Perimeter and area
Perimeter is the distance around a two-dimensional shape.
The perimeter of a circle is called the circumference:
Circumference = 2π × radius
The perimeter of a circle is called the circumference:
Circumference = 2π × radius
Math Live (learnalberta.ca)
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Sample Activities for Teaching Conservation of Area
- Quilts
Mrs Carter is making a quilt with three patches of blue cloth on a white background for Catholic Week. She needs help deciding where to put the patches. If Mrs Carter wants the patches to cover the same amount of space on the white background, should she scatter them about or put them together in a group? Explain your answer.
b. Provide the students with three pieces of blue paper to represent the patches of blue cloth. Ask them to move the papers around on their desk, which can be the white background for the quilt, and decide which arrangement would be best for the quilt. If necessary, provide scaffolding by moving three pieces of paper on the overhead projector into different positions. Example:
c. Through discussion, have the students verbalize that grandma can put her three patches of blue cloth anywhere on the white background and they will always cover the same amount of surface.
- Changing Shapes
b. Have the students cut one of their squares along the diagonal to make two triangles. Instruct them to rearrange the two triangles to make as many different shapes as possible with two sides aligned.
Possible shapes:
c. Encourage the students to make other designs by cutting a square in different ways and rearranging the pieces. Reinforce that the pieces of one square must be rearranged to make one design—the pieces are the same colour. The students may glue their designs on newspaper and place them into groups on the floor, justifying the categories.
Ask the students to describe the differences and similarities among the designs. Guide the discussion to generalize that all the designs cover the same amount of surface or have the same area because each design was cut from a congruent square—same size and shape.
d. Focus the students' attention on the group of designs that were made by rearranging two halves of a square. Ask the students what fraction is shown by one part of each design. Reinforce that when a whole is divided into halves, each half has the same size (area) but not necessarily the same shape. Ask the students the following question:
If you take one-half of one square and made a design with one-half of a different square, will the design still cover the same surface (or have the same area) as the other designs? Explain your answer.