This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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 place the numbers from 1 to 10 in the grid?
This package will help introduce children to, and encourage a deep
exploration of, multiples.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
You can make a calculator count for you by any number you choose.
You can count by ones to reach 24. You can count by twos to reach
24. What else can you count by to reach 24?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Help share out the biscuits the children have made.
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?
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?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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?
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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
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?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these
Got It game for an adult and child. How can you play so that you know you will always win?
This activity focuses on doubling multiples of five.
Are these statements always true, sometimes true or never true?
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 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?
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?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
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?
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?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
An investigation that gives you the opportunity to make and justify
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Look at the squares in this problem. What does the next square look
like? I draw a square with 81 little squares inside it. How long
and how wide is my square?
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.