This task combines spatial awareness with addition and multiplication.

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

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?

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

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

A game that tests your understanding of remainders.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

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?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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

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?

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?

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.

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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?

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?

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 find different ways of creating paths using these paving slabs?

Number problems at primary level that may require resilience.

Number problems at primary level that require careful consideration.

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

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

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

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

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

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?

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?

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

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

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

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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

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