A linear relationships ‘menu’

Nat Banting wrote recently on his blog about a type of task he calls a ‘menu’: Given a list of features, the task for students is to build as few functions as possible to satisfy each requirement at least once.

Nat’s original post is about a quadratics functions menu. My attention was captured by Dylan Kane’s tweet in which, inspired by Nat, he wrote a trigonometric functions menu. Later, Sheri Walker was inspired to write an exponential functions menu.

I was similarly inspired, and so included the following linear relationships ‘menu’ in our most recent #math1057 tutorial.

Not only does this style of task elicit strategic thinking and emphasise understanding, it also helps students make connections between certain properties of linear equations.

My favourite tasks have a variety of ways for students to start. With the ‘menu’, I noticed a few strategies. For example:

• Some students found the equation of the line through the two given points (2,-3) and (4,0), and proceeded from there.
• Some started with the equation of a specific line (like from the previous tutorial question) and worked out which requirements it met. Later, they realised they could make adjustments to the line so that it met more of the requirements. Once they met as many requirements as they could, they thought of another specific line with at least one of the remaining requirements, and repeated their process.
• Some started with a rough sketch of a line with the first requirement, and made adjustments as they progressively considered additional requirements. Once they could no longer alter their line, they chose specific values (like two points, or a point and a slope) from which to build a specific linear equation.
• Some students identified requirements that can not be paired, and put them in separate lists. Later, once all requirements were assigned to a list, they built specific equations that satisfied the properties on the list.

Like Nat, I suspect this style of task will become a staple in my classroom. I look forward to expanding it to other topics, like geometry, statistics and probability. If you design your own, please share!