Number Sentences Sort (update)

One of the smaller expectations we have to deal with is the ability for students to interpret algebraic equations. You know: "what does 2x + 1 mean"?. We created this very simple sorting activity where students are given expressions (and equations) and the sentence to describe them and have to match them up. This is meant to be an activity that is relatively quick. We have two versions here. One for grade 7 that only has expressions and one for grade 8 that has equations as well. We also have an Explain Everything version of each so that if you have an iPad (or Chromebook), with that app, you can have your students sort them electronically. This can also be used as review in Grade 9.
Note: This is an update to the same activity posted last year but now with a grade 8 and Explain Everything version
Double Note: This has been updated again to now include a Desmos card sort. So both card sorts are now transferred to this new Desmos feature. You can learn about Desmos Card Sorts by clicking here. Download the Teacher versions (which you can copy) of these activities below in the download section.

• Gr7PA - translate phrases describing simple mathematical relationships into algebraic expressions using concrete materials
• Gr8PA - translate statements describing mathematical relationships into algebraic expressions and equations
• MPM1D, MFM1P - As review

• For the grade 7 version there are four different (but similar) sets. One set per page. For the grade 8 version there are three different (but similar) sets. One set per page. 
• Print each page on card stock (we also suggest laminating). We suggest that each set be printed on different colour card stock for easy sorting. Cut each out and put each set in an envelope.
• Obviously you will have to decide how many sets you will need for your class depending on whether you pair students up or not. 
• Note that in the version with equations, there are some algebraic expressions that do not have matching sentences. In these cases, students will have to write their own.
• If you choose to use the Explain Everything version, then you probably want to download that .xpl file and put it on a server where your students can get easy access to it. 

Explain Everything Screenshot

1. Depending on how many students you have you may want to do this individually, in pairs or in larger groups. The activity is not super complex so we don't recommend anything bigger than pairs. 
2. Students take each set and sort the algebraic expression with the written version. 
3. When they are done their set they can trade with another group that has a different colour of cards. If they are using the Explain Everything version then they can just go to the next slide. 
4. There is a homework sheet for consolidation that includes both expressions and equations as well.

• NumberSentences-Expressions (doc. PDF, XPL, Desmos)
• NumberSentences-Equations (doc, PDF, XPL, Desmos)
• NumberSentencesHomework-Equations (doc, PDF)
• Entire Folder

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Simplifying Expressions with Algebra Tiles Matching Cards

This is a very simple matching activity where students are given a bunch of algebraic expressions (in one variable) and simplified expressions (both in algebraic and algebra tile form) and all they have to do is match up each expression with their simplified form. This is not meant to be a long or complex activity and could best be used as a warm up or end of class review or possibly just in the middle of a long class to switch up the period.

• MPM1D - add and subtract polynomials with up to two variables [e.g., (2x – 5) + (3x + 1), (3x²y + 2xy²) + (4x²y – 6xy²)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);
• MFM1P - add and subtract polynomials involving the same variable up to degree three [e.g., (2x + 1) + (x²– 3x + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);

• There are four sets of cards (each group would get a set so they aren't all working on the same questions). Each set of cards will have answers that have the same characteristics (Set 1 - answer is a trinomial, Set 2 - answer is a binomial with no squared term, Set 3 answer is a binomial with no x term, Set 4 - answer is a binomial with no constant term). A set should contain 12 cards. Four long expressions, four algebraic answers and four algebra tile answers.
• Print and cut out the cards (we suggest laminating them to). Note that each card has what set number it belongs to so that if you mix them up you can easily sort them back into their sets. You may wish to put each set in an envelope or ziplock bag for easy distribution.
• You will probably want to have physical algebra tiles for students to use while doing the actual simplification.
• Note that because there doesn't seem to be a consensus on which colour algebra tiles represent positive or negative, there are two sets. One that assumes red is positive and one that assumes red is negative. Keep which ever is the protocol for your class and discard the other.

1. Students could be put into groups or do this individually. Ether way, since there are only four sets you will need to have multiple copies of each set. 
2. Give each group an envelop and tiles and ask them to match the unsimplified expression with the simplified expression and algebra tile representation. 
3. Once each group is done, have groups switch their envelopes. (1 gives to 2, 2 gives to 3 etc). You can do this 4 times. 

• SimplifyingPolynomialsMatching (pdf, doc)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks

Sort Students into Groups using Linear Representations

In this activities students are each given one card. The card will either have a graph, table of values or equation of a linear relation. Their job is to find the two other students who have the other two representations of the same linear relationship. This shouldn't take too long and could be repeated every couple of days to solidify conversion between representations

MPM1D, MFM2P  - 

• graph lines by hand, using a variety of techniques
• identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b

• Download the cards and cut them out (you may want to laminate them)

1. Shuffle the cards and distribute one per student. Note that there are 11 sets of 3 cards so you may want to remove sets to more closely match your student population.
2. Students will find the other people who have the same linear relationship

• GraphTableLineMatch (doc) (pdf)

Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks