Lesson Plan Guide

Georgia Learning Connections

By Page Bird

Title:

Investigating the properties of a circle

Annotation:

In this lesson students will first use wax paper to look at different properties of circles such as chords, tangent lines, inscribed angles, and inscribed angles in a semi-circle, as well as finding the center of the circle. After investigating with the wax paper, students will then use GSP to investigate cyclic quadrilaterals as an extension of the initial investigation.

Primary Learning Outcomes:

Students will find the center of a circle, draw tangents to a circle, and investigate angles inscribed in a semicircle.

Students will find that a circle inscribed in a semicircle is a right angle.

The last part of the lesson will require students to investigate the relationship between the angles in a cyclic quadrilateral.

Students will find that opposite angles are supplementary angles both with the wax paper and with GSP.

Assessed QCC:

M 6.1 Solves problems, reasons, and estimates throughout mathematics

M 6.2 Describes orally and in writing, using the appropriate mathematical vocabulary, mathematical concepts and procedures, such as the reasoning involved in solving problems or computing

M 6.3 Uses scientific calculator and computer skills to solve problems, to discover patterns and sequences, to investigate situations and to draw conclusions

M 6.12 Uses characteristics and properties of lines and line segments to determine relationships between lines.

M 6.13 Identifies the component parts of an angle, its vertex, and sides; and classifies angles as acute, right, obtuse, or straight

M 6.14 Identifies lines of symmetry

M 6.17 Identifies effects of basic transformations on geometric shapes.

M 6.20 Identifies terms associated with a circle.

M 6.22 Measures angles using a protractor

Total Duration:

60 —130 minutes

Materials and equipment:

1. 8 pieces of square wax paper per student with circle drawn on paper (try not to use a compass)

2. protractor

3. compass

Technology Connection:

GSP

Procedures:

Step One:

During this step, students will use wax paper to find the center of a circle and tangents lines to a circle.

Estimated Time:

15-25 minutes

Step Two:

During this step students will look at inscribed angles in semicircles. Students will compare will angles inscribed in circles and investigate this with the wax paper.

Estimated Time:

10-20 minutes

Step Three:

Students will use wax paper to investigate cyclic quadrilaterals. Lead students to find that opposite angles are supplementary.

Estimated Time:

10-25 minutes

Step Four:

Use GSP to construct a cyclic quadrilateral. This will require using rotations, translations, and possibly reflections. Find out what other quadrilaterals have opposite angles supplementary.

Estimated Time:

25-60 minutes

Assessment:

Students will be assessed based on GSP write ups and investigation reports made during the first three steps. Also, student participation will be considered.