Building Powerful Numeracy from Whole Numbers to Ratios

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

Math is figure-outable! pharris@byu. net

0. 26 x 24 pharris@byu. net

Counting Strategies Additive Thinking Multiplicative Thinking Proportional Reasoning Algebraic Reasoning pharris@byu. net

15 - 7 pharris@byu. net

Counting Rack Rekenrek pamelawharris. com

Counting Rack Rekenrek

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 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 + ONE

ZERO FACTS ONE FACTS DOUBLE + ONE DOUBLE, DOUBLE

ZERO FACTS ONE FACTS DOUBLE + ONE DOUBLE, DOUBLE TENS

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

ZERO FACTS ONE FACTS DOUBLE + ONE DOUBLE, DOUBLE 5 IS HALF OF 10 DOUBLE, DOUBLE NINES TENS

ZERO FACTS ONE FACTS DOUBLE + ONE DOUBLE, DOUBLE 5 IS HALF OF 10 5 AND ONE MORE DOUBLE, DOUBLE NINES TENS

Practice with a Game pharris@byu. net

TI-Nspire, 84, 83 and APPS pharris@byu. net

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

Problem 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 • What questions could • you ask? pharris@byu. net

2 x 3. 24 x 3. 28 x 3. 210 x 3. 29 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 Problem Strings pharris@byu. net

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

pharris@byu. net

Problem 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. 76 x 24

pharris@byu. net

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