This problem looks at how one example of your choice can show something about the general structure of multiplication.
These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
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?
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?
Would you rather: Have 10% of Â£5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
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.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Can you work out some different ways to balance this equation?
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
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?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.
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.
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?
Can you match pairs of fractions, decimals and percentages, and beat your previous scores?
There are nasty versions of this dice game but we'll start with the nice ones...
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.
Can you sort these triangles into three different families and explain how you did it?
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
This problem explores the shapes and symmetries in some national flags.
How many different triangles can you make on a circular pegboard that has nine pegs?
How much do you have to turn these dials by in order to unlock the safes?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
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?
Can you place the blocks so that you see the reflection in the picture?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
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.
Can you place these quantities in order from smallest to largest?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
How many tiles do we need to tile these patios?
How will you find out how much a tank of petrol costs?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
Can you use this information to estimate how much the different fruit selections weigh in kilos and pounds?
These watermelons have been entered into a competition. Use the information to work out the number of points each one was awarded.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Use the information on these cards to draw the shape that is being described.
How many faces can you see when you arrange these three cubes in different ways?
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?
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
Can you draw a square in which the perimeter is numerically equal to the area?
Can you put these mixed-up times in order? You could arrange them in a circle.
How many of this company's coaches travelling in the opposite direction does the 10 am coach from Alphaton pass before reaching Betaville?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
If you asked your mum/dad/friend to take you to the park today, what sort of response might you get?
What is the most common coin in this shopkeeper's till?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Play this dice game yourself. How could you make it fair?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?
Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?