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Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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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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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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A game in which players take it in turns to choose a number. Can you block your opponent?

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

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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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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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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 complete this jigsaw of the multiplication square?

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

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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 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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A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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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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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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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 rectangles can you make using this set of rods?

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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?

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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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How will you work out which numbers have been used to create this multiplication square?

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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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Play this game and see if you can figure out the computer's chosen number.

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

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Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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

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Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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Can you sort numbers into sets? Can you give each set a name?

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Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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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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Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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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?

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

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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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Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?