I. Curricular Framework

Concept:

Similarity

Essential Question:

What is the concept of geometric similarity and how is it useful in real life?

Bridge:

Ratios

Content:

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To provide students with personal experience involving similarity.

Pose the question, “Are all of the students in this class ‘similar’?” With a partner, measure the following body parts and put the measurement into ratio form:
Height-waist to floor
Arm Length-finger tip to elbow
Head Length-top of ear to chin

Evaluation: Participation and interest

2. Attend: Attending to the Connection

Objective: To analyze and compare data found in “body ratios”.

In small groups, students discuss their ratios found in the previous activity. Are the ratios close for most individuals? Are we all “similar”?

Evaluation: Observe and listen to discussion

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To discover the relationship between angles and sides of similar polygons

Students are given pairs of polygons that are similar. They are instructed to measure the angles and sides of each polygon. Corresponding sides are written as ratios. Students discuss findings and write a conjecture about what they think it means for polygons to be similar.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To inform students of principles of similar polygons

Lecture on properties of similar polygons. Demonstrate similarity principles of triangle altitudes, medians, and segment parts formed by angle bisectors. Have students construct and measure these and write conjectures. Discuss findings.

Evaluation: Student questions, participation and conjectures

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: to give students practice in recognizing similar polygons, finding missing parts of similar polygons and solving problems using the principles of similar polygons

Worksheets or problems from a text.

Evaluation: Quality and accuracy of work

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To allow students to try a hands-on experiment using similarity

Students will conduct indirect measurement techniques using the shadow method, mirrors and hypsometers

Students will choose one of the following projects:
1. Group project. Research “golden rectangles”. Design and conduct a survey to determine if people really do prefer “golden rectangles” to rectangles which are not “golden”. Report on your findings.

2. Write a report on NASA’s uses of similarity.

3. Complete a scale drawing of the school grounds.

4. Report on fractals. Choose a fractal that utilizes “self-similarity”. Develop a part of the fractal during your presentation.

5. Using HyperStudio, write a story, with illustrations, that utilizes similarity as a main idea in the story.

Evaluation: Do the indirect measurements and projects demonstrate an understanding of similarity?

7. Refine: Refining the Extension

Objective: Evaluate indirect measurements. Complete projects and discuss them in small groups

Record all indirect measurement findings from the various groups. Discuss which method is believed to be most accurate. Discuss projects in small groups or with partners. Complete project self-evaluations, and answer the essential question.

Evaluation: Quality of product and discussion

8. Perform: Creative Manifestation of Material Learned

Objective: To allow students to share their projects with classmates

Students eill present projects to the whole class and if possible share projects between sections.

Evaluation: Quality of presentations and involvement of students

Assessment, Phase Five,Performance, Creative Use of Material Learned: