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Reasoning, Convincing and Proving is part of our Thinking Mathematically collection.
Can you select the missing digit(s) to find the largest multiple?
In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
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?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
How much of the square is coloured blue? How will the pattern continue?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Which set of numbers that add to 100 have the largest product?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Are these games fair? How can you tell?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Choose any three by three square of dates on a calendar page...
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
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?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Can you describe this route to infinity? Where will the arrows take you next?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A collection of short Stage 3 and 4 problems requiring Reasoning, Convincing and Proving.
Sequences of multiples keep cropping up...
There are lots of different methods to find out what the shapes are worth - how many can you find?
Can you find the values at the vertices when you know the values on the edges?
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Can you make sense of these three proofs of Pythagoras' Theorem?
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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
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?
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?
Have you ever wondered what it would be like to race against Usain Bolt?
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
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.
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?
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?
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?
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove 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.
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
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?
Can you make a square from these triangles?
Which of these triangular jigsaws are impossible to finish?
Sort these mathematical propositions into a series of 8 correct statements.