Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

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?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

Can you find the chosen number from the grid using the clues?

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

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

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?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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

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

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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

56 406 is the product of two consecutive numbers. What are these two numbers?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

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 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.