Reflection: Adjustments to Practice Which is the blackest? - Section 2: Warm up


I was really nervous going into this lesson that the students would not be able to make the necessary observations and conclusions to define the idea of ratio. I want to do less of the telling and have them do more of the figuring and discovering, but I was not entirely sure that they would be able to. I found that students are much more capable than I thought and they often exceed my expectations

The most important thing for me as a teacher in this lesson was to listen to the language students were using to explain their observations and encourage them to elaborate their thinking. Because they don't initially use academic language it can be difficult to understand their meaning. Don't fear that their observations are on the wrong track! Instead, probe them for more detail. When they say things like "As the floors get smaller, the white tiles are being taken away" ask them to tell you a little more about that (or "how does that make this floor blacker?"). They may reply that when only the white tiles are taken away and none of the black tiles are, the floor ends up with more black than white tiles. 

The students may be thinking much more concretely than you do. When I first heard some of the ways in which students were explaining their ideas my heart sank, because I didn't really understand what they were thinking and how it applied. Once I probed for more, however, their thinking and its relevance became clear.

Using their own language helps them attach meaning to the quantities and will help them make sense of the new terminology. It also creates a need for more precise language which they will more readily recognize and accept when it is introduced. When students work in a group and hear all the different ways to explain the same idea, they gain a more complete nuanced understanding of the concept and the terminology.

  The students will get there!
  Adjustments to Practice: The students will get there!
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Which is the blackest?

Unit 5: Writing and comparing ratios
Lesson 1 of 14

Objective: SWBAT understand and explain the meaning of a ratio.

Big Idea: A ratio is a comparison of two or more quantities or amounts.

  Print Lesson
Math, Number Sense and Operations, cooperative learning activity, ratio, using text, ratios, pattern, sense making, perserverance
  54 minutes
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