## Understanding Area

### Dorothy Wagner

#### Description

Students make the transition from measuring in linear units to measuring in the square units of area. Area formulas for rectangle, parallelogram and triangle will be developed.

#### Objectives

Uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of two- and three- dimensional shapes including rectangular solids, cylinders, cones and pyramids.

#### Materials

-Rulers with inches and centimeters (one per student)
-A rectangle for each student with dimensions in inches (sizes vary- 5x8,4x10,7x6 etc)
-Paper and pencil for each student

#### Preparations

1. Get a ruler for each student.
2. Prepare the rectangles by cutting colored copy paper into various sized rectangles making sure the dimensions are cut to whole inches.

#### Procedures

1. Begin by reviewing, with the students, the three dimensions which are length, width and depth. Ask for verbal examples from the class of different types of linear units and geometric figures that they have studied having two dimensions (length and width).

2. Make sure each student has a rectangle. Have each student use the ruler to mark off one-inch notches around the perimeter of the rectangle and do the same on the board as a sample. Then have the students connect the opposite notches making a grid and do the same on the board sample.

3. When all students are finished with their grids, ask them what one of the little spaces in the grid is called. Establish that the unit of measure is changing from linear units to square units and also that the grid represents area. Explain area as a covering represented by the number of square units inside a polygon. At this point, do some conversions on the board using square units emphasizing the change from linear to square units.

4. On the board, label the length and width of the rectangle and receive responses from the students that the area formula for a rectangle is length times width

5) (See associated file)

6) Use examples to establish the steps that the students need to write while completing each problem.
Step 1: Write the formula.
Step 2: Substitute any given information into the formula.
Step 3: Use previous geometric concepts to find the missing information and complete the area.
Example 1: Find the area of a triangle with base 4 in. and height 6 in.
A = (1/2)(b)(h)
A = (1/2)(4)(6)
A = 12 sq in
Note: Have the students follow these steps every time to establish good work habits that will carry over to the third dimensional problems.

Example 2: Find the dimensions of a rectangle with a length five times its width and an area of 80 sq. in.

#### Assessments

To grade the students work assign point values to the required steps.
For example:

Step 1:
3 points if student completely and neatly writes the formula
2 points if formula is not complete
0 point if no formula appears

Step 2:
3 points if student substitutes all given information into step 1.
2 points if partial substitution of given information into step 1.
0 points if random arithmetic steps appear.

Step 3:
3 points if equation in step 2 is completed by solving or using other Geometric concepts to obtain the area correctly.
2 points if equation in step 2 is completed mentally
0 points if no solution is reached

This lesson does not address the entire benchmark.

#### Attached Files

This is step five of procedures containing a figure.     File Extension: pdf