Friday, 8 May 2015

9 Applied 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.


MFM1P (for a similar activity for MFM1D, click here)
  • solve first-degree equations with nonfractional 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)
  • 6 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. Note: After doing this activity a few times, I needed an envelope with no integer solutions so I created the purple (1st) envelope.
  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 to 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 white envelope that matches the 9 applied curriculum.  Since our goal is to get them to the white 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 pink envelope so to challenge them further the yellow envelope has equations with fractions.  These are not part of the 9 applied curriculum but they can use their prior knowledge to try to solve these equations.
  6. The assigned homework handout are just the questions from the cards. Student would just continue from where they left off on the continuum.
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. Note this video is from an academic class which has slightly different envelopes


  • 9 Applied Solving Equations Continuum Cards (pdf) (doc)
  • 9 Applied 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

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