Fractions Nancy Hughes Olathe District Schools. Standards Seventh Grade N M7.1.4.K2d The student...

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Transcript of Fractions Nancy Hughes Olathe District Schools. Standards Seventh Grade N M7.1.4.K2d The student...

FractionsNancy Hughes

Olathe District Schools

Standards

Seventh GradeN M7.1.4.K2d The student adds,

subtracts, multiplies, and divides fractions and expresses answers in simplest form.

Eighth GradeM8.1.4.A1bThe student models, performs,

and explains computation with rational numbers, the irrational number pi, and algebraic expressions in a variety of situations.

VocabularyAddendCommon denominatorsDenominatorDividendDivisionEquivalent fractionFractionImproper fractionLeast common denominatorLowest termsMinuendMixed numberNumeratorProper fractionQuotientSimplifySubtrahendUnit fraction

Objectives

Develop concepts of fractions and mixed numbers

Use models to add, subtract, multiply and divide fractions

Add, subtract, multiply, divide fractions and mixed numbers

Adding Fractions – Using Fraction Circles

Pull out your fraction circles and sort them by colors. The clear circle is the number 1 or 1 whole.

Do the same with the fraction tiles. Sort them by color.

1

2

1

4

1

2

1

4

1

4

1

4

1

5

1

5

1

5

1

5

1

5

1

6

1

6

1

6

1

6

1

6

1

6

1

8

1

8

1

8

1

8

1

8

1

8

1

8

1

8

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

3

1

3

1

3

1

Adding Fractions – Using Fraction Circles or Fraction Tiles

4

2

4

1Let’s add

Which colored circle or tile will you need to add these fractions? Explain.

•Because the fraction has a denominator of 4, find the fraction piece that has been divided into fourths.

•Take the ¼ piece and add to it the piece.

+4

34

1

4

14

1=

+ =4

3

4

2

Adding Fractions – Using Fraction Circles or Tiles

5

2

5

1

5

3

Use either fraction circles or tiles to model

Again, look at the denominator and choose your tiles accordingly.

5

1+

5

1

5

1=

+5

3=

Adding Fractions – Using Fraction Circles or Tiles

3

1

2

1Use either fraction circles or tiles to model

•Notice we do not have like denominators. This makes it more of a challenge. Begin by taking the ½ and the 1/3 and find tiles or circles that are exactly the same size.

•Did you find like tiles? Explain.

•If you found tiles or parts of a circle that have a denominator of 6, you were correct.

•Notice the ½ matches up with 3/6 and the 1/3 matches up with 2/6.

½ ½6

1

6

1

6

1

6

1

6

16

1

3

1

3

1

3

1

6

1

6

1

6

1

6

1

6

1

6

1

Now we can add!

Adding Fractions – Using fraction circles or tiles

3

1

2

1Use either fraction circles or tiles to model

6

1

6

1

6

1

6

1

6

1

6

16

1

6

1

6

1

6

1

6

1

6

1

+ =6

5

+ =6

5

6

3

6

2

You Try

Use your fraction circles or fraction tiles to find 10

3

5

1

+ =

2

1

10

5

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1+ 10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1 =

2

1

10

5

Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions, and then add.

Roll 1st Fraction

2nd Fraction

Sum

#1

#2

#3

#4

#5

Quick Review

How to use your calculator to check!

Fraction bar

Change to a decimal

Change to a fraction

Simplify Mixed Number and Improper Fraction

Subtracting Fractions

Visual approach using fraction tiles or fraction circles

Subtracting Fractions using fraction circles or fraction tiles

What is ? Again we will have to find like denominators. Which sets of tiles or circles will work? Explain.

If you guessed the 10th’s you were right, 6/10 = 3/5

5

3

10

7

5

1

10

1

10

1

5

1

5

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

5

1

5

1

5

1

10

1

-

Subtracting Fractions using fraction circles or fraction tiles

What is ? If you used fraction circles, your work should be identical to the fraction tiles.

5

3

10

7

5

3

10

6

10

1

10

6

10

7

=

-

You Try – Use fraction tiles or fraction circles to show your answer.

What is ? 2

1

12

9

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

12

1

2

1

-12

1

12

1

12

1or ¼

4

1

- =

Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then subtract.

Roll 1st Fraction

2nd Fraction

Difference

#1

#2

#3

#4

#5

Quick Review

Multiplying fractions

Multiplying fractions is like finding what one fraction is of another.

Multiplying fractions

For example, to find , we begin with an area model.

4

303

2f

12

6

4

3

3

2x

3/4

2/31 2 3

4 5 6

7

8

1211109

Multiplying Fractions

To simplify ,find the prime factorization of 6 and 12.

