Post on 03-Nov-2014
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Focusing on Fractions
Presented by Kathleen Cotter LawerBased on the work of Joan A. Cotter, Ph.D.
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© Activities for Learning, Inc. 2012
Joan A. Cotter, Ph.D.
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin• Montessori Educator
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin• Montessori Educator• Math Games
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin• Montessori Educator• Math Games• Tutor
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin• Montessori Educator• Math Games• Tutor• AL Abacus
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin• Montessori Educator• Math Games• Tutor• AL Abacus• Middle-School Teacher
Joan A. Cotter, Ph.D.
• Engineer from University of Wisconsin• Montessori Educator• Math Games• Tutor• AL Abacus• Middle-School Teacher• Ph.D. in Math Education
How are fractions usually taught?
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Fraction Model: “Fish Tank”
© Activities for Learning, Inc. 2012
Fraction Model: “Fish Tank”
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Fraction Model: “Fish Tank”
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Fraction Model: “Words”
This is fourths.
© Activities for Learning, Inc. 2012
Fraction Model: “Words”
This is fourths. This is thirds.
© Activities for Learning, Inc. 2012
Fraction Model: “Words”
This is fourths. This is thirds.
If this were chocolate…
© Activities for Learning, Inc. 2012
Fraction Model: “Words”
This is fourths. This is thirds.
If this were chocolate…
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Fraction Model: “Rounded Corner”
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Fraction Model: “Rounded Corner”
The middle fractions are greater than the fractions at the ends!
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Fraction Models: Circles
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Fraction Models: Circles
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Try to compare 4/5 and 5/6 with this model.© Activities for Learning, Inc. 2012
Fraction Models: Circles
Are we comparing angles, arcs, or area?© Activities for Learning, Inc. 2012
Fraction Models: Circles
Experts in visual literacy say that comparing quantities in pie charts is difficult because most people think linearly. It is easier to compare along a straight line than compare pie slices. askoxford.com
© Activities for Learning, Inc. 2012
Fraction Models: Circles
Experts in visual literacy say that comparing quantities in pie charts is difficult because most people think linearly. It is easier to compare along a straight line than compare pie slices. askoxford.com
Specialists also suggest refraining from using more than one pie chart for comparison.
www.statcan.ca
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So how should we teach fractions?
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Fraction Model: Linear Chart
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Fraction Model: “Color”
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1 1 1 1 1 1
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Fraction Model: “Missing Parts”
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Fraction Chart1
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Fraction Chart
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Ask the children to put it together like a puzzle.
© Activities for Learning, Inc. 2012
Definition of a Fraction
© Activities for Learning, Inc. 2012
Definition of a Fraction
A fraction is part of a set or part of a whole.Textbook definition
© Activities for Learning, Inc. 2012
Definition of a Fraction
32What about ?
A fraction is part of a set or part of a whole.Textbook definition
© Activities for Learning, Inc. 2012
Definition of a Fraction
An expression that indicates the quotient of two quantities.
American Heritage Dictionary
© Activities for Learning, Inc. 2012
Definition of a Fraction
An expression that indicates the quotient of two quantities.
American Heritage Dictionary
A number in the form where b ≠ 0.Arizona Standards
ab
© Activities for Learning, Inc. 2012
Fraction Chart1
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© Activities for Learning, Inc. 2012
Fraction Chart
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© Activities for Learning, Inc. 2012
Fraction Chart
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© Activities for Learning, Inc. 2012
Fraction Chart
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© Activities for Learning, Inc. 2012
Fraction Naming
© Activities for Learning, Inc. 2012
Fraction Naming
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 2 equal parts.
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 2 equal parts.
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 2 equal parts.
One divided into 3 equal parts.
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 2 equal parts.
One divided into 3 equal parts.
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 2 equal parts.
One divided into 3 equal parts.
One divided into 4 equal parts.
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
1 One whole
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
1 One whole
divided into
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
1 One whole
divided into
3 three equal parts
© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
1 One
divided by
3 three
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Fraction Naming
One divided into 3 equal parts.
