Challenge Level

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?

Challenge Level

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?

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

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

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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

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

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

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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?

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

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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.

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

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

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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.

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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?

Challenge Level

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

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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?

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"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 ...?

Challenge Level

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

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

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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?

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

Challenge Level

Number problems at primary level that may require resilience.

Challenge Level

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.

Challenge Level

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?

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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?

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

Challenge Level

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

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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?

Challenge Level

Number problems at primary level to work on with others.

Challenge Level

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?

Challenge Level

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

Challenge Level

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

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Can you complete this jigsaw of the multiplication square?

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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?

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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?

Challenge Level

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.

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

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Got It game for an adult and child. How can you play so that you know you will always win?

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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

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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?"

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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.

Challenge Level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

Challenge Level

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