Post on 16-Aug-2020
© Activities for Learning, Inc. 2017
Taking the Fear Out of Fractions
presented by Kathleen Cotter Lawler based on the work of Dr. Joan A. Cotter
3 5
2 5
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count the blue fish
count all the fish
What fraction of the fish are blue?
Fraction Model: “Fish Tank”
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Fraction Model: “Words”
This is fourths. This is thirds.
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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. 2017
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. www.askoxford.com
Specialists also suggest refraining from using more than one pie chart for comparison.
www.statcan.ca
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Problems Teaching Fractions
• Common meaning is “small amount.”• Introduced as part of a whole (not whole story).• Fraction names use ordinal words.• Are “improper” fractions somehow
undesirable?• Mixed numbers different in arithmetic, algebra.• Our culture implies fractions are difficult.• Many adults have only a partial understanding.
© Activities for Learning, Inc. 2017
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Fraction Model: Linear Chart
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© Activities for Learning, Inc. 2017
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Fraction Model: “Color”
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Fraction Model: “Missing Parts” 1
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© Activities for Learning, Inc. 2017
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Fraction Chart
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Ask the children to put it together like a puzzle.
© Activities for Learning, Inc. 2017
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Fraction Chart
An interesting pattern.
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Fraction Stairs
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Fraction Stairs
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A hyperbola.
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Fraction Stairs
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Two hyperbolas.
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What about ?
Definition of a Fraction
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A fraction is part of a set or part of a whole.Textbook definition
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Definition of a Fraction
A number in the form where b ≠ 0.Mathematical Definition
ab
An expression that indicates the quotient of two quantities.
American Heritage Dictionary
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Fraction Naming
• Until now, 1 was considered the smallest unit.
• Fraction – to fracture, to break, to divide.• Today, we will fracture 1, although always
into equal pieces.
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Fraction Naming
1 One wholedivided into
3 three equal parts
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Fraction Naming
1 Onedivided bythree3
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Fraction Naming 1
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In English, we use ordinal numbers to name fractions, with the exception of half.
1Read as “one-third.”
3
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= Books Reading
Games provide interesting repetition needed for automaticity.
Games also provide an application for new information.
Games Math
Games
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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. 2017
Unit Fraction War
1 4
1 5
© Activities for Learning, Inc. 2017
1
Fraction Chart
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How many fourths in a whole?
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© Activities for Learning, Inc. 2017
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Fraction Chart
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How many sixths?How many fourths in a whole?
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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
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3 5
Concentrating on One
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More Fraction Naming
Read as “two-thirds.”
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1Two is3
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s
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More Fraction Naming
1 Onedivided by
3 three
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More Fraction Naming 1 1
2 Twodivided into
3 three equal parts
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More Fraction Naming 1
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1
1two
3s=
2 Twodivided by
3 three
© Activities for Learning, Inc. 2017
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Fraction Chart
Which is more, 3/4 or 4/5?
© Activities for Learning, Inc. 2017
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Fraction Chart
Which is more, 7/8 or 8/9?
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Fraction Circles
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Which is more, 4/5 or 5/6? Which model is easier?
© Activities for Learning, Inc. 2017
Partial Chart
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© Activities for Learning, Inc. 2017
Partial Chart
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© Activities for Learning, Inc. 2017
Partial Chart
© Activities for Learning, Inc. 2017
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. 2017
Fraction War 1
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© Activities for Learning, Inc. 2017
Advanced Fraction War
*
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Equivalent Fractions
How many fourths equal a half?
© Activities for Learning, Inc. 2017
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Equivalent Fractions
How many fourths equal a half? Eighths?
© Activities for Learning, Inc. 2017
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Equivalent Fractions
How many fourths equal a half? Eighths?
© Activities for Learning, Inc. 2017
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Equivalent Fractions
How many fourths equal a half? Eighths? Sevenths?
© Activities for Learning, Inc. 2017
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Fractions Greater Than 1
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Mixed to Improper Fractions Each row of connected rectangles represents 1.
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Mixed to Improper Fractions Each row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
© Activities for Learning, Inc. 2017
Mixed to Improper Fractions Each row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
3 4 2 = 11
4
© Activities for Learning, Inc. 2017
Mixed to Improper Fractions Each row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
3 4 2 = 11
4
two 4s + 3 = 11
© Activities for Learning, Inc. 2017
Mixed to Improper Fractions Each row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
3 4 2 = 11
4
two 4s + 3 = 11 1 3 4 = 13
3
© Activities for Learning, Inc. 2017
Mixed to Improper Fractions Each row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
3 4 2 = 11
4
two 4s + 3 = 11 1 3 4 = 13
3
four 3s + 1 = 13
© Activities for Learning, Inc. 2017
Mixed to Improper Fractions Each row of connected rectangles represents 1.
