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.
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?
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?
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?
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?
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 find any perfect numbers? Read this article to find out more...
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
A game that tests your understanding of remainders.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Follow the clues to find the mystery number.
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.
This activity focuses on doubling multiples of five.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
Have a go at balancing this equation. Can you find different ways of doing it?
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.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Got It game for an adult and child. How can you play so that you know you will always win?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. 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?
If there is a ring of six chairs and thirty children must either
sit on a chair or stand behind one, how many children will be
behind each chair?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Can you place the numbers from 1 to 10 in the grid?
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.
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Help share out the biscuits the children have made.
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 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?
Are these domino games fair? Can you explain why or why not?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you work out some different ways to balance this equation?
Can you complete this jigsaw of the multiplication square?
An investigation that gives you the opportunity to make and justify
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.