## Reflection: Flexibility Comparing ratios - Section 3: Exploration

I needed to adjust this lesson in two ways the second time around. Firstly, I decided not to make students come up with the idea for a table or to work in small groups to figure out what types of ratios could be written. I felt that these both detracted from the focus on common denominators, which is the main point I wanted them to notice. Instead I asked the whole class what types of ratios we could write for the three tile designs (black:white, white:black, black/total, white/total) and built the table as a whole class. This made the time go faster as small groups just filled in the ratios giving more time to focus on which of the types of ratios were easier to compare and why.

The other adjustment came in response to a student during class. When I asked her to explain which design she thought was blackest she chose the correct one, but used part:part reasoning instead of part/total reasoning. She said that the black to white tile ratio for her choice was 5:4 which meant that there were more black tiles than white tiles. Her explanation was absolutely correct, but it didn't lead to the intended discussion of common denominators. The problem is that only one of the designs contains more black than white tiles, which makes this a viable argument, but doesn't emphasize the usefulness of common denominators.

To fix the problem I drew a fourth design with 9 total tiles and all but the center are black.With two designs containing more black than white tiles, one with a black to white ratio of 5:4 and the other with 8:1, it's a little harder to compare the part:part ratios. My students more easily came to the conclusion that it was easier to compare the black to total ratios of 5/9 and 8/9.

# Comparing ratios

Unit 5: Writing and comparing ratios
Lesson 6 of 14

## Big Idea: It's easier to compare ratios when one of the quantities is the same and easiest with common denominators.

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Standards:
Subject(s):
Math, Number Sense and Operations, equivalent ratios, ratios, comparing, common denominator, part to part, part to whole, ratio table, pattern
54 minutes

### Erica Burnison

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