Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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?

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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?

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

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

These clocks have been reflected in a mirror. What times do they say?

Find at least one way to put in some operation signs (+ - x รท) to make these digits come to 100.

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

What do you think is going to happen in this video clip? Are you surprised?

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.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Dotty Six is a simple dice game that you can adapt in many ways.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

This problem explores the shapes and symmetries in some national flags.

Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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?

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

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Can you replace the letters with numbers? Is there only one solution in each case?

Can you draw a square in which the perimeter is numerically equal to the area?

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.