MSIS #5 Rational Numbers & Ratios

The final institute in Shanghai. Ramblings and note takings

Opening with convince us that 1/10 of 450 is 45.

  • Equivalence
  • “Who did it differently?”
    • chop of the zero
    • move the decimal to the left
    • percent
    • multiply by a tenth
    • divide by 10
  • Record – why?

“This is unquestionably the hardest piece of mathematics to teach and the second most important to learn (after operations).”

Rates / ratios – do they “live” on the number line?

  • 6/10 + 6 /10 = 12/10, but…
  • In the first half, someone made 6 out of 10 free throws. In the second half, an additional 6 shots out of 10 were made. 12 out of 20 were made
  • Examine the relationship between the values (double number line versus single)


Bridge to HS -shift from additive thinking to multiplicative thinking

Model – what happens between the problem and the solution

Convince us in two different ways. How do the two different ways talk to each other?


A blurry miserable image but…writing ratios as fractions. Should a part:part ratio be written as a fraction as it does not represent a part to whole?


Student Talk

  • Who is struggling? Let us know what you are thinking.

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