Find the frequency distribution for ordinary English, and use it to help you crack the code.
Substitution and Transposition all in one! How fiendish can these codes get?
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.
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?"
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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 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?
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 is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you complete this jigsaw of the multiplication square?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Given the products of diagonally opposite cells - can you complete this Sudoku?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
If you have only four weights, where could you place them in order
to balance this equaliser?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
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.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Use the interactivities to complete these Venn diagrams.
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 collection of resources to support work on Factors and Multiples at Secondary level.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Given the products of adjacent cells, can you complete this Sudoku?
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 three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
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?
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.
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you work out what size grid you need to read our secret message?