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-out-able! 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 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

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 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 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 pharris@byu.net

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

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 pharris@byu.net

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

pharris@byu.net

Problem Strings 25 x 36 1/4 x 36 0.25 x 36 0.26 x 36 0.24 x 36 pharris@byu.net

pharris@byu.net

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 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