sorting to algebra developing mathematical thinkers
TRANSCRIPT
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Sorting to AlgebraDeveloping Mathematical
Thinkers
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Algebraic Ideas Breaking it up
4 40 45591940
121 11
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What does the “thick line” do?
4
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What does the “thick line” do?
4 21
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What does the “thick line” do?
4 21 25
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What about this way?
100
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What about this way?
100
27
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What about this way?
100
73
27
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Kindergarten Sorters
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4 + 5 = 9
3 + 1 = 4
7
Addition and SubtractionFrom sorting to algebra
Challenge: can you find some
that don’t work?
5x + 3y = 23
2x + 3y = 11
Is there anything interesting about Is there anything interesting about addition and subtraction addition and subtraction sentences?sentences?
13+ =6 51 4
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Back to the very beginningsPicture a young child with a small pile of buttons.
Natural to sort.
We help children refine and extend what is already natural.
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6
4
7 3 10
Back to the very beginnings
Children can also summarize.
“Data” from the buttons.
blue gray
large
small
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large
small
blue gray
AbstractionIf we substitute numbers for the original objects…
6
4
7 3 10
6
4
7 3 10
4 2
3 1
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A Cross Number PuzzleDon’t always start with the question!
5
21
8
13
912
7 6
3
1st grade
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Building the addition algorithmOnly multiples of 10 in yellow. Only less than 10 in blue.
63
38
25
1350
20 5
830
2nd grade
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Relating addition and subtraction6
4
7 3 10
4 2
3 16
4
7 3 10
4 2
3 1
2nd grade
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The subtraction algorithm
63
38
25
1350
20 5
830
25
38
63
-530
60 3
830
25 + 38 = 63 63 – 38 = 25
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The subtraction algorithm
63
38
25
1350
20 5
830
25
38
63
520
60 3
830
25 + 38 = 63 63 – 38 = 25
50 13
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597
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Place Value Bonus235 + 597 = 832
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Cross Number Puzzles and Multiplication
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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Developing a familiar multiplication algorithm
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The algebra connection: adding
4 2
3 1
10
4
6
37
4 + 2 = 6
3 + 1 = 4
10+ =7 3
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The algebra connection: subtracting
7 3
3 1
6
4
10
24
7 + 3 = 10
3 + 1 = 4
6+ =4 2
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The eighth-grade look
5x 3y
2x 3y 11
23 5x + 3y = 23
2x + 3y = 11
12+ =3x 0x = 4
3x 0 12
All from sorting buttons!
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Algebra At the Core Kindergarten – Grade 5
Focus on underlying principles allows“two for the price of one”
subtraction is un-additiondivision is un-multiplication
Mastery of traditional algorithms Easier and more exciting to learn and explore
More competently used
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For more information about Cross Number Puzzles
and Think Math! visit thinkmath.edc.org