## The Great Collatz Collab

Proving the Collatz Conjecture is a famous unsolved problem in mathematics. It can be understood by school students and can be explained using artistic diagrams. Introduce your students to the Collatz Conjecture by using these map (graph) drawing worksheets. The Great Collatz Collab was a project in 2022 where, using maps drawn by students all around the world, we made a giant collaborative Collatz map featuring sections from as many student maps as possible. You can view the final poster and watch the video about it below.

## Festive Fold and Cut

The Fold and Cut Theorem tells us it is possible to cut any straight-edge shape out of a piece of paper with a single cut, provided you fold the paper correctly first. In this collection of resources students can explore the Fold and Cut Theorem with festive shapes, and can go on to make and decorate a Fold and Cut Christmas Tree.

## Squared Squares

A perfect squared square is a square that can be composed of a set of entirely unique smaller squares. Explore squared squares with your class via this collection of puzzles that involve deduction and spatial reasoning.

## Wrapping Presents Mathematically

We can use mathematics to wrap presents efficiently, minimising the amount of wrapping paper we use. Explore this with your students!

## Fold-and-Cut Bat

It is possible to cut any straight-edge shape out of a piece of paper with a single cut. Provided you fold the paper the correct way first. These instructions show how to make a one-cut bat. There is an additional challenge to find the folding pattern for a different bat.

## Frog Jumps

A frog needs to cross a pond by stepping on all, some or none of nine lily pads floating across the pond. How many different ways are there that the frog could cross the pond? Use our activity sheets to investigate this problem with your students.

## Bar Code Check Digit Trick

Bar codes have a pattern in their digits to help detect errors. A magic trick can be done where one person reads out all but the final digit on the bar code of a product, and the second person ‘predicts’ this final digit (the check digit) by using the pattern in the digits. Teach your class to do this trick and get them thinking about the maths that makes the trick work.

## Giant Sierpinski Triangle

In this video below Matt Parker and Steve Mould manage to create recursive fractals using Powerpoint. Here we've collected some ideas for making giant fractals with your class. Including a brand new guide for a low-prep paper Sierpinski triangle the whole class can help build.

## Difference of Two Squares

In the video below, Matt Parker and James Grime get us thinking about the sorts of numbers that can be expressed as the difference of two squares. Use the video and our task ideas to get your students playing around with squares and constructing proofs.

## Graceful Trees

Can you arrange five consecutive odd numbers in a line, so that the differences between adjacent pairs of numbers are all different? What if the numbers are connected in a way other than in a line? The Graceful Tree Conjecture in graph theory says that we will always be able to arrange n evenly-spaced numbers in a tree (with n nodes) so that differences between adjacent pairs are all different. Explore this with your students!