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# Step 1. Understanding our Strategies for Solving Multi-Step Word Problems

Lesson 5 of 6

## Objective: SWBAT solve multi-step word problems and defend their reasons for choosing specific strategies.

## Big Idea: This differentiated lesson focuses on key vocabulary, reviewing specific word problem solving strategies, and metacognitive awareness of how to solve one step and multi-step problems.

*60 minutes*

**Rationale:** The lesson today is a response to data I have collected over the course of the year that says that my students have not mastered the standard of solving multi-step word problems. The purpose of this lesson is to have students practice being more aware of their thinking process in solving word problems and how they go about making choices of how to solve them. There are three levels of students for whom I have chosen to focus on different strategies and approaches. They are:

**Novice:** Those who need language support and practice the most. These students are called "Keys to Success!" I had placed keys on each of their desks prior to class.* These students will focus on only the key words we find in word problems and learning to turn the "TV" on in their heads as they think about the operation. Their workstation should have word problems cut in strips and put in a container they can draw from. I use a little bear can with a mouth you can reach into. I do not use the multi-step problems for this group.*

**Emerging:** Those who have language skills down and need practice at thinking about the strategies and using the key words to solve. These are the "Explorers." These students found magnifying glasses. They will be solving word problems and explaining why they used specific strategies. These students use the Word Problem Word List and Problem Solving Strategy Chart Resource above. They will use their iPads and IXL.com, Level F F.2 & F.4. One problem from F.2 and 3 from F.4. If you don't use IXL, just choose multi-step and other problems from the Word Problem Resource sheet.

**Advanced:** Those who have mastered the skills of using strategies and key words, but need to be challenged about thinking why a word problem would be classified in certain categories.These were my "Contractors." They found small hand tools on their desks. These students will design a game for all of us to play. These students received a variety of word problems cut up in strips and spread out over a table,

Word Problem Strategy Discussion SB File

I set the stage for all in a short ten minute whole class review of word problem strategies that we have used in the past by using the SB file. I wanted them to understand that they needed to think really hard during this lesson and that they would be accountable for a product at the end of the lesson.

**I asked: What do you remember about each of these strategies? What helps you? Which ones do you like best?**

Key words popped up first from one student. She told us that key words help her figure out what her variable will be. ( I think she meant variable label). KWS ( What we Know, Want to Know and How so Solve) was discussed as one of their favorites. One boy said it helps him sort the information in the problem. Another favorite was Start, Change, Result because it helped us get the equation in the right order.

**Resources: Create Stations for students to work from. Post Signs and Resources at these places.**

Problem solving strategy chart for Explorers

Word Problem Resource All Operations.

Directions to Designing The Word Problem Game.

Word Problem Vocabulary Chart

Large Note cards, markers, highlighters & iPads

Large Color Coded Note Cards Designed from Word Problem Vocabulary Chart ( I chose one color for each operation)

Small Note cards with the words from the vocabulary sheet written on them.

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#### Groupings and Expectations

*15 min*

The next step was to explain why they had the items on their desks. I posted signs with the group names at work stations and I explained the meaning behind each name. I called each group and had them hold up their items as I explained:

**Keys to Success: **"You hold the key by studying key words in word problems. We will study these key words together!"

**Contractors:** "You will build us a game today that will tie together all that we have been working on! We will play it Friday!"

**Explorers:** "You will be exploring word problems and telling us why you used the strategies you did!" I assigned IXL.com Level F. I assigned 1 problem from F.2 and 3 problems from F.3

They were excited! I told them that they would be working on IXL.Com on their assigned pages while I met with each group and explained what the learning task would be.

**All set to work! ** **I visited the Contractors first.** (All the other students logged onto IXL and got busy). I explained the resources to them and went over their instruction sheet with them, making sure they understood each expectation. They set to work and I pulled the Explorers together.

**The Explorers were the largest group today. **I sat them on the floor at their station and explained that they would be using their Chart as they worked on IXL Level F F.2 & F. 4. I explained that their job was to solve four word problems, filling out the chart and explaining why they chose the strategy they did. I was careful to explain that I expected them to solve the problems using their best work and thinking. I explained that they could choose a partner to work with and that I needed them to do their working out on one looseleaf paper and to fill out one chart together. The entire work should be done as a team.