1Read as “one-third.”
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© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
1Read as “one-third.”
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© Activities for Learning, Inc. 2012
Fraction Naming
One divided into 3 equal parts.
1Read as “one-third.”
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In English, we use ordinal numbers to name fractions, with the exception of half.
© Activities for Learning, Inc. 2012
How should we practicewhat we learned?
© Activities for Learning, Inc. 2012
Games
© Activities for Learning, Inc. 2012
© Activities for Learning, Inc. 2012
GamesMath
Games
=GamesMath
Games
© Activities for Learning, Inc. 2012
=Books
ReadingGamesMath
Games
© Activities for Learning, Inc. 2012
=Books
Reading
Games provide interesting repetition needed for automaticity.
GamesMath
Games
© Activities for Learning, Inc. 2012
=Books
Reading
Games provide interesting repetition needed for automaticity.
Games also provide an application for new information.
GamesMath
Games
© Activities for Learning, Inc. 2012
Unit Fraction War
© Activities for Learning, Inc. 2012
Unit Fraction War
Purpose: Practice for naming and comparing unit fractions.
© Activities for Learning, Inc. 2012
Unit Fraction War
Purpose: Practice for naming and comparing unit fractions.
To help the children realize a unit fraction decreases as the denominator increases.
© Activities for Learning, Inc. 2012
Unit Fraction War
Purpose: Practice for naming and comparing unit fractions.
To help the children realize a unit fraction decreases as the denominator increases.
Goal: To collect all, or most, of the cards by comparing unit fractions.
© Activities for Learning, Inc. 2012
Unit Fraction War
© Activities for Learning, Inc. 2012
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Unit Fraction War
© Activities for Learning, Inc. 2012
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Unit Fraction War
© Activities for Learning, Inc. 2012
Unit Fraction War
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Unit Fraction War
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Unit Fraction War
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Unit Fraction War
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Unit Fraction War
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Unit Fraction War
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Unit Fraction War
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© Activities for Learning, Inc. 2012
Unit Fraction War
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Unit Fraction War
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© Activities for Learning, Inc. 2012
More Fraction Naming
© Activities for Learning, Inc. 2012
More Fraction Naming1
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More Fraction Naming
One-third taken 2 times.
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More Fraction Naming
One-third taken 2 times.
1Two
3s
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© Activities for Learning, Inc. 2012
More Fraction Naming
One-third taken 2 times.
1Two is
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© Activities for Learning, Inc. 2012
More Fraction Naming
One-third taken 2 times.
Read as “two-thirds.”
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1Two is
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© Activities for Learning, Inc. 2012
More Fraction Naming1
© Activities for Learning, Inc. 2012
More Fraction Naming1 1
© Activities for Learning, Inc. 2012
More Fraction Naming
Two divided into 3 equal parts.
1 1
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More Fraction Naming
Two divided into 3 equal parts.
1 1
2 Two
divided by3 three
© Activities for Learning, Inc. 2012
More Fraction Naming
Two divided into 3 equal parts.
1 1
2 Two
divided by3 three
© Activities for Learning, Inc. 2012
More Fraction Naming
Two divided into 3 equal parts.
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2 Two
divided by3 three
© Activities for Learning, Inc. 2012
More Fraction Naming
Two divided into 3 equal parts.
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1two
3s=
2 Two
divided by3 three
© Activities for Learning, Inc. 2012
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© Activities for Learning, Inc. 2012
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How many fourths in a whole?
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© Activities for Learning, Inc. 2012
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How many fourths in a whole?
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© Activities for Learning, Inc. 2012
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How many fourths in a whole?
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© Activities for Learning, Inc. 2012
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How many fourths in a whole?
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© Activities for Learning, Inc. 2012
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Fraction Chart
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How many fourths in a whole?
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© Activities for Learning, Inc. 2012
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Fraction Chart
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How many sixths?How many fourths in a whole?
© Activities for Learning, Inc. 2012
Purpose: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole.
Concentrating on One Game
© Activities for Learning, Inc. 2012
Purpose: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole.
