Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Use the interactivities to complete these Venn diagrams.
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!
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you complete this jigsaw of the multiplication square?
Each light in this interactivity turns on according to a rule. What
happens when you enter different numbers? Can you find the smallest
number that lights up all four lights?
A game that tests your understanding of remainders.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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?
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.
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?
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. . . .
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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...
Given the products of adjacent cells, can you complete this Sudoku?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?"
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?
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?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Given the products of diagonally opposite cells - can you complete
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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.
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.
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
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?
Can you find a way to identify times tables after they have been shifted up?
What is the smallest number with exactly 14 divisors?
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?
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?
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?
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.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?