Composite Prime Composite Prime

6 2 12 2 3 6 2 3

12

6

6 2 • 3 = 1

12 2 • 2 •3 2

Multiplying fractions

What is?

?4

1

5

4x

¼

5

4

5

1

20

4

4

1

5

4x

Multiplying FractionsTo find the answer to ½ x 3/5, we will use another model.

Show 3 out of 5

Show 1 out of 2

Shade the answer

10

3

5

3

2

1x

You try! To find the answer to . Model your answer.

Show 2 out of 3

Show 1 out of 5

Shade the answer

15

2

5

1

3

2x

5

1

3

2x

Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then multiply.

Roll 1st Fraction

2nd Fraction

Product

#1

#2

#3

#4

#5

Quick Review

Dividing Fractions – Fraction Tiles

Find 4

1

8

5

8

1

8

1

8

1

8

1

8

1

4

1

4

1

4

1

2

12

4

1

8

5

Visualize how many ¼’s will go into 5/8. Using fraction tiles, visualize how many ¼’s you can place upon 5/8.

Dividing Fractions – Fraction Tiles

Find 5

2

10

8

25

2

10

8

10

1

10

1

10

1

10

1

10

1

10

1

10

1

10

1

5

1

5

15

1

5

1

You try! Use your fraction circles or tiles.

Find 3

1

6

5

2

12

2

12

6

5

6

1

6

1

6

1

6

1

6

1

3

1

3

1

3

1

Quick ReviewUse two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then divide.

Roll 1st Fraction

2nd Fraction

Quotient

#1

#2

#3

#4

#5

Quick Review

Adding Fractions – Using Arithmetic

Method 1 3 x5 15 4 x5 20 2 x4 8+5 x4 20 23 20

Method 2 3 x5 15 + 2 x4 8 = 23 4 x5 20 + 5 x4 20 20

Method 3

20

23

20

815

5

2

4

320

45

xx

You try!

Use one of the three methods to find

24

19

3

2

8

1

If you do not know the common denominator, find the LCM.

Composite

Prime

8 4

222

Composite

Prime

3

222

3

LCM = 2x2x2x3=24

Subtracting Fractions – Using Arithmetic

Method 1 3 x5 15 4 x5 20 2 x4 8-5 x4 20 7 20

Method 2 3 x5 15 - 2 x4 8 = 7 4 x5 20 5 x4 20 20

Method 3

20

7

20

815

5

2

4

320

45

xx

You try!

Use one of the three methods to find

04

3

12

9

If you do not know the common denominator, find the LCM.

Composite

Prime

12 6

223

Composite

Prime

4

22

223

LCM = 2x2x3=12

Multiplying Fractions – Using Arithmetic

Method 1

5222

52

40

10

5

2

8

5

Composite

Prime

10

25

Composite

Prime

40 20 20

2225

¼

Method 2

4

1

5

2

8

5

1

4

You Try!

Use one of the two methods to multiply fractions.

2

1

16

18

9

4

Dividing Fractions Using Arithmetic

Divide the following:

52

16

8

5

16

2

8

5

Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign.

Multiply the fractions.

You try!

Divide the following:

212

28

7

6

28

12

7

6

Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign.

Multiply the fractions.

JournalingAnswer two of the following questions in your journal:1. Explain how to add fractions using either fraction circles

or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.

2. Explain how to subtract fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.

3. Explain how to multiply fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.

4. Explain how to divide fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.

Practice Operations with Fractions

What is the value of….. ?

6

5

3

1

6

11:Answer

What is the value of….. ?

18

7

6

1

9

5:Answer

What is the value of….. ?

14

9

7

4

14

31:Answer

What is the value of….. ?

13

3

26

9

26

15:Answer

What is the value of….. ?

16

3

8

7

16

11:Answer

What is the value of….. ?

21

5

7

6

21

13:Answer

What is the value of….. ?

10

7

9

8

90

17:Answer

What is the value of….. ?

3

1

2

1

6

1:Answer

What is the value of….. ?

12

7

8

7

24

7:Answer

What is the value of….. ?

5

3

9

7

45

8:Answer

What is the value of….. ?

2

1

2

1

4

1:Answer

What is the value of….. ?

3

1

4

3

4

1:Answer

What is the value of….. ?

9

8

4

3

3

2:Answer

What is the value of….. ?

15

14

7

5

3

2:Answer

What is the value of….. ?

5

3

11

6

55

18:Answer

What is the value of….. ?

5

2

4

1

8

5:Answer

What is the value of….. ?

5

4

8

5

32

25:Answer

What is the value of….. ?

5

3

9

2

27

10:Answer

What is the value of….. ?

2

3

5

3

5

2:Answer

What is the value of….. ?

8

33

4

5

33

10:Answer