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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
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?
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.
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?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
56 406 is the product of two consecutive numbers. What are these
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
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.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
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.
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?
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?
Are these statements always true, sometimes true or never true?
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?"
Can you complete this jigsaw of the multiplication 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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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 find any perfect numbers? Read this article to find out more...
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
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 activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?