Illuminations: Area Contractor

# Area Contractor

 This lesson gives students the opportunity to explore surface area in the same way that a contractor might when providing an estimate to a potential customer. Once the customer accepts the estimate, a more detailed measurement is taken and a quote prepared. In this lesson, students use estimation to determine the surface area of the walls and floor of their classroom. They check the reasonableness of their estimates, and then measure the classroom for accuracy.

### Learning Objectives

 Students will: Estimate area of walls and floor using reference items or points in a room Estimate area of windows, doors, and any obstructions that cannot be moved or that the customer does not want moved Estimate net surface area of walls and floor by subtracting the area of any obstructions from the appropriate wall or floor gross estimate Calculate actual gross surface area of walls and floor using a tape measure, within ±1 inch tolerance (or as determined by you) Determine net surface area of walls and floor through actual measurement of surface area less any obstructions such as chalkboards, cabinets, windows, doors, etc., within a tolerance determined by you

### Materials

 Measuring tape (1 per group; tapes 25 feet or longer provide the best accuracy) Chart paper and markers Area Contractor Activity Sheet

### Questions for Students

 If you were the customer, would you want your contractor to overstate or understate the estimate? Which would be better if you were the contractor? Why? [From both the customer’s and the contractor’s perspective it is better to overestimate than to underestimate. The contractor could lose money on the job if the cost comes out higher than the estimate. The customer may feel misled if the final cost is higher than the estimate. However, contractors need to take care that they do not grossly overestimate the cost because they may scare their potential customer off.] What are some situations in which an estimate is usually sufficient? [Answers will vary but may include distance, value of the contents of a shopping cart, cost of a meal when eating out, etc.] Describe a situation where precision is critical. [Answers will vary. A good example to get students talking is the fabrication of an airplane. Would they want to fly in a plane were the parts were not measured with precision? In any situation where integrity of the construction could mean the difference between life and death or injury, precision is critical.]

### Assessment Options

 Collect the completed activity sheets. Have students present their results to the class. Have groups prepare a written report of their findings that includes a description of the mathematics used to justify their estimates. Consider having students repeat this activity for a room in their home. This could also be a family-night assignment that encourages other family members to participate.

### Extensions

 Groups can compete for accuracy of estimates without being under. As well, as part of the opener for Part 2, let students know that bonus points will be awarded for the most accurate measurement. Note: In order to offer this extension, you will need accurate measurements of the classroom before starting this lesson. Your school’s building engineer may have that information available. Add additional elements to the estimation task, such as the ceiling and any trim. Invite a guest speaker to talk about the process of providing estimates. Consider asking your building engineer to come in and present the estimate request to your students.

### Teacher Reflection

 Did students have sufficient knowledge of estimation to work on this activity independently within their groups? Did students experience difficulties with using the measuring tapes? If so, what could be done to make it easier for them? If you used ability grouping or differentiation, were the results positive or negative? Why? What would you do differently next time? Do you feel that group dynamics were important in this activity? Why? If time was a constraint for this activity, what would you change? Were concepts presented too abstractly? too concretely? How would you change them? What were some of the ways in which students showed that they were actively engaged in the learning process? Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments? Were these adjustments effective? What worked with respect to classroom behavior management? What didn't work? How would you change what didn’t work?

### NCTM Standards and Expectations

 Measurement 6-8Use common benchmarks to select appropriate methods for estimating measurements. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
 This lesson was prepared by Julie Healy as part of the Illuminations Summer Institute.

2 periods

### Lessons

 More and Better Mathematics for All Students
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