During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

This article for teachers suggests ideas for activities built around 10 and 2010.

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Here is a chance to play a version of the classic Countdown Game.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Resources to support understanding of multiplication and division through playing with number.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

There were 22 legs creeping across the web. How many flies? How many spiders?

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.

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

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

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

Number problems at primary level that require careful consideration.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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?

How would you count the number of fingers in these pictures?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

This task combines spatial awareness with addition and multiplication.

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

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.