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Reasoning, Convincing and Proving is part of our Thinking Mathematically collection.
In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
Try out some calculations. Are you surprised by the results?
You'll need to know your number properties to win a game of Statement Snap...
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
The Number Jumbler can always work out your chosen symbol. Can you work out how?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Choose any three by three square of dates on a calendar page...
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
These Olympic quantities have been jumbled up! Can you put them back together again?
Imagine a very strange bank account where you are only allowed to do two things...
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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...
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Play around with the Fibonacci sequence and discover some surprising results!
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Just because a problem is impossible doesn't mean it's difficult...
Can you find ways to put numbers in the overlaps so the rings have equal totals?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Where should you start, if you want to finish back where you started?
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
A collection of short Stage 3 and 4 problems requiring Reasoning, Convincing and Proving.
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Can you find the values at the vertices when you know the values on the edges?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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?
Can you make sense of these three proofs of Pythagoras' Theorem?
The clues for this Sudoku are the product of the numbers in adjacent squares.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
Have you ever wondered what it would be like to race against Usain Bolt?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
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?
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
Can you find the hidden factors which multiply together to produce each quadratic expression?
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
What is special about the difference between squares of numbers adjacent to multiples of three?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
If you know the perimeter of a right angled triangle, what can you say about the area?
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?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Can you explain what is going on in these puzzling number tricks?
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Use the differences to find the solution to this Sudoku.
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Can you create a Latin Square from multiples of a six digit number?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
What do you get when you raise a quadratic to the power of a quadratic?
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Can you make sense of the three methods to work out what fraction of the total area is shaded?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Can you match the charts of these functions to the charts of their integrals?
Can you work through these direct proofs, using our interactive proof sorters?
Do you have enough information to work out the area of the shaded quadrilateral?
Sort these mathematical propositions into a series of 8 correct statements.
Which of these triangular jigsaws are impossible to finish?