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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
A number game requiring a strategy.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Number problems at primary level that require careful consideration.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Number problems at primary level that may require resilience.
Find the next number in this pattern: 3, 7, 19, 55 ...
Use the information to work out how many gifts there are in each pile.
If the answer's 2010, what could the question be?
It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
An old game but lots of arithmetic!
What is happening at each box in these machines?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
How would you find out how many football cards Catrina has collected?
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,. . . .
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
This number has 903 digits. What is the sum of all 903 digits?
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?
Can you find different ways of creating paths using these paving slabs?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
How would you count the number of fingers in these pictures?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
How will you work out which numbers have been used to create this multiplication square?