## Cut It Out

#### Description

Using a graphic model, students are asked to derive an original formula for calculating the area of an irregular figure. This lesson requires that students use critical thinking, visual perception, and mathematical computation.

#### Objectives

The student knows the relationship between the area or perimeter of an original figure and that of a newly created figure.

#### Materials

-Paper
-Pencil
-Calculator
-Cut It Out student worksheet (See Associated File)
-Graphic Model (See Associated File)
-Safety scissors

#### Preparations

2. Make a copy of the Graphic Model for each student. (See Associated File)
3. Make a copy of the Cut It Out worksheet for each student. (See Associated File)
4. Draw examples of known shapes (various triangles, rectangles, trapezoids) on the board.
5. Draw an example of an irregular figure on the board. The irregular figure should be composed of several smaller known shapes. (See Sample Sheet in Associated File)
6. Make sure each student has access to a pair of safety scissors and a calculator.

#### Procedures

1. Review the concept of area with the students. Distribute the Grades 6-8 Mathematics Reference Sheet (See Weblinks) so students can see the various area formulas provided.

2. Model how to calculate the area of various triangles, rectangles, and trapezoids.

3. Draw students’ attention to the irregular figure drawn on the board. Explain that a real-life example of an irregular figure would be something like a floor plan. A floor plan may consist of many different shapes formed together to create one shape, for instance, a house.

4. Discuss the importance of being able to calculate the area of items that may not be regularly shaped. Perhaps this floor plan is the plan for the building of your new house. You should want to know how much living space you will have before your house is built. This kind of information would help you decide whether to put a king or queen size bed in your bedroom, what size stove or refrigerator to put in your kitchen, etc. In order to determine this information, it is important to be able to develop a procedure or formula to do so.

5. Invite the students to answer the question of how they would go about finding the area of an irregular figure. Select two or three students to provide answers. Give feedback.

6. Demonstrate, using the example on the board, how to separate the irregular figure into several smaller shapes. A good demonstration would be to highlight in a different color or circle the smaller shapes within the irregular one.

7. Demonstrate finding the area of each shape and adding them together to find the area of the irregular figure.

8. Entertain any questions at this point and prepare students for the activity.

9. Pass out material to students.

10. Give the following instructions to students.

a. You should have a graphic model (drawing or picture), pair of scissors, pencil, reference sheet, calculator, and worksheet on your desk. (See Associated File)

b. Look at your drawing and decide what regular shapes are present and can be created from the irregular figure.

c. On your worksheet, in the space provided, explain how you would divide the irregular figure to create regular shapes. Use the correct name of each shape (triangle, rectangle, trapezoid, etc.) in your writing. Several different explanations are possible.

d. Once you have completed your writing, take the scissors and your drawing and carefully cut out each shape you named in your explanation.

e. Using your reference sheet, locate the area formula for each shape and write the formula in the center of your shape.

f. Using your shapes and their area formulas, create a formula that could be used to calculate the area of the irregular figure. Write your new formula on your worksheet in the space provided.

h. Make sure your name is on your worksheet and turn it in at the end of class.

11. While students are engaged in the activity, teacher should circle the room and provide assistance as needed.

#### Assessments

1. EXPLANATION: The student uses a drawing of an irregular figure to explain in words how to subdivide the figure into smaller shapes. Each shape (triangle, rectangle, trapezoid, etc.) should be named in the writing assignment.

2. DEMONSTRATION: The student takes the drawing and using the above explanation and a pair of safety scissors, demonstrates the subdivision of the irregular figure into smaller shapes by cutting each shape out.

3. IDENTIFICATION: Using the reference sheet, the student identifies the area formulas for each shape.

4. CALCULATION: The student demonstrates how to use the formulas of known shapes to calculate the area of the irregular figure by writing an original formula.

CRITERIA:
1. Provide a formula to calculate the area of the irregular shape. The final formula should include the use of the area formulas of the smaller shapes created in the evidence portion of the assessment.

2. Students should demonstrate that they understand that they must add the area formulas of the known shapes in order to create their final formula. Submission of a formula which when used, provides the correct area of the irregular figure is proof of understanding.