# 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. 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.