##
* *Reflection: Diverse Entry Points
Comparing Fractions - Section 3: Closing

We all have our "plans" when we begin a lesson. We have decided what the outcomes need to be, how we will get there, and what we will do to wrap up the lesson. However, when we trust our students enough, sometimes we go way off course into learning that surprises us.

When these two boys, one a strong math learner, and another that struggles, began working together to explain to me an understanding they arrived at, I couldn't contain my excitement. One student was talking about cross multiplying while the other was making sense of using multiplication to find equivalent fractions, all while using one of the day's strategies for representing a comparison.

Trust yourself enough to trust the students and let them take you as far as their curiosity will allow. You will never be bored:)

*Let Them Go...*

*Diverse Entry Points: Let Them Go...*

# Comparing Fractions

Lesson 2 of 5

## Objective: Students will be able to compare fractions with different numerators and denominators by creating various models.

## Big Idea: Children need to "see" math in order to begin explaining their knowledge. This lesson pairs fraction comparisons with modeling math.

*45 minutes*

#### Mini Lesson

*10 min*

To open today's lesson, I placed a comparison (3/4 > 1/2) on the board and ask the students to turn and describe how they know it is true. The strategies are varied. One of my students remarks that he understood 2/4 equals 1/2, so an extra 1/4 makes 3/4 larger. Many students draw models on their white boards to grapple with and prove.

Following the partner discussions, I ask the students why it seems they are struggling with this more than when we compared fractions with same denominator. They tell me exactly what I thought I would hear…everything is different, so they couldn't visualize it.

Now I remind them that we can only compare fractions when we have two of the same whole. If your students need this type of reminder as well, draw the standard small and large pizza and ask if half of each is the same, or why they are not equal. This is usually all it takes.

It is critical that students have various ways of comparing fractions, so we make a list on the board of models they can use. We came up with number lines, Cuisenaire rods, sketches, and fraction circles.

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#### Active Engagement

*25 min*

I put several comparison sentences on the board and ask students to use their choice of model to help them solve. The sentences for my class to model are:

5/8_____3/5

3/4_____2/3

2/4_____1/3 (on this one I was hoping someone would see the 2/4 and think about 1/2)!

2/8_____3/4

You may use any fraction pairs for this lesson. The real task is in the students creating and using models to support their responses.

This partnership still struggles with how to begin. At the end, they stop "guessing" and start drawing!

In this video, my student is using number lines and hoping to find the solution. When I approach him, he has the lines drawn and labeled at the beginning, but has not partitioned the line. I ask him to go ahead and do that, and I was very pleased with his strategy!

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#### Closing

*10 min*

My closing starts out as a review of using models to represent comparisons, remembering to use the same size whole. However, we take a sharp turn when the students start asking questions about fractions that take my breath away.

One student asks if there is a way to use fourths to create fifths. I did not have my camera in my hand to video the discussion, but it was fantastic because everyone just starts sketching, wondering, debating. Finally, the class decides you cannot use fourths to create fifths, because fourths are not multiples of fifths.

The next wondering comes from a student who receives extra support; fractions were a bit difficult at the beginning. He starts out asking a question and goes to the board to explain what he is wondering. Another student literally jumps up and adds his thinking.

The following two videos are what came from a little wondering.

*expand content*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities