Measuring with Mathematics

Kenneth BlackmanSanta Rosa District Schools

Description

Students discover how the change in the dimensions of a shape will cause a change in the overall area of the shape, but the perimeter will stay the same.

Objectives

The student knows how a change in a figure's dimensions affects its perimeter, area, circumference, surface area, or volume.

The student knows how changes in the volume, surface area, area, or perimeter of a figure affect the dimensions of the figure.

Materials

- Stake Flags (Minimum of 8)
- Land Tape Measures (6 Tapes)
- String
- Paper
- Pencil
- Calculator (One calculator for each group)

Preparations

1. Copy Area Review Worksheet and Data Chart (one copy per student).
2. Assemble needed material stated earlier. (Flags, Strings, Tape Measures)
3. Stake piece of property with flags and string. (Rectangle shape is recommended.)
4. Copy Group Activity Evaluation Form.

Procedures

Day 1:
1. Discuss with the students the mathematical concepts embedded within real estate careers. Discuss the concept of land measurement and how it is related to the total price of a piece of property. Work examples of the cost of a piece of property if the area is known. Discuss how the price of land can change if the shape of the land is changed.

2. Review with the students the area formulas related to a square, a rectangle, and a triangle.
Area of square = Side* Side
Area of rectangle = Length * Width
Area of triangle = Base * Height / 2

3. Model problems related to the area formulas listed above. Work problems on the board related to each formula. Use questioning techniques with the students to check for understanding.

4. Hand out Area Review Worksheet and assign to class for classwork and homework. Circulate throughout the classroom and observe students checking for comprehension.

5. Review the concepts discussed during the class period. Question the students and work example problems looking for student comprehension.

Day 2:
1. Review with the students the area formulas studied the day before. Model to the students problems related to the area of squares, rectangles, and triangles.

2. Review with the students the problems from the homework assigned the day before.

3. Arrange the class in groups of four. (The students or the teacher can select the groups.) Have the students select a team leader, recorder, and two people for measuring the dimensions of the shape.

4. Lead students outside to measure the land that has previously been staked.

5. Distribute tape measures to the groups. (Select one member from each group who is responsible for returning the tape measure.)

6. Instruct the students to make a scale drawing of the piece of property including the dimensions. Circulate among the students to check students' drawings of the piece of property.

7. Instruct the students to measure the dimensions of the property staked off, to record the data on the Data Chart, and to find the area of the shape. Model to the students where the measurements are recorded on the Data Chart.

8. When students are finished measuring and recording, reposition the staked flags in a different shape that has the same perimeter. Have the students check their data while you are changing the position of the flags.

9. Instruct the students to measure the new shape and calculate the area for the new shape. Circulate among the students using questioning techniques to check for understanding. Check the students’ Data Charts to insure the correct information is being measured.

10. Lead the students back to class.

11. Instruct group leaders to share the groups' answers with the entire class. Lead the students in discussing incorrect answers and why some answers may be different than others. Discuss the concept of precision in measuring a shape. Demonstrate to the students why changing the dimensions of a shape will change the area.

12. Explore with the class why changing the dimensions of a figure changes the area. Give the students several examples demonstrating this concept.
“4 in by 6 in rectangle = 24 in. squared and a 2 in by 8 in rectangle = 16 in squared.”

13. Instruct the students to calculate the cost of each piece of property if it is \$45.00 per square foot. Circulate throughout the room using questioning techniques to check for understanding.

14. Instruct the students to evaluate the other members of their group using the Group Activity Evaluation Form. Evaluate each student using the Group Activity Evaluation Form.

Assessments

The Data Chart for each student is collected and assessed for correctness. Calculations are checked and the writing portion will be evaluated for evidence of a correlation between the dimensions of an object and the area. Area Review Worksheets will also be collected and graded. Questioning techniques are used to check for understanding. Group Activity Evaluation Forms are collected and used as documentation of instructing students in developing cooperative learning techniques.

Extensions

This lesson could lead into social studies concepts related to map drawing through the use of the scale drawings. Business concepts related to real estate and the cost of land are also embedded within the lesson. This lesson could be used with a series of lessons related to a range of geometric concepts (area, surface area, recognition of geometric shapes, similar figures, and congruent figures).

Attached Files

A review worksheet, a data collection form, and a group evaluation form.     File Extension: pdf