View
219
Download
0
Category
Tags:
Preview:
Citation preview
Sorting to AlgebraDeveloping Mathematical
Thinkers
Algebraic Ideas Breaking it up
4 40 45591940
121 11
What does the “thick line” do?
4
What does the “thick line” do?
4 21
What does the “thick line” do?
4 21 25
What about this way?
100
What about this way?
100
27
What about this way?
100
73
27
Kindergarten Sorters
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
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.
6
4
7 3 10
Back to the very beginnings
Children can also summarize.
“Data” from the buttons.
blue gray
large
small
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
A Cross Number PuzzleDon’t always start with the question!
5
21
8
13
912
7 6
3
1st grade
Building the addition algorithmOnly multiples of 10 in yellow. Only less than 10 in blue.
63
38
25
1350
20 5
830
2nd grade
Relating addition and subtraction6
4
7 3 10
4 2
3 16
4
7 3 10
4 2
3 1
2nd grade
The subtraction algorithm
63
38
25
1350
20 5
830
25
38
63
-530
60 3
830
25 + 38 = 63 63 – 38 = 25
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
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597
Place Value Bonus235 + 597 = 832
Cross Number Puzzles and Multiplication
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
Developing a familiar multiplication algorithm
The algebra connection: adding
4 2
3 1
10
4
6
37
4 + 2 = 6
3 + 1 = 4
10+ =7 3
The algebra connection: subtracting
7 3
3 1
6
4
10
24
7 + 3 = 10
3 + 1 = 4
6+ =4 2
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!
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
For more information about Cross Number Puzzles
and Think Math! visit thinkmath.edc.org
Recommended