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?
Can you explain how this card trick works?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This activity involves rounding four-digit numbers to the nearest thousand.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Delight your friends with this cunning trick! Can you explain how
What happens when you round these numbers to the nearest whole number?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
This challenge asks you to imagine a snake coiling on itself.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
An investigation that gives you the opportunity to make and justify
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
What happens when you round these three-digit numbers to the nearest 100?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
Find the sum of all three-digit numbers each of whose digits is
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
Find out what a "fault-free" rectangle is and try to make some of
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in