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 DOUBLE + ONE ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE DOUBLE, DOUBLE DOUBLE ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE DOUBLE, DOUBLE DOUBLE TENS ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE DOUBLE, DOUBLE DOUBLE NINES TENS ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE 5 IS HALF OF 10 DOUBLE, DOUBLE DOUBLE NINES TENS ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE DOUBLE, DOUBLE 5 IS HALF OF 10 5 AND ONE MORE DOUBLE, DOUBLE DOUBLE NINES TENS ZERO FACTS ONE FACTS DOUBLE DOUBLE + ONE 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 Proble m 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 f (x)1 •What questions could •you ask? pharris@byu.net 2 x 3.24 x 3.28 x 3.210 x 3.29 x 3 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 Proble m Strings pharris@byu.net PB CC 2 4 Proble m Strings 8 10 9 6 5 3 400 450 456 18 25 pharris@byu.net 270 18 pharris@byu.net Proble m 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 0.75 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