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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My Favorite Unit to Teach – Linear Functions

My favorite unit to teach is Linear Functions. Not sure why…I just think y=mx+b is a fun equation.  I always tell my students that I am going to get a y=mx+b tattoo on my forehead as soon as I get over my fear of needles.  As a result, I’ve had a couple of students make me t-shirts with the equation on it so that I don’t have to get the tattoo 🙂

y=mx+b t-shirt

y=mx+b t shirt

A couple of my favorite activities from this unit:

Rule of 4 for Linear Equations  (worksheets)  Throughout the unit we practice defining variables and translating word problems into equations, then creating a table of values and graphing the equation to show the relationship among the representations.

Desk Hop Linear Equations (activity in pairs): I have each of the 20 problems on an 8.5 x 11 piece of paper, spread out all over the library. The students get the answer sheet and rotate through the problems in any order to write and interpret the linear equations.  Unfortunately, I can’t find the original word document of the individual problems.  The link includes the answer sheet and the 2 pages that have all 20 problems on them that I made for students who were absent. This takes most of my students about 60 minutes to complete.

Writing an Equation from 2 Points Template I always a few students who really struggle with writing an equation if they are given two points. They do use the TI-84 graphing calculator eventually, but I want them to really understand where the equation comes from.  I put this template in a sheet protector or plastic communicator for those students and let them write on it with dry erase markers to do the substitution.

Matching Graphs to Standard Form and Matching Graphs to Slope Intercept Form and Graphs (activity in pairs) Copy each document onto cardstock.  Every pair gets the same graphs. Students who are ready use the equations in standard form, others use equations in slope-intercept form. Match the graphs to the equations.

I have two versions of a “y = mx+b” song: This one  is from a CD of math songs by Bob Garvey to the tune of  “YMCA.”  This one is a youtube video. My students prefer the beat of the video, but we sing the YMCA version in class and I have several of them act out the letters/symbols.

students doing y=mx+b dance

We also have the  Slope Song which we sing with a country twang (especially the “y’s over x” part).

My students really like Hot Seat reviews – they get so competitive!  Students are in lines in group of 4. The last person in each line gets the  Hot Seat Cards which are printed on card stock, one set per group of students, cut apart. The last person in the line chooses an answer then passes it to the person in front of them. That students looks at the answer and if he agrees, passes it up. If he disagrees, he passes it back. When the first person in the line gets and agrees with the answer, he holds it against his chest and turns toward me. The first group to get the correct answer gets 2 points, every group with a correct answer gets 1 point.

I do several foldables in this unit. One is the slope foldable. (I have my students do all the writing in their foldables). I tell them the mostly true story (except for the cliff part) about my first skiing experience.  Going UP the chair lift, I had a very POSITIVE attitude – skiing was going to be great! I had a new outfit and felt like a snow bunny.  Going DOWN the hill, I spent more time on my behind than on my skis and my friends made fun of me, I cried, and the snot froze to my face. So not the look I was going for.  It was a very NEGATIVE experience.  By the time I got to the bottom of the hill, I was having ZERO fun, was exhausted, and closed my eyes. I failed to see the very steep cliff and skied right off the edge – words could not describe that feeling – it was UNDEFINED.  (One parent stopped me at the market to tell me they were so sorry about my sad skiing experience – too funny) Under each flap, the students draw a graph of a linear equation with each slope, write an equation in slope-intercept form with each type of slope, and describe what slope is all about.

inside the foldable

back of the foldable

Another foldable is for the whole unit. This one has “tabs” that we write the main topics on, then open the foldable to reveal the notes for each topic. This one used three pieces of paper, folded, then stapled together at the top.

Students add additional notes – this is my copy.

I teach mostly freshmen in my Algebra I class at the high school and adults in the developmental algebra class at the community college. I use these activities with both groups and they are very engaged!