For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
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.
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.
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?"
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.
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you complete this jigsaw of the multiplication square?
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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 smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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!
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Got It game for an adult and child. How can you play so that you know you will always win?
An investigation that gives you the opportunity to make and justify
If you have only four weights, where could you place them in order
to balance this equaliser?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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 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.
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
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?
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.
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
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?
An environment which simulates working with Cuisenaire rods.
56 406 is the product of two consecutive numbers. What are these
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
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The clues for this Sudoku are the product of the numbers in adjacent squares.