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Ratios & Proportional Relationships: Building Mathematical Understanding

Discover effective strategies for developing proportional reasoning skills and building mathematical relationships among numbers. Learn from Pamela Weber Harris, a renowned math educator, how to make math figure-out-able for all students.

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Ratios & Proportional Relationships: Building Mathematical Understanding

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

  2. Math is figure-out-able!

  3. 0.26 x 24

  4. Counting StrategiesAdditive ThinkingMultiplicative ThinkingProportional ReasoningAlgebraic Reasoning

  5. Unitizing • Considering multiple items as one thing

  6. Counting RackRekenrek Counting Additive

  7. Counting RackRekenrek

  8. Counting RackRekenrek

  9. Consider the Multiplication and Division Algorithms

  10. 11 x 12

  11. 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.

  12. 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!

  13. How to Build Multiplicative & Proportional Reasoning at the Same Time? • Good, rich contexts • Mini-lesson: Problem Strings

  14. 2 x 274 x 278 x 2710 x 279 x 275 x 27100 x 2799 x 27 324/27 405/27 Problem Strings

  15. Graph it

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

  17. 2 x 3.24 x 3.28 x 3.210 x 3.29 x 3.25 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

  18. Problem Strings

  19. 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 Problem Strings

  20. 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

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

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