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?
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 planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Is there an efficient way to work out how many factors a large number has?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
56 406 is the product of two consecutive numbers. What are these
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?
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?
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?
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.
Number problems at primary level that may require determination.
Can you find any perfect numbers? Read this article to find out more...
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.
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...
An investigation that gives you the opportunity to make and justify
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Are these statements always true, sometimes true or never true?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
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?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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.
Can you find a way to identify times tables after they have been shifted up?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Follow the clues to find the mystery number.
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?
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?
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Number problems at primary level to work on with others.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?