Goal: To find the pairs that make a whole.
Concentrating on One Game
© Activities for Learning, Inc. 2012
Concentrating on One
© Activities for Learning, Inc. 2012
Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
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Concentrating on One
© Activities for Learning, Inc. 2012
Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
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Concentrating on One
© Activities for Learning, Inc. 2012
Concentrating on One
© Activities for Learning, Inc. 2012
Let’s begin to comparefractions….
© Activities for Learning, Inc. 2012
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Fraction Chart
Which is more, 3/4 or 4/5?
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Fraction Chart
Which is more, 3/4 or 4/5?
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Fraction Chart
Which is more, 3/4 or 4/5?
© Activities for Learning, Inc. 2012
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Fraction Chart
Which is more, 7/8 or 8/9?
© Activities for Learning, Inc. 2012
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Fraction Chart
Which is more, 7/8 or 8/9?
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Fraction Chart
Which is more, 7/8 or 8/9?
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Fraction Chart
An interesting pattern.
© Activities for Learning, Inc. 2012
Fraction Stairs
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Fraction Stairs
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Fraction Chart
How many fourths equal a half?
© Activities for Learning, Inc. 2012
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Fraction Chart
How many fourths equal a half?
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Fraction Chart
How many fourths equal a half? Eighths?
© Activities for Learning, Inc. 2012
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14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
How many fourths equal a half? Eighths?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
How many fourths equal a half? Eighths? Sevenths?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
How many fourths equal a half? Eighths? Sevenths?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
What is 1/4 plus 1/8?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
What is 1/4 plus 1/8?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
What is 1/4 plus 1/8?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
What is 1/4 plus 1/8?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
What is 1/4 plus 1/8? [3/8]
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
If the chance of rain is 3/4, the chance it won’t rain is .
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
If the chance of rain is 3/4, the chance it won’t rain is .
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fraction Chart
If the chance of rain is 3/4, the chance it won’t rain is 1/4 .
© Activities for Learning, Inc. 2012
Partial Chart
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Partial Chart
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Partial Chart
© Activities for Learning, Inc. 2012
Partial Chart
© Activities for Learning, Inc. 2012
Fraction War
Purpose: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler.
© Activities for Learning, Inc. 2012
Fraction War
Purpose: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler.
Goal: To capture all the cards.
© Activities for Learning, Inc. 2012
Fraction War1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
14
18
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
14
18
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
14
18
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
34
58
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
34
58
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
34
58
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
34
34
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
34
34
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War
34
34
38
14
1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Fraction War1
14
14
14
14
12
12
18
18
18
18
18
18
18
18
© Activities for Learning, Inc. 2012
Advanced Fraction War
© Activities for Learning, Inc. 2012
What about fractions bigger than 1?
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fractions > 1
© Activities for Learning, Inc. 2012
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
Fractions > 1
18
© Activities for Learning, Inc. 2012
Mixed to Improper Fractions
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s
© Activities for Learning, Inc. 2012
2 =
34
114
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
two 4s
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
four 3s© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
four 3s + 1 © Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
four 3s + 1 = 13© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
four 3s + 1 = 13
353
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
four 3s + 1 = 13
353 =
185
© Activities for Learning, Inc. 2012
Mixed to Improper FractionsEach row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
342 =
114
two 4s + 3 = 11 134 =
133
four 3s + 1 = 13
353 =
185
three 5s + 3 = 18
© Activities for Learning, Inc. 2012
Help the student discover the algorithm.
