Preparation Prepare a set of standard triangle shapes for each student. The shapes are found in the Guess My Rule Cards handout.

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1 Classifying Triangles Student Probe How are triangles A, B, and C alike? How are triangles A, B, and C different? A B C Answer: They are alike because they each have 3 sides and 3 angles. They are different because A is a right triangle, B is an equilateral (or equiangular) triangle, and C is an obtuse triangle. Lesson Description This lesson uses triangles and their properties to help students develop an understanding of classifying two-dimensional figures. Rationale The study of geometry is dependent upon deductive reasoning and syllogism. Student success in geometry, evidenced by van Hiele s work, is dependent upon students understanding of spatial ideas. Before students can be successful in a rigorous geometry course, they must be able to make use of informal deduction and make sense of the relationships among geometric objects. This lesson provides students with opportunities to make sense of triangles and their properties. At a Glance What: Classify triangles by their properties Common Core Standard: CC.5.G.4. Classify two-dimensional figures in a hierarchy based on properties. Mathematical Practices: Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Who: Students who cannot classify triangles according to their properties Grade Level: 5 Prerequisite Vocabulary: right angle, congruent, equilateral triangle, isosceles triangle, scalene triangle, acute angle, right triangle, obtuse angle, obtuse triangle Delivery Format: Small Groups of 2 to 3 Lesson Length: 30 minutes Materials, Resources, Technology: Pre-cut shapes Student Worksheets: Guess My Rule Cards (.pdf) Preparation Prepare a set of standard triangle shapes for each student. The shapes are found in the Guess My Rule Cards handout.

2 Lesson The 1. We are going to work with triangles today. Sort all of the triangles out of your set and put the rest away. What are triangles? 2. In what ways are triangles alike? 3. In what ways can triangles be different? Let s take a look at some of their differences. 4. Make a group of all the right triangles. 5. Do all these figures look the same? How are they different? 6. Now make a group of Cards 3, 11, and 12. We call these triangles equilateral. That means the sides are congruent. 7. Look at the angles of the triangles in this group. What do you notice? Are any of the angles right angles? Are the angles acute? Are the angles obtuse? Polygons with exactly 3 sides. Answers may vary. They all have: 3 sides 3 angles 3 vertices Answers may vary, but listen for: Different side lengths Different angles Group contains cards 1, 4, 5, and 8. They all contain a right angle. The lengths of their sides are different. Their sides are the same. The angles are congruent. We will only be using cards numbered Put the rest of the cards away for now. What is a right triangle? Are their sides the same length?

3 The 8. We also call these triangles equiangular. That means the angles are all congruent. 9. Make a group using Cards 2, 7, and 9. Look at the angles of the triangles in this group. What do you notice? Are any of the angles right angles? Are the angles acute? Are the angles obtuse? 10. These are obtuse triangles. That means they have exactly one obtuse angle. 11. Make a group using Cards 3, 4, 6, 9, 11, and 12. We have used some of these cards before. This time I want you to focus on the lengths of the sides. Do they all have 3 congruent sides? (Yes, some of them do, but that does not describe the whole group.) That means they cannot be. 12. Do they have at least 2 congruent sides? We call triangles that have at least 2 congruent sides isosceles triangles. Answers may vary. They have one obtuse angle. Equilateral Yes

4 The 13. Can someone make a statement about equilateral and isosceles triangles? 14. Is it possible to have a right triangle that is isosceles? Show me a card with a right isosceles triangle? 15. Is it possible to have an obtuse triangle that is isosceles? Show me a card with an obtuse isosceles triangle. 16. Is it possible to have a right triangle that is obtuse? Show me a card with a right obtuse triangle. (See Teacher Notes.) 17. Repeat with additional groupings to deepen students understanding of the properties of triangles. Answers may vary, but listen for, All equilateral triangles are isosceles. Some isosceles triangles are equilateral. Yes, Card 4 Yes, Card 9 No, it is not possible Are all equilateral triangles isosceles? Are all isosceles triangles equilateral? Teacher Notes 1. An important property of triangles is the sum of the measures of the interior angles is 180 o. To demonstrate this property, cut a triangular region from a sheet of paper or note card. Tear the three corners off and lay them side by side with the vertices ( points ) together. They will form a straight line, which measures 180 o. 2. Since the sum of the measures of a triangle is 180 o, no triangle can contain more than one right or obtuse angle. Variations None Formative Assessment Grant said that he drew a right triangle that was also isosceles. Draw a triangle like Grant s.

5 References Mathematics Preparation for Algebra. (n.d.). Retrieved 1 4, 2011, from Doing What Works. TERC. (2008). Investigations in Number, Data, and Space. Boston: Pearson. Van de Walle, J. A., & Lovin, L. H. (2006). Teaching Student-Centered Mathematics Grades 5-8 Volume 3. Boston, MA: Pearson Education, Inc.

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