Lessons Integrating Information and Communication Technology within a Curriculum Area

Author

Cara Mac Lean

Title

Pythagorean Theorem

***Though the instructions are given in English, student sheets are also available in French

8

Subject Area

Mathematics

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

1.      Introduction: Students will draw right triangles and identify the parts of a right triangle: right angle, interior and exterior angles, hypotenuse and legs. They will also try to predict and identify any relationships that exist between the sides of a right triangle.

2.      Students will visit a website with a java applet that allows them to prove the relationship between the sides of right triangles.

3.      They will then try some sample problems on the same website, and self-evaluate.

4.      Students will fill out a concept frame of their understanding of the Pythagorean theorem.

5.      To apply this knowledge, students will use dot paper in graphics software to draw three connecting right triangles. Using the side lengths of the first triangle, students calculate the length of the hypotenuse of the largest triangle.

Correlations to ICT and curriculum outcomes

Math Outcomes:        D9                  demonstrate an understanding of the Pythagorean Theorem using models

D10                apply the Pythagorean theorem in problem situations

ICT Outcomes:           PTS 9.2        explore curriculum concepts under study using specialized software; measuring, sampling and recording equipment; and computer-based simulations, with teacher assistance

PTS 9.3         explore the curriculum through a wide range of print and electronic forms; accessing and processing information by means of the specialized techniques associated with the technology they select

PTS 9.6         use information and communication technology to explore increasingly complex numerical and spatial situations for the purpose of developing and testing conjectures

Projected timeline for preparation and for carrying out activities

2 or 3 1-hour periods

Equipment Requirements: (computers, software, etc)

A computer for each student or pair of students

MS Paint

Internet access

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

Several student worksheets and teacher masters are included:

 Word processor Acrobat Reader Parts of a Triangle parts_of_triangle.rtf parts_of_triangle.pdf Parties du triangle parties_du_triangle.rtf parties_du_triangle.pdf Student Instructions Handout (English) student_sheet.rtf student_sheet.pdf Student Instructions Handout (French) student_sheet_french.rtf student_sheet_french.pdf Blank Concept Frame (English) concept_frame.rtf concept_frame.pdf Blank Concept Frame (French) concept_frame_french.rtf concept_frame_french.pdf Sample Concept Frame (English) concept_frame_sample.rtf concept_frame_sample.pdf Sample Concept Frame (French) concept_frame_sample_french.rtf concept_frame_sample_french.pdf MS Paint Help ms_paint_help.rtf ms_paint_help.pdf Sample - Connecting Triangles sample_connect_triangles.rtf sample_connect_triangles.pdf Rubric - Pythagorean Relationships pyth_relation_rubric.rtf pyth_relation_rubric.pdf

Dot grid (1 cm)                                     Dot grid (0.5 cm)

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

http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html applet to prove the theorem

http://www.pbs.org/wgbh/nova/proof/puzzle/use.html problems to solve

http://mathkang.org/swf/pythagore2.html French video of Proof

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

1.      Distribute Pythagorean Relationship – Parts of a Right Triangle. Have students draw and label a right triangle, and try to think about the relationships that might exist between the lengths of the sides.

2.      Now that they have made their own predictions about the relationship between the lengths of the sides of the right triangle, introduce the relationship a2 + b2 = c2. Invite them to go to http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html to see a proof, and follow the directions to see the relationship. Another way to show the relationship is to draw a right triangle on chart paper, and cut out squares with side lengths equal to the lengths of the sides of the triangle, and then cut up the two smaller squares so they cover the larger one.

3.      After they have seen and understood the relationship between the sum of the squares of the lengths of the shorter sides (legs) and the square of the hypotenuse, try the sample problems here: http://www.pbs.org/wgbh/nova/proof/puzzle/use.html

4.      Once they have tried all the problems, and feel they understand the Pythagorean Relationship, show them the sample concept frame, and have them open the template in MS word and complete their own.

5.      After they have completed their frame and had it checked, have them open the dot paper template in MS Paint. Show them the example of the connected triangles. Then have them make three connected triangles, and use the Pythagorean Relationship to calculate the length of the hypotenuse of the largest triangle.

6.      In order to evaluate their work, it might be easiest if they copy and paste their connected triangles into Ms Word and show their work there, as shown in the connected triangles example. This also forces them to redraw two of the triangles from another perspective.

Student products expected

 Parts of a Triangle parts_of_triangle.rtf parts_of_triangle.pdf Parties du triangle parties_du_triangle.rtf parties_du_triangle.pdf Student Instructions Handout (English) student_sheet.rtf student_sheet.pdf Student Instructions Handout (French) student_sheet_french.rtf student_sheet_french.pdf Blank Concept Frame (English) concept_frame.rtf concept_frame.pdf Blank Concept Frame (French) concept_frame_french.rtf concept_frame_french.pdf

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

 Sample Concept Frame (English) concept_frame_sample.rtf concept_frame_sample.pdf Sample Concept Frame (French) concept_frame_sample_french.rtf concept_frame_sample_french.pdf Sample - Connecting Triangles sample_connect_triangles.rtf sample_connect_triangles.pdf

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)

 Rubric - Pythagorean Relationships pyth_relation_rubric.rtf pyth_relation_rubric.pdf

Possible extensions

Students could be asked to find examples of right triangles where is not possible to measure one side, but it is possible to measure the other two, and then calculate the missing side using the Pythagorean Relationship.