Perimeter and Area
This activity consists of two tasks looking at the relationships between area and perimeter.
Task 1
Make as many rectangles as you can with a perimeter of 16 using the red squares.
What areas can you make?
What is the biggest area?
Can you predict which rectangle with perimeter 12 will have the biggest area? Check using the red squares.
Which rectangle with perimeter 24 will have the biggest area?
Predict which rectangle with perimeter 18 will have the biggest area. Check with the red squares.
Extension
Can you make a generalisation as to which rectangle will produce the biggest area for any given perimeter?
Make as many rectangles as you can with a perimeter of 16 using the red squares.
What areas can you make?
What is the biggest area?
Can you predict which rectangle with perimeter 12 will have the biggest area? Check using the red squares.
Which rectangle with perimeter 24 will have the biggest area?
Predict which rectangle with perimeter 18 will have the biggest area. Check with the red squares.
Extension
Can you make a generalisation as to which rectangle will produce the biggest area for any given perimeter?
Task 2
Make as many rectangles as possible of area 24 using the red squares below. How many are there?
What possible perimeters can you get?
Which rectangle gives the biggest/smallest perimeter?
Can you predict how many rectangles there will be for an area of 20? Find them using the red squares.
How about for an area of 16? Which of these will have the biggest/smallest perimeter?
In general, which rectangle of a given area will have the biggest/smallest perimeter?
Extension
How does this change if we say that the shapes don't have to be rectangles, and that the only constraint is that each red square must be touching another red square full side to full side?
What if we allow them to only touch at corners?
Make as many rectangles as possible of area 24 using the red squares below. How many are there?
What possible perimeters can you get?
Which rectangle gives the biggest/smallest perimeter?
Can you predict how many rectangles there will be for an area of 20? Find them using the red squares.
How about for an area of 16? Which of these will have the biggest/smallest perimeter?
In general, which rectangle of a given area will have the biggest/smallest perimeter?
Extension
How does this change if we say that the shapes don't have to be rectangles, and that the only constraint is that each red square must be touching another red square full side to full side?
What if we allow them to only touch at corners?
Ideas for Teachers
Two great activities for use as a starter. Either give students access to computers to explore themselves, or get them to do the working on paper. The person who gives best description can show on the board. These are both classic investigations, and the underlying maths is vitally important.
Two great activities for use as a starter. Either give students access to computers to explore themselves, or get them to do the working on paper. The person who gives best description can show on the board. These are both classic investigations, and the underlying maths is vitally important.
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