Reflection: Flexibility The Decimal Slide - Section 3: Revisiting Proportion


It is really important to take time for student questions. It may mean you need to take two days for a lesson you expected to take one or that you take a completely different turn, but many student questions can help push student learning forward and can serve to clarify student understanding. Sometimes it is hard to recognize when a student question contains an idea worth exploring with the whole class, which is why it is really important to try to fully understand what the student is trying to say. I like to encourage student questions as much as I can. Some I just answer, some I expect and have a demo ready, and some I want to turn back to the whole class for further investigation. This last type is the one I'm talking about here. When a question truly comes from student curiosity about the math or when it makes connections to other topics we have or will cover or when it really highlight's a tricky part of the math that's when I want to take some extra time. I like to make a big deal and get extra nerdy and excited about it!

When we were discussing how all the representations of 1/10 were proportional students had come up with several equivalent fractions like 2/20 and had provided context from earlier lessons (lady bug lessons). Students said that if 2 lady bugs were spotted out of a total of 20 lady bugs that was the same ratio as 1 spotted lady bug for every 10 total lady bugs. One student, Cristina, asked if the part to part ratio 2/18 would be proportional as well. After turning this question back to the class who initially thought that it couldn't be proportional, but they were uncomfortable with their conclusion. We spent some time defining the terms (spotted, non-spotted, and total) before they concluded that as long as we defined the fraction as a part to part fraction it was proportional, but if that was not defined they would say 2/18 was not proportional to 2/20.

Exploring this idea helped students gain a greater understanding of the nuances of part to part and part to whole ratios and the need for precision.

  Flexibility: Allowing time to investigate student questions
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The Decimal Slide

Unit 8: Exploring Rational Numbers
Lesson 16 of 20

Objective: SWBAT mentally calculate 10% of any number.

Big Idea: Students connect to prior knowledge of place value and fraction sense to help understand the "decimal slide".

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Math, Fractions, Number Sense and Operations, Decimals, Place Value, percent, proportional relationships, prior knowledge, Mental Math, ratios, equivalence, box diagra, rational numbers
  54 minutes
different representations
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