Transcript From Buttons to Algebra: Learning the Ideas and Language

Sorting to Algebra
Developing Mathematical
Thinkers
Cross Number Puzzles
Puzzles are not "dessert" for after the "real" work is done.
Selected properly and introduced thoughtfully, they can be
the real work.
EDC
What am I supposed to do?
What CAN I do?
Algebraic Ideas Breaking it up
59
4
40
45
19
40
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
Addition and Subtraction
From sorting to algebra
4+5=9
5x + 3y = 23
3+1=4
2x + 3y = 11
5
17 + 46 = 13
Challenge: can
you find some
that don’t work?
Is there anything interesting about
addition and subtraction
sentences?
Back to the very beginnings
Picture a young child
with a small pile of
buttons.
Natural to sort.
We help children refine
and extend what is
already natural.
Back to the very beginnings
blue
gray
6
small
4
large
7
3
10
Children can also
summarize.
“Data” from the buttons.
Abstraction
If we substitute numbers for the original objects…
blue
gray
small
6
4
2
6
large
4
3
1
4
10
7
3
10
7
3
A Cross Number Puzzle
Don’t always start with the question!
7
6
13
5
3
8
12
9
21
1st grade
Building the addition algorithm
Only multiples of 10 in yellow. Only less than 10 in blue.
20
5
25
30
8
38
50
13 63
2nd grade
Relating addition and subtraction
2nd grade
4
10
2
3
6
7
3
4
1
1
4
3
7
6
3
2
10
4
The subtraction algorithm
20
5
25
60
3
63
30
8
38
30
8
38
50
13 63
30
-5
25
25 + 38 = 63
63 – 38 = 25
The subtraction algorithm
20
5
25
50
60 13
3 63
30
8
38
30
8
38
50
13 63
20
5
25
25 + 38 = 63
63 – 38 = 25
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 597
Place Value Bonus
235 + 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
6
4+2=6
3
1
4
3+1=4
7
3
10
7 + 3 = 10
The algebra connection: subtracting
7
3
10
7 + 3 = 10
3
1
4
3+1= 4
4
2
6
4 +2 = 6
The eighth-grade look
5x
3y 23
5x + 3y = 23
2x
3y
11
2x + 3y = 11
3x
0
12
3x + 0 = 12
x=4
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-addition
division 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