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

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?

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!

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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

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?

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 use the numbers on the dice to reach your end of the number line before your partner beats you?

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

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

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?

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

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

Can you hang weights in the right place to make the equaliser balance?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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?

This challenge extends the Plants investigation so now four or more children are involved.

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.