An investigation that gives you the opportunity to make and justify
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Can you place the numbers from 1 to 10 in the grid?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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 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.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Follow the clues to find the mystery number.
Can you find the chosen number from the grid using the clues?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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 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?
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?
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.
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?
This package will help introduce children to, and encourage a deep
exploration of, multiples.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
If there is a ring of six chairs and thirty children must either
sit on a chair or stand behind one, how many children will be
behind each chair?
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.
Are these domino games fair? Can you explain why or why not?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
This activity focuses on doubling multiples of five.
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
A game that tests your understanding of remainders.
Help share out the biscuits the children have made.
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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 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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you make square numbers by adding two prime numbers together?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?