For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
A game that tests your understanding of remainders.
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?"
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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
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.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each 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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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.
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. . . .
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 complete this jigsaw of the multiplication square?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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...
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Given the products of adjacent cells, can you complete this Sudoku?
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!
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Nearly all of us have made table patterns on hundred squares, that
is 10 by 10 grids. This problem looks at the patterns on
differently sized square grids.
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 find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
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 article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Use the interactivities to complete these Venn diagrams.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?