Post on 17-Jan-2016
2015 The Institute for the Professional Development of Adult Educators
Using Fraction Tileswww.floridaipdae.org
2015 The Institute for the Professional Development of Adult Educators
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A linear model gives an overview and shows relationships.A linear model gives an overview and shows relationships.
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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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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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How many fourths equal a half? Eighths? Sevenths?
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What is half of a half? That’s multiplying fractions.
Fraction Tiles
2015 The Institute for the Professional Development of Adult Educators
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?
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2015 The Institute for the Professional Development of Adult Educators
11 1
or 3 ÷ 2.
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means three s12
What is a fraction?
2015 The Institute for the Professional Development of Adult Educators
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*9/8 is 1 plus 1/89/8 is 1 plus 1/8
Fraction Tiles
2015 The Institute for the Professional Development of Adult Educators
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
2015 The Institute for the Professional Development of Adult Educators
2 =34
114 4 =2
314324
two 4s
11
Write each quantity as a mixed numberand as an improper fraction.
3
four 3s + 2 = 14
+ 3 = 11
Mixed to Improper Fractions
Each row of connected rectangles represents 1.Write each quantity as a mixed number and as an
improper fraction.
2015 The Institute for the Professional Development of Adult Educators
2 =34
114 4 =2
3143 4 =3
5235
Write each quantity as a mixed numberand as an improper fraction.
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two 4s
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four 5s + 3 = 23
four 3s + 2 = 14
+ 3 = 11
Mixed to Improper Fractions
Each row of connected rectangles represents 1.Write each quantity as a mixed number and as an
improper fraction.
2015 The Institute for the Professional Development of Adult Educators
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.
2015 The Institute for the Professional Development of Adult Educators
Circle the wholes and write each quantity asan improper fraction and as a mixed number.
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= 2115
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Improper to Mixed Fractions
The correlation to division becomes obvious here.The correlation to division becomes obvious here.
Circle the wholes and write each quantity as an improper fraction and as a mixed number.
2015 The Institute for the Professional Development of Adult Educators
Circle the wholes and write each quantity asan improper fraction and as a mixed number.
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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.
Improper to Mixed Fractions
Circle the wholes and write each quantity as an improper fraction and as a mixed number.
2015 The Institute for the Professional Development of Adult Educators
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14Shade . Shade . Shade .
Fractional Parts of Geometric Figures
2015 The Institute for the Professional Development of Adult Educators
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14Shade . Shade . Shade .
Fractional Parts of Geometric Figures
2015 The Institute for the Professional Development of Adult Educators
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14Shade . Shade . Shade .
Fractional Parts of Geometric Figures
2015 The Institute for the Professional Development of Adult Educators
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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
2015 The Institute for the Professional Development of Adult Educators
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
2015 The Institute for the Professional Development of Adult Educators
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Simplifying Fractions
2015 The Institute for the Professional Development of Adult Educators
36
= 12
Simplifying Fractions
2015 The Institute for the Professional Development of Adult Educators
48
= 12
Simplifying Fractions
2015 The Institute for the Professional Development of Adult Educators
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.
Simplifying Fractions
2015 The Institute for the Professional Development of Adult Educators
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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6 12 18 24 30 36 42 48 54 60
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
10 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
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
Simplifying Fractions
2015 The Institute for the Professional Development of Adult Educators
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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30
40
6 12 18 24 30 36 42 48 54 60
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
10 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
*
12 12 1616
Simplifying Fractions
2015 The Institute for the Professional Development of Adult Educators
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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
2015 The Institute for the Professional Development of Adult Educators
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x =12
The square represents 1.The square represents 1.
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
12
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.
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
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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.
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
23
x =34
Another example. Another example.
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
23
x =34
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
23
x =34
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
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x = =34
612
12
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
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x =34
The total number of of rectangles is 3 x 4.
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
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.
Multiplying Fractions
2015 The Institute for the Professional Development of Adult Educators
÷ =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
2015 The Institute for the Professional Development of Adult Educators
÷ =121 2
÷ =131 3
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÷ =1 3
÷ =1 4
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34÷ =1 4
3÷ =231 3
2
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
2015 The Institute for the Professional Development of Adult Educators
÷ = __342
1 114
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2 sets of ¾ plus 2 of the 3 needed for the next set = 2 2/3
Dividing Fractions
Find
2015 The Institute for the Professional Development of Adult Educators
23 ÷ = __To find
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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
2015 The Institute for the Professional Development of Adult Educators
IPDAE