Can you find a way of counting the spheres in these arrangements?

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these numbers to the nearest whole number?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

This challenge is about finding the difference between numbers which have the same tens digit.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

This activity involves rounding four-digit numbers to the nearest thousand.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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?

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?

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Find the sum of all three-digit numbers each of whose digits is odd.

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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

Watch this animation. What do you see? Can you explain why this happens?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Try out this number trick. What happens with different starting numbers? What do you notice?

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

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

This challenge asks you to imagine a snake coiling on itself.

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

This task follows on from Build it Up and takes the ideas into three dimensions!

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

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?