Teacher Component

General Overview: Our unit plan is geared toward students in a mid-level freshman or sophomore geometry class. We cover a variety of topics that include a review of the types of triangles, triangle sum theorem, triangle conjectures, discovery of congruency methods, and similar triangles. Through a variety of activities, an on going journal, final project, and multiple forms of assessment it is our intent that our students would build a solid foundation of the most basic polygon. Our activities and assessments cater to a variety of students in that they address students who are kinesthetic learners, auditory learners, and visual learners. They also make use of hands on activities, emergent technology, and connect to the real world.

Lesson Plan:

Day 1: Introduction Lesson. In this lesson, students are reaquainted with the different types of triangles. They will be given magazines in which to find examples of triangles in the real world. This search will lead into a discovery project of the different triangles that exist. Students will work to construct the various combinations of acute, obtuse, or right triangles, and equilateral, isosceles, or scalene triangles. The unit project assignment, as described in day 7, will be handed out at the end of the class period (combined effort).

Day 2: Triangle Sum Theorem. In this lesson, students are encouraged to discover the triangle sum theorem. After doing a short review of important postulates and properties, such as those pertaining to congruent vertical angles and corresponding angles, students will then complete an activity on Geometer's Sketch Pad. During this activity they will discover that the sum of the three interior angles of a triangle is equal to 180 degrees. This lesson not only makes use of technology, but also leads the student through a discovery process which they will then reflect upon in their journal (John Bassler).

Day 3: Triangle Conjectures. This lesson is set up in more of a lab format in which students formulate hypotheses about the various components of a triangle. Through discovery activities that utilize a variety of manipulatives, students will develop an understanding of the Triangle Inequality Conjecture, the Side-Angle Inequality Conjecture, and the Triangle Exterior Angle Conjecture. These activities, paired with short class discussions will then allow students to reflect upon their findings in their journal and support or negate their original hypotheses (Kathleen Weber).

Day 4: Congruent Triangles 1. In this lesson, students participate in a hands-on activity which allows them to realize the importance of triangles in the real world. With the help of "Lazy Lawrence," students will develop an understanding of the angle-side-angle, side-angle-side, and side-side-side congruency theorems. Not only do students realize one of the real world application of the lesson, but they also have fun using fettuccine noodles to discover them on their own (Elizabeth Lord).

Day 5: Congruent Triangles 2. In this lesson, students take the congruency theorems a step further, and discover why certain combinations of a triangle will not work to prove congruency. Specifically, they develop an understanding of counterexamples. Students are shown counterexamples to prove why the side-side-angle and the angle-angle-angle combinations fail to work. They are then encouraged to discover how the angle-angle-side congruency method works through a hands-on activity that utilizes various manipulatives. Students then discuss their findings and reflect upon their learnings in their journal (Rachelle Tompkins).

Day 6: Similar Triangles. In this lesson students develop an understanding of what similarity means. Through various discussions and activities students will discover the difference between similar and congruent triangles. Students will then build a knowledge base pertaining to the various theorems that deal with similar triangles. Weather permitting, students will then venture outdoors to calculate the height of the school building using similar triangles. Students will then report their findings in the form of a journal entry (Kristen Thomas).

Day 7: Concluding Activity. Through out the unit students have been discovering the many properties of triangles. Today, the final day of the unit, students will present their final projects. These projects have encouraged students to find examples of how triangles play a role in an activity that interests them. Students are urged to classify these triangles and apply the ideas that have been discussed in this unit to them. In addition to this presentation, students have been instructed to write up a short essay of their findings, accompanied by a visual. Completed journals will be collected and assessed, as well (combined effort).

Day 8: Unit quiz. (combined effort)

Back to Frontpage Student Component

	Day 1: Introduction Lesson. In this lesson, students are reaquainted with the different types of triangles. They will be given magazines in which to find examples of triangles in the real world. This search will lead into a discovery project of the different triangles that exist. Students will work to construct the various combinations of acute, obtuse, or right triangles, and equilateral, isosceles, or scalene triangles. The unit project assignment, as described in day 7, will be handed out at the end of the class period (combined effort).
	Day 2: Triangle Sum Theorem. In this lesson, students are encouraged to discover the triangle sum theorem. After doing a short review of important postulates and properties, such as those pertaining to congruent vertical angles and corresponding angles, students will then complete an activity on Geometer's Sketch Pad. During this activity they will discover that the sum of the three interior angles of a triangle is equal to 180 degrees. This lesson not only makes use of technology, but also leads the student through a discovery process which they will then reflect upon in their journal (John Bassler).
	Day 3: Triangle Conjectures. This lesson is set up in more of a lab format in which students formulate hypotheses about the various components of a triangle. Through discovery activities that utilize a variety of manipulatives, students will develop an understanding of the Triangle Inequality Conjecture, the Side-Angle Inequality Conjecture, and the Triangle Exterior Angle Conjecture. These activities, paired with short class discussions will then allow students to reflect upon their findings in their journal and support or negate their original hypotheses (Kathleen Weber).
	Day 4: Congruent Triangles 1. In this lesson, students participate in a hands-on activity which allows them to realize the importance of triangles in the real world. With the help of "Lazy Lawrence," students will develop an understanding of the angle-side-angle, side-angle-side, and side-side-side congruency theorems. Not only do students realize one of the real world application of the lesson, but they also have fun using fettuccine noodles to discover them on their own (Elizabeth Lord).
	Day 5: Congruent Triangles 2. In this lesson, students take the congruency theorems a step further, and discover why certain combinations of a triangle will not work to prove congruency. Specifically, they develop an understanding of counterexamples. Students are shown counterexamples to prove why the side-side-angle and the angle-angle-angle combinations fail to work. They are then encouraged to discover how the angle-angle-side congruency method works through a hands-on activity that utilizes various manipulatives. Students then discuss their findings and reflect upon their learnings in their journal (Rachelle Tompkins).
	Day 6: Similar Triangles. In this lesson students develop an understanding of what similarity means. Through various discussions and activities students will discover the difference between similar and congruent triangles. Students will then build a knowledge base pertaining to the various theorems that deal with similar triangles. Weather permitting, students will then venture outdoors to calculate the height of the school building using similar triangles. Students will then report their findings in the form of a journal entry (Kristen Thomas).
	Day 7: Concluding Activity. Through out the unit students have been discovering the many properties of triangles. Today, the final day of the unit, students will present their final projects. These projects have encouraged students to find examples of how triangles play a role in an activity that interests them. Students are urged to classify these triangles and apply the ideas that have been discussed in this unit to them. In addition to this presentation, students have been instructed to write up a short essay of their findings, accompanied by a visual. Completed journals will be collected and assessed, as well (combined effort).
	Day 8: Unit quiz. (combined effort)