Reflection: Intervention and Extension Dominant Traits in Division (day 5 of 5) - Section 3: Exploration


The first time I taught this lesson I really didn't what my kids were going to notice. My original objective was simply to get them to notice that some fractions have equivalent decimals that repeat and some have equivalent decimals that terminate. My hope was that they would find some patterns, but I didn't know what patterns they might find. After teaching the lesson I now have a better idea of what ideas to expect from my students and have a deeper appreciation of the value of this task.

  • Some kids will notice that when the numerator is a multiple of a three the decimal will terminate in a 5
  • Some may look at equivalent fractions with denominators of powers of ten.

Originally I had planned it as primarily an intervention task, but now see that there is opportunity for extension. Because my goal was framed by the standard of knowing that some decimals terminate and some repeat my questions tended to be limited by that. I primarily asked them which ones terminate and which repeat, but neglected to ask them the more meaningful question of why these patterns were happening. Their observations in this lesson were approaching the foundational math and I didn't notice.

I would also modify the worksheet in two ways.

  • I would eliminate the "simplify" column, because I think they would come up with the idea themselves and possibly come up with other equivalent fractions like hundredths.
  • I would also cut off the list at 5 twelfths and then have them use the patterns they've noticed and predict what the next fractions would be equal to.

6 twelfths is an easy one and would get them to think about equivalent fractions & simplifying on their own. I would also like to get them to think about adding 1 twelfth each time to emphasize the equivalence of the fractions and decimals.

  Intervention and Extension: Letting my students take the lead
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Dominant Traits in Division (day 5 of 5)

Unit 8: Exploring Rational Numbers
Lesson 6 of 20

Objective: SWBAT discover patterns in division that result in a repeating or a terminating decimal.

Big Idea: Students observe when and how division produces repeating and terminating decimals when dividing by 12.

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Math, Number Sense and Operations, division, terminating decimals, repeating decimals, student led inquiry, pattern, rational numbers
  54 minutes
trying out some division
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