Building Powerful Numeracy
Pamela Weber Harris
@pwharris
pamelawharris.com
pharris@byu.net
facebook.com/numeracy
Math is
figure-outable!
pharris@byu.net
Counting Strategies
Additive Thinking
Multiplicative
Thinking
Proportional
Reasoning
Algebraic
Reasoning
pharris@byu.net
Proble
m
Strings
pharris@byu.net
28 + 14
4x7+2x7
49 + 21
7x7+3x7
28 + 49
4x7+7x7
48 + 54
8x6+9x6
10 x 6 + 7 x 6
36 + 18
4a + 2a
Relational Thinking
36 + 97 = ______ + 100
3,554+2,849 = 3,403+ ____
True or False?
19.8 + 2.03 = 20 + 0.03
Relational Thinking
36 - 19 = ______ - 20
3,554 - 2,849 = ______ - 3,000
True or False?
6.2 - 3.8 = 6 - 4
19.8 - 1.98 = 20 - 2
Counting Strategies
Additive Thinking
Multiplicative
Thinking
Proportional
Reasoning
Algebraic
Reasoning
pharris@byu.net
11 x 12
pharris@byu.net
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!
pharris@byu.net
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
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
pharris@byu.net
TI-Nspire, 84, 83 and
APPS
pharris@byu.net
Proble
m
Strings
pharris@byu.net
2 x 27
4 x 27
8 x 27
10 x 27
9 x 27
5 x 27
100 x 27
99 x 27
324/27
405/27
Consider the
Multiplication and
Division Algorithms
pharris@byu.net
Graph it
pharris@byu.net
What kind of relation?
•Open:
•packs sticks.tns
•Enter the values in lists
•Enter the equation in
f (x)1 
•What questions could
•you ask?
pharris@byu.net
Proble
m
Strings
pharris@byu.net
2 x 3.2
4 x 3.2
8 x 3.2
10 x 3.2
9 x 3.2
5 x 3.2
15 x 3.2
100 x 3.2
99 x 3.2
44.8/3.2
323.2/3.2
313.6/3.2
480/3.2
PB
CC
2
4
Proble
m
Strings
8
10
9
6
5
3
400
450
456
18
25
pharris@byu.net
270 18
pharris@byu.net
Proble
m
Strings
pharris@byu.net
25 x 36
1/4 x 36
0.25 x 36
0.26 x 36
0.24 x 36
0.25 x 24
0.75 x 24
0.76 x 24
Math is Figure-outable
• Look to most efficient strategies and
build proportional reasoning at the same
time
• Teachers build own numeracy
• It’s about relationships:
-
Among numbers to solve problems
Between teachers and students to
build young mathematicians
pharris@byu.net
Building Powerful Numeracy
from Whole Numbers to
Ratios, 5-7
Pamela Weber Harris
@pwharris
pamelawharris.com
pharris@byu.net
facebook.com/numeracy