© Activities for Learning, Inc. 2012
Improper to Mixed Fractions
© Activities for Learning, Inc. 2012
Improper to Mixed Fractions
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
© Activities for Learning, Inc. 2012
Improper to Mixed FractionsWrite each quantity as an improper fraction,
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
© Activities for Learning, Inc. 2012
Improper to Mixed FractionsWrite each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
© Activities for Learning, Inc. 2012
Improper to Mixed FractionsWrite each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
115
© Activities for Learning, Inc. 2012
Improper to Mixed Fractions
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
115
© Activities for Learning, Inc. 2012
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
Improper to Mixed Fractions
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
115 = 21
5
© Activities for Learning, Inc. 2012
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
Improper to Mixed Fractions
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
53
115 = 21
5
© Activities for Learning, Inc. 2012
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
Improper to Mixed Fractions
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
53
115 = 21
5
© Activities for Learning, Inc. 2012
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
Improper to Mixed Fractions
15
13
15
15
15
15
15
15
15
15
15
15
13
13
13
13
53 = 12
3
115 = 21
5
© Activities for Learning, Inc. 2012
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
Remember, let the student discover the algorithm.
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
12Shade
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
12Shade
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
12
23Shade Shade
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
12
23Shade Shade
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
12
23
14Shade Shade Shade
© Activities for Learning, Inc. 2012
Fraction of Geometric Figures
12
23
14Shade Shade Shade
© Activities for Learning, Inc. 2012
Making the Whole
© Activities for Learning, Inc. 2012
Making the Whole
13
23
© Activities for Learning, Inc. 2012
Making the WholeDraw the whole.
13
23
© Activities for Learning, Inc. 2012
Making the WholeDraw the whole.
13
13
13
13
23
© Activities for Learning, Inc. 2012
Making the WholeDraw the whole.
13
13
13
13
23
13
23
© Activities for Learning, Inc. 2012
How about a fraction of a number?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
© Activities for Learning, Inc. 2012
A Fraction of Twelve
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/2 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/2 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/2 of 12? [6]
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/3 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/3 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/3 of 12? [4]
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/4 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/4 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/4 of 12? [3]
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/5 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/5 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/5 of 12? It’s not even; there is a remainder.
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/6 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/6 of 12?
© Activities for Learning, Inc. 2012
A Fraction of Twelve
What is 1/6 of 12? [2]
© Activities for Learning, Inc. 2012
A Fraction of 100
© Activities for Learning, Inc. 2012
A Fraction of 100100
© Activities for Learning, Inc. 2012
A Fraction of 100100
50 50
© Activities for Learning, Inc. 2012
A Fraction of 100100
50 50331
3 3313 331
3
© Activities for Learning, Inc. 2012
A Fraction of 100100
50 50
25 2525 25331
3 3313 331
3
© Activities for Learning, Inc. 2012
10050 50
25 2525 25
A Fraction of 100
20 2020 20 20
3313 331
3 3313
© Activities for Learning, Inc. 2012
A Fraction of 100100
50 50
25 2525 25331
3
20 2020 20 20
1212 121
2 1212 121
2 1212 121
2 1212 121
2
3313 331
3
© Activities for Learning, Inc. 2012
A Fraction of 100100
50 50
25 2525 2520 2020 20 20
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
© Activities for Learning, Inc. 2012
Percents
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
2of 1001
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
2of 100 =
1001 50
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
2of 100 = = 50%
1001 50
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
4of 100 1
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
4of 100 =
1001 25
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
4of 100 = = 25%
1001 25
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
10of 1001
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
10of 100 =
1001 10
© Activities for Learning, Inc. 2012
PercentsPercent means a fraction of 100 or per 100.
10of 100 = = 10%
1001 10
© Activities for Learning, Inc. 2012
Now let’s simplify fractions.
© Activities for Learning, Inc. 2012
Simplifying Fractions
12
© Activities for Learning, Inc. 2012
Simplifying Fractions
36
= 12
© Activities for Learning, Inc. 2012
Simplifying Fractions
48
= 12
© Activities for Learning, Inc. 2012
Simplifying Fractions
© Activities for Learning, Inc. 2012
Simplifying Fractions
912
© Activities for Learning, Inc. 2012
Simplifying Fractions
912 3
© Activities for Learning, Inc. 2012
Simplifying Fractions
912 3
© Activities for Learning, Inc. 2012
Simplifying Fractions
912
= 343
© Activities for Learning, Inc. 2012
Simplifying Fractions
© Activities for Learning, Inc. 2012
Simplifying Fractions
© Activities for Learning, Inc. 2012
Simplifying Fractions
© Activities for Learning, Inc. 2012
Simplifying Fractions
© Activities for Learning, Inc. 2012
Simplifying Fractions
2128
© Activities for Learning, Inc. 2012
Simplifying Fractions
2128
© Activities for Learning, Inc. 2012
Simplifying Fractions
2128
© Activities for Learning, Inc. 2012
Simplifying Fractions
4572
© Activities for Learning, Inc. 2012
Simplifying Fractions
4572
© Activities for Learning, Inc. 2012
Simplifying Fractions
4572
© Activities for Learning, Inc. 2012
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2012
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2012
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2012
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2012
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2012
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2012
So how does multiplying fractions work?
