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Between 2 Numbers • Chewable Math • Visual Patterns

 

Lessons From the Classroom

Fawn Nguyen Fawn Nguyen

Comparing Fractions

I was taught to find a common denominator when comparing or ordering fractions. Find the LCM. Even change them into decimals.

Instead, I want to compare fractions in these three ways:

  1. Using number sense and the fraction 1/2

  2. Finding a common numerator

  3. Thinking of them as perfect pinks or not

Compare 3/4 and 5/12.

3/4 is more than 1/2, and 5/12 is less than 1/2, hence 3/4 > 5/12.

Compare 1/5 and 2/7.

1/5 is the same as 2/10, and 2/10 is smaller than 2/7 because pizza.

Compare 5/7 and 6/9.

A perfect pink color is made from 1 part red and 2 parts white, expressed as 1/2. I have a visual sense of this color, this red/white ratio of 1/2. Anything greater than 1/2 is dark pink, and anything less is light pink.

So 5/7 is darker, and to get to the color of 6/9, I’d need to do this: 5/7 + 1/2 = 6/9. If I’m adding something less dark than what I’d started with, then I’m going to dilute the color, so 6/9 is less dark than 5/7. I conclude 5/7 > 6/9.

Of course if I add the exact same color to itself, then there should be no change: 2/3 + 2/3 = 4/6.

Compare 19/60 and 21/55.

19/60 is light pink, so is 21/55. To get from 19 to 21, I’d need to add 2 reds, and to get from 60 to 55, I’d take away 5 whites. The net effect is more red, making 21/55 darker, or 19/60 < 21/55.

This is not unlike how batting averages work.

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Teach Teach

Smallest and Largest

Most of my 6th graders struggled with this handout today. Only 4 of 36 students scored 8 out of 8 on it. I offered no help on this except my reading the instructions to them and reiterating that for each operation, the two numbers must be different.

I retyped this task from the Noyce Foundation.

If you teach 6th grade math or if you could share this with a colleague who does, I'd be very curious to learn how your kids might do on this. (Guess I'm now wondering how 7th and 8th graders fare on this too.)

I'm feeling disheartened and ineffective with this group of 37 kids. If I squinted really hard, then maybe I could spot just a few tiny specks of mathematical growth in them.

This teaching thing is tough.

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