# Area and Perimeter of Rectangles with Cheezits

Cheez-It Math

Area and Perimeter

Objectives:

• Students will measure area and perimeter and have experience using manipulatives to visualize the concepts.
• Students will explore relationships between area and perimeter and recognize that shapes with the same area can have different perimeters, and vice versa.
• Students will hear and use mathematical language in context  including:   area, perimeter, prime, square, factor.

Supplies:

•   Cheez-Its (2 boxes is good enough for a class of 24-30)
• Worksheets

Lesson

• Give each student (or group) 16 Cheez-Its. Have them assemble a Cheez-It rectangle.
• Find the area and perimeter of that rectangle in “Cheez-it” units (which are about 1 x 1 inch; ‘generic’ brand tend to be smaller).   For area, count the squares (“area, square-y-a”); for perimeter, trace the lines on the edges (“perimeter – the line around the edges”)
• Display different rectangles with 16 Cheez-its.   Review the concept that area means the space taken up in two dimensions or two directions, while perimeter is one dimension, like a straight line.
• Draw rectangles of those sizes on the grid paper;  look for patterns (e.g., the more like a square the rectangle is, the smaller the perimeter will be).  Note that the scale is smaller – the rectangles on the paper will have perimeters in centimeters and area in cm2 .
• Be sure to include 1 x 16.
• Note that the lengths of the sides are “factors” of the area number.
• Encourage students who are counting from one to practice working with larger numbers in their thinking (so if the area was 8 x 2, to trace the line for the perimeter but know that it is going to be 8 w/0 counting each line again).

EAT 2CHEEZ ITS – or set them aside if you’re disinclined to do so.

Repeat the pattern above with 14 Cheez-Its.  Note that you can make  fewer rectangles with 14 Cheez-its.   (Don’t draw all the rectangles… we’ll pick our favorites at the end. )

EAT 2CHEEZ ITS

Repeat the pattern above with 12 Cheez-Its.  Note that you can make lots of different rectangles…

Eat 1 CHEEZIT:

Repeat the pattern – note that you can only make a 1 x 11 rectangle... this is what makes 11 a “prime” number.

Eat 2 CheezIts (you should have 9):

Repeat the pattern – note that  you can only make the lo-o-ong rectangle and… the nice square.

Eat 5 Cheez-Its…

Repeat the pattern – note that  you can only make the long rectangle and… the nice square.

……………..sick of cheezits yet?   Hope not!

EAT 3 CHEEZ ITS

Repeat the process with 1 Cheez-It. (Note: A perimeter of 4 might be a surprise!  Make sure they count the edges.

When the process is done, discuss data in groups. Draw conclusions. What patterns do they see? Have students record conclusions on back of Record Sheet.

Pick your four favorite rectangles and draw them on the grid paper, and note their areas and perimeters.

Possible Discussion Points

1. Discuss what would happen if you compared rectangles with the same perimeter. (The more the shape looks like a square, the larger the area will be. The more the shape looks like a line, the smaller the area.
2. What would happen to the area if you doubled the side of a given square? For example, instead of a 2x2 square, you would have a 4x4 square. (The area actually quadruples when the side is doubled.)

NOTE Adapt!   Do fewer or more “repeat the procedure” as befits the situation.