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Broad Topics > Calculations and Numerical Methods > Multiplication & division

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Going Round in Circles

Stage: 3 Challenge Level: Challenge Level:1

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

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Countdown

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

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The Remainders Game

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

A game that tests your understanding of remainders.

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Power Mad!

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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Tug Harder!

Stage: 2 Challenge Level: Challenge Level:1

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?

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Shape Times Shape

Stage: 2 Challenge Level: Challenge Level:1

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

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Secret Number

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Route Product

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Round and Round and Round

Stage: 3 Challenge Level: Challenge Level:1

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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Method in Multiplying Madness?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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A Chance to Win?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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Integrated Product Sudoku

Stage: 3 and 4 Challenge Level: Challenge Level:1

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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Factor-multiple Chains

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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What's in the Box?

Stage: 2 Challenge Level: Challenge Level:1

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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Multiplication Square Jigsaw

Stage: 2 Challenge Level: Challenge Level:1

Can you complete this jigsaw of the multiplication square?

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More Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Little Man

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Fair Feast

Stage: 2 Challenge Level: Challenge Level:1

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

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The Deca Tree

Stage: 2 Challenge Level: Challenge Level:1

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.

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A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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Trebling

Stage: 2 Challenge Level: Challenge Level:1

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

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The Brown Family

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Sixty-seven Squared

Stage: 5 Challenge Level: Challenge Level:1

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

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Remainders

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Multiplication Squares

Stage: 2 Challenge Level: Challenge Level:1

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.

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All the Digits

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Tomato and the Bean

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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Mystery Matrix

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Super Shapes

Stage: 2 Short Challenge Level: Challenge Level:1

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

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Twenty Divided Into Six

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Amy's Dominoes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Forgot the Numbers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Make 100

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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Watch the Clock

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Number Rules - OK

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

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Expenses

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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The Puzzling Sweet Shop

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Amazing Splitting Plant

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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Magic Plant

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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Doubling Fives

Stage: 1 Challenge Level: Challenge Level:1

This activity focuses on doubling multiples of five.

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Division Rules

Stage: 2 Challenge Level: Challenge Level:1

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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Multiply Multiples 3

Stage: 2 Challenge Level: Challenge Level:1

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

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Multiply Multiples 2

Stage: 2 Challenge Level: Challenge Level:1

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

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Multiply Multiples 1

Stage: 2 Challenge Level: Challenge Level:1

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

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Learning Times Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

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Current Playing with Number Upper Primary Teacher

Stage: 2 Challenge Level: Challenge Level:1

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

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Exploring Number Patterns You Make

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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Square Subtraction

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Ordering Cards

Stage: 1 and 2 Challenge Level: Challenge Level:1

This problem is designed to help children to learn, and to use, the two and three times tables.