The Price is Right (& other tasks to foster reasoning about fractions)

As I mentioned in my previous post, the start of the school year in my Grade 9 class is dedicated to reviewing some basic concepts from elementary school – in particular, integer operations, fractions, and fraction operations. I try to embed these skills as components of tasks that ask students to make decisions, generalize, problem solve, and/or engage with novel or less-familiar mathematical ideas – or, as Nat Banting (who does this so well) describes it, “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.” At the beginning of the year, these kinds of activities allow me to simultaneously identify and assess the needs of students who are still struggling with basic concepts and to challenge students who are ready to learn something new. Continue reading “The Price is Right (& other tasks to foster reasoning about fractions)”

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Integer Bingo

During the first week or so of the school year, I take time to review some basic concepts from previous years with my Grade 9 students – in particular, integer operations, fractions, and fraction operations. The challenge is designing tasks that embed review and practice within problems or activities that also call for generalization, problem solving, or engagement with novel or less-familiar mathematical ideas. I deem this necessary because, of course, not all students come to high school with the same understandings and strengths, and while some do need the opportunity to review basic concepts, others are ready to move on. For the latter group, review activities are at a high risk of being perceived as baby-ish and not worth the time, which means that I need to design these tasks very carefully – that is, in such a way that I can simultaneously assess the needs of students who are still struggling with basic concepts and challenge students who are ready to learn something new.

I’d like to share one task that, I think, had something to offer to all of my students: Integer Bingo, which is based on a task developed by and discussed in Serradó (2016). I chose this task for several reasons: Continue reading “Integer Bingo”

Love the questions

There are a lot of quotes (maybe as many as there are teachers) that begin something like this: “The goal of education is…” For example,

“The one real goal of education is to leave a person asking questions.” Max Beerhohm

Undoubtedly, many of these are spoken in a hyperbolic manner, and should be interpreted as such. (Myself, I would be wary of anyone who believed that there are precisely N goals of education, true for all places and at all times.) Nevertheless, this sentiment came to my mind last week, the first week of school. Continue reading “Love the questions”