Seeing Things Differently – Hexagonal Numbers
A problem for secondary students familiar with triangle numbers. Try to give time for them to come up with their own structures that help them see ways of extending the sequence.
Seeing hexagonal numbers
Able Adder
This task and related ideas have been inspired by the “Twist and Lock” problem below.
Task 1: Investigate all the shapes Able Adder can make.
Task 2: Adder Tracks
Twist and Lock
I was visiting the Tate Modern in London and found these in the shop. A string of cubes linked together with some elastic and which allow you to twist each cube onto different sides of adjacent cubes. Find some related mathematical ideas here.
A version for Farhan
Just seen a reference to the NRICH problem ‘Farhan’s Poor Square’. Though I am not excited by this problem – it made me think of this:
- AB is the diameter of the circle on ABC and part of a diagonal of the large square.
- The large square has a side length of 2x.
- The triangle is isosceles and right angled.
What is the area of the large square that is left white?
Is it possible to make the grey shape larger and reduce the white area? What is the best you can do? Does a constraint that the grey shape has to remain similar matter? For example, you don’t have to stick to a semicircle, just a segment of a circle.
Diameter, circumference and Pi
Three tasks that are designed to help develop a firm understanding of the relationship between the diameter and the circumference of a circle and multiples of Pi.
Patterns and Coordinates
A series of whole class and group activities to explore, conjecture and generalise (using algebra if appropriate) in the context of coordinates in all four quadrants.
Inferring and Extending
Can you describe what you see in the images which introduce this problem and can you extend the idea if there were three circles and not two?
This page has the following sub pages.
Thanks, Jenny–I’ll show some students today and see what they think.
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