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/2 of 1/2?
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/2 of 1/2?
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/2 of 1/2?
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/3 of 1/2?
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/3 of 1/2?
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/3 of 1/2?
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
What is 1/3 of 1/2? That’s multiplying fractions!
1
14
14
14
14
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Multiplying Fractions
© Activities for Learning, Inc. 2012
Multiplying Fractions
Multiplying is not exclusively repeated addition.
© Activities for Learning, Inc. 2012
Multiplying Fractions
Multiplying is not exclusively repeated addition.
Area is another facet of multiplication.
© Activities for Learning, Inc. 2012
Multiplying Fractions
12
x =12
© Activities for Learning, Inc. 2012
Multiplying Fractions
One half of one half
12
x =12
© Activities for Learning, Inc. 2012
Multiplying Fractions
One half of one half
12
x =12
© Activities for Learning, Inc. 2012
Multiplying Fractions
12
x =12
One half of one half
© Activities for Learning, Inc. 2012
Multiplying Fractions
12
x =12
One half of one half
© Activities for Learning, Inc. 2012
Multiplying Fractions
12
x =12
One half of one half
© Activities for Learning, Inc. 2012
Multiplying Fractions
12
x =12
One half of one half
© Activities for Learning, Inc. 2012
Multiplying Fractions
One half of one half
12
x =12
14
© Activities for Learning, Inc. 2012
Multiplying Fractions
One half of one half
12
x =12
14
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
Three fourths of two thirds
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
Three fourths of two thirds
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
Three fourths of two thirds
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
Three fourths of two thirds
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
Three fourths of two thirds
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
34
Three fourths of two thirds
x =
© Activities for Learning, Inc. 2012
Multiplying Fractions
Three fourths of two thirds
23
x = 34
612
© Activities for Learning, Inc. 2012
Multiplying Fractions
Three fourths of two thirds
23
x = 34
612
© Activities for Learning, Inc. 2012
Multiplying Fractions
Three fourths of two thirds
23
x = 34
612
© Activities for Learning, Inc. 2012
Multiplying Fractions
Three fourths of two thirds
23
x = =34
612
12
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
612
The total number of rectangles is
© Activities for Learning, Inc. 2012
Multiplying Fractions
x =
The total number of rectangles is 3 x 4.
23
34
612
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
612
The total number of rectangles is 3 x 4.
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
612
The total number of rectangles is 3 x 4.
The number of double crosshatched rectangles is
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
612
The total number of rectangles is 3 x 4.
The number of double crosshatched rectangles is 2 x 3.
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
612
The total number of rectangles is 3 x 4.
The number of double crosshatched rectangles is 2 x 3.
© Activities for Learning, Inc. 2012
Multiplying Fractions
23
x = 34
612
The total number of rectangles is 3 x 4.
The number of double crosshatched rectangles is 2 x 3.
© Activities for Learning, Inc. 2012
What about dividing fractions?
© Activities for Learning, Inc. 2012
What is Division?
© Activities for Learning, Inc. 2012
Process of separating into equal groups
What is Division?
© Activities for Learning, Inc. 2012
Process of separating into equal groups
either number of groups, or
What is Division?
© Activities for Learning, Inc. 2012
Process of separating into equal groups
either number of groups, or
size of the groups
What is Division?
© Activities for Learning, Inc. 2012
6 ÷ 2 = __
What is Division?
