## Good Work! - Section 3: Decomposition and Drawings to Solve those Word Problems

# Applying Strategies to Word Problems and Fractions

Lesson 3 of 8

## Objective: SWBAT solve addition and subtraction word problems using like denominators.

## Big Idea: Students apply strategies they have used for whole number word problems, but use fractions this time. They also discover that they can use fractional models to help them solve problems.

*45 minutes*

#### I am thinking of a number!

*10 min*

As we continue to master solving factor pairs to 100, I noticed my students are becoming acutely aware of how many factor pairs certain products contain. In other words, they know that 24 has 4 factor pairs. So, I thought of this fun little brain teaser to help further their thinking. It is played in a circle. One person is in the middle and says " I am am thinking of a number that has 4 factor pairs. This number contains a 4 in its ones place and is between 1 and 30." Students have to give each other enough information for them to be able to process what number it could be.

We played about seven rounds in 10 minutes. I think the most fun was when one boy picked out 72 as his number. He told the class that it has 6 factor pairs and a two in the ones place. Three kids shouted out 72 before he could even give them the range of numbers!

My below grade level students were able to keep up with the easier problems. The one that stumped them the longest was 22. We didn't include prime numbers this time, but I suppose we could say: " I am thinking of a number** **between one and 100 that has one factor pair and a one in its ones place and then list how many prime numbers fit that criteria. It would be too easy if you gave it a shorter range. This is so much fun!!!

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The SB file provided today is a short and simple three page file that helped get my students minds wrapped around their word problem strategies. I opened up the Fraction Word Problems SB lesson in a whole class review with them sitting on the floor in front of the Smart Board. They offered up answers to each question and did a wonderful job connecting what strategies were ones they could use to solve the word problem.

One student told us that that Math Mountains help her know where the total should go. I asked for more equation forming strategies. One student blurted out Start, Change and Result. ( This strategy focuses on what the start of the problem is, and follows the changes to arrive at the result. We noted it as SCR.) Another student said "KWS." ( What do we know? What do we want to know? How do we solve?). I explained that that strategy just helps us sort out the information, but doesn't always help us find an equation. It sure makes it easier to look at!

As we kept going, our list depleted to the strategies listed on Solving Fraction Word Problems SB Class Notes. I asked a student to read the problem aloud. I drew their attention back to Math Mountain. I asked if this particular problem would work well with a math mountain? Could we find the total in this problem? Was it clear?

We determined together that the math mountain wasn't much help this time. One boy raised his hand and suggested drawings! This was a great time to talk about how we could use the drawing to compare the two fractions. Through this comparison, we could determine how much larger one fraction was from the other. That student came to the board and drew the picture.

After we solved the problem, we turned to the next SB page and talked about decomposition and drawings.

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As we started to work on the second page to solve the problem, I asked students to work on solving it in their notebooks. I asked them to look for the key word that told them what operation to use. As students solved the word problem, I roved the class. I saw one student made a comparison drawing for the problem. I told him that it was a good idea, but it might be a clearer picture to produce drawing in circles. Good Work!

The first two students who finished were asked to come to the board and write their solutions as well as copy the strategies they used. Solving Fraction Word Problems Both boys used KWS ( What do I Know, Want to Know and How to Solve?). One student struggled a bit with where the numbers should go. Classmates looked on and interjected supporting his work. We finished and compared. The fraction needed to be decomposed because it was a improper fraction . We continued as a class to find different ways to decompose or draw the fraction. It was fun! Students started to see the many ways we could pull apart an improper fraction to produce the mixed number. I noticed that there was one more way that would be a simpler way of thinking about decomposition. Ohhhh! I get it! is what I heard in the back ground as I gave them one more way of thinking about decomposition.

As we finished up this page on the SB, I switched to the third page and asked that if anyone was still struggling, we would be working on the last word problem together. Otherwise, if they felt ready, I would give them their class assignment and they could work for awhile.

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Fraction Word Problems Resource

I assigned IXL.com Level F R.2 word problems for them to work on. I expected them to work independently at their desks. Word problems were to be dissected using strategies, equations with variables and drawings. Any improper fraction needed to be decomposed. If it was necessary to solve a mixed number subtraction problem that needed to be regrouped, I reminded them that they needed to decompose both to produce equivalent fractions that were improper. I quickly wrote an example of that on the board as I explained that I strongly thought they wouldn't run into any of them. I wrote the equation 2 5/8 - 1 7/8 and quickly solved it using decomposition.

For my students who struggle with words, I had created word problem solving sheets using a colored paper and a word problem glued to it. This worked beautifully for them to be able to highlight the key word, have plenty of room to work on their word problems and remove the worry of the technology. My students need the paper space and the word problem there in front of them so they don't need to look back and forth. They all found their key words quickly! There was a lot of talk about how easy it was to see them and how much they liked the colored paper. Proud Problem Solvers. As soon as they achieved the word problem, they could log on to IXL and work on those problems, use more colored paper, or a paper of their choice. I also had more word problems glued to colored paper for them to continue on as they had in case they didn't feel ready. It was a great transition! All logged onto IXL before class was over!

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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: Understanding Composing and Decomposing: Day 1
- LESSON 2: Using Decomposition As a Tool to Prove The Why Behind Simplifying
- LESSON 3: Applying Strategies to Word Problems and Fractions
- LESSON 4: Snicky Snacks & Fractions: Using Our Skills to Make a Treat.
- LESSON 5: Quiz 1 : Assessing addition and subtraction of like denominators
- LESSON 6: Quiz 2: Assessing Decomposition & Mixed Number Problems
- LESSON 7: RTI Decomposing: Dice, Drawing and Explicit Instruction
- LESSON 8: Unit Assessment of Addition and Subtraction of Fractions With Like Denominators