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. In this two part lesson, an estimation is done first and then an actual measure to check for accuracy.

Standards & Objectives

Academic standards
CCSS.Math.Content.6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge...
CCSS.Math.Content.6.G.A.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures....
CCSS.Math.Content.7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between...
CCSS.Math.Content.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles,...
CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
GLE 0606.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0606.1.3
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
GLE 0606.4.3
Develop and use formulas to determine the circumference and area of circles, and the area of trapezoids, and develop strategies to find the area of composite shapes.
GLE 0606.4.4
Develop and use formulas for surface area and volume of 3-dimensional figures.
SPI 0606.4.4
Calculate with circumferences and areas of circles.
SPI 0606.4.5
Determine the surface area and volume of prisms, pyramids and cylinders.
SPI 0606.4.6
Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.
TSS.Math.6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and...
TSS.Math.6.G.A.4
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these...
TSS.Math.7.G.B.3
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the...
TSS.Math.7.G.B.5
Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles,...
TSS.Math.8.G.C.7
Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
Learning objectives: 

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.
Essential and guiding questions: 

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? 
  • What are some situations in which an estimate is usually sufficient?  
  • Describe a situation where precision is critical.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

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.

Helpful Hints

Materials:

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

References

Contributors: