Reflection: Intervention and Extension Building Block Percents - Section 3: Exploration with white boards


Unfortunately, many of my students have learned to rely on procedures when working with fraction concepts. They know tricks and try to remember rules, but many lack number sense with fractions. This fact is a challenge when trying to teach a rigorous Grade 7 curriculum. 

This lesson surfaced some concept gaps that I didn't expect. I was really surprised how many students didn't intuitively know that 20% would be 10% + 10%. The Cup Model  helped a little, particularly when I asked students how much more they needed to get from 10% to 20%. But, it became very clear, very fast, that the majority of my students were unsure that 10/100 + 10/100 is the same as 20/100. When I realized this fact I knew that my students:

  1. Do not interpret a denominator as the name (and size) of the object (unit) being counted
  2. Do not understand that the numerator is the counting number (or the number of pieces of size denominator)

Today, I ended up teaching a mini-lesson. In it I had students counting unit fractions (see Scaffolding fraction sense) and writing out the denominator name in words. I gave the groups piles of fraction circle pieces and had them count up the one-fourths, for example. When they were done I asked how many one-fourths each group had and wrote it on the board: 3 fourths, 9 fourths, 5 fourths, 4 fourths, etc. I asked two questions to emphasize the definitions of numerator and denominator:

  1. what is being counted?
  2. which number tells the count? 

Using this information, we were also able to review equivalent mixed number names. I asked questions like, "What is another way to write this same amount?" Using fraction circles was especially helpful for this mini-lesson because it made the whole obvious and concrete.

I had another boy find 10% by dividing the quantity by 10. He was right, but, because I was afraid he was using the wrong 10, I asked him where he got the 10 and he said from the numerator in 10% (10/100). To scaffold &clarify, I asked if he would divide by 30 if he has to find 30% and he confirmed. This told me he didn't understand that the denominator is a divisor and tells how many peices the whole is divided into. I did a brief sidebar with fraction circles with his group relating the denominator to the division and also reminded him of the earlier box diagrams we did. 

I could spend a lot more time revisiting fraction concepts with concrete models.


  Intervention and Extension: Processing vs Reasoning with Fractions
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Building Block Percents

Unit 8: Exploring Rational Numbers
Lesson 17 of 20

Objective: Students will be able to calculate any whole number percent of a number mentally.

Big Idea: From 10% students can build 30%, 120%, 5%, etc.

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Math, Number Sense and Operations, percent of a number, Mental Math, rational numbers
  60 minutes
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