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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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!