2015 The Institute for the Professional Development of Adult Educators Using Fraction Tiles .

2015 The Institute for the Professional Development of Adult Educators

Using Fraction Tileswww.floridaipdae.org


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A linear model gives an overview and shows relationships.A linear model gives an overview and shows relationships.

Fraction Tiles


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How many fourths in a whole? How many sixths?

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What is more, 1/4 or 1/3? What is more, 1/9 or 1/10?

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Which is more, 3/4 or 4/5?

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Which is more, 3/4 or 4/5? Which is more, 7/8 or 8/9?

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The pattern of 1/2, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10.

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How many fourths equal a half? Eighths? Sevenths?

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What is half of a half? That’s multiplying fractions.

Fraction Tiles


A fraction is part of a set or part of a whole.textbook definition

What about ?

Another common meaning of fraction is fragment or a small part.Another common meaning of fraction is fragment or a small part.

What is a fraction?

32


11 1

or 3 ÷ 2.

1 112

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32

means three s12

What is a fraction?


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*9/8 is 1 plus 1/89/8 is 1 plus 1/8

Fraction Tiles


2 =34

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Write each quantity as a mixed numberand as an improper fraction.

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two 4s

3

+ 3

11

= 11

Each row of connected rectangles represents 1.Write each quantity as a mixed number and as an

improper fraction.

How did you find the 11?How did you find the 11?

Mixed to Improper Fractions


2 =34

114 4 =2

314324

two 4s

11


3

four 3s + 2 = 14

+ 3 = 11



improper fraction.


2 =34

114 4 =2

3143 4 =3

5235


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two 4s

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four 5s + 3 = 23

four 3s + 2 = 14

+ 3 = 11



improper fraction.


Circle the wholes and write each quantity asan improper fraction and as a mixed number.

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Improper to Mixed Fractions

Circle the wholes and write each quantity as an improper fraction and as a mixed number.



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= 2115

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The correlation to division becomes obvious here.The correlation to division becomes obvious here.




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= 2115

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= 153

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The correlation to division becomes obvious here.The correlation to division becomes obvious here.




12

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14Shade . Shade . Shade .

Fractional Parts of Geometric Figures


12

23

14Shade . Shade . Shade .

A study showed that many students and adults thought this was impossible.A study showed that many students and adults thought this was impossible.

Fractional Parts of Geometric Figures


10050 50

25 2525 25

10 10 10 10 10 10 10 10 10 10

3313 331

3 3313

*

1212 121

2 1212 121

2 1212 121

2 1212 121

2

Dividing 100


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Simplifying Fractions


36

= 12



48

= 12



912

= 343

Writing the common multiple in a circle, in this example, 3, helps students remember what they’re dividing by.

Writing the common multiple in a circle, in this example, 3, helps students remember what they’re dividing by.



1 2 3 4 5 6 7 8 9

2 4 6 8 10 12 14 16 18

3 6 9 12 15 18 21 24 27

4 8 12 16 20 24 28 32 36

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7 14 21 28 35 42 49 56 63 70

8 16 24 32 40 48 56 64 72 80

9 18 27 36 45 54 63 72 81 90

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00

The fraction 4/8 can be reduced on the multiplication table as 1/2.The fraction 4/8 can be reduced on the multiplication table as 1/2.

21212828

45457272



1 2 3 4 5 6 7 8 9

2 4 6 8 10 12 14 16 18

3 6 9 12 15 18 21 24 27

4 8 12 16 20 24 28 32 36

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7 14 21 28 35 42 49 56 63 70

8 16 24 32 40 48 56 64 72 80

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5 10 15 20 25 30 35 40 45 50

00

*

12 12 1616



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4–

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3– 4

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2 37

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5– 2

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*

Subtracting Fractions


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x =12

The square represents 1.The square represents 1.

Multiplying Fractions


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x =12

We are thinking 1/2 of 1/2. First find 1/2 of it vertically. We are thinking 1/2 of 1/2. First find 1/2 of it vertically.



12

x =12

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Now find 1/2 of it horizontally. The solution is the double crosshatched area.

Now find 1/2 of it horizontally. The solution is the double crosshatched area.



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x =34

Another example. Another example.



23

x =34



23

x = =34

612

12



23

x =34

The total number of of rectangles is 3 x 4.



23

x =34

The number of double crosshatched rectangles is 2 x 3.

The total number of rectangles is 3 x 4.

That’s why to multiply fractions, we multiply the numerators and the denominators.

That’s why to multiply fractions, we multiply the numerators and the denominators.



÷ =121 2

÷ =131 3

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The third problem can be thought of as how many 2/3s are in 1 or half of 1 ÷ 1/3.The third problem can be thought of as how many 2/3s are in 1 or half of 1 ÷ 1/3.

÷ =231 3

2

2 sets of ½ = 1

3 sets of 1/3 = 1

1 set of 2/3 plus 1/2 of another set of 2/3 = 1

Dividing Fractions


÷ =121 2

÷ =131 3

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14

÷ =1 3

÷ =1 4

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34÷ =1 4

3÷ =231 3

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1 ÷ 3 is simply the definition of a fraction. Notice the pattern.1 ÷ 3 is simply the definition of a fraction. Notice the pattern.

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Dividing Fractions


÷ = __342

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2 sets of ¾ plus 2 of the 3 needed for the next set = 2 2/3

Dividing Fractions

Find


23 ÷ = __To find

34

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(Is the answer more or less than 1?)

Another example: How many 3/4s are in 2/3?Another example: How many 3/4s are in 2/3?

Dividing Fractions


IPDAE

2015 The Institute for the Professional Development of Adult Educators Using Fraction Tiles .

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Transcript of 2015 The Institute for the Professional Development of Adult Educators Using Fraction Tiles .