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.

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

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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?

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In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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

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

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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?

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Can you find the chosen number from the grid using the clues?

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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.

Challenge Level

Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

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

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?

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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?

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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?

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Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

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You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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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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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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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.

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Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

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Can you complete this jigsaw of the multiplication square?

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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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How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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Number problems at primary level that may require resilience.

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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 ...?

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If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

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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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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?

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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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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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

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

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Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?