Ratios Proportional Relationships for All Pamela Weber Harris

Ratios & Proportional Relationships for All Pamela Weber Harris @pwharris pamelawharris. com pharris@byu. net

Math is figure-outable!

0. 26 x 24

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

Consider the Multiplication and Division Algorithms

11 x 12

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

2 x 274 x 278 x 2710 x 279 x 275 x 27100 x 2799 x 27 324/27 405/27 Problem Strings

Graph it

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

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

Problem Strings CC 2 4 8 10 9 6 5 3 400 PB 450 456 18 25

Problem 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

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 pharris@byu. net