## As we cut the paper, what was essential? - Section 2: New Games for Comparing Fractions

# 2 Games that Compare Fractions with a Little RTI on the Side

Lesson 4 of 12

## Objective: SWBAT compare fractions using fractional models.

Today I listed all the factor pairs for 12,18,15,24,27,36, 40,56,72 and told students needed to find all of factor pairs that were less than 50. For example, after they would find all of the factor pairs for say 18, they had to list them in order correctly, 1x18, 2x9, etc. I timed them at 4 minutes to see if they could get all the factor pairs listed correctly. I told them I would give them free math app time if they were the first done and the most accurate! I set the timer and the mayhem began! This was just a riot. They were pointing, writing and scratching off what they had made mistakes on. Finally, the timer went off and not a soul got them all! I heard a lot of "Awwwwssss!" One student was just about finished, but was still missing all the factor pairs for 40. They still thought it was great!

I told them that we were going to try it again tomorrow and see what happens. I roved the class and only one student was really struggling, but everyone else had their factors lined up quite nicely. They just needed to be a little faster!

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**Materials:** Fraction cards all cut out and placed in envelopes. Directions to the War Game. iPad ap *Oh No Fractions!* Writing paper. Rolls of adding machine paper.

**Get going**! I wanted to get right to working on comparing fractions so I opened the lesson by reminding students about how we had used dominoes to create equivalent fractions. I told them that we would be comparing fractions that might not be equivalent and we needed to use fractional models like we had before.

I demonstrated how to compare 2/3 and 5/8 by drawing two equal sized bars on the board, one above another. This helped students see that the bars needed to be the same size. I continued by drawing 3/3 in the first bar and shading in two of them. Then I did the same with the second bar but drew 8/8 and shaded in five of them. Right away students could see the comparison.

**I asked them if they knew how to play the game War?** Many raised their hands. I explained that they needed to dole out the cards in the envelope until they were all passed out between them and their partner. Next, they would each draw a card from their pile, look at them both, draw both the fractions in a comparison bar model as I had instructed ( I pointed to my previous drawing) and that they needed to prove which was larger. I told them that the exception would be if they received a card whose fraction was representative of one whole. That would be an automatic win. The person with the largest fraction won the pair of cards. When all cards were gone, the person with the most cards wins. However, their drawings would be checked and they would have to prove their winning.

Once students finished, they needed to work independently on the second game. They were to open up their iPad and find the ap Oh No! Fractions. Like the game of War, I wanted them to draw out their fractions to prove they were correct.Oh No Fractions & Drawing Then, they could check their work using the "Prove it" button on the ap.

I told them that I was going to have them partnered in different groups and that one group would be with me for a little while to experiment with a new idea I had. I separated the students who I knew were not understanding equivalent fractions to help them use a manipulative idea I had using cash register tape. Then, I told the other students to partner up and get busy with War first.

**Small Intervention Group**

I drew 1/2, 1/4, 1/8 on the board. I told students that they should cut three tapes that were the same size from their roll and fold the fractions. I demonstrated on a tape as we talked about accuracy in folding, cutting the same size strip of paper, and labeling the fractions. These students were amazed at the folding. We talked about what happened when we folded in half. One student said that it doubled. They folded the first set. I asked them to lay out the strips and explain what they noticed. Together, they talked about how it "sort of" lined up and that they could see how the lines came right in the middle of the fraction above it.

Next, I taught them to fold thirds, then sixths. We did the same process. Then we switched the tapes and compared fractions using them. Some students didn't have the same size wholes to start with, so they realized that they couldn't compare effectively.As we cut the paper, what was essential was the question that led them to understand that *we must have the same size wholes to compare*. This realization will help them fully master the standard.

I roved about the room looking for progress and proof of learning. I saw some wonderful things going on as I looked at work. Two girls used the < > signs on their own without my coaching!Comparing using signs. We also discussed and students changed their practice during War to be more accurate.Why can't we compare using these drawings? shows how students recognize that the fractional models must be drawn accurately. This supports Math Practice Standard 5.

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I asked students for an Aha! moment as I often do to wrap up a lesson. I love hearing how they have discovered something great in their learning. One student talked about learning about accuracy.Commenting on learning about how to compare and the importance of accuracy of drawing the model. The student who talked earlier about the sizes of fractions piped up to mention that she didn't realize how it all worked but the drawing helped her see it. One paper folder told me that he learned that all the fractions had to be the same size in the fold. I clarified it for him to help him understand that the whole had to be the same size and so did the pieces in the fractional group. I explained that their next journey would be to learn about decimals and be able to compare those too.

I assigned IXL math Level F Q.1, Q.6 & 7 for homework. I asked them to start with Q.1 and draw. If that got too easy they should move on to the next lessons but to work toward mastery for at least a half hour. I expected to see the drawing on paper.

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Pre-Test Fractions 1. & Eggsciting Spiral Review
- LESSON 2: Understanding The Whole Through the iPad
- LESSON 3: The Equivalence: The Domino Effect
- LESSON 4: 2 Games that Compare Fractions with a Little RTI on the Side
- LESSON 5: Quiz 1: Creating and Comparing Equivalent Fractions
- LESSON 6: Fractions: Using Graph Paper to Prove Equivalency of Hundreths and Tenths
- LESSON 7: Comparing Fractions on a Numberline
- LESSON 8: The Depth of Decimals: Comparing Using A Fractional Model
- LESSON 9: Decimal War: Comparing Fractions Using Place Value
- LESSON 10: Comparing Decimals Using a Numberline
- LESSON 11: Quiz 2 Showing Our Understanding of Decimals
- LESSON 12: Fractions 1: Comparing Fractions and Decimals Assessment