When students are given a factoring worksheet, most will become disengaged quickly. But during this activity, we heard a student say "Can we do this type of activity more often?". In the above envelopes there are expressions that need to be factored 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.

- MPM 2D - factor polynomial expressions involving common factors, trinomials, and differences of squares
- MFM 2P - factor binomials and trinomials involving one variable up to degree two, by determining a common factor using a variety of tools, factor simple trinomials of the form x
^{2}+ bx + c, factor the difference of squares of the form x^{2}– a^{2} - MCF 3M - factor quadratic expressions in one variable, including those for which a ≠ 1 ,differences of squares and perfect square trinomials by selecting and applying an appropriate strategy
- MBF 3C - factor trinomials of the form ax
^{2}+ bx + c, where a = 1 or where a is the common factor, by various methods - MCR 3U - as review

- 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 after each equation, 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 at a Scholastic's book fair or on eBay or Amazon.

- 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.
- Tape the envelopes 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. 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.
- As they move through the continuum, the hope is that they reach envelope 4 (blue) that matches the grade 10 academic curriculum. Since our goal is to get them to the blue card, students should solve ALL equations on that card instead of just the first five.
- The last 2 envelopes are set up to challenge students who are moving forward quickly. They should solve all questions in these envelopes. Let students try to figure out for themselves how to factor these expressions.
- The assigned homework are just the questions from the cards. Student would just continue from where they left off on the continuum. I just have students take a picture of the card(s) with their phone.

- Factoring Continuum Cards (Word doc, pdf)
- Factoring Continuum Answers (Word doc, pdf)
- Factoring Continuum Exit Card (Word 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

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