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What is it?
Often when scrolling through my Twitter timeline I come across one of those puzzles that shows you a square split up into regions by intersecting lines and challenges you to calculate the fraction of the square contained in one on the regions. I’ll be honest, I struggle because I don’t have a framework to approach such problems. I scrabble around for a bit, and then sneak a peek in the replies to see the answer.

This resource provides such a framework. By showing us how we can take such problems out of the world of geometry and into the world of straight-line graphs, all of a sudden there is a route in. This resource has been a game-changer for me, but more importantly, by sharing these problems with students, we can show them how different areas of maths combine, and get them to practice working with concepts such as coordinate geometry, fractions, simultaneous equations, substitution and more.

How can it be used?
As the author says, a sound knowledge of straight line graphs – in particular calculating their equations and their point of intersection – is required to get the most out of this resource. Fortunately, that is covered in the starter. With such knowledge established, working through the first example as a class seems a sensible starting point. The teacher could model a stage and then challenge the students to consider what would come next, then resume the modelling.

There are plenty of practice questions provided on the accompanying worksheet for students to get stuck into following the teacher-led demonstration, so they can consolidate and develop their skills and many of the solutions are incredibly satisfying in their simplicity. This really is a fine example of a resource that combines lots of different areas of maths in a challenging, fun, and ultimately useful way.

Thanks for sharing!
Craig Barton

Download: Graphs and geometry
View the author’s other resources