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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Here are two kinds of spirals for you to explore. What do you notice?
Find out what a "fault-free" rectangle is and try to make some of
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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
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
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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 a route from the outside to the inside of this square, stepping on as many tiles as possible.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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?
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.
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?
This challenge asks you to imagine a snake coiling on itself.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Are these statements always true, sometimes true or never true?
What happens when you round these three-digit numbers to the nearest 100?
This activity involves rounding four-digit numbers to the nearest thousand.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?