![Subtraction Surprise](/sites/default/files/styles/medium/public/thumbnails/content-id-11014-icon.png?itok=VAg2GirR)
![Method in multiplying madness?](/sites/default/files/styles/medium/public/thumbnails/content-id-5612-icon.png?itok=ZHpntMLH)
problem
Method in multiplying madness?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
![spaces for exploration](/sites/default/files/styles/medium/public/thumbnails/content-id-5531-icon.png?itok=qpsPwmmx)
article
spaces for exploration
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
![Keep it simple](/sites/default/files/styles/medium/public/thumbnails/keep-it-simple.gif?itok=xXs1GgR6)
![How much can we spend?](/sites/default/files/styles/medium/public/thumbnails/content-id-6650-icon.png?itok=VYEcWe-l)
problem
How much can we spend?
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
![Charlie's delightful machine](/sites/default/files/styles/medium/public/thumbnails/content-id-7024-icon.png?itok=TnFInR1F)
problem
Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
![Your number was...](/sites/default/files/styles/medium/public/thumbnails/content-id-7216-icon.png?itok=gedgqfRa)
problem
Your number was...
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
![What numbers can we make?](/sites/default/files/styles/medium/public/thumbnails/content-id-7405-icon.png?itok=AGBx2S5H)
problem
What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
![Forwards Add Backwards](/sites/default/files/styles/medium/public/thumbnails/content-id-11111-icon.png?itok=qNzPZE6G)
![Multiple Surprises](/sites/default/files/styles/medium/public/thumbnails/content-id-11173-icon.jpg?itok=djf7nIS-)
![Frogs](/sites/default/files/styles/medium/public/thumbnails/content-00-12-game1-icon.gif?itok=HbJX89ir)
problem
Frogs
How many moves does it take to swap over some red and blue frogs? Do you have a method?
![Interactive Spinners](/sites/default/files/styles/medium/public/thumbnails/content-id-6033-icon.png?itok=h8ACE9q-)
problem
Interactive Spinners
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
![Crossed Ends](/sites/default/files/styles/medium/public/thumbnails/content-id-6261-icon.png?itok=w601cT6o)
problem
Crossed Ends
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
![Can they be equal?](/sites/default/files/styles/medium/public/thumbnails/content-id-6398-icon.png?itok=MaCLt6SR)
problem
Can they be equal?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
![Cuboid challenge](/sites/default/files/styles/medium/public/thumbnails/content-id-6399-icon.png?itok=5nRc6gv3)
![Power mad!](/sites/default/files/styles/medium/public/thumbnails/content-id-6401-icon.png?itok=Ukk2Xjef)
problem
Power mad!
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
![Seven Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-8111-icon.png?itok=_4UM0hZd)
problem
Seven Squares
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
![Same Answer](/sites/default/files/styles/medium/public/thumbnails/content-id-11124-icon.jpg?itok=51IjjMJv)
problem
Same Answer
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
![Fibonacci Surprises](/sites/default/files/styles/medium/public/thumbnails/content-id-11164-icon.png?itok=MkOhkYT5)
problem
Fibonacci Surprises
Play around with the Fibonacci sequence and discover some surprising results!
![Where can we visit?](/sites/default/files/styles/medium/public/thumbnails/content-00-12-six3-icon.jpg?itok=fnQnUDU6)
problem
Where can we visit?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
![Egyptian Fractions](/sites/default/files/styles/medium/public/thumbnails/content-03-05-penta5-icon.gif?itok=zV3qUZmO)
problem
Egyptian Fractions
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
![Farey Sequences](/sites/default/files/styles/medium/public/thumbnails/content-02-04-six3-icon.jpg?itok=wOYGWvuN)
![Coordinate Patterns](/sites/default/files/styles/medium/public/thumbnails/content-id-2292-icon.png?itok=tWsgfytK)
problem
Coordinate Patterns
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
![Stars](/sites/default/files/styles/medium/public/thumbnails/content-id-2669-icon.png?itok=Ez9pJPne)
problem
Stars
Can you work out what step size to take to ensure you visit all the dots on the circle?
![Route to infinity](/sites/default/files/styles/medium/public/thumbnails/content-id-5469-icon.png?itok=277vYUz4)
problem
Route to infinity
Can you describe this route to infinity? Where will the arrows take you next?
![Consecutive negative numbers](/sites/default/files/styles/medium/public/thumbnails/content-id-5868-icon.jpg?itok=Ym7OX3hn)
problem
Consecutive negative numbers
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?