Finding Area

Overview
Students will compete to find the area of irregular shapes by counting tiles.

 

Standards Addressed
Grade 4, Mathematics — Measurement

03-04 Benchmark
D. Identify appropriate tools and apply counting techniques for measuring side lengths, perimeter and area of squares, rectangles, and simple irregular two-dimensional shapes, volume of rectangular prisms, and time and temperature.

Y2003.CMA.S02.G03-04.BD.L04.I04 / Use Measurement Techniques and Tools

04. Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume.

 

Grade 7, Mathematics — Geometry and Spatial Sense

05-07 Benchmark
J. Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.

Y2003.CMA.S03.G05-07.BJ.L07.I06 / Spatial Relationships

06. Determine and use scale factors for similar figures to solve problems using proportional reasoning.

 

Materials
Computers with Internet connection

 

Procedure
Part 1: O’Neil Woods Metro Park

  1. Tell the students that there is going to be a contest to see who can come the closest to finding the area of Cuyahoga Valley National Park (CVNP). You can announce that there will be a prize for the winning group, such as getting to leave class first or earning points for the next activity.
  2. Break the students into groups of two or three.
  3. Distribute the O’Neil Woods Metro Park — Outline Map student handout. Each square on the map represents 2.14 acres, and students are to find the area of the park. Review that area is the plane surface of an object.
  4. Ask each group to come up with a method to determine the area of the park.
  5. When each group has calculated the area, record the answers publicly and let the groups tell how they figured it out. The correct answer is an area of about 295 acres. Students should end up with about 138 squares when they combine whole and partial squares.

Part 2: Cuyahoga Valley National Park

  1. Now that students have had some practice calculating area for an irregular shape, tell them that they are going to work with a very irregular shape — Cuyahoga Valley National Park.
  2. Distribute the Cuyahoga Valley National Park — Outline Map.
  3. Tell the students that their goal is to find the area of the CVNP. Each square represents 128 square acres.
  4. The correct answer is that there are approximately 258 squares in the CVNP outline. Since each square is worth 128 square acres, the actual area is about 33,000 square acres.
  5. Once again, award a prize to the group that has the closest answer.
  6. Have each group write the following:
    1. What procedure they used to find their estimate.
    2. What their estimate was.
    3. How they got that estimate (show mathematics involved).
    4. What they thought about the accuracy of their attempt.

 

Evaluation
Each part of their writing could equal 25 points.

Category 4
3 2 1
Explanation Is a complete response with a detailed explanation. Is a good, solid response with clear explanation. Is an unclear explanation. Misses key points.
Mechanics Has no math errors. Has no major math errors or serious flaws in reasoning. Has some serious math errors or flaws in reasoning. Has major math errors or serious flaws in reasoning.
Demonstrated Knowledge Shows complete understanding of the questions, mathematical ideas and processes. Shows substantial understanding of the problem, ideas and processes. Shows some understanding of the problem. Shows a complete lack of understanding of the problem.


 

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