Category: tasks

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.

area scale tasks

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.

Pythagorean theorem tasks

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 “

classroom structure discourse tasks whiteboards

Creating Communities of Discourse: Large Whiteboards

Post author By natbanting
Post date November 5, 2013
1 Comment on 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?

reflection tasks

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 of 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 to do as a teacher–make the students think.

factors fractions games investigation logic tasks

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.

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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 project approach; student initiative and autonomy is a powerful thing. I, however, don’t like that the experiment involves humans. Here’s why…

logic numerical flexibility pattern tasks

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).

measurement ratios tasks unit analysis

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.

logic probability tasks

Fair Dice Task

The recent curriculum renewal has placed a (well-deserved) heightened emphasis on counting, set theory, and probability. Just under a half of a Grade 12 “Foundations of Mathematics” course now covers the three topics. This is a huge improvement from the token, disjointed topics strewn around the last courses. It allows teachers to set a different tone–a tone of curiosity that seems inherent in probability.

I came across the idea of Grime Dice (named and pioneered by Dr. James Grime @jamesgrime) late last year after I knew I was to be teaching probability this winter. I knew right away this was a great task to get students tinkering with probability before defining its inter-workings theoretically. A great description of their function can be found on the PlusMath website written by Dr. Grime himself. They are available for purchase from MathGear.co.uk.