This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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 task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
Here are two kinds of spirals for you to explore. What do you notice?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
An investigation that gives you the opportunity to make and justify
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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?
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.
Find out what a "fault-free" rectangle is and try to make some of
This challenge asks you to imagine a snake coiling on itself.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
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.
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.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
What happens when you round these three-digit numbers to the nearest 100?