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?

Can you match these calculation methods to their visual representations?

In this article for primary teachers, Ems outlines how we can encourage learners to be flexible in their approach to calculation, and why this is crucial.

More resources to support understanding multiplication and division through playing with numbers

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

Related resources supporting pupils' understanding of multiplication and division through playing with numbers.

Can you put these four calculations into order of difficulty? How did you decide?

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

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

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

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?

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?

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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

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.

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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

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

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

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

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

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

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

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

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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

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

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.

Ben’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?

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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

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?

This task combines spatial awareness with addition and multiplication.

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

Can you find different ways of creating paths using these paving slabs?

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,. . . .

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Given the products of adjacent cells, can you complete this Sudoku?

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.