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Building Powerful Numeracy from Whole Numbers to Ratios, 5-7
Pamela Weber Harris @pwharris pamelawharris.com facebook.com/numeracy
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Math is figure-out-able!
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0.26 x 24
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Counting Strategies Additive Thinking Multiplicative Thinking Proportional Reasoning Algebraic Reasoning
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15 - 7
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Counting Rack Rekenrek
pamelawharris.com
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Counting Rack Rekenrek
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Problem Strings
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As Close As It Gets a) 400 b) 410 c) 419 d) 500
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As Close As It Gets ,989 a) 14 b) 1,900 c) 2,000 d) 2,100
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As Close As It Gets a) 0 b) 0.5 c) 0.75 d) 1
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Relational Thinking 36 + 97 = ______ + 100 3,554+2,849 = 3,403+ ____
True or False? =
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As Close As It Gets 14,009 - 9.19 a) 14,000 b) 5,000 c) 13,000
d) 4,000
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As Close As It Gets 1, a) 3 b) 100 c) 200 d) 300
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As Close As It Gets a) 5 b) 6 c) 4 d) 3
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Relational Thinking 36 - 19 = ______ - 20
3, ,849 = ______ - 3,000 True or False? = 6 - 4 =
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Counting Strategies Additive Thinking Multiplicative Thinking Proportional Reasoning Algebraic Reasoning
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11 x 12
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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.
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I didn’t ask you if you know it, I asked you what it is
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!
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ZERO FACTS ONE FACTS
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ZERO FACTS ONE FACTS DOUBLE
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ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE
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ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE
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ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE DOUBLE, DOUBLE
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ZERO FACTS ONE FACTS DOUBLE TENS DOUBLE + ONE DOUBLE, DOUBLE
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ZERO FACTS ONE FACTS DOUBLE NINES TENS DOUBLE + ONE DOUBLE, DOUBLE
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ZERO FACTS ONE FACTS DOUBLE NINES TENS DOUBLE + ONE 5 IS HALF OF 10
DOUBLE, DOUBLE 5 IS HALF OF 10 DOUBLE, DOUBLE DOUBLE NINES TENS
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ZERO FACTS ONE FACTS DOUBLE NINES TENS DOUBLE + ONE 5 IS HALF OF 10
DOUBLE, DOUBLE 5 IS HALF OF 10 5 AND ONE MORE DOUBLE, DOUBLE DOUBLE NINES TENS
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ZERO FACTS ONE FACTS DOUBLE NINES TENS DOUBLE + ONE 5 IS HALF OF 10
DOUBLE, DOUBLE 5 IS HALF OF 10 5 AND ONE MORE DOUBLE, DOUBLE DOUBLE NINES TENS
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Practice with a Game
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TI-Nspire, 84, 83 and APPS
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How to Build Multiplicative & Proportional Reasoning at the Same Time?
Good, rich contexts - See Cathy Fosnot Mini-lesson: Problem Strings
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Problem Strings 2 x 27 4 x 27 8 x 27 10 x 27 9 x 27 5 x 27 100 x 27
324/27 405/27 Problem Strings
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Consider the Multiplication and Division Algorithms
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Graph it
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What kind of relation? Open: packs sticks.tns
Enter the values in lists Enter the equation in What questions could you ask?
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Problem Strings 2 x 3.24 x 3.28 x 3.210 x 3.29 x 3.25 x 3.2
44.8/3.2 323.2/3.2 313.6/3.2 480/3.2 Problem Strings
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Problem Strings pharris@byu.net PB CC 2 4 8 10 9 6 5 3 400 450 456 18
25 Problem Strings
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Problem Strings 25 x 36 1/4 x 36 0.25 x 36 0.26 x 36 0.24 x 36
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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
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Building Powerful Numeracy from Whole Numbers to Ratios, 5-7
Pamela Weber Harris @pwharris pamelawharris.com facebook.com/numeracy
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