Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
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?
Are these domino games fair? Can you explain why or why not?
56 406 is the product of two consecutive numbers. What are these
Investigate the different shaped bracelets you could make from 18
different spherical beads. How do they compare if you use 24 beads?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
"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
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 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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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 many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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...
Explore the relationship between simple linear functions and their
Twice a week I go swimming and swim the same number of lengths of
the pool each time. As I swim, I count the lengths I've done so
far, and make it into a fraction of the whole number of lengths. . . .
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.
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?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each time?
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?