Thursday, 20 April 2017

Fraction Operation Continuum

As math teachers we definitely want our students to practice to become proficient but piles of problems or worksheets aren't going to be very engaging to students. We think this tweak to the standard worksheet is a way to turn those boring questions into something more engaging.

In Ontario, grade 7s are introduced to operations with fractions. Addition & subtraction and multiplication & division with whole numbers. The premiss here is fairly simple. Students are presented with multiple cards of questions (in this case of adding and subtraction of fractions (with a little of division and multiplication with whole numbers). The cards represent problems that increase in difficulty as you go from one to the next. Students can all start at the first envelope or you could give them an exit card the day before to help place them in a particular card to start. Students check their own answers using answer cards with the answers written with "invisible" ink that can be revealed by shining a UV light on it.

Students really seem to like this style of activity as they feel empowered to move from card to card when they are ready and the added feature of checking the answers with the UV pen gives a sense of novelty. This could be used as practice or review.

  • Gr7 - divide whole numbers by simple fractions
  • Gr7 - use a variety of mental strategies to solve problems involving the addition and subtraction of fractions
  • Gr7 - add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;
  • Gr7 -  demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number
  • Gr8 - As review (we plan an extension so that this could be used for grade 8 with multiplying and dividing fractions)
  • Enough copies of each of the question cards for your class (there are four cards per page at each level) in different colour card stock for each level,  laminated (use colours that allow seeing the magic pen writing - you may want to test this). You will likely not need as many cards in the last few envelopes as students work at different paces. You will need as many as you have in your class if you decide to start everyone at the first level. Fewer if you let students start at different levels (see below)
  • 3 sets of the answer cards (use magic pen to write the answers anywhere along each equation, they could be sideways, upside-down, (the answers are on the last page of the Google Doc). The answer cards are the same as the question cards but you write the answers in invisible ink on them. To help distinguish the answer cards to the question cards you should put a stamp or sticker on the back. Write on the cards first then laminate them. If you write on the card after lamination then the ink tends to wear off. There is a separate answer card on the last page of the download. That is for you to carry around (or not) but not for showing students but more for your reference.
  • 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 or Amazon.

  1. Place the questions in piles (or in envelopes taped to the wall) in order of difficulty and set up three stations for the answer cards. Students will get a card and answer the first 5 questions. 
  2. You could have all students start at level 1 but for this activity to be most successful, students should 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 (the day before) to help you decide which envelope each student should start in. When given back the exit card write down the level they will start in. 
  3. 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 card. If not there are more questions on the card until they master that type. You can decide whether you want them to do the other 5 or just do enough to get a total of five correct. 
  4. As they move through the continuum, the hope is that they reach level 6 which matches the grade 7 curriculum. Since our goal is to get them to level 6, students should solve ALL equations on that card instead of just five. 
  5. The seventh level is set up to challenge students who are moving forward quickly. They should solve all questions on this card.  


  • Fraction Operation Continuum (with Answers) - (PDF, Google Doc)
Did you use this activity? Do you have a way to make it better? If so tell us in the comment section. Thanks