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. ShouldÂ 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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