Author

Danielle Boyd - SRSB

Title

Constructing and Evaluating Similar Triangles using The Geometer’s Sketchpad

Grade Level

10

Subject Area

Math

Overview of unit/lessons/activities (assumptions of prior knowledge/learning)

Unit 5- Geometry and Trigonometry

This activity serves as a beginning point for students with regards to trigonometry.

• The first handout requires students to revisit the concept of similar triangles addressed earlier years. In doing so students must describe properties of similar triangles. Furthermore, the worksheet introduces the idea of naming various sides of a right-angled triangle and reinforces the idea of ratios of corresponding sides of similar triangles.
• The second part of the idea focuses on students constructing and evaluating similar triangles in Geometer’s Sketchpad. The original idea came from page 155 of the curriculum document where students were to construct similar triangles by drawing with pencils, rulers, and protractors. In this adapted activity rather, students are demonstrating their knowledge of these concepts by using the software program.

Correlations to ICT and curriculum outcomes

Mathematics 10 Outcomes:

• D2 apply the properties of similar triangles
• D8 solve problems involving similar triangles and right triangles

ICT Integration Outcomes:

• PTS 12.2 Evaluate, select, and use the following to learn and to represent curriculum concepts under study: specialized software, including computer-based simulations; and measuring, sampling and recording devices, including complex calculators.
• BOC 12.3 Demonstrate facility with the specialized vocabulary associated with the technology they use
• CT 12.3 Design and create electronic documents to accomplish curricular task

Projected timeline for preparation and for carrying out activities

With the assumption that students will take approximately an hour to construct the triangles, time in class should also be allotted to review what students must do with the data they collected. Some students will finish the construction aspect quickly and as a result, they will begin their calculations during the first class. Others will struggle with the technological aspect therefore the hour for computer access will be needed. If a pod of computers is available, students then can work at various levels within the classroom setting without the need of a lab to be booked. Peer-to-peer mentoring is also pivotal in this process. Final calculations can be completed at home if need be.

Equipment Requirements: (computers, software, etc)

Computers with The Geometer’s Sketchpad installed on each

Teaching materials provided (Blacklines, worksheets, templates, teacher materials)

• Similar Triangles Worksheet (Word format) (pdf format)
• Constructing and Evaluating Similar Triangles using Geometer’s Sketchpad (Word format) (pdf format)
• Instructions for using Geometer’s Sketchpad
• Instructions for Constructing a Right Angle Triangle in Geometer’s Sketchpad (Word format) (pdf format)
• Instructions for Measuring Line Segments (Word format) (pdf format)
• Instructions for Measuring Angles (Word format) (pdf format)
• Teacher Resource: Sample Triangles and Ratio Table (Word format) (pdf format)

Resources available for teacher/student use (websites, references, etc)

Exploring Geometry with The Geometer’s Sketchpad: Chapter 10 Trigonometry and Fractals

Mathematical Modeling: Book 1, Chapter 5.1 Ratios Based on Right Triangles

Detailed instructions for each activity or lesson (teacher notes, activity information, learning strategies, teacher role, student roles)

1. Revisit the concept of similar triangles. In doing so, have students complete the handout: Similar Triangles Worksheet (Word format) (pdf format). This will allow students to start thinking about the properties of similar vs. congruent triangles that were learned in previous years.
2. As a class, read over the remainder of the worksheet and discuss the ideas of similar triangles and ratios. The example included on this handout will allow you to name the sides of the right triangle in relation to theta. Some students may have to be introduced to the idea of theta.
3. Once the sides of the triangles have been named and the corresponding ratios have been discussed, students can begin the activity using the handout: Constructing and Evaluating Similar Triangles using Geometer’s Sketchpad (Word format) (pdf format). I suggest doing a walkthrough to outline the assignment and expectations as an entire group before students begin.
4. Students can then proceed through the activity, using the handouts:

   Instructions for Constructing a Right Angle Triangle in Geometer’s Sketchpad (Word format) (pdf format)
   Instructions for Measuring Line Segments (Word format) (pdf format)
   Instructions for Measuring Angles (Word format) (pdf format)

5. Once students complete the construction and labeling of the triangles, they then can move to the questions on the, Constructing and Evaluating Similar Triangles using Geometer’s Sketchpad (Word format) (pdf format).

• First they student examine the similarities and differences of the 2 triangles.
• Next students will complete the ratio table using the dimensions from their triangles.

Lastly, students will conclude the activity by summing up what they have learned about similar right triangles & trigonometric ratios by writing an email to their friend. This final email should be completed individually and perhaps at home. It will be sent to the teacher for evaluation.

Student products expected

1. An email with an attachment of the completed right triangle & a summary of similar right triangles in relation to trigonometric ratios.
2. Completion to Questions 1 to d as well as the ratio table from the handout:

Constructing and Evaluating Similar Triangles using Geometer’s Sketchpad (Word format) (pdf format)

Samples (include teacher notes, assessment information, student work if available)

Sample Triangles and Ratio Table (Word format) (pdf format) provides a sample diagram (from The Geometer’s Sketchpad) of a constructed right triangle as well as the corresponding ratio table.

Assessment: The following rubric can be used to evaluate the material students are asked to send via email:

Rubric for Sketchpad file and Email Summary (Word format) (pdf format)
made from RubiStar

Logistics (organization, grouping, management issues, access to technology)

Students can work individually or in pairs.

Assessment information (e.g., rubrics for products and/or process)

Assessment: The following rubric can be used to evaluate the material students are asked to send via email:

Rubric for Sketchpad file and Email Summary (Word format) (pdf format)
made from RubiStar

An additional assessment of their ratio table should be given to assure student understanding of :

naming sides of a right triangle in relation to theta
proper use of ratio formulas.

Possible extensions

An addition to the activity could include changing the sizes of the other two angles while maintaining the 90° angle. This could serve as reinforcement for the concepts in the activity.

Other activities are included in the resource, Exploring Geometry with The Geometer’s Sketchpad. Chapter 10: Trigonometry and Fractals may be helpful in the next stage of the unit. You may have students model a river problem using The Geometer’s Sketchpad.
This resource is available for purchase through the Nova Scotia School Book Bureau (NSSBB #23064).

Adaptations for students requiring additional support

A sample triangle could be provided for a student who needs additional assistance. This way, the student would focus on understanding the ratios as the core of the activity.