Find the sum of all three-digit numbers each of whose digits is odd.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Try out this number trick. What happens with different starting numbers? What do you notice?
An investigation that gives you the opportunity to make and justify predictions.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Here are two kinds of spirals for you to explore. What do you notice?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task follows on from Build it Up and takes the ideas into three dimensions!
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Are these statements always true, sometimes true or never true?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
This activity involves rounding four-digit numbers to the nearest thousand.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
This challenge asks you to imagine a snake coiling on itself.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
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.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?