Decimal Multiplication &
Division Like You’ve Never
Seen
Pamela Weber Harris
@pwharris
pamelawharris.com
pharris@byu.net
Book Signing
Pamela Weber Harris
Heinemann #516
Math is
figure-outable!
Counting
Additive
Multiplicative
Proportional Reasoning
Algebraic Reasoning
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11 x 12
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132 ... Um, I knew 10 x 12 = 120, and um, then I just
add 12 because 1 x 12 = 12 and um I just add 12 to
120 and I got 132.
I didn’t ask you if you know
it, I asked you what it is.
What do you know...
and figure it out from there!
ZERO FACTS
ONE
FACTS
ZERO FACTS
ONE FACTS
DOUBLE
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
DOUBLE, DOUBLE
DOUBLE
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
DOUBLE, DOUBLE
DOUBLE
TENS
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
DOUBLE, DOUBLE
DOUBLE
NINES
TENS
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
5 IS HALF OF 10
DOUBLE, DOUBLE
DOUBLE
NINES
TENS
ZERO FACTS
ONE FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
5 IS HALF OF 10
5 AND ONE MORE
DOUBLE, DOUBLE
DOUBLE
NINES
TENS
Practice with a Game
Proble
2 x 274 x 278 x 2710 x 279
275 x 27100 x 2799 x 27
m
324/27
405/27
Strings
2 x 3.24 x 3.28 x 3.210 x 3.29 x 3
x 3.2
15 x 3.2100 x 3.299 x 3.2
44.8/3.2
323.2/3.2
313.6/3.2
480/3.2
Proble
m
Strings
Proble
m
Strings
3x8
6x4
8x6
4 x 12
16 x 3
25 x 64
2.5 x 3.2
1.8 x 3.5
Proble
m
Strings
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Proble
m
Strings
9 x 10
9x4
9 x 14
10 x 11
7 x 11
17 x 11
12 x 16
1.2 x 16
Proble
m
Strings
7 x 60
7 x 59
30 x 12
29 x 12
6x4
6 x 40
6 x 39
6 x 0.1
6 x 4.1
6 x 3.9
Proble
m
Strings
8 x 60
8 x 59
8 x 0.1
8 x 0.2
8 x 6.2
8 x 5.8
48.8 / 8
47.2 / 8
Counting
Additive
Multiplicative
Proportional Reasoning
Algebraic Reasoning
Not just about any
way to do a
problem......
The Landscape of
Learning
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Math is Figure-outable
• Look to most efficient strategies
• Teachers build own numeracy
• It’s about relationships:
-
Among numbers to solve problems
Between teachers and students to
build young mathematicians
Decimal Multiplication &
Division Like You’ve Never
Seen
Pamela Weber Harris
facebook.com/numeracy
@pwharris
pamelawharris.com
pharris@byu.net
Book signing
Heinemann #516