Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Are these statements always true, sometimes true or never true?
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?
56 406 is the product of two consecutive numbers. What are these
Can you find any perfect numbers? Read this article to find out more...
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?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Can you work out what a ziffle is on the planet Zargon?
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?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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?
Number problems at primary level that may require determination.
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 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?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you work out some different ways to balance this equation?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Is there an efficient way to work out how many factors a large number has?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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...
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. 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 can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Benâ€™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. Can you find
all the numbers in each set from these clues?
Number problems at primary level to work on with others.
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?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?