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?
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
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?
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.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
56 406 is the product of two consecutive numbers. What are these
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.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Can you complete this jigsaw of the multiplication square?
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!
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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
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.
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 that tests your understanding of remainders.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
If you have only four weights, where could you place them in order
to balance this equaliser?
An investigation that gives you the opportunity to make and justify
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 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?
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?
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?
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...
The clues for this Sudoku are the product of the numbers in adjacent squares.