The Algebra Toolbox

If the only tool you have is a hammer, you tend to see every problem as a nail. – Abraham Maslow


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Activities for Solving Equations

I use lots of practice activities for solving one-, two-, and multi-step equations with my Algebra I class. Solving equations is part of their middle school curriculum but most still need much practice to achieve “fluency.”

Here are some of the activities I use:

By the Shapes Activity that I got at an NCTM conference years ago, but don’t know who the presenter was. If these are your creation, please let me know so I can credit you! 

Summary of Activity: Students work in groups of 4 to determine the value of each of 3 shapes, using 4 clue cards (equations).  The By the Shapes Teacher Notessay to use counters, but I don’t. I put the By the Shapes Recording Sheet in a plastic sleeve and students record the value of each shape on the sleeve. When they have the solution, they raise their hands and show me. If they are correct (By the Shapes Answers), they mark off that clue set number at the bottom of the recording sheet (to keep track of which sets they have completed) and I give them another set.  The best part of this activity is the conversation that happens within the groups. Students engage in some really good discussions about the value of each shape, verifying solutions by substituting the values into each of the 4 clues (equations) and eliminating possible values of the shapes based on the clues.

Preparation:  Copy the By the Shapes cards onto card stock. There is page of icons that can be copied onto the back of each clue page, but this isn’t really necessary…just pretty. It’s nice if each clue set is a different color. I made 2 sets of clues (16 sets total) so that as groups finished I could be sure to give them one they hadn’t done yet.  Give each group 1 By the Shapes Recording sheet and a dry erase marker/eraser. It helps to do the Teacher demo so they have an idea of what they are supposed to do.  I told them to use all the clues at the same time to figure out the value of each shape.

Solving Equations Song– even my high school boys will clap and sing along to this one.

2 step equations model for students who struggle with getting started solving two-step equations.

Gallery Walk Variables on Both Sides– I post each sheet of 3 problems around the room and give each student an answer sheet. Students work with a partner and rotate among the 10 sheets of problems, choosing one problem from each sheet to complete. I ask them to challenge themselves to complete the “hardest” problem on each sheet if they are able.

Crumple and Shoot (also known as Trashketball) – powerpoint of equations with variables on both sides of the equals sign. Students work in teams of 4, each studnet has a number from 1-4.  Every student does every problem on white board. I use a random number generator to call a number from 1-4. That student holds up their board – if the answer is correct, their team gets one point and they have the opportunity to get extra points by shooting a piece of scrap paper into our recycle box.  I have a “one point line,”  “two point line” and “three point line” from which to shoot to make extra points.  Students are encouraged to work together with their team to complete the problems since they never know who will be called to show the answer. Great communication encourager.

Pass the Probem – Equations– in groups of 4, students pass one problem around the group, each student doing one step of the problem. Directions are on the first page of this document.

Placemat Equations– I put one “placemat” in a plastic sleeve. Students work in groups 4, each student completes one of the problems on the placemat. They find the sum of their solutions and write the sum in the center of the placemat. I only have to check one number to know if they have all solved their problems correctly.  After using this activity, I found that it was better for me to write the equations onto the placemats so that the problems were oriented so that the students could see the problems easily without the problem being upside down. I also used markers so it was more colorful.

Hot Seat Solving Equations– powerpoint of equations. Students have to determine what the first step would be in solving the given equations (includes literal equations).  Students are in 4 teams. Each team has four cards:  “Add/Subtract,”  “Multiply/Divide”  “Combine like terms” and “Use Distributive Property to simplify.”  Hot Seat directions can be found here in this post.

Study Guide– prior to taking the unit assessment, we prepare a study guide.

I also played a game of Risk using equations.  I gave the students a blank recording sheet. I put the problems on the board and showed them one problem at a time. They did the work on the back of the recording sheet and wrote the answer only on the front along with how many points they wanted to risk on that answer. I revealed the answer, we discussed it, and they calculated their points (working in pairs to keep them honest).

**Update: I just read a great post by Julie at I Speak Math about solving equations.  I love this math community!

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