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# Building Powerful Numeracy from Whole Numbers to Ratios, 5-7

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Building Powerful Numeracy Pamela Weber pamelawharris.com facebook.com/numeracy.

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Building Powerful Numeracy from Whole Numbers to Ratios, 5-7
Pamela Weber Harris @pwharris pamelawharris.com facebook.com/numeracy

Math is figure-out-able!

0.26 x 24

Counting Strategies Additive Thinking Multiplicative Thinking Proportional Reasoning Algebraic Reasoning

15 - 7

Counting Rack Rekenrek
pamelawharris.com

Counting Rack Rekenrek

Problem Strings

As Close As It Gets a) 400 b) 410 c) 419 d) 500

As Close As It Gets ,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? =

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, 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, ,849 = ______ - 3,000 True or False? = 6 - 4 =

Counting Strategies Additive Thinking Multiplicative Thinking Proportional Reasoning Algebraic Reasoning

11 x 12

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
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

ZERO FACTS ONE FACTS DOUBLE TENS DOUBLE + ONE DOUBLE, DOUBLE

ZERO FACTS ONE FACTS DOUBLE NINES TENS DOUBLE + ONE DOUBLE, DOUBLE

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

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

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

Practice with a Game

TI-Nspire, 84, 83 and APPS

How to Build Multiplicative & Proportional Reasoning at the Same Time?
Good, rich contexts - See Cathy Fosnot Mini-lesson: Problem Strings

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

Consider the Multiplication and Division Algorithms

Graph it

What kind of relation? Open: packs sticks.tns
Enter the values in lists Enter the equation in What questions could you ask?

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

Problem Strings pharris@byu.net PB CC 2 4 8 10 9 6 5 3 400 450 456 18
25 Problem Strings

Problem Strings 25 x 36 1/4 x 36 0.25 x 36 0.26 x 36 0.24 x 36

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 pamelawharris.com facebook.com/numeracy

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