Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Have a go at balancing this equation. Can you find different ways of doing it?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

How many different rectangles can you make using this set of rods?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

Number problems at primary level that may require resilience.

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?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

How many different sets of numbers with at least four members can you find in the numbers in this box?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Can you make square numbers by adding two prime numbers together?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Given the products of diagonally opposite cells - can you complete this Sudoku?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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?

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

Can you complete this jigsaw of the multiplication square?

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

Number problems at primary level to work on with others.

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you find different ways of creating paths using these paving slabs?