Reflection: Developing a Conceptual Understanding Exploring Equivalence - Section 2: Guided Practice


When I circulated around the room during the launch, I noticed multiple students attempting to demonstrate fraction equivalence with addition and subtraction.  They were adding the numerator and denominator by the same number. I was surprised by this confusion and made a note to have a small group intervention to follow up.

However, when I asked the students to explain mathematically how to simplify fractions, a different student shared, "You subtract".  Then, another student said, "You divide by 2".  The language confusion was something I expected, but I wasn't expecting the students to use subtraction to simplify. 

Rather than wait to address this, and move into my lesson, I told students that division is actually used to simplify and multiplication is used to create equivalent fractions.  I am going to show you why that it is the case right now.

This lesson took an important tangent.  Rather than let the students practice finding equivalent fractions, we made connections between whole numbers and fractions and explored the identity property.  The Identity Property of 1 is a critical understanding when working with fractions. Dividing the numerator and denominator by 3/3 or 2/2 etc is the same as dividing by 1. The value of the fraction doesn't change. 

Students need to have the conceptual, not just procedural, understanding of "whatever you do to the bottom, you have to do to the top".  

  Misconception Highlighted
  Developing a Conceptual Understanding: Misconception Highlighted
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Exploring Equivalence

Unit 2: Adding and Subtracting Fractions
Lesson 2 of 11

Objective: SWBAT simplify fractions and find equivalent fractions using representations such as models, pictures, or symbols.

Big Idea: Students have opportunities to connect the different representations, including models, to make sense of equivalent fractions.

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Math, modeling, Fractions, equivalent fractions
  40 minutes
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