Mathematics TEKS Refinement 2006 – 6-8

Tarleton State University

Geometry and Spatial Reasoning Activity:

Triangle Properties

TEKS:

(6.6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: (A) use angle measurements to classify angles as acute, obtuse, or right; (B) identify relationships involving angles in triangles and quadrilaterals; (6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. (6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; (6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (B) validate his/her conclusions using mathematical properties and relationships. Measurement Connection: (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to: (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; (C) measure angles;

Geometry and Spatial Reasoning Triangle Properties

Grade 6 Page 1

Mathematics TEKS Refinement 2006 – 6-8

Tarleton State University

Overview:

Students will identify, compare, and contrast triangles according to properties of sides and properties of angles.

Materials:

Paper Rulers Protractors Blackline master (various triangles) Possible or Impossible game cards on transparency Large index cards, 1 per teams of 2

Grouping:

Pairing of two students

Time:

60 minutes

Lesson: Procedures 1. (5-10 minutes) Review the fact that triangles are classified: by properties of sides and properties of angles. Give students the meaning of equilateral, isosceles, scalene, acute, obtuse, and right triangles.

Notes Have students repeat definitions of the triangles using correct mathematical attributes. Encourage note taking during this time.

2. (20 minutes) Provide each student with a ruler, protractor, and backline master that contains a variety of triangles. With their partner, each student is to classify each triangle according to both properties of angles and sides. They must justify the naming of each triangle through use of the ruler and protractors and provide the measures of the angles and length of sides.

Question: Consider equilateral, isosceles, and scalene triangles. Which of these triangles can have right angles? Acute angles? Obtuse angles?

Vocabulary: congruent, equilateral, isosceles, scalene, acute, obtuse, and right triangles.

Watch for misreading of the protractor. Have students measure side lengths in cm units. Student responses must be justified by providing an example of each case that they state is possible.

3. (10-15 minutes) Play Possible or Impossible. Have students write the words Possible and Impossible on an index card, each word on a different side using a marker.

Geometry and Spatial Reasoning Triangle Properties

Students must justify their answer by either drawing a picture or stating orally why they chose the answer being held. Oral explanations and/or drawings must be justified with correct math Grade 6 Page 2

Mathematics TEKS Refinement 2006 – 6-8

Procedures Make a transparency of the master for the game. Cut out each card from the transparency master, shuffle.

Tarleton State University

Notes terminology and reasoning. You may add additional attribute cards to extend the game.

Place two cards on the overhead at a time. One card must be the type of triangle (right, acute, obtuse, scalene, isosceles, or equilateral). Ask students if this type of triangle is possible or impossible. Allow teams to discuss. Once a decision has been made, students hold up the card to indicate whether it is possible or impossible. 4. (5 minutes) Student Reflection: Write a brief paragraph that compares and contrasts equilateral, isosceles, scalene, acute, obtuse, and right triangles. Select 4 types of triangles and explain how they are alike and how they are different. Give an example of a triangle that is impossible.

Homework:

Use a ruler and protractor to draw triangles based on angle measures and side lengths that fit into each classification of triangles. Note triangles which may be considered as more than one type. Support each drawing with mathematical terminology and measurements. You may extend this to have students find the perimeter and area for each triangle drawn to make a connection to measurement.

Assessment:

Use student reflections to identify any misconceptions that still exist.

Extensions:

Extend the Possible or Impossible game to include having pictures of triangles placed on the overhead and students providing the type of triangle.

Modifications: While playing the game, students may have several triangles drawn on a worksheet. Students would identify which triangle on the sheet matches the description placed on the overhead.

Geometry and Spatial Reasoning Triangle Properties

Grade 6 Page 3

Geometry and Spatial Reasoning Triangle Properties

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Mathematics TEKS Refinement 2006 – 6-8

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Grade 6 Page 4

Tarleton State University

Tarleton State University

Acute

Obtuse

Two One angle One angle angles = greater measures 90º than 90º 67º Sum of Sum of All angles angles angles less than measures measures 90º less than equals 180º 180º Scalene Equilateral No sides congruent

Geometry and Spatial Reasoning Triangle Properties

Right

Sum of angles measures greater than 180º Two sides congruent

One angle = 90º

Grade 6 Page 5

Isosceles

One angle measures 85º All sides congruent

Possible or Impossible Game Transparency Master

Mathematics TEKS Refinement 2006 – 6-8