Using A Grid To Calculate The Area Of An Irregular Figure

Using A Grid To Calculate The Area Of An Irregular Figure

Lake Chad

Opening

Lake Chad

  • Use the map to locate where Lake Chad is in Africa.

  • This picture of Lake Chad in Africa was taken by the Apollo 7 astronauts from space in 1968. The area of Lake Chad has decreased significantly since this photograph was taken.
    • Discuss why the changes in the area of Lake Chad might be interesting to scientists, and how they might determine the surface area of the lake.

An Irregular Figure

Opening

An Irregular Figure

This map shows the shape of Lake Chad when it is full. The shape of Lake Chad would be called an irregular figure.

  • What strategy can you use to find the area of the surface of the lake?

Math Mission

Opening

Estimate the area of an irregular figure using a grid.

Estimate the Surface Area of Lake Chad

Work Time

Estimate the Surface Area of Lake Chad

One method geographers use to find the area of an irregularly shaped lake is to use a grid.

The scale of the grid shown on this image of Lake Chad is each small square represents a 10 mile by 10 mile area.

  • Why do you think the grid is slanted?
  • Make an estimate of the area of the lake using the grid.

Hint:

  • What is the area of one square?
  • If a square completely overlaps the lake, what do you know?
  • If a square only partially overlaps the lake, what can you do?

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain how you found the area of Lake Chad.
  • Support your explanation mathematically.

Challenge Problem

Suppose the grid were a different size—either smaller or larger.

  • What would be the advantages and disadvantages of using a smaller versus a larger grid size?

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about other classmates’ methods for finding the area of Lake Chad.
  • How close is your estimate to that of the rest of the class?
  • If your estimate is larger or smaller, can you explain why? What did you do differently?

Hint:

As your classmates present, ask questions such as:

  • How did you calculate the area?
  • What strategy did you use to calculate the area in a square that did not completely cover the lake?
  • Why would you use this method to determine the area, as opposed to dividing the figure into composite figures as in the last lesson?
  • Why do you think the problem used the term surface area rather than justarea ?

Compare Methods of Finding Area

Formative Assessment

Summary of the Math: Compare Methods of Finding Area

  • Write a summary that describes and compares the method for finding area using a grid versus the method for finding area by decomposing a figure into smaller figures.
  • Discuss when you would use each method and the advantages and disadvantages of each method.

Hint:

Check your summary.

  • Do you explain how to use the grid method to find area?
  • Do you explain how to use the decomposition method to find area?
  • Do you discuss when to use each method?
  • Do you discuss the advantages and disadvantages of each method?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Something new I learned today about finding areas is …