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?
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.
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
56 406 is the product of two consecutive numbers. What are these
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Can you find any perfect numbers? Read this article to find out more...
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
Can you work out what a ziffle is on the planet Zargon?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
What is the smallest number with exactly 14 divisors?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
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.
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Number problems at primary level that may require determination.
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Can you find a way to identify times tables after they have been shifted up?
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?
An investigation that gives you the opportunity to make and justify
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you work out some different ways to balance this equation?
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?
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?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Follow the clues to find the mystery number.