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.
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Can you make square numbers by adding two prime numbers together?
One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
An environment which simulates working with Cuisenaire rods.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
An investigation that gives you the opportunity to make and justify predictions.
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 some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Follow the clues to find the mystery number.
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?
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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?
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.
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?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Can you complete this jigsaw of the multiplication square?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
If you have only four weights, where could you place them in order to balance this equaliser?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
Got It game for an adult and child. How can you play so that you know you will always win?
Can you explain the strategy for winning this game with any target?