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?
There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
An investigation that gives you the opportunity to make and justify predictions.
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
How many different sets of numbers with at least four members can you find in the numbers in this box?
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
Got It game for an adult and child. How can you play so that you know you will always win?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
Number problems at primary level that may require determination.
An environment which simulates working with Cuisenaire rods.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you find any perfect numbers? Read this article to find out more...
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Are these statements always true, sometimes true or never true?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
Can you find a way to identify times tables after they have been shifted up?
Number problems at primary level to work on with others.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you make square numbers by adding two prime numbers together?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
56 406 is the product of two consecutive numbers. What are these two numbers?