NCTM Standards:

Analyze characteristics and properties of two- and three-dimensional geometric shapes and development mathematical arguments about geometric relationships.

§ Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

§ Use geometric models to represent and explain numerical and algebraic relationships.

Geometry Subtopic	Maryland Learning Outcome	Activities	Technology Integration	Time Required
Interior Angles of a Polygon	MLO 2.1 Describe two- and three-dimensional geometric figures using number of sides, faces, vertices, diagonals, and sums of angles.	Objective: Given a polygon of n sides, find the sum of the degrees of the interior angles of the polygon. Materials: Worksheet on Interior Angles Procedure: Give the students one piece of information: The sum of the interior angles of a triangle is 180°. Have the students construct a table with three columns – (1) polygons from triangle to octagon, (2) number of adjacent triangles inside, and (3) sum of interior angles. Draw a quadrilateral on the board and count the number of triangles and the sum of the interior angles. Complete the table for the quadrilateral. Complete the table for polygons with 5, 6, 7, and 8 sides, naming each polygon. Have the students describe the pattern that is occurring in the sum of interior angles column. The students should be able to conclude that the sum of the interior angles is 180(n – 2).	Use Geometer’s Sketchpad to prove the sums of interior angles. Construct a triangle, quadrilateral, pentagon, hexagon, and octagon and add the interior angles to show that the sum is always 180(n-2).	1 class period (45-60 minutes)

Assessment:

Informal: Observe students’ calculations as they find the sum of interior angles for each polygon; Assess students’ ability to find the formula by observing their responses.

Formal: Quiz on interior angles of polygons – assesses the students’ ability to apply the formula that they have found. Include a writing piece on HOW the students found the formula for interior angles of a polygon.

NCTM Standards:

Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships.

§ Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Geometry Subtopic	Maryland Learning Outcome	Activities	Technology Integration	Time Required
Sorting Polygons	MLO 2.1 Describe two- and three-dimensional geometric figures using number of sides, faces, vertices, diagonals, and sums of angles.	Objective: Given polygons of different types, students will be able to sort the polygons into categories and name the characteristics by which they have sorted the polygons. Materials: “Geodee’s Sorting Scheme” worksheet, various cutouts of polygons from construction paper Procedure: Give each student one shape from the set of cutouts. Divide them into groups of four to five and have them sort their shapes into two groups. The students should be able to describe their rationale for sorting to each other and to the rest of the class. Repeat this activity with the students, having them mix up the shapes, and eventually having the whole group work together. Have the students return to their seats and sketch a Venn diagram of one of their sorting strategies. Hand out “Geodee’s Sorting Scheme” and have the students discuss their answers to question 1 with each other and write their answers on the paper. The students should complete the activity, discussing Geodee’s rational for putting the final rhombus in either side of the table. Lesson Extensions: See Lesson Plan for “Geodee’s Sorting Scheme”	Demonstrate “Shape Sorter” applet on CD ROM from NCTM Navigating Through Geometry	1 class period (45-60 minutes)

Assessment:

Informal: Observe students as they sort the polygons and observe their reasoning for sorting the shapes. Ask questions as the students sort the shapes. Students can assess each other based on their rationales for sorting the shapes.

Formal: Quiz using Venn Diagram, having students give rationale for shapes sorted within the Venn Diagram.

NCTM Standards:

Use visualization, spatial reasoning, and geometric modeling to solve problems.

§ Draw geometric objects with specified properties, such as side lengths or angle measures.

§ Use visual tools such as networks to represent and solve problems.

Geometry Subtopic	Maryland Learning Outcome	Activities	Technology Integration	Time Required
Constructions	MLO 2.4 Use a compass and straightedge to construct angles, rectangles, circles, and other geometric figures.	Objective: Given only a compass and a straightedge, students will be able to construct a perpendicular bisector to a straight line and will be able to construct a rectangle. Materials: compass and straightedge for each student, activity sheet for each student Procedure: Discuss the vocabulary terms perpendicular and bisector with the students. Use a protractor to create a 90° angle, then discuss with the students how a person might go about constructing an angle without using a protractor. Hand an activity sheet to each student. Hand out the Safe-T compasses and have the students practice constructing circles of various sizes on the backs of their papers. Demonstrate how to construct a perpendicular bisector, and then have the students construct a few of their own. Lead the students in a discussion of how one might use this knowledge of perpendicular lines to construct a rectangle. Have the students construct a rectangle on their papers.	After the students construct their rectangles on their papers using compasses and straightedges, the teacher can demonstrate how to use Geometer’s Sketchpad to do constructions using straight lines and circles.	1 class period (45-60 minutes)

Assessment:

Informal: Observe students’ ability to control the compass and draw basic circles and angles.

Formal: Have students turn in their constructions and give a grade for them. As part of a quiz at a later time, have the students use the Safe-T Compass to construct perpendicular lines or angle bisectors.

NCTM Standards:

(Measurement) Apply appropriate techniques, tools and formulas to determine measurements.

§ Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more complex shapes.

Geometry Subtopic	Maryland Learning Outcome	Activities	Technology Integration	Time Required
Circles	MLO 2.8 Estimate and determine the circumference and area of circles.	Objective: Given a number of circles of different sizes, students will find the relationship between circumference and diameter and recognize that relationship as the value pi. Materials: five round objects of various sizes, string, meter sticks, activity sheet Procedure: SEE ATTACHED LESSON PLAN FOR THIS ACTIVITY	Students can use TI-83 Graphing Calculators to plot the linear regression of the points created by the circumference-diameter graph.	2 class periods (45-60 minutes each)

Assessment:

Informal: Observe students’ ability to use the meter sticks to measure the distances across and around the circular objects.

Formal: Quiz on circle area and circumference; Maryland School Assessment.
NCTM Standards:

Apply transformations and use symmetry to analyze mathematical situations.

§ Describe sizes, positions, and orientations of shapes under formal transformations such as flips, turns, slides, and scaling.

Geometry Subtopic	Maryland Learning Outcome	Activities	Technology Integration	Time Required
Transformations	MLO 2.5 Draw and describe the results of translations, reflections, rotations, dilations and combinations of transformations.	Objective: Given a polygon on a Cartesian grid, students will be able to transform the polygon so that it is translated, reflected, and rotated across the x- and y-axes. Materials: coordinate grid paper for each student Procedure: Hand out grid paper to each student. Have the students construct x- and y-axes in the middle of the paper, then have them draw a triangle of any size in the second quadrant of their grid. Discuss reflection and have the students reflect the three points of the triangle across the y-axis, then connect the points to construct a new triangle. This is a reflection. Have the students reflect the points again across the x-axis, from the first quadrant to the fourth quadrant. Discuss that this transformation is not only a reflection of the triangle in quadrant I. It is a 180° rotation of the first triangle they drew. The students can translate their shape by “sliding” the points to the left or right any number of spaces. They must remember that each point must be moved in the same direction, and the same number of spaces. This activity can also be completed in Geometer’s Sketchpad and demonstrated for the class as a whole. If possible, it can be done in a computer lab where every student has the opportunity to use the program.	Geometer’s Sketchpad integration (discussed in Procedure #5)	1 to 2 class periods (45-60 minutes each)

Assessment:

Informal: Observe students as they draw their transformations. Ask questions about they types of transformations they have constructed.

Formal: Part of a quiz should cover different types of transformations.