Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
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?
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Can you find any perfect numbers? Read this article to find out more...
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Help share out the biscuits the children have made.
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
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?
A game that tests your understanding of remainders.
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
Can you find the chosen number from the grid using the clues?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
"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 ...?
Follow the clues to find the mystery number.
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you work out what a ziffle is on the planet Zargon?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
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?
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?
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
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?
If you have only four weights, where could you place them in order to balance this equaliser?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
An investigation that gives you the opportunity to make and justify predictions.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Are these domino games fair? Can you explain why or why not?
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.
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Can you place the numbers from 1 to 10 in the grid?
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?