**Lastly, I gathered my "Keys to Success" people **.

**A Classifying Activity:** They were last because this is where I would be spending most of my time. This group needed the most attention. Language skills need to be honed. I asked students to spread the Cards to Sort out and place the word problem key words under each operation card. There was one set for all of them to work on and they spread them widely across the floor so there was plenty of room to work. I told them to take a stroll and look at the words to become familiar with them before we started looking for these words in the word problems. They roved about looking at the words.

I asked if the same words were under different operations? They noticed that "each" was in both division and in multiplication. I asked them how they would know where to place the word problem? One student said that maybe the numbers would be different.

I responded that maybe the numbers would have different meanings and that is how we could tell. I brought them back to the floor and pulled a strip from my bear and read the word problem. Sure enough, I had picked one they thought was multiplication because of the word "each" and it turned out to be division. From this word problem, I explained that taking flowers from one big vase and putting them into nine vases was division. I needed to turn that TV on in my head and envision the word problem much like we do a story. This supports Math Practice MP2.

I grouped these students with others whom I thought they would work well. I passed the bear container and had each team draw out a problem.** Their group task was to read the word problem and place the word problem strip under the correct key word to identify the operation that would be used to solve it.** *I could hear each group read the problem aloud and knew I was able to leave at this point and rove the room to see what other groups were up to. I visited them often to make sure they were on task placing the strips in correct places.*

#### Resources

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**Guiding the Process:** After I left the Keys to Success group, I found the Explorers very busily working with iPads, solving problems and we discussed their strategies, explanations and success. They were having fun and were engaged.Working on IXL. The Dog Problem shows us how these students used their strategies well in order to solve their problems. We laughed at the dog problem because it was about things in a household that a dog destroyed. It was exaggerated and funny.

I stopped by the Contractors to find them busily grouping word problems into operations categories. I asked them what group they put the multi-step word problems in? Were they under one operation or in their own group?

They said they wondered about that. So, I told them to make it into its group. I asked them what strategies were they using? Key words, and having to set up the problem mentally was discussed. One very dramatic member of the team said they acted it out and then they would decide after they acted it out. He said they actually acted out one of the problems. That's taking another strategic method! This decision making is an example of Math Practice 3. They have to listen to each other and decide what is going on.

I went back to my "key" group. They were struggling. I got out highlighters and they highlighted key words. We discussed some of them together and replaced them in their proper categories. I asked a Contractor student to join us for a moment to lead a discussion on why does this not belong here? . I did this to test his thinking, but also to give him a chance to lead others because I thought he would lead them well.

A little more time was spent with him reading and figuring out the words to another word problem to discuss the answer to why is the placement correct?.

I encouraged them to keep visualizing their word problems and think about where the total was. They moved about and continued to be busy sorting, arguing their ideas well, and really hashing over the words as the Contractor student went back to his work. After a few minutes, before the group closure, I had a little closure with just the small group. This clip shows some discussion about awareness. Aha moments make them accountable for their work."You have to look for the key words" was a response to what one student learned.

I gave them the two minute warning. They moaned when I told them it was time to stop!

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#### Closure

*5 min*

When students were finished and time was up, I drew them together to find out what they had discovered. I wanted them to share what they had learned about their thinking in terms of word problems and how they go about knowing how to solve them.

**I asked a simple metacognitive question:** How did thinking about how you solved word problems help you? Did thinking about your strategies make a difference in how you solved the problem? One student said yes. She liked the chart because she realized how much she used equations and KWS to solve. IXL said their solutions were correct. She was happy about it.

I told them that I wanted them to take a stroll around the room and look at what had been done. I wanted Explorers to leave their word problem samples out. I wanted the Contractors to leave their work out for viewing. And of course, the Keys to Success group had an interesting display of strips of word problems placed near the operations for people to view with highlighted key words.

I assigned the Explorers and Contractors the IXL F F.4 (multi-step). The Keys to Success group needed to work on IXL F F.2. Each group should do 4 more problems.

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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: Start! Change! Result! A Strategy to understand solving word problems.
- LESSON 2: Writing a Simple Word Problem From Scratch by Using Strategies Learned
- LESSON 3: Understanding How to Find a Variable in a Word Problem
- LESSON 4: Using Strategies in Working Backwards to Solve Multi-Step Word Problems
- LESSON 5: Step 1. Understanding our Strategies for Solving Multi-Step Word Problems
- LESSON 6: Step 2: Game Day: A Student Designed Class Game for Word Problem Solving