Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Number problems at primary level that require careful consideration.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

Can you use the information to find out which cards I have used?

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

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you find all the different ways of lining up these Cuisenaire rods?

This Sudoku, based on differences. Using the one clue number can you find the solution?

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.