Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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 focuses on finding the sum and difference of pairs of two-digit numbers.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Find the sum of all three-digit numbers each of whose digits is
Got It game for an adult and child. How can you play so that you know you will always win?
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
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find out what a "fault-free" rectangle is and try to make some of
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 ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
What happens when you round these three-digit numbers to the nearest 100?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
An investigation that gives you the opportunity to make and justify
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens when you round these numbers to the nearest whole number?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
This activity involves rounding four-digit numbers to the nearest thousand.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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 challenge asks you to imagine a snake coiling on itself.
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.