Are these statements always true, sometimes true or never true?
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?
Number problems at primary level that may require determination.
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?
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?
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?
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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 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 work out what a ziffle is on the planet Zargon?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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.
An investigation that gives you the opportunity to make and justify
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level to work on with others.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Follow the clues to find the mystery number.
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!
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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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.
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.
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.
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you find any perfect numbers? Read this article to find out more...
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?
Explore the relationship between simple linear functions and their
Can you work out some different ways to balance this equation?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
If you have only four weights, where could you place them in order
to balance this equaliser?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
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?
Can you make square numbers by adding two prime numbers together?