Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many different sets of numbers with at least four members can you find in the numbers in this box?
56 406 is the product of two consecutive numbers. What are these two numbers?
"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 ...?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
How many trains can you make which are the same length as Matt's, using rods that are identical?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Follow the clues to find the mystery number.
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
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?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Can you place the numbers from 1 to 10 in the grid?
Are these domino games fair? Can you explain why or why not?
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?
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?
Can you complete this jigsaw of the multiplication square?
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?
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Number problems at primary level that may require determination.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
An investigation that gives you the opportunity to make and justify predictions.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This activity focuses on doubling multiples of five.
Got It game for an adult and child. How can you play so that you know you will always win?
Are these statements always true, sometimes true or never true?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
If you have only four weights, where could you place them in order to balance this equaliser?
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?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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?
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?
Can you make square numbers by adding two prime numbers together?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.