Learning Context

Goals / Purpose:

• Increase students' confidence and improve their problem-solving skills.
• Clear up students' misconceptions about area.
• Use students' prior knowledge of geometry to generate new knowledge.

Essential Question:

• How can one determine the amount of space taken up by a shape?

Enduring Understanding:

• Relationships among shapes can be expressed through formulas.
• Objects used for play can also be used to help us learn.
• Prior knowledge of shapes can lead to new discoveries.
• Creating a model can reveal patterns / relationships among shapes.

Guiding Questions:

• What does perimeter represent?
• What are the properties of a square, a rectangle, and a right triangle? What properties do they share?
• What is a "square unit"? How is it different from a linear unit?

Diagnostic/Summative Questions:

• What does area represent? How is it different from perimeter?
• How do you determine the area of a rectangle?
• How do you determine the area of a right triangle that sits inside the rectangle?

Objectives:

• Construct squares of various sizes and compile data to develop a formula for area of a square.
• Review the properties of rectangles and develop a formula for area of a rectangle.
• Compare the properties of right triangles to their corresponding rectangles and develop a formula for area of a triangle.

Grade Level/Ability:

This learning experience is designed for a sixth grade Math class. All students are taught in the regular classroom. Math lessons take place five days a week, for approximately 40 minutes per day. A few students may receive additional tutoring in Math skills approximately one hour per week from the Title I Math teacher.

Overview of What Students Need to Know:

In order for students to successfully complete the objectives of this learning experience, students need to recognize the following:

• Area is a measure of two-dimensional space; as such it should consistently be expressed in square units(to distinguish it from linear measurement).
• If adjacent sides of a rectangle are known, area can easily be determined.
• If the students can visualize a right triangle as a component of a rectangle with the same length and width, the area of the right triangle can also be determined.

The final product of this learning experience requires the students to:

• follow written directions and to execute them correctly and neatly on grid paper.
• use a ruler for drawing straight lines to ensure accuracy.
• explain their reasoning in writing.
• draw upon the classroom experiences to complete the task.

Classroom rules are essential in maintaining order and in allowing children to focus on the task-at-hand. Students should be aware of the classroom rules and practice them consistently. Adherence to these rules creates a positive work environment with few distractions. Students should:

• follow the teacher's directions promptly.
• wait their turn to speak.
• keep their bodies to themselves.
• use school-appropriate language.

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Updated: September 8, 2009
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