Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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 is about finding the difference between numbers which have the same tens digit.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
An investigation that gives you the opportunity to make and justify
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
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 the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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 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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
This problem challenges you to find out how many odd numbers there
are between pairs of numbers. Can you find a pair of numbers that
has four odds between them?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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
Stop the Clock game for an adult and child. How can you make sure you always win this game?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
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
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This activity focuses on rounding to the nearest 10.
This challenge asks you to imagine a snake coiling on itself.
What happens when you round these three-digit numbers to the nearest 100?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
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?
What happens when you round these numbers to the nearest whole number?