factors pattern polynomial tasks

Trinomial Factoring Match

Fractions, factors, and functions.

A large portion of my career to date has been spent musing over how to engineer classroom environments that infuse meaning into these three mathematical structures. When it comes to polynomial factoring, the area model has provided the most success. After connecting 2-digit by 2-digit multiplication, the area model becomes a beautiful visual to make sense of the “adds to ___; multiplies to ___” phrase that echoes around the room.

But we don’t keep the area model around forever. Once we’ve used the model to build meaning, we mobilize that understanding in more symbolic situations in a careful, deliberate march toward mathematical abstraction.

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Report on a Math Tournament

**This post contains the materials and advice you’ll need to run a distanced math tournament with your district, division, school, province, state, classroom, family, coworkers, neighbours, etc., etc., etc.**

Honestly, the more math love, the better! (IMHO)

In mid-October, I designed a math provincial math tournament open to all middle school teachers in my home province of Saskatchewan, Canada. After writing up a blog post that served as a formal invitation, the tournament (which I affectionately called the Saskatchewan Mathematics Invitational Tournament–or #SMIT2020 for short) has been running for just over a month with over 80 classrooms from across the province playing Federico Chialvo’s delightful game MULTI. (see here for more information).

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A Math Tournament

**Update: Nov 23, 2020: Follow along on Twitter with some of the thinking at the hashtag #SMIT2020

COVID has created a global (and now chronic) pressure on all teachers in all classrooms, and the shifting, local realities have made teacher collaboration a precious commodity. It’s hard enough to find time to confer with colleagues under the best of situations, and now our major professional muster points are not currently viable–adding further value to any sense of connection that can be generated.

Bummer, right?

factors primes squares tasks

Counting Factors with Grade 7/8s

One of the great parts of my job as a split classroom teacher and division consultant is that I get to spend time in classrooms from grades six to twelve. This means I often need to be in one head space to teach my own Grade 12s and then switch gears to act with younger mathematicians. It also means that the classroom experiences are sporadic and involve teachers working in several different places in several different curricula.

On this particular occasion, I was working with a 7/8 split class that had just finished a unit on perfect squares and divisibility rules, and we wanted an activity that could serve as a sort of review of divisibility rules but also reveal something cool about perfect squares. I thought about the locker problem, but it doesn’t require students to factor in order to see the pattern. Instead, I took some of the underlying mathematical principles (namely: that perfect squares have an odd number of factors) and wrapped it in a structure suited for a Friday afternoon.

factors probability tasks

100 Rolls Task

**Update November 2020. Jamie Mitchell–a fantastic teacher from Ontario, Canada–sent me this google doc that his student prepared to justify her solution. After you wrestle with the prompt for a while, take a second to read this brilliant response!

Most probability resources contain a familiar type of question: the two-dice probability distribution problem. 

Often times, it is accompanied with questions concerning the sums of the faces that appear on each dice. 

For example:

Roll two fair, 6-sided dice. What possible sums can be made by adding the faces together?
What is the probability that:
a) the sum is 6
b) the sum is a multiple of 4
c) the sum is greater than 15?

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Fraction War Task

A while ago I wrote a post on embedding atomic skills into tasks so that the basic skills are developed and used as tools of mathematics rather than the ultimate goal of mathematics. I try to develop tasks that follow this framework. I want the student to choose a pathway of thought that enables them to use basic skills, but doesn’t focus entirely on them.

Recently, I was reading Young Children Reinvent Arithmetic: Implications of Piaget’s Theory by Constance Kamii and came across one of her games that she plays with first graders in her game-driven curriculum.

factors games numeracy primes tasks

The Guess Who Conundrum

Every so often, an idea comes out of left field. I woke up with this on my mind–must have been a dream.
Back in the day, my family had a dilapidated copy of the game “Guess Who?” My siblings and I would take turns playing this game of deduction. You essentially narrowed a search for an opponent’s person by picking out characteristics of their appearance.
circles circumference factors pattern tasks

Bike Trail Task

There is two hour parking all around University of Saskatchewan. I once went to move my car (to avoid a ticket) and found that the parking attendant had marked–in chalk–the top of my tire. I wanted to erase the mark so began driving through as many puddles as possible.
I then convinced myself to find a puddle longer than the circumference of my tire–to guarantee a clean slate and a fresh two hours.
As I walked back to campus, I got thinking about the pattern left behind by my tires. For simplicity, let’s take the case of a smaller vehicle–a bike.
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Painting Tape

I came across the following situation while shopping for paint at a local home improvement store:

Admittedly, the three varieties were not positioned like this, but this positioning does raise an interesting question.
“We can see the packages are the same height, what is that height?”
factors polynomial reflection

All Factors Considered

I have only been teaching for 2 years, but am already beginning to encounter the recursive nature of the profession. I have had several repeat classes in my 4 semesters of teaching, and they require the achievement of the same outcomes. This does not bother me, in general, because I am excited to see the improvement in my teaching. There is one unit, however, that has already frustrated me. Its ability to sabotage creative exploits is unrivalled throughout the mathematics curriculum; I am speaking of the unit on polynomial factoring.