Download Classifying*Triangles - Math Interventions Matrix

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, or 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 into categories based on their properties. Classify two-­‐
dimensional figures in a hierarchy based on properties. Matched Arkansas Standard: AR.5.G.8.1 (G.8.5.1) Characteristics of Geometric Shapes: Identify and model regular and irregular polygons including decagon 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 Preparation Prepare a set of standard quadrilateral shapes for each student. The shapes are found in the Guess My Rule Cards handout. Lesson The teacher says or does… 1. We are going to work with quadrilaterals today. Sort all of the quadrilaterals 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 alike? How are they different? Expect students to say or do… Polygons with exactly 3 sides. If students do not, then the teacher says or does… We will only be using cards numbered 1-­‐12. Put the rest of the cards away for now. Answers may vary, but listen Prompt students. for they all have: 3 sides 3 angles 3 vertices Answers may vary, but listen Prompt students. for: Different side lengths Different angles Group contains cards 1, 4, 5, and 8. No. They all contain a right angle. The lengths of their sides are different. 6. Now make a group of Cards 3, 11, and 12. How are they alike? Their sides are the same. We call these triangles equilateral. That means the sides are congruent. 7. Look at the angles of the The angles are congruent. triangles in this group. What do you notice? Are any of the angles right No. angles? Are the angles acute? Yes. Are the angles obtuse? No. What is a right triangle? Are their sides the same length? Are their angles congruent? Do they have any angles equal to ? Do they have any angles less than ? Do they have any angles greater than ? The teacher says or does… 8. We also call these triangles equiangular. That means the angles are all congruent. Expect students to say or do… If students do not, then the teacher says or does… Are their angles congruent? Do they have any angles equal to ? Do they have any angles less than ? Do they have any angles greater than ? 9. Make a group using Cards 2, 7, Are their angles and 9. congruent? How are they alike? Do they have any angles Look at the angles of the Answers may vary. equal to ? triangles in this group. What They have one obtuse angle. Do they have any angles do you notice? less than ? Do they have any angles Are any of the angles right No. greater than ? angles? Are the angles acute? Yes. Are the angles obtuse? Yes. 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 No. sides? (Yes, some of them do, but that does not describe the whole group.) That means they cannot be __. Equilateral 12. Do they have at least 2 Yes congruent sides? We call triangles that have at least 2 congruent sides isosceles triangles. The teacher says or does… 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. Expect students to say or do… Answers may vary, but listen for, “All equilateral triangles are isosceles. Some isosceles triangles are equilateral.” Yes, Card 4 If students do not, then the teacher says or does… Are all equilateral triangles isosceles? Are all isosceles triangles equilateral? Yes, Card 9 Prompt students. No, it is not possible Prompt students. Teacher Notes 1. An important property of triangles is the sum of the measures of the interior angles is . To demonstration of 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 . 2. Since the sum of the measures of a triangle is , 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. References
Mathematics Preparation for Algebra. (n.d.). Retrieved 1 4, 2011, from Doing What Works: http://dww.ed.gov/practice/?T_ID=20&P_ID=48 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.