Move around slider a.
What happens to the area of the shaded region?
Move around slider b. What do you notice?
Can you write some mathematical statements to describe the relationship between a, b and the area?
What will the area be when a = 5 and b = 4?
How do you know?
How many different ways can you make an area of 24?

Larger Numbers

What happens as you move the sliders around now?
How many ways can you find to make a rectangle with an area of 1000?

Decimals

Imagine we have zoomed into the corner of the diagram and so the area of the large square with the black outline is 1.
Move the sliders a and b.
What happens now?
Can you write some mathematical statements to describe the relationship between a, b and the area?
What will the area be when a = 0.3 and b = 0.6?
Can you find some different ways of making an area of 0.12?

More Decimals

Now try with the following interactive.
What is the same and what is different?
Can you write down some mathematical statements to describe the relationship between a, b and the area of the purple region?