Understanding How to Find a Variable in a Word Problem

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SWBAT identify a variable that represents the unknown within a word problem, create equations with the variable, and solve using the equation.

Big Idea

Students will work together and independently in this lesson to successfully determine an appropriate variable, situation equation and solution to word problems.

Warming up!

10 minutes

Our warm up today started right in with reviewing our strategies we have learned throughout this unit in solving short word problems.

I pulled up my Smart Board File Notebook to the first page to discuss Two Step Word Problem Strategies.

I asked students to contribute a strategy and come write it up on the page one by one. They handed the  SB pen off to another student with raised hands as they sat on the floor in front of the Smart Board. I like to let them take charge of their reviews and select people to contribute.This gets  my kids engaged right away and take ownership for their learning.

I loved how each strategy was explained by several students in the class. They all wanted to contribute! There was a lot of noise and excitement. One student popped up and said, "Mrs. Kanthack, we forgot situation and solution equations!" That is a hard concept and he remembered!

When we were done listing, we talked about how each of the strategies are related to one another and how we need to choose carefully. After comparing, we all decided that KWS strategy is the best one for sorting out a word problem. This discussion connected understanding of the "how" to solve word problems with the "why" strategies are used. It got us to think about the many ways of solving.

*Start, Change and Result, helps a student pick out what is going on. What are we starting with? What is the change? And what will be my result?

*The Math Mountains are sometimes called break apart drawings. This triangular shape shows where the total is located, the two addends and how subtraction and addition are related. It also works for multiplication and division, but of course it is factor, factor, product on the triangle.

*KWS Chart is by far one of the best methods for tearing apart a problem. This is something I designed from KWL charts in language arts. I am certain there are different ways of doing this, but I like this because my students are familiar with KWL charts from ELA and it transfers easily.

*We also talked about situation equations and solution equations. The situation equation is simply the equation that tells us what is really going on. The solution equation is the equation is what we use to solve. So, that supports the CCSS concepts of why and how in equations. Sometimes situations equations and solution equations are the same. It gives students a structure to solve and sets them up in logical thinking. All of the strategies can be related in some way and can be used together.


Introducing the variable and how to find it in a word problem.

10 minutes

I turned to the second page of my SB Notebook. I introduced Two Step Word Problem Strategies with the concept of variables by first reading the standard to help them understand that variables are a part of mastering the standard.

We listed letters that could be variables on the board, just for fun and to understand that certain letters represent certain ideas in math. I explained that x and y turn up in certain algebraic equations when we graph. I told them that we can use variables to our advantage to understand a word problem, as I turned to the third page of the SB Notebook.

We read through the third page and discussed the concepts of looking at the question to the story problem to find out what we need to know. There weren't too many questions and students could clearly see and understand the connection between eggs and "e". It worked well.

To take notes, I had students photograph the pages with their iPads rather than writing it all down. Snapping photos of their notes. They can upload it to a Google Doc or use a note taking ap to organize it. I told them I would help them with that in the near future as we strive to be more paperless and have quick notes to refer to.

I moved on. It was time to solve a problem together, step by step. 

Solving Together to Master the Standard.

20 minutes

I proceeded to change to the next slide to introduce how to find the variable. I asked for a volunteer to come up and set up a KWS chart. We read the problem together out loud and my student started to write down the K ( What we know) part of the chart when he was interrupted! A student blurted out, Find the W first! She explained that it was better to think about what we want to know right away and that helps us focus on what we are solving.

I loved it!  Such energy! It is an awesome teaching moment when students take charge and offer up their profound understanding! We completed the chart, student by student. 

Find the Variable in the Word Problem: Look for the noun in the question.I announced it was time to find the variableLeading them to find the variable using the "W" shows us how we use the noun in the question to find a good letter to use for the variable and then the label.

Word Problem: My garden has 78 varieties of plants in it this year. There are 24 different varieties of tomatoes and 14 different varieties of beans. The rest of the varieties are greens. How many different varieties of greens are there?

I guided them to find a "g" for greens. I asked for a show of thumbs up to confirm we all agreed. Then a discussion broke out among them about what greens were. Most did not know what greens were! It was important to discuss this not only from a nutritional aspect, but from a math aspect because if they don't understand what they are reading, or a least have some mental image going, the problem will be harder to solve. One strategy we sometimes use is to "turn the tv on" in their head, like we do in any other reading. I was thinking about how if they didn't know spinach was a green, they would have a harder time envisioning what the problem was about. It might seem trivial, but for some students, it makes a world of difference.

Guiding Thinking: We continued to solve the problem and discussed how we would use the other strategies. I asked what we started with? I asked if there was an easy "change" we could pinpoint. The students responded with "no". I asked if they thought we should abandon the Start, Change, Result strategy. One student said, " Well we know the start, and I think it's the total, so how about using a math mountain?" I listed the math mountain placing the total on top and drawing the two numbers we knew were part of the total. And something clicked with two of my students.

"Wait, how about the "g"?  I drew another line in green and placed the g at the bottom. Suddenly our math mountain had three lines in the triangle. There appeared to be another addend in the equation for this problem.

I asked if them what I should do with those numbers and how were they related to the total? We created an equation using all of the addends and the variable. We finished by solving the problem and labeling it correctly using the variable.


Group Solutions

10 minutes

Source: Houghton Mifflin Math Expressions Volume 1, p. 136. or use any resources for mixed multi- step addition and subtraction word problems.  I told them I would give them 10 minutes to solve a word problem cooperatively in their groups. They turned to page 136 of their textbook as the SB Notebook showed.  As they solved, I roved about the room checking their interactions with one another and made sure everyone was reading the problem, contributing, and on task. To my amazement, they wasted no time figuring out who would be the scribe and they set up the KWS charts immediately. I heard them discussing what the variable should be.

The story problem they solved was from Math Expressions ( Houghton Mifflin). It was similar to my garden problem, except it was a one step problem. I wanted to first see if they could find the variable, so I chose to start with an easier problem to solve. I worked to clarify some confusion about the variable and the unknown.

As I stopped to listen to groups, I did see a few misconceptions about where the total should go. Some students cannot pinpoint where the total is in the word problem by using the "key" words. I need to work more with this! Locating the total cold be tricky, but we worked using our strategies.

Some were done quickly with correct set up and answers. They continued on to problem number 5. This problem was a two step problem to solve. I questioned the students to be able to tell me how they knew it was a two step? They did an exceptional job simply setting up their equation using a variable. I reminded them to put in their parentheses.

After the time was up, we spent a few minutes discussing if they thought finding the variable was easy using their strategies. There was some confusion about finding the variable that we worked through. My plan for the next lesson is a whole class period of working on word problems and more of what was done today.


Homework IXL

10 minutes

I assigned IXL math C.2 for practice at home. I told them I expected them to take each word problem and set it up with a KWS chart, find the variable, write the situation and solution equation, solve using the variable and label in the solution. I assigned them 30 minutes of practice. 

I think this assignment is great because the website records the amount of time they spent ( I have an account). I can check on their effort. 

Even though we are trying to be more paperless, I still believe that paper and pencil and proof of thinking is essential to master CCSS standards. I need to see their thinking. Once that thinking is established, I plan to ease up on the planning for word problems. But for now, it is important that they establish a pattern of thinking through writing it down systematically.

Even though students are following through and solving their word problems, my main assessment goal for this assignment is whether they can pick out a logical variable to represent the unknown. Accuracy in the solution will be dependent on how they decide what operations to choose. 

I will address that in the next lesson to build on mastery of the standard.