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.

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?

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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

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

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

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

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

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

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?

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?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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

This task combines spatial awareness with addition and multiplication.

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Try out some calculations. Are you surprised by the results?

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

Investigate the number of faces you can see when you arrange three cubes in different ways.

This challenge combines addition, multiplication, perseverance and even proof.

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

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Take turns to place a decimal number on the spiral. Can you get three consecutive numbers?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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.

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