How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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.
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?
Number problems at primary level that may require determination.
An investigation that gives you the opportunity to make and justify
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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 find a way to identify times tables after they have been shifted up?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
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?
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?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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 find any perfect numbers? Read this article to find out more...
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...
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you make square numbers by adding two prime numbers together?
What is the smallest number with exactly 14 divisors?
Number problems at primary level to work on with others.
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 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.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
"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 ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
An environment which simulates working with Cuisenaire rods.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture