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...
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
A game that tests your understanding of remainders.
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?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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!
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?
What is the smallest number with exactly 14 divisors?
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 complete this jigsaw of the multiplication square?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
If you have only four weights, where could you place them in order
to balance this equaliser?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Got It game for an adult and child. How can you play so that you know you will always win?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Can you work out what a ziffle is on the planet Zargon?
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?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Number problems at primary level that may require determination.
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?