Grade 7 Math Activities

People often think of numbers and geometry as belonging to branches of mathematics that are hardly related. In fact, exploring relationships between numbers and geometry can lead to fascinating insights in both areas. In this activity, your child will gain a deep understanding of an exciting topic where numbers and geometry intersect: perfect squares.

	Square grid paper (you can make your own using a centimeter or inch ruler to fill paper with squares) or another square material such as square tiles

	Toothpicks

	Pencil

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:

	Do you notice any pattern with the rectangles that have the greatest area?

	Do you think this shape will always have the greatest area? Why?

	Try it now with a perimeter of 24 and see.

	Does it work with 24, too?

	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:

	Why do you think these numbers are called “squares”?

	What happens when you build perfect squares in order of size? Do you see any patterns in the numbers as they get larger?

	How can you build the next perfect square from the previous one? (more grid paper or toothpicks can be used here)

	Can you find the next five perfect squares (numbers) without building the shapes?

Encourage your child to continue exploring patterns in perfect squares and to also look at other number-shape relationships. Try staircases made of squares next. Exploring perfect squares (and other “number shapes”) will help your child make connections between numbers and geometry, and to commit these important numbers to memory.

 Grade 7 Math Activities