Math Challenge Activity

I built this activity for a group of 120 students from grades 7-10 at a provincial math contest. The problems themselves are a mixture of created, adapted, and stolen. I chose them because they fit fairly nicely into a multiple choice format while still eliciting deep thinking.The puzzle moves forward as follows:There are 10 stations, and 10 problems. Each problem is responsible for giving a unique letter for the final word scramble. Some of the letters are repeated more than once in the final answer (i.e. have a frequency more than one), but no problem leads to the same letter. Each …

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Garbage Can Task

The following task happened by accident:I was about to introduce a problem to my Math 9 Enriched class that we were going to complete with group whiteboards. Before I could introduce, life got in the way. Students wanted to know about their most recent examination. As I launched into a speech on their performance, a student got up to sharpen their pencil. She walked right in front of me. I made a comment, and she replied that the garbage can should be in the back corner where it would be more convenient. I told her that having it by my desk …

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Basketball Golf Task

The other day, a future teacher asked what one piece of advice I would give to a soon-to-be mathematics teacher. I immediately had several. I settled on one that I felt encapsulated my belief both in and out of class: Honour curiosity.  In class, this finds me wandering through student suggestions and constantly posing new problems that create relevant challenges. Curiosity (both student and teacher) keeps a vibrant ecology going, and I would argue that the intellectual tension so often provided through curiosity is necessary for a positive ecology to thrive.Outside of class, this has me interacting with my curios …

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Road Building Task

The Pythagorean Theorem is often taught in isolation. It has connections to solving equations, but often appears in curriculum long before other equations involving radicals. It also has unique ties to both radicals as well as geometry.Despite these connections, the theorem has developed the reputation of a surface skill. It involves the  repetition of the rule alongside numerous iterations. Something so fundamental to geometry is reduced to a droning chorus of: ” ‘a’ squared plus ‘b’ squared equals ‘c’ squared “ This task aims to find a middle ground between where critical problem solving and collaboration can meet the technical …

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Creating Communities of Discourse: Large Whiteboards

I have talked about individual whiteboards on this blog before. My school bought me supplies and I was loving the various classroom activities. While the grouping questions facilitated good mathematical talk between peers, I was still searching for a method to encourage more collegiality where my role could diminish to interested onlooker or curious participant.  So I had this brilliant idea.  Why don’t we get group-sized whiteboards created where students could work collaboratively on tasks? In my mind I had just stumbled upon something uniquely genius, but soon discovered that it had been done by Frank Noschese years previous.  I …

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What Makes a Task “Rich”?

In my short career, I have seen the death of the lesson. I remember creating ‘lesson plans’ to the exact standards of my college of education, and then never looking at them when I began to teach. I was never really in tune with the rigidity of the plan, but knew that there were certain learning goals I needed to get to by the end on an hour. The scene has shifted away from the harshness of a ‘lesson’ toward more student-action-centred words like project, problem, prompt, or task. I like these words because they accurately describe what I am trying …

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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.The game was called double …

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Spinner Data Task

The difference between what should happen and what does happen is a difficult distinction for students. They are so used to finding exact answers in the back of textbooks, that differing experimental results create an sense of uneasiness. At an early age (Grade 9 in my province) we begin to introduce students to the ideas of sampling and experimental probability.  The topic is usually approached with a project or survey of schoolmates. The results are then tallied and then used to create “probabilities” of various things such as favourite sports team, food, or colour. I love the philosophy behind the …

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Dice Sums Task

Dice are familiar tools in most mathematics classrooms. Their use in primary school games allows students to build preliminary notions of number and autonomy. (see Kamii) As the grades progress, dice sums become too simple and the tool is pushed into the realm of probability and chance. There, alongside decks of cards and coloured spinners, it enjoys almost godly status; it seems that there is no better way to calculate odds than to role dice and spin spinners (in outrageous cases—simultaneously). The greatest thing dice have going for them is familiarity. Teachers can use this to upset the thinking of …

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Leaky Faucet Task

This idea is not my own. The only problem is, I don’t exactly know who it belongs to. I remember tweeps talking about about a task where a leaky faucet’s effect was analysed on a water bill. When I encountered the situation at my Uncle’s house, I had to capture the modelling in action. The best part was the conversation from intrigued (and weirded out) relatives as I ducked and dived around the tap to get a good angle. We got into a conversation about teaching, and they were happy to present any questions that came to their minds. The …

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