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### Method in multiplying madness?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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### spaces for exploration

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

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### Keep it simple

Can all unit fractions be written as the sum of two unit fractions?

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### 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?

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### 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?

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### 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?

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### 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?

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### Forwards Add Backwards

What happens when you add a three digit number to its reverse?

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### Frogs

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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### Interactive Spinners

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

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### Crossed Ends

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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### Can they be equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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### Seven Squares

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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### Same Answer

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

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### Fibonacci Surprises

Play around with the Fibonacci sequence and discover some surprising results!

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### 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?

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### 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.

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### Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

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### Coordinate Patterns

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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### Stars

Can you work out what step size to take to ensure you visit all the dots on the circle?

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### Route to infinity

Can you describe this route to infinity? Where will the arrows take you next?

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### Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

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### Power mad!

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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### Consecutive negative numbers

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?