Friday, 8 May 2015

9 Academic Solving Equations Continuum

When students are given a solving equations worksheet, most will become disengaged quickly. But during this activity, we heard a student say "Am I sick because I think this is fun".  In the above envelopes there are equations that need to be solved that increase in complexity as you go from left to right.  Students start in a particular envelope based on a formative assessment (eg. exit card) and move themselves along the continuum at their own pace.  As an added bonus rather than checking answers at "the back of the book", they will check using an ultraviolet "magic" pen on the answer cards.  Solving equations is like finding that mystery number.

MPM1D (for a similar activity for MFM1P, click here)
  • solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies
One Set of Answer Cards
  • 20 copies of each of the question cards in different colour cardstock, cut and laminated (use colours that allow seeing the magic pen writing)
  • 7 envelopes of the same colour as question cards (made from cutting cardstock, taped and laminated)
  • 3 sets of the answer cards (use magic pen to write the answers anywhere along each equation, they could be sideways, upside-down, ...- use the homework sheet to see the answers to the questions) To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back.
  • 3 "magic" pens can be purchased at Chapters/Indigo or we found these at a Scholastic's book fair. We have since purchased some on eBay.

  1. For this activity to be successful, students must start at the appropriate envelope. If they start in one that is too hard they will be frustrated and if they start in one that is too easy they will be bored. Use an exit card to help you decide which envelope each student should start in. When given back the exit card write down the colour of the envelope they will start in.
  2. Tape the envelopes to the wall in order of difficulty and set up three stations for the answer cards.
  3. Students will get a card and answer the first 5 questions.  To check their answers, they will go to a station and use the magic pens. Students may decide to do one question at a time and then go check their answer or they may do all 5 and then check. Students are monitoring themselves so they decide.  If they get the first 5 right, they have a level of mastery to move themselves to the next envelope.  If not there are more questions on the card until they master that type.  
  4. As they move through the continuum, the hope is that they reach the yellow envelope that matches the 9 academic curriculum.  Since our goal is to get them to the yellow card, students should solve ALL equations on that card instead of just the first five.
  5. The last 2 envelopes are set up to challenge students who are moving forward quickly.  They should solve all questions in these envelopes. We had a few students that were able to solve all the questions in the purple envelope so to challenge them further I created the brown envelope with quadratic equations.  These would not formally be taught but instead let them use something like guess and check.  
  6. The assigned homework are just the questions from the cards. Student would just continue from where they left off on the continuum (up to the yellow).
The video, below, is only visible in the WECDSB domain. That is, only teachers in our school board can see the video if they are logged into their MyTools2Go accounts

  • 9 Academic Solving Equations Continuum Cards (pdf) (doc)
  • 9 Academic Solving Equations Continuum Homework (pdf) (doc)
  • Solving Equations Continuum Exit Card (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


  1. Interesting to read that the video "only teachers in our school board can see the video if they are logged into their MyTools2Go accounts" -- tho' I suppose that's because YouTube is blocked where teachers are (it's not blocked here)?
    Wondering if you've considered giving things a Creative Commons license

  2. Originally we started this blog as a resource for teachers in our school board but knew others would be interested. Getting all the permissions is a bit of a hassle (from students and teachers) so we either block out faces (on pictures - which is easy) or just only make it available locally (on video).