Write each quantity as a mixed number and as an improper fraction.
3 4 2 = 11
4
two 4s + 3 = 11 1 3 4 = 13
3
four 3s + 1 = 13
3 5 3 = 18
5
three 5s + 3 = 18
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Help the student discover the algorithm.
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Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
1 5
1 3
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 3
1 3
1 3
1 3
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Improper to Mixed Fractions
11 5 = 2 1
5
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
1 5
1 3
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 3
1 3
1 3
1 3
© Activities for Learning, Inc. 2017
Improper to Mixed Fractions
= 1 2 3
11 5 = 2 1
5
Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number.
1 5
1 3
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 5
1 3
1 3
1 3
1 3
5 3
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Remember, let the student discover the algorithm.
© Activities for Learning, Inc. 2017
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Simplifying Fractions
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
21 28
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
45 72
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
Why does this work?
45 72
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1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
12 16
© Activities for Learning, Inc. 2017
1 2 3 4 5 6 7 8 92 4 6 8 10 12 14 16 183 6 9 12 15 18 21 24 274 8 12 16 20 24 28 32 36
10203040
6 12 18 24 30 36 42 48 54 607 14 21 28 35 42 49 56 63 708 16 24 32 40 48 56 64 72 809 18 27 36 45 54 63 72 81 9010 20 30 40 50 60 70 80 90 1
5 10 15 20 25 30 35 40 45 50
00
Simplifying Fractions
12 16
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Simplifying Fractions
12 16
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Simplifying Fractions
12 16 4
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Simplifying Fractions
12 16 = 3
4 4
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Let’s look at adding fractions….
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Fraction Chart
What is + ?
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© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
1
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© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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© Activities for Learning, Inc. 2017
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Fraction Chart
What is + ?14
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© Activities for Learning, Inc. 2017
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Fraction Chart
What is + ?14
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© Activities for Learning, Inc. 2017
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Fraction Chart
What is + ?14
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38
© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
1
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19
13
13
13
15
15
15
15
15
16
16
16
16
16
16
17
17
17
17
17
17
17
12
13
© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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
12
13
© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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
12
13
© Activities for Learning, Inc. 2017
Fraction Chart
What is + ?
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
12
13
56
© Activities for Learning, Inc. 2017
Fraction Chart
What is of ?
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
12
12
© Activities for Learning, Inc. 2017
Fraction Chart 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
What is of ?12
12
© Activities for Learning, Inc. 2017
Fraction Chart 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
What is of ?13
12
© Activities for Learning, Inc. 2017
Fraction Chart 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
What is of ? That’s multiplying fractions! 13
12
© Activities for Learning, Inc. 2017
Multiplying Fractions
Multiplying is not exclusively repeated addition.
1 2 × = + ? 1
21 2
4 × 4 = 4 + 4 + 4 + 4
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Multiplying Fractions
Multiplying is not exclusively repeated addition.
Area is a better model.
4 × 4 =
© Activities for Learning, Inc. 2017
Multiplying Fractions
One half of one half
1 2 × = 1
2
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Multiplying Fractions
1 2 × = 1
2
One half of one half
© Activities for Learning, Inc. 2017
Multiplying Fractions
1 2 × = 1
2
One half of one half
© Activities for Learning, Inc. 2017
Multiplying Fractions
One half of one half
1 2 × = 1
21 4
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Multiplying Fractions
One half of one half
1 2 × = 1
21 4
© Activities for Learning, Inc. 2017
Multiplying Fractions
2 3 × = 3
4
Three fourths of two thirds
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Multiplying Fractions
2 3 × = 3
4
Three fourths of two thirds
© Activities for Learning, Inc. 2017
Multiplying Fractions
2 3 × = 3
4
Three fourths of two thirds
© Activities for Learning, Inc. 2017
Multiplying Fractions
2 3 × = 3
4
Three fourths of two thirds
© Activities for Learning, Inc. 2017
Multiplying Fractions
Three fourths of two thirds
2 3 × = 3
4 6
12
© Activities for Learning, Inc. 2017
Multiplying Fractions
2 3 × = 3
4 6
12
The total number of rectangles is 3 × 4.
© Activities for Learning, Inc. 2017
Multiplying Fractions
2 3 × = 3
4 6
12
The total number of rectangles is 3 × 4.
The number of colored crosshatched rectangles is 2 × 3.
© Activities for Learning, Inc. 2017
Process of separating into equal groups
w either number of groups, or
w size of the groups
What is Division?
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How many 2s in 6?
6 ÷ 2 = __
What is Division?
© Activities for Learning, Inc. 2017
How many 2s in 6?
6 ÷ 2 = __
Number of groups of 2s; 3 groups
What is Division?
© Activities for Learning, Inc. 2017
How many 2s in 6?
6 ÷ 2 = __
Two groups; 3 in each group
What is Division?
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 1
112
12
14
14
14
14
13
13
13
How many 1/2s in 1?
© Activities for Learning, Inc. 2017
Dividing Fractions
112
12
14
14
14
14
13
13
13
÷ = 1 2 1
How many 1/2s in 1?
© Activities for Learning, Inc. 2017
Dividing Fractions
112
12
14
14
14
14
13
13
13
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Dividing Fractions
112
12
14
14
14
14
13
13
13
How many 1/3s in 1?
1 3 1 ÷ =
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Dividing Fractions
112
12
14
14
14
14
13
13
13
1 3 1 ÷ = 3
÷ = 2 1 2 1
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Dividing Fractions
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 3
How many 2/3s in 1?
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 3
How many 2/3s in 1?
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 3
3 2
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 3
3 2
÷ = 1 3 4
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
How many 3/4s in 1?
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 3
3 2
÷ = 1 = 1 3 4
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
How many 3/4s in 1?
1 3
4 3
© Activities for Learning, Inc. 2017
Dividing Fractions
÷ = 1 2 3
3 2
÷ = 1 3 4
4 3
÷ = 1 2 5
5 2
÷ = 1 5 8
8 5
÷ = 1 4 7
7 4
Guide the student to making the discovery that the answers are the inverted form of the divisor, the number by which another number is to be divided.
1 6 1 ÷ = 6
1 5 1 ÷ = 5
1 4 1 ÷ = 4
1 3 1 ÷ = 3
÷ = 2 1 2 1
© Activities for Learning, Inc. 2017
Fraction Division War
Purpose: Practice in dividing fractions. To help the children realize the
quotient is the inverted form of the divisor.
Goal: To collect all, or most, of the cards by having the greatest quotient.
© Activities for Learning, Inc. 2017
Fraction Division War
© Activities for Learning, Inc. 2017
Fraction Division War
1
1
© Activities for Learning, Inc. 2017
Fraction Division War
1 2
1 4
= 2
= 4
1
1
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
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÷ = 8
More Dividing Fractions
÷ = 1 4 1 4
1 4 2
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More Dividing Fractions
÷ = 1 4 1 4
÷ = 2 × (1 ÷ ) 1 4 2 1
4
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More Dividing Fractions
÷ = 1 4 1 4
= 2 × 4 = 8
÷ = 2 × (1 ÷ ) 1 4 2 1
4
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More Dividing Fractions
÷ = 1 4 1 4
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
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More Dividing Fractions
÷ = 1 4 1 4
÷ = 12 1 4 3 1 1
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
÷ = 3 × (1 ÷ ) 1 4 3 1
4 1
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
= 3 × 4 = 12
÷ = 3 × (1 ÷ ) 1 4 3 1
4 1
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
÷ = 2 × (1 ÷ ) = 2 × 4 = 8
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = 1 4
1 2
1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
÷ = 2 × (1 ÷ ) = 2 × 4 = 8
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = 2 1 4
1 2
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = × (1 ÷ ) 1 4
1 4
1 2
1 2
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
= × 4 = 2 1 2
÷ = × (1 ÷ ) 1 4
1 4
1 2
1 2
÷ = 2 × (1 ÷ ) = 2 × 4 = 8
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = × (1 ÷ ) = × 4 = 2 1 4
1 4
1 2
1 2
1 2
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
© Activities for Learning, Inc. 2017
More Dividing Fractions
÷ = 1 4 1 4
÷ = × (1 ÷ ) = × 4 = 1 4
1 4
1 3
1 3
1 3
4 3
÷ = × (1 ÷ ) = × 4 = = 3 1 4
1 4
3 4
3 4
3 4
12 4
÷ = 2 × (1 ÷ ) = 2 × 4 = 8 1 4 2 1
4
÷ = 3 × (1 ÷ ) = 3 × 4 = 12 1 4 3 1
4 1
÷ = × (1 ÷ ) = × 4 = 2 1 4
1 4
1 2
1 2
1 2
© Activities for Learning, Inc. 2017
Harder Fraction Division War
1 2
1 4
1 6
2 3
*
© Activities for Learning, Inc. 2017
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. 2017
Fraction Chart
Allow the student to explore the whole picture and relationships within the whole using the linear perspective.
© Activities for Learning, Inc. 2017
In Conclusion …
Math needs to be taught so95 percent is understood andonly 5 percent memorized.
Richard Skemp -- major pioneer in
mathematics education
© Activities for Learning, Inc. 2017
In Conclusion …
Our goal as a teacher of mathematics is to help our students transform, expand, and refine these beginning ideas into deeper mathematical thinking.
– Dr. Joan A. Cotter
© Activities for Learning, Inc. 2017
Taking the Fear Out of Fractions
presented by Kathleen Cotter Lawler based on the work of Dr. Joan A. Cotter
3 5
2 5