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?
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.
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. . . .
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 work out some different ways to balance this equation?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you replace the letters with numbers? Is there only one
solution in each case?
Follow the clues to find the mystery number.
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?"
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?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What could the half time scores have been in these Olympic hockey
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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...
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Can you substitute numbers for the letters in these sums?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Given the products of adjacent cells, can you complete this Sudoku?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
In how many ways can you stack these rods, following the rules?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?