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Lesson Plans and Worksheets for Geometry

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More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 3, Lesson 1

Student Outcomes

- Students review the area formula for rectangles with rational side lengths and prove the area formula for an arbitrary rectangle.
- Students use a square grid to estimate the area of a curved region using lower approximations, upper approximations, and average approximations.

**What Is Area?**

Classwork

**Exploratory Challenge 1**

a. What is area?

b. What is the area of the rectangle below whose side lengths measure 3 units by 5 units?

c. What is the area of the 3/4 × 5/3 rectangle below?

**Exploratory Challenge 2**

a. What is the area of the rectangle below whose side lengths measure √3 units by √2 units? Use the unit squares on the graph to guide your approximation. Explain how you determined your answer. b. Is your answer precise?

**Discussion**

Use Figures 1, 2, and 3 to find upper and lower approximations of the given rectangle.

**Discussion**

If it takes one can of paint to cover a unit square in the coordinate plane, how many cans of paint are needed to paint the region within the curved figure?

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