Reflection: Complex Tasks Numerators and Denominators - Section 3: Independent Time


As the students worked on the independent practice and I circulated around, I realized that students were adding and subtracting fractions on their own. The first student I saw said, well, there were 2 out of the box and 12 in all so 12 - 2 = 10 so there has to be 10/12 left in the box. 

I was amazed at how easily he visualized the subtraction of the numerators to subtract fractions. I had not mentioned any of this to the students, but they figured it out on their own. It seemed so obvious to them. 

By learning through these hands on activities, students were gaining a conceptual understanding of what a fraction really is (i.e. part of a whole, or part of a whole set) so understanding that you don't change the denominator is understood rather than memorized. 

 As I circulated around I saw this scene reenacted by other children. Sometimes the best learning happens when children figure things out on their own.

  Complex Tasks: Figuring It Out On Your Own
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Numerators and Denominators

Unit 9: Fractions
Lesson 4 of 10

Objective: Students will develop a conceptual understanding of what a numerator and denominator stand for in a fraction

Big Idea: Students always think of unit fractions (1/2, 1/3, 1/4), but the numerator can change. What happens when it changes? What does that mean for how much of the whole I have?

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