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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Universal Design for Learning

One of my favorite planning tools is this UDL (Universal Design for Learning) wheel.  Even though all good teachers do these things in their lessons all the time, my district is requiring us to list the specific UDL principles and learning supports in each of our lessons, so this is a convenient way for me to access them.

According to “Universal Design for Learning is a set of principles for curriculum development that give all individuals equal opportunities to learn.  UDL provides a blueprint for creating instructional goals, methods, materials, and assessments that work for everyone–not a single, one-size-fits-all solution but rather flexible approaches that can be customized and adjusted for individual needs.”

The wheel can be found at  Click the arrows to the right or left of the viewing window to rotate the wheel to the desired Principle of UDL.  Principle 1 is to Provide Multiple Means of Representation (presenting content in a variety of ways). Principle 2 is Provide Multiple Means of Expression (how students express what they know). Principle 3 is Provide Multiple Means of Engagement (how students are engaged and how they interact with the content).

Picture of UDL wheel



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!

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Activities for Translating Algebraic Expressions

These are quick, review-type activities that I use after I teach translating Algebraic expressions. I will start with the cool notes from @Middle School Math Madness in her post for Translating Words into Math.

The rest of the week will include a variety of review activites to provide practice with the operation words.  All of my classes sit in teams of 4, so most activities are for small groups.

Word Sort – copy the words on card stock and cut apart, one set for each group.  I put the heading cards (addition, sub, mult, div, parentheses) on a different color paper. These heading cards are used again in Hot Seat and the rest are used again with Four Corners.  Give each group an envelope with all the operation words and the heading cards in it. They work together to sort all the words under the correct heading (add, sub, etc). Operation Words sort

Four Corners (except there are 5, so I guess it’s five corners??) – post the large operation symbols and the parentheses on the wall around the room (I made an x and a dot for multiplication – use whichever). Give each student a card with a phrase on it (from Word Sort). They go stand near the operation sign corresponding to their card.  They compare cards and check to see if everyone is in the right place.  4 Corners Operation Signs

Language of Algebra Game – copy the cards onto card stock. One set for each group of 4.  The game plays like Rummy.  Pass out 7 cards to each player. The rest go face down in a pile. The goal is to make a “book” of cards – 4 expressions that are that same. The directions are with the cards.  Language of Algebra Matching

Hot Seat – use the heading cards (add, sub, mult, div, parentheses) from the Word Sort.  Students get in single file lines of 4 or 6 facing the board. The last person in the row gets the heading cards. Everyone else faces forward so they can’t help each other. I show a word/phrase from the powerpoint and the last person decides which card is the right operation and passes it the person in front of him. If that person agrees, he passes it forward. If he disagrees, he passes it back. When a card makes it to the first person in line, if they agree, they hold it against their chest in and face me so I know they are registering their “final answer.” The first team with correct answer gets 2 points, any team with a correct answer gets 1 point. They rotate the front person to the back and start over.  Hot Seat Operation Words