8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

1/14

The Number System

Day 7Van Siclen Community Middle School

Mr. E Grade 6 Mathematics

Class 602/603/604/605

November 2014

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

2/14

www.tinyurl.com/vscmath62

Todays Lesson Link

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

3/14

Do Now 4 minutes

A) How many1

are in

2

? You may use a model.

B) How many

9are in

2

9?

How many1

cups of orange juice are in 2 cups of orange juice? Show your work.

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

4/14

Lesson Overview

So far weve been using a lot ofmodels in order to solve problems.

Today, we are going to stop usingthem in favor of a much faster

way.

Today we will learn about using

multiplicative inverses tounderstand why division with

fractions also works asmultiplication.

Today we will use fraction strips to

divide fractions by fractions andmake this easier to understand.

Reciprocal/Multiplicative Inverse Two numwhose product is equal to 1 are reciprocals

one another.

Example:2

and

2are multiplicative inverse

because2

x

2= 1.

Example #2 4 and1

are multiplicative

inverses because

1x

1

= 1.

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

5/14

Write your own! 2 minutes

Take 1 minute to write three of your own multiplicative inverses.

One of your examples include a whole number.

Is their product equal to 1?

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

6/14

Dividing Fractions with a Model

2

5

Why are there 5 boxes in this model?

In other words,2

5

of what number is

? (We can also say

is equal to2

5

of

what number?)

How many boxes of the model above should be shaded in? How do you know?

Now two boxes are shaded. What fraction do these shaded boxes represent?

How do you know?

?

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

7/14

Dividing Fractions with a Model 5 minutes

2

5

If 2 units =

, how much is 1 unit? How do we know?

What is the answer? (What is the sum of all 5 units?)

How did we find the answer?

?

3

4

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

8/14

Dividing Fractions with a Model - Recap

2

5

So 1 unit is half of

= (1

2

x

) =

Since 1 unit is

, 5 units =

x 5 =

15

or 1

7

So

1

2=

15

or 1

7

3

4

3

8

3

8

3

8

3

8

3

8

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

9/14

Dividing Fractions with a Model - Recap

2

5

Solve: (1

2x

x 5) = __________

Solve:

x (

1

2x 5) = __________

Are these both equal?

What can we say about the following two problems?

2

5and

x

5

2

3

4

3

8

3

8

3

8

3

8

3

8

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

10/14

Invert and Multiply.

This way to solve division with fractions is called invert and multiply.

We only invert the SECONDfraction (the divisor), not the first one (dividend).

Example:

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

11/14

Dividing Fractions with a Model 4 minutes

We need to find out..does the invert and multiply rule always work?

Lets solve1

2

using a model.

1) How many boxes should your model have? How many boxes should weshade in?

2) What fraction do each of these shaded boxes represent?

3) What is the answer?

4) Use the invert and multiply rule. Is the answer the same?

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

12/14

Dividing Fractions with a Model 4

minutes

Solve2

by using a model AND by using the invert and multiply rule.

Compare both of your answers.

Are the answers the same?

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

13/14

What did we learn?

Dividing fractions by fractions is equivalent to multiplying by its reciprocal.

In the future, we can use models or the invert and multiply rule to solve

division with fraction questions.

8/10/2019 Lesson #23 - Visual Fraction Models to Algorithm

14/14

Homework Due November 19, 2014

Finding reciprocals

Comparing models to the invert and multiply rule.