We’re stretching our #MondayMaths puzzle to the limit this week with a transformation of our very own Mathematics Mastery logo. From the information given, can you and your class work out the coordinate of B and find the area of trapezium AOBC?
It’s easy to observe interesting geometrics in the things we see around us every day, be it the patterns of a wallpaper, the spacing of bathroom tiles, or in this case, our logo! In this perplexing puzzle we’re looking specifically at the floating trapezium right in the middle.
What’s the best way to start?
This problem can be approached in several ways – either by making calculations using knowledge of linear graphs and linear equations, or by building from what we know about properties of shapes.
Need some top tips?
With either method, the best possible starting point is to label all the coordinates we do know. It may be useful to extend BC to meet the y-axis and find that any other coordinate that will help pinpoint the position of B.
As shown below, students may want to divide the trapezium shape into individual triangles – the isosceles triangle, OBC and the right-angled triangle, AOC.
If using a linear approach, students need to think about the fact that OA and BC are parallel – and so what does this mean in terms of the formulae of those lines?
However, if students are tackling it by thinking about properties of shapes, they can identify that OBC is an isosceles triangle. What does this reveal about the coordinate of B compared to the coordinates of O and C?
Can this be used as a depth task?
This would work well for our Year 9 mastery students who have been studying Cartesian coordinates and linear graphs this term – but is also suitable for a Year 10 lesson as students start to look at more complex graphical problems.
How can the puzzle be extended?
Why not look around to find some other well-known logos and pull out a few fun questions about their structure, geometry or patterns that can be solved by calculation and/or estimation.
Hope you enjoy – we’d love to hear your ideas for using this in a lesson. And remember the answer is posted on Twitter later this week!
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