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Ratios & Proportional Relationships for All Pamela Weber Harris @pwharris pamelawharris.com [email protected] Math is figure-outable! 0.26 x 24 QuickTime™ and a H.264 decompressor are needed to see this picture. 270 18 QuickTime™ and a H.264 decompressor are needed to see this picture. QuickTime™ and a H.264 decompressor are needed to see this picture. QuickTime™ and a H.264 decompressor are needed to see this picture. Counting Strategies Additive Thinking Multiplicative Thinking Proportional Reasoning Algebraic Reasoning Unitizing • Considering multiple items as one thing Counting Rack Rekenrek Counting Additive Counting Rack Rekenrek Counting Rack Rekenrek Consider the Multiplication and Division Algorithms 11 x 12 QuickTime™ and a YUV420 codec decompressor are needed to see this picture. 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! How to Build Multiplicative & Proportional Reasoning at the Same Time? • Good, rich contexts • Mini-lesson: Problem Strings Proble 2 x 274 x 278 x 2710 x 279 x 275 x 27100 x m 2799 x 27 324/27 Strings 405/27 Graph it 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? 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 CC PB 2 4 Proble m Strings 8 10 9 6 5 3 400 450 456 18 25 Proble m Strings 25 x 361/4 x 360.25 x 360.26 x 360.24 x 360.25 x 24 0.75 x 240.76 x 24 QuickTime™ and a H.264 decompressor are needed to see this picture. 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 Ratios & Proportional Relationships for All Pamela Weber Harris @pwharris pamelawharris.com [email protected]