Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Can you use the information to find out which cards I have used?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Find all the numbers that can be made by adding the dots on two dice.

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

If you have only four weights, where could you place them in order to balance this equaliser?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Use the number weights to find different ways of balancing the equaliser.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Dotty Six is a simple dice game that you can adapt in many ways.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Investigate what happens when you add house numbers along a street in different ways.

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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