Reflection: Discourse and Questioning Ratio soup assessment day - Section 2: Warm up


I was really happy with the way this warm up went. I was afraid students would try to compare one fraction at a time using a whole variety of ratios when I really wanted them to focus on the simplified part to total ratios. Normally I am happy with multiple methods, but here I really just wanted to focus on using common denominators. It worked out really well because three of the ratios I had given them simplify to a common denominator and only one that didn't. Most of them immediately recognized that the three were easy to put in order because of the common denominator. They got stuck exactly where I had anticipated and didn't know where the last one fit.

When my students asked for help I asked them to explain their thinking to me first. Then I had my questions ready for them. Sometimes it helps just to revoice their thinking in mathematical terms.

  • What made the first three so much easier to compare?
  • So, it would be easier if this last one had the same denominator too?

As I watched my "peer instructors" working with their groups I noticed that the information they were relying on most was the visual "scaling". I took my cue from them and asked students to focus on the designs when answering my questions:

  • "Show me in the picture where we see the (2/9 or 4/9) in the designs?"
  • "What does the 9 represent in the picture?"
  • "Do we see that in the other designs?"
  • "So, these three (A,B,C) are all the same size, but this last one isn't?"
  • "So, it's easier when you can scale the design to '9 squares'?"

My role also included helping students listen to and understand each other's thinking. One student in the group might explain their thinking visually, but another student in the group might need to see how it relates to the math.


  Discourse and Questioning: Teacher's role during student discourse
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Ratio soup assessment day

Unit 5: Writing and comparing ratios
Lesson 7 of 14

Objective: SWBAT explain the concept of "building up" a ratio pattern as a model for making equivalent fractions in order to make common denominators.

Big Idea: Repeating the same pattern over and over is a concrete model for understanding the abstract process of multiplying the numerator and denominator by a common factor.

  Print Lesson
Math, modeling, Number Sense and Operations, common denominator, simplifying ratio, ratios, part to part, writing, part to whole, comparing ratio, pattern
  54 minutes
model for scaling
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