Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
A game that tests your understanding of remainders.
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
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.
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
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.
Can you find any perfect numbers? Read this article to find out more...
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
A game in which players take it in turns to choose a number. Can you block your opponent?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
An environment which simulates working with Cuisenaire rods.
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each time?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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.
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
"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
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Arrange any number of counters from these 18 on the grid to make a
rectangle. What numbers of counters make rectangles? How many
different rectangles can you make with each number of counters?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
Use the interactivity to sort these numbers into sets. Can you give
each set a name?
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?
Are these domino games fair? Can you explain why or why not?
Can you find just the right bubbles to hold your number?
Can you place the numbers from 1 to 10 in the grid?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?