## 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.

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

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.

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 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.

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.

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.

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!

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!

Chinese New Year in 2019 (5 February) welcomes in the year of the Earth-Pig. In Chinese Mythology, each year has a Zodiac which comprises of an animal and an element. When will the next Earth-Pig year be? What was the Chinese Zodiac of the year of your birth? Celebrate Chinese New Year by using maths to answer these questions.

Which week day will your birthday be this year? Or in 2020? When will you next be able to re-use your 2019 calendar? This set of tasks is about the maths of calendars, and is inspired by Matt Parker's video 'How many calendars are there?'

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