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## PowerPoint Slideshow about ' Modeling Multiplication of Fractions' - ferris-atkinson

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### Modeling Multiplication of Fractions

Isabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

Isabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

MCC4.NF.4; MCC5.NF.4; MCC5.NF.5; MCC5.NF.6

Deanna Cross – Hutto Middle School

Multiplying on a Number Line

- Fraction by a WHOLE number

Isabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

Suggestions on how to solve?

Number Line

Number Lines

Start and end with an arrow

Divided into equal (equivalent) increments

Can start and end at any number

Are there any numbers that can be “renamed” or written as an equivalent fraction?

Isabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

- Isabel has used only ¾ of the paper. What if she had used ½ of the paper? How much would she have used?
- You have to multiply 8 x ¾.

8 x ¾

- First – Model what you have on a number line – “She had 8 feet of wrapping paper”
- Now, she is multiplying by ¾ . What is the denominator?

0 1 2 3 4 5 6 7 8

8 x ¾

- Now, divide the total amount (8) into 4 pieces. (8 ÷ 4 = 2 – so each piece is equal to 2)
- Shade in 3 of the four pieces.
- Look to see if this lines up with a number on your number line.

0 1 2 3 4 5 6 7 8

Isabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

- So, 8 x ¾ = 6.
- Why is the answer smaller than 8?
- Because whenever you multiply a whole number by a fraction, you will get a smaller answer.

0 1 2 3 4

3 x

- Now, look at your denominator – 3
- Divide your bar into three EQUAL pieces.
- Shade in 1 of the three pieces.
- Does this line up with a number on the number line?

0 1 2 3 4 5 6

6 x

- Now, look at your denominator – 4
- Divide your bar into four EQUAL pieces.

HINT: Divide 6 by 4 and determine the decimal portion to divide this piece into

- Shade in 2 of the four pieces.
- Does this line up with a number on the number line?

Practice

- Optional Practice problems
- 8 x
- 9 x
- 12 x
- 10 x
- 4 x

Multiplying with an AREA MODELIsabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

- Fraction by a WHOLE number

Area models

- Reminder of area – length x width = area
- Area is the amount INSIDE a rectangular shape.
- To determine area, you multiply TWO numbers – the length and the width.

- Isabel has used only ¾ of the paper.
- You have to multiply 8 x ¾.
- Suggestions to solve using area model?

8 x ¾

- Draw a rectangle.
- Divide the rectangle into smaller rectangles to represent your WHOLE number.

8

8 x ¾

- Next, along the vertical side, divide your rectangle into the number of pieces representing your denominator 4

4

8 x ¾

- Now, count how many ¼’s you have shaded green.
- 24 boxes =

8

4

- Can we leave like this, or is there another way to write this improper fraction?

8 x ¾

- = 24 ÷ 4 = 6
- Proof: If you divided 8 dollars up among 4 people, how much would each get?
- TWO
- Now, how much would 3 people get?
- SIX
- So, ¾ of 8 = 6

4 x ½

- This is one you already know the answer to – if you have ½ of 4 you have 2. Let’s prove that with an area model.

4 x ½

- Next, divide your rectangle into the number of pieces for your denominator along the vertical edge.

4

2

3 x 1/3

- Now, think about what each square represents…

3

So, each square = 1/3, there are 3 thirds…

3

3 x 1/3 = 1

Practice

- Optional Practice problems
- 8 x
- 6 x
- 12 x
- 5 x
- 4 x

Multiplying with TAPE DIAGRAMIsabel had 8 feet of wrapping paper to wrap Christmas gifts with. She Used 3/4 of the paper. How much paper did she use? How much paper did she have left over?

- Fraction by a WHOLE number

Tape diagrams

- Tape diagrams are like adding strips of paper together to determine lengths. For example, if I had 3 chocolate cupcakes and someone gave me 2 more, I would have five.

3 chocolate

2 more

5 chocolate cupcakes

Multiplying with Tape Diagrams

- Fraction by Whole numbers are easy with tape diagrams…it is like repeated addition.

- Isabel has used only ¾ of the paper.
- You have to multiply 8 x ¾.
- Suggestions to solve using tape diagram model?

8 x 3/4

- Think, how many 3/4ths do you need?
- 8
- Make a tape model to represent 3/4. Copy this eight times.

8 x 3/4

How do you change an improper fraction to a mixed number?

4 x ½

- Draw a diagram to represent ½.
- Repeat this 4 times.

Practice

- Optional Practice problems
- 12 x
- 9 x
- 5 x
- 6 x
- 4 x

Algorithm?

- Now…let’s look at our practice problems and try to determine an algorithm to solve multiplication of a whole by a fraction.

Is there a pattern? What is being done each time?

Algorithm

( ) x q = (a x q) ÷ b

HUH??? LETTERS???

Each letter is a variable. It represents or takes the place of a number. Let’s look at an example of what these letters mean.

Practice

- Optional Practice problems
- x 5
- x 18
- x 32
- x 10
- x 4

of a class are boys. Of those boys, are wearing tennis shoes. What fraction shows how many boys are wearing tennis shoes?

- Suggestions on how to solve this?

Multiplying on a Number Line

- Next, divide this bar into the denominator of the first fraction (3). Shade in the numerator (2).

0

Multiplying on a Number Line

- Finally, see if this matches any of your points on the number line.

Can 2/4 be written any other way?

0

Multiplying on a Number Line

These are both even numbers, so the fraction can be reduced (or simplified) by dividing the numerator and denominator by 2.

Divide this amount into two equal sections (how can you divide 7 in half?)

- When you divide 7 by 2, it does not produce an even number. Instead, you get 3.5 - Model this amount (three sections and half of a section).

0

This does NOT fall at an exact mark on the number line, which means more numbers must be added to the number line.

What could fall between 3/8 and 4/8???

0

We need a number half way in between these two fractions, which means we need two TIMES as many increments (or lines) on the number line. What is 2 x 8?

0

Model the second fraction (factor).

- Divide into 3 sections and shade 2.

0

- Check to see if this lines up with a number on the number line.

Divide the numerator and denominator by 2.

Can this fraction be reduced (simplified) or written in any other way?

0

Practice

- Optional Practice problems

Multiplying with an AREA MODEL

- Fraction by a Fraction

- of a class are boys. Of those boys, are wearing tennis shoes. What fraction shows how many boys are wearing tennis shoes?
- Suggestions on how to solve this using an area model?

Can you reduce or simplify this?

- So, your numerator = 6
- Your denominator = 12

Can you reduce or simplify this?

- So, your numerator = 7
- Your denominator = 16

Can you reduce or simplify this?

- So, your numerator = 12
- Your denominator = 30

Algorithm?

- Now…let’s look at our practice problems and try to determine an algorithm to solve multiplication of a whole by a fraction.

Is there a pattern? What is being done each time?

Algorithm

HUH??? LETTERS???

Each letter is a variable. It represents or takes the place of a number. Let’s look at an example of what these letters mean.

Algorithm

a = your numerator of your first fraction

b = your denominator of your first fraction

c = your numerator of your second fraction

d = your denominator of your second fraction

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