This task follows on from Build it Up and takes the ideas into three dimensions!

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

This challenge is about finding the difference between numbers which have the same tens digit.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

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?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Benâ€™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?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

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?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Try out this number trick. What happens with different starting numbers? What do you notice?

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Find the sum of all three-digit numbers each of whose digits is odd.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Are these statements always true, sometimes true or never true?

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.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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.

An investigation that gives you the opportunity to make and justify predictions.

This challenge asks you to imagine a snake coiling on itself.

Find out what a "fault-free" rectangle is and try to make some of your own.

Here are two kinds of spirals for you to explore. What do you notice?

This activity involves rounding four-digit numbers to the nearest thousand.