Reasoning, Convincing and Proving - Secondary Students

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

How much can you read into a t-shirt?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Can you find the values at the vertices when you know the values on the edges?

Can you find triangles on a 9-point circle? Can you work out their angles?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Imagine a very strange bank account where you are only allowed to do two things...

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Can you work out which drink has the stronger flavour?

Join pentagons together edge to edge. Will they form a ring?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Just because a problem is impossible doesn't mean it's difficult...

Can you make sense of these three proofs of Pythagoras' Theorem?

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Play around with the Fibonacci sequence and discover some surprising results!

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Have you ever wondered what it would be like to race against Usain Bolt?

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Is it possible to find the angles in this rather special isosceles triangle?

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?

Why does this fold create an angle of sixty degrees?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Two ladders are propped up against facing walls. At what height do the ladders cross?

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.