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?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
56 406 is the product of two consecutive numbers. What are these
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Can you make square numbers by adding two prime numbers together?
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?
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?
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.
An investigation that gives you the opportunity to make and justify
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
"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?
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 is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you work out what a ziffle is on the planet Zargon?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
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!
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
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.