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?
An investigation that gives you the opportunity to make and justify
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
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.
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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 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 make square numbers by adding two prime numbers together?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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...
56 406 is the product of two consecutive numbers. What are these
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?
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?
Follow the clues to find the mystery number.
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?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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!
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
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.
Can you work out what a ziffle is on the planet Zargon?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
If you have only four weights, where could you place them in order
to balance this equaliser?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
A game that tests your understanding of remainders.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Can you find a way to identify times tables after they have been shifted up?
Can you complete this jigsaw of the multiplication square?
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?
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 see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Have a go at balancing this equation. Can you find different ways of doing it?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two
digit numbers are multiplied to give a four digit number, so that
the expression is correct. How many different solutions can you
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?
Given the products of adjacent cells, can you complete this Sudoku?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.