Begin by giving your child a material such as square grid paper
or other squares. Ask him to draw or make as many different rectangles
as he can that have a perimeter (total length around the shape) of
16. For example, one rectangle could have two sides of length 2, and
two sides of length 6, which total 16. Remember; it is possible to
have a rectangle with four equal sides — a square!
Then, ask your child to find the area (total number of squares
used) for each rectangle. Ask: Have you found all the rectangles?
Which rectangle has the greatest area?
Next ask your child to find rectangles that have a perimeter of
12. What are their areas? Which rectangle has the greatest area? Ask:
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| Do you notice any pattern with the rectangles that have
the greatest area? |
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| Do you think this shape will always have the greatest area?
Why? |
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| Try it now with a perimeter of 24 and see. |
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| Does it work with 24, too? |
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| What is a quick way for finding the area of these biggest
shapes? |
Your child should have found that the rectangles that have the
greatest area for a given perimeter are always squares. Now have your
child make a series of squares in size order (1 x 1, 2 x 2, 3 x 3,
and so forth). Ask him to write the area of each square beneath the
square itself. These numbers are called “perfect squares.”
In discussing the perfect squares, ask him some of the following questions:
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| Why do you think these numbers are called “squares”? |
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| What happens when you build perfect squares in order of
size? Do you see any patterns in the numbers as they get larger? |
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| How can you build the next perfect square from the previous
one? (more grid paper or toothpicks can be used here) |
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| Can you find the next five perfect squares (numbers) without
building the shapes? |
