lesson 6-4)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
6-56-5 Divide by 5
6-56-5 Divide by 5
Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.
Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
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?
Five-Minute Check (over Lesson 6-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
6-66-6 Problem-Solving Investigation: Choose a Strategy
6-66-6 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
6-66-6 Problem-Solving Investigation: Choose a Strategy
Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
6-66-6 Problem-Solving Investigation: Choose a Strategy
Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.
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.
6-66-6 Problem-Solving Investigation: Choose a Strategy
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.
6-66-6 Problem-Solving Investigation: Choose a Strategy
Plan
You need to look at how to arrange items. So, the draw a picture strategy is a good choice.
6-66-6 Problem-Solving Investigation: Choose a Strategy
Solve
The picture shows 6 + 5 + 5 or 16 plants. There are 4 equal groups of 4 plants.
6-66-6 Problem-Solving Investigation: Choose a Strategy
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.
6-66-6 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 6-6)
Main Idea
California Standards
Example 1: Real-World Example
6-76-7 Divide by 10
6-76-7 Divide by 10
Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results.
6-76-7 Divide by 10
Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
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
Five-Minute Check (over Lesson 6-7)
Main Idea
California Standards
Key Concept: Division Properties
6-86-8 Division Properties
6-86-8 Division Properties
• I will learn to use properties about using 1 and 0 in division.
6-86-8 Division Properties
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.
66Division Concepts and Facts
66Division Concepts and Facts
Five-Minute Checks
Math Tool Chest
Image Bank
Understand Division
Relate Multiplication to Division
66Division Concepts and Facts
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.
66Division Concepts and Facts
66Division Concepts and Facts
66Division Concepts and Facts
66Division Concepts and Facts
66Division Concepts and Facts
66Division Concepts and Facts
Lesson 6-1 (over Chapter 5)
Lesson 6-2 (over Lesson 6-1)
Lesson 6-3 (over Lesson 6-2)
Lesson 6-4 (over Lesson 6-3)
Lesson 6-5 (over Lesson 6-4)
Lesson 6-6 (over Lesson 6-5)
Lesson 6-7 (over Lesson 6-6)
Lesson 6-8 (over Lesson 6-7)
66Division Concepts and Facts
(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
66Division Concepts and Facts
(over Lesson 6-1)
Divide. Use a number line or paper and pencil.
A. 3
B. 6
C. 2
D. 8
16 ÷ 8
66Division Concepts and Facts
(over Lesson 6-1)
Divide. Use a number line or paper and pencil.
A. 3
B. 6
C. 1
D. 9
9 ÷ 3
66Division Concepts and Facts
(over Lesson 6-1)
Divide. Use a number line or paper and pencil.
A. 10
B. 5
C. 7
D. 12
35 ÷ 7
66Division Concepts and Facts
(over Lesson 6-1)
Divide. Use a number line or paper and pencil.
A. 6
B. 7
C. 12
D. 14
24 ÷ 4
66Division Concepts and Facts
(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
66Division Concepts and Facts
(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
66Division Concepts and Facts
(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
66Division Concepts and Facts
(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
66Division Concepts and Facts
(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
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
A. 2; 2 × 3 = 6
B. 4; 2 × 4 = 8
C. 3; 2 × 3 = 6
6 ÷ 2
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
A. 6; 2 × 6 = 12
B. 6; 2 × 3 = 6
C. 10; 2 × 10 = 20
12 ÷ 2
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
16 ÷ 2
A. 4; 4 × 4 = 16
B. 8; 2 × 8 = 16
C. 32; 2 × 16 = 32
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
A. 10; 5 × 2 = 10
B. 5; 5 × 3 = 15
C. 5; 2 × 5 = 10
10 ÷ 2
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
8 ÷ 2
A. 4; 2 × 4 = 8
B. 6; 2 × 4 = 8
C. 3; 2 × 3 = 6
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
A. 9; 3 × 3 = 13
B. 7; 2 × 7 = 14
C. 12; 4 × 3 = 12
14 ÷ 2
66Division Concepts and Facts
(over Lesson 6-4)
Divide. Write a related multiplication fact.
A. 2; 2 × 2 = 4
B. 8; 2 × 4 = 8
C. 6; 3 × 4 = 12
4 ÷ 2
66Division Concepts and Facts
(over Lesson 6-5)
Divide. Write a related multiplication fact.
A. 5; 5 × 5 = 25
B. 10; 6 × 6 = 36
C. 15; 3 × 5 = 15
25 ÷ 5
66Division Concepts and Facts
(over Lesson 6-5)
Divide. Write a related multiplication fact.
A. 25; 5 × 5 = 25
B. 10; 10 × 5 = 50
C. 15; 3 × 5 = 15
50 ÷ 5
66Division Concepts and Facts
(over Lesson 6-5)
Divide. Write a related multiplication fact.
A. 10; 2 × 5 = 10
B. 5; 1 × 1 = 1
C. 1; 1 × 5 = 5
5 ÷ 5
66Division Concepts and Facts
(over Lesson 6-5)
Divide. Write a related multiplication fact.
A. 7; 5 × 7 = 35
B. 5; 5 × 6 = 30
C. 12; 3 × 4 = 12
35 ÷ 5
66Division Concepts and Facts
(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
66Division Concepts and Facts
(over Lesson 6-7)
Divide 70 ÷ 10.
A. 7
B. 10
C. 11
D. 70
66Division Concepts and Facts
(over Lesson 6-7)
Divide 30 ÷ 10.
A. 10
B. 13
C. 3
D. 11
66Division Concepts and Facts
(over Lesson 6-7)
Divide 50 ÷ 10.
A. 5
B. 10
C. 15
D. 20
66Division Concepts and Facts
(over Lesson 6-7)
Divide 20 ÷ 10.
A. 2
B. 10
C. 15
D. 20
66Division Concepts and Facts
(over Lesson 6-7)
Divide 90 ÷ 10.
A. 9
B. 15
C. 90
D. 100
66Division Concepts and Facts
(over Lesson 6-7)
Divide 100 ÷ 10.
A. 1
B. 100
C. 0
D. 10
This slide is intentionally blank.