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Building Powerful Numeracy from Whole Numbers to Ratios, 5-7
Pamela Weber Harris@pwharris
facebook.com/numeracy
Counting Strategies
Additive ThinkingMultiplicative
ThinkingProportional ReasoningAlgebraic Reasoning
Counting RackRekenrek
pamelawharris.com
Counting RackRekenrek
Problem Strings
As Close As It Gets
409 + 1.19
a) 400 b) 410
c) 419 d) 500
As Close As It Gets
13.2 + 1,989
a) 14 b) 1,900
c) 2,000 d) 2,100
As Close As It Gets
a) 0 b) 0.5
c) 0.75 d) 1
Relational Thinking
36 + 97 = ______ + 100
3,554+2,849 = 3,403+ ____
True or False?
19.8 + 2.03 = 20 + 0.03
As Close As It Gets
14,009 - 9.19
a) 14,000 b) 5,000
c) 13,000 d) 4,000
As Close As It Gets
1,002 - 899
a) 3 b) 100
c) 200 d) 300
As Close As It Gets
a) 5 b) 6
c) 4 d) 3
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 ThinkingMultiplicative
ThinkingProportional ReasoningAlgebraic Reasoning
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!
ONE FACTS
ZERO FACTS
ONE FACTS
ZERO FACTS
DOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
DOUBLE, DOUBLEDOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
TENS
DOUBLE, DOUBLEDOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
TENS
NINES
DOUBLE, DOUBLEDOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
TENS
NINES
5 IS HALF OF 10
DOUBLE, DOUBLEDOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
TENS
NINES
5 IS HALF OF 10
5 AND ONE MOREDOUBLE, DOUBLEDOUBLE
ONE FACTS
ZERO FACTS
DOUBLE
DOUBLE + ONE
DOUBLE, DOUBLE
TENS
NINES
5 IS HALF OF 10
5 AND ONE MOREDOUBLE, DOUBLEDOUBLE
How to Build Multiplicative & Proportional Reasoning at the
Same Time?
•Good, rich contexts - See Cathy Fosnot
•Mini-lesson: Problem Strings
Problem
Strings
2 x 274 x 278 x 27
10 x 279 x 275 x 27
100 x 2799 x 27324/27405/27
What kind of relation?
•Open:
•packs sticks.tns
•Enter the values in lists
•Enter the equation in
•What questions could•you ask?
f (x)1 =
Problem
Strings
2 x 3.24 x 3.28 x 3.210 x 3.29 x 3.25 x 3.2
15 x 3.2100 x 3.299 x 3.244.8/3.2
323.2/3.2313.6/3.2480/3.2
Problem
Strings
25 x 361/4 x 360.25 x 360.26 x 360.24 x 360.25 x 24 0.75 x 240.76 x 24
Math is Figure-out-able
•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
Building Powerful Numeracy from Whole Numbers to Ratios, 5-7
Pamela Weber Harris@pwharris
facebook.com/numeracy
