# Circumference and Area of Circles

## Learning Topics:

Geometry of a Circle, line segment, chord, plane, radius, diameter, pi, Circumference of Circles, and Area of Circles.

Learning Objectives for all Circumference and Area of Circles lessons in Unit 2.

#### Geometry and the Circle

The student will be able to:

• Define point, center, radius, diameter, chord, line segment, plane.
• Identify a point, diameter, radius and chord from a diagram.
• Explain the relationship between diameter and chord.
• Recognize that every diameter is a chord, but not every chord is a diameter.
• Give examples of parts of a circle from the real world.
• Describe how a circle divides the plane into three parts.
• Apply definitions and concepts to complete five interactive exercises.

#### Circumference of Circles

The student will be able to:

• Define circle, circumference.
• Recognize that Pi is constant for any circle.
• Explain the relationship between diameter and radius.
• Restate the formula and procedure for finding the circumference of a circle.
• Recognize that a circle has many different radii and diameters passing through its center.
• Compute the circumference of a circle, given its diameter.
• Compute the circumference of a circle, given its radius.
• Compute the diameter of a circle, given its circumference.
• Give examples of circumference from the real world.
• Evaluate five interactive exercises with real-world problems.
• Analyze each problem to identify the given information.
• Formulate a strategy for solving each problem.
• Apply circumference concepts and formulas to solve real-world problems.

#### Area of Circles

The student will be able to:

• Define area of a circle.
• Recognize the difference between circumference and area of a circle.
• Restate the formula and procedure for finding the area of a circle.
• Compute the area of a circle, given its radius.
• Compute the area of a circle, given its diameter.
• Compute the radius and diameter of a circle, given its area.
• Give examples of area of a circle from the real world.
• Evaluate five interactive exercises with real-world problems.
• Analyze each problem to identify the given information.
• Formulate a strategy for solving each problem.
• Apply circle area concepts and formulas to solve real-world problems.

#### Practice Exercises

The student will be able to:

• Examine ten interactive exercises for all topics in this unit.
• Determine which concepts and formulas are needed to complete each practice exercise.
• Compute answers by applying appropriate formulas and procedures.
• Self-assess knowledge and skills acquired from this unit.

#### Challenge Exercises

The student will be able to:

• Evaluate ten interactive exercises with word problems for all topics in this unit.
• Analyze each word problem to identify the given information.
• Formulate a strategy for solving each problem.
• Apply strategies to solve routine and non-routine problems.
• Synthesize all information presented in this unit.
• Connect circumference and area of circles to the real world.
• Develop problem-solving skills.

#### Solutions

The student will be able to:

• Examine the solution for each exercise presented in this unit.
• Identify which solutions need to be reviewed.
• Compare solutions to completed exercises.
• Identify and evaluate incorrect answers.
• Amend and label original answers.
• Identify areas of strength and weakness.
• Decide which concepts, formulas and procedures need to be reviewed from this unit.