Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Use the interactivities to complete these Venn diagrams.
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
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!
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
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?
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.
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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 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?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
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?
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 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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 game that tests your understanding of remainders.
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?
56 406 is the product of two consecutive numbers. What are these
Follow the clues to find the mystery 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.
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?
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?
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?
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
An environment which simulates working with Cuisenaire rods.
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?
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...