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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
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?
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 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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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 and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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.
"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
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?
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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Follow the clues to find the mystery number.
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these
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?
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you place the numbers from 1 to 10 in the grid?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Can you find any perfect numbers? Read this article to find out more...
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
This activity focuses on doubling multiples of five.
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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
An investigation that gives you the opportunity to make and justify
A game that tests your understanding of remainders.
Help share out the biscuits the children have made.