© Activities for Learning, Inc. 2012
How many 2s in 6?
6 ÷ 2 = __
What is Division?
© Activities for Learning, Inc. 2012
How many 2s in 6?
6 ÷ 2 = __
What is Division?
© Activities for Learning, Inc. 2012
How many 2s in 6?
6 ÷ 2 = __
Number of groups of 2s
What is Division?
© Activities for Learning, Inc. 2012
How many 2s in 6?
6 ÷ 2 = __
Number of groups of 2s
What is Division?
© Activities for Learning, Inc. 2012
How many 2s in 6?
6 ÷ 2 = __
Number of groups of 2s; 3 groups
What is Division?
© Activities for Learning, Inc. 2012
Dividing Fractions
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121
112
12
14
14
14
14
13
13
13
How many 1/2s in 1?
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121
112
12
14
14
14
14
13
13
13
How many 1/2s in 1?
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121
112
12
14
14
14
14
13
13
13
How many 1/2s in 1?
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121
112
12
14
14
14
14
13
13
13
How many 1/2s in 1?
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/2s in 1?
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
131 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
131 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
131 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
131 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
131 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
131 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
131 ÷ = 3
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
131 ÷ = 3
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
112
12
14
14
14
14
13
13
13
131 ÷ = 3
231 ÷ =
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
12÷ = 1
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231
How many 2/3s in 1?
112
12
14
14
14
14
13
13
13
12÷ = 1 =
32
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231
112
12
14
14
14
14
13
13
13
÷ = 32
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2 12
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2 12
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
How many 4/3s in 1? [Less than 1]
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
12
12
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
14
14
14
14
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
14
14
14
How many 4/3s in 1?
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
14
14
14
How many 4/3s in 1?
34
© Activities for Learning, Inc. 2012
13
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
112
12
14
14
14
14
13
13
13
14
14
14
34
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
34
Each green pair is a reciprocal,
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
34
Each green pair is a reciprocal, sometimes called a multiplicative inverse.
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
34
Each green pair is a reciprocal, sometimes called a multiplicative inverse.
When multiplied together, they equal 1.
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
34
Sometimes textbooks put a 1 under a whole number to make it look like a fraction,
© Activities for Learning, Inc. 2012
Dividing Fractions÷ =
121 2
131 ÷ = 3
231 ÷ =
32
÷ =1 2
÷ =1 3
12
13
÷ =1 43
34
Sometimes textbooks put a 1 under a whole number to make it look like a fraction, but it is not necessary.
1
1
1
1
© Activities for Learning, Inc. 2012
Dividing Fractions
÷ =34
112
12
14
14
14
14
13
13
13
23
© Activities for Learning, Inc. 2012
Dividing Fractions
÷ =34
112
12
14
14
14
14
13
13
13
Is the answer more or less than 1?
23
© Activities for Learning, Inc. 2012
Dividing Fractions
÷ =34
112
12
14
14
14
14
13
13
13
Is the answer more or less than 1?
23
© Activities for Learning, Inc. 2012
Dividing Fractions
÷ =34
112
12
14
14
14
14
13
13
13
Is the answer more or less than 1?
23
© Activities for Learning, Inc. 2012
Dividing Fractions
÷ =34
112
12
14
14
14
14
13
13
13
23
89
© Activities for Learning, Inc. 2012
1
14
14
14
14
Fraction Chart
12
12
110
110
110
110
110
110
110
110
110
110
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
© Activities for Learning, Inc. 2012
Fraction Chart
© Activities for Learning, Inc. 2012
Allow the student to explore the whole picture
Fraction Chart
© Activities for Learning, Inc. 2012
Allow the student to explore the whole picture
and relationships within the whole
Fraction Chart
© Activities for Learning, Inc. 2012
Allow the student to explore the whole picture
and relationships within the whole using the
linear perspective.
Focusing on Fractions
Presented by Kathleen Cotter LawerBased on the work of Joan A. Cotter, Ph.D.
35
25
© Activities for Learning, Inc. 2012