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Use two of your straws placed along the edges of your notebook paper as the legs of the right triangle. Use the corner of a piece of notebook paper for a right angle. Group Members _īefore We Begin Can a right triangle be formed using any three lengths of sides? Select three straws from the bag. The Pythagorean Theorem and Special Right Triangles Ask students to summarize individually in their math journals what they learned today.Īssessments  Observation  Class Discussion  Written solutions and explanations  Math Journals  Future quiz and/or test At conclusion of activities, debrief as a whole class. Have students work in same groups on these activities.

2 Pass out Extension Sheets on 30°, 60°, right triangles and 45°, 45°, right triangles. Ask students to summarize individually in their math journals what they learned today. Remember to let students determine conjectures and solutions – do not give answers! After completion of this activity sheet, facilitate a debrief discussion of the activity. o Pass out Pythagorean Theorem activity sheet and have students work on this activity sheet within their groups. Facilitate class discussion after 2 minutes. o Attention Getter: Pass out Ziploc bags with straws to students and pose the question “Can you get a right triangle from any 3 side lengths?” Ask students to work individually on this question and then discuss their findings with their group members.  Day 1 o Group students into heterogeneous groups of 3.  Calculators  Activity and extension activity sheets  Pencils Suggested Procedure  The time frame for this lesson is 2 days. Use lengths so that not all combinations will result in a triangle. Learning Objectives  Understand Pythagorean Theorem  Apply Pythagorean Theorem to real-world scenario  Understand the difference between rational versus irrational numbers  Recognize the relationships of side lengths in special right triangles  Apply knowledge of special right triangles to real-world scenarios Materials  Ziploc bags containing colored straws of different lengths. o Grade 7: Number and Number Systems  Indicator #3: Describe differences between rational and irrational numbers e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non-terminating and non-repeating decimals. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Number, Number Sense and Operations Standard: Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Indicator #1: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects. o Grade 8: Characteristics and Properties Use triangle angle sum relationships to solve problems. Use Pythagorean Theorem to solve problems involving right triangles. o Grade 7: Characteristics and Properties  Indicator #3: Use and demonstrate understanding of the properties of triangles. Students use spatial reasoning, properties of geometric objects and transformations to analyze mathematical situations and solve problems. NCTM Standards Addressed  Geometry and Spatial Sense Standard: Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Lastly, we assume students have basic graphing calculator proficiency in finding squares, finding square roots, and using the table function. We are also assuming they have a strong background in basic geometry concepts including finding area and perimeter and classifying angles. Key Words  Hypotenuse  Irrational Numbers  Legs  Pythagorean Theorem  Rational Numbers  Right Triangles  Simplest Radical Form Background Knowledge We are assuming the students are proficient at calculating square roots and squares, solving multi-step equations as well as basic quadratic equations. Lesson Plan: Pythagorean Theorem and Special Right Triangles Lesson Summary This lesson will provide students with the opportunity to explore concepts including the Pythagorean Theorem, rational and irrational numbers, and the relationship of side lengths of special right triangles.