Ext 6-8 Sampler

44 PartB Grade7 Lesson29, 7ETeacherGuide 82 Objective31: To identify conditionswhen side lengths and angles form a triangle. Materials: Raw spaghetti noodles, copies of Skill Builders 31-2, large triangles cut fromMaster 30 TriangleSides andAngles In this lesson, studentswill investigatewhether ornot a triangle canbe formedgivenmeasures of the sides and angles. In the first activity, studentswill discover that the sumof the lengths of the two shortest sides of a triangle is always greater than the lengthof the third side. In the second activity, studentswill find the sumof the interior angles of a triangle. Studentswill thendetermine if three anglemeasures canbeused to form a triangle GivenSide Lengths Distribute5 raw spaghetti noodles and a copyof Skill Builders 31-2 to eachpair of students. Todaywearegoing to construct trianglesgiven lengthsof the3 sides.The side lengths for the first trianglearegiven inproblem1. Holdup1 raw spaghetti noodle. Wearegoing touseour spaghetti noodles to construct a triangleusing these side lengths.Wearegoing tobreakour spaghetti noodles to match the lengthsof the three segments inproblem1. Model for studentshow to break anoodle andmake it the lengthof the first segment shown inproblem1. Now Iwant you touseyournoodles tomakea triangle with the side lengths shown inproblem1.Afteryouand yourpartnerhave finishedproblem1, pleaseuseyour spaghetti noodles to completeproblems2and3. Be prepared for student questions.Only the side lengths inproblem1 actually canbeused to form a triangle. Encourage students toverbalizewhy the side lengths in problem2donot form a triangle. (The two shortest sides arenot long enoughor the longest side seems too long.) Encourage the students to continue their investigation withproblem3. The goal is for students todiscover that the sumof the lengths of the two shortest sides of a triangle is always greater than the lengthof the longest side. They can then complete the statement at the topof the Skill Builder. GivenAngleMeasures Using a copyof the larger triangles cut fromMaster 30, have studentsmeasure each anglewith aprotractor. Thenhave them tear the angles at eachof the three corners andplace the vertices of the3 angles together to form a straight line. The sumof the3anglesof any triangle is a straight line. A B B C C A Review the fact that a straight anglehas ameasurment of 180°. What is the sumof the three interioranglesof a triangle? (180degrees) Write the followingon theboard: A. 30°, 80°, 50° B. 20°, 80°, 80° C. 70°, 90°, 40° Ask the students towork inpairs todecide if these lists of anglemeasures couldbeused to form a triangle. Ask the students to share their conclusions.Write the following statement on theboard and ask students to complete the statement: The sumof the three interior angles of a triangle is always ____________ Read through the information at the topof thepage together.Workproblems 1 and7 togetherwith the class. Have students complete thepageon their own. Skill Builders 31-2 Conceptual Understanding 82 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. The sum of the two shortest sides is greater than the longest side. 2 + 3 > 4 The sum of the two shortest sides is NOT greater than the longest side. Will these side lengths form a triangle?Write yes or no. Will these anglesmake a triangle?Write yes or no. (Remember: The sum of the angles of a triangle always equals 180°.) 1. 5m, 7m, 4m ____________ 3. 8 in., 3 in., 11 in. ____________ 5. 9 ft., 2 ft., 8 ft. ____________ 2. 3 ft., 7 ft., 5 ft. ____________ 4. 10m, 6m, 2m ____________ 6. 4 in., 1 in., 3 in. ____________ 7. 30°, 100°, 50° ____________ 9. 60°, 70°, 80° ____________ 8. 45°, 45°, 80° ____________ 10. 90°, 30°, 60° ____________ Micah drew this triangle. What is wrongwith the triangleMicah drew? ______________________________ ______________________________ ______________________________ 3 cm 4 cm 5 cm 3 cm 2 cm 2 cm 2 + 3 > 5 3 cm 8 cm 40° 75° 60° 7 cm Conditions for Forming a Triangle The sum of the angles in a triangle always equals 180°. The sum of the length of the two shorter sidesmust be greater than the length of the longest side. Part B yes yes yes yes no no no no no yes 7.G.2 Conditions for FormingaTriangle