• Assess student understanding using the Triangle Classification sheet and question/answer time.
• Formally evaluate students using the brief summary of the lesson that each student wrote after the Types of Triangles activity.

As students enter the room, give all of them a copy of the Lesson 2 Entrance Ticket (M-6-2-2_Lesson 2 Entrance Ticket and KEY.docx). Have students work independently at their seats. After a few minutes have them share their answer to question 1 with a partner. Then have each group share one fact they know about triangles (keeping a list on the board). Have them share until everyone has all of what they know about triangles on the board (and then have them add new facts to their list). Go through the answers to question 2 (showing them that they can “measure” a 90 degree angle with the corner of a piece of paper). After finishing the angle classifications, go over the answers to questions 3 and 4. Emphasize that for obtuse and right triangles, there need only be one angle that is either obtuse or right, but for an acute triangle all three angles must be acute. If there is time, pose the question “Can you have a triangle that has both an obtuse angle and a right angle?”

Lastly say “We were looking at the triangles and grouping them by their angle measures. How else could we group them?” Wait for students to answer. “Correct, side lengths. How many types of triangles do we have when we look at their side lengths?” As students come up with the three categories write them on the board with space below to draw an example. Optional: Have a student come up to the board to draw an example of one of the three categories. Then once an example of each has been drawn, challenge someone to come up and draw a different triangle that is still in the same category.

Continue with another activity focusing on the types of triangles. Students may work individually or in partners. Each group or student will need their pencils, one ruler, and one protractor. Hand out to each student a copy of the Triangle Classifications activity sheet (M-6-2-2_Triangle Classifications and KEY.docx). First have a few (7) volunteers read the types of triangles and their definitions. Next have someone read the directions. After that say, “In summary, for each of these triangles in the chart, you (and your partner) must use the ruler and measure all three of the side lengths of each triangle in centimeters, and record your results in the appropriate place.” Draw a basic triangle on the board and label the three corners A, B, and C. Then label the side lengths arbitrarily (e.g., 3cm, 4cm, 5cm). Then off to the right write the notation . Ask, “Which number goes with which side? What is the length of side ? How do you know?” Be sure students know that the sides are labeled with the endpoints. “Then, once you have measured the side lengths you will need to measure how many degrees each angle of the triangle measures. Be sure to add up all three angles to see what they equal all together. You can divide the work up so that each of you do two triangles or do them all together. But both partners need to measure the side lengths and angles of at least two triangles. You have 20 minutes to complete this assignment. [IS.4 - Struggling Learners] Be sure to write in the triangle type(s) in the last column.” If needed, remind students that it will be easier to measure the angles if they use the straight edge to extend one of the sides of the triangle. [IS.5 - Struggling Learners]

While students are working, use the opportunity to walk around and help those who are having trouble using a ruler and protractor correctly.

Once the time is up, have students share their answers with the rest of the class. Some questions to ask would be:

• “How many degrees did the angles equal in each triangle?
• Can a triangle have only one classification?
• Can the longest side equal or be longer than the sum of the other two sides? Shorter than their differences?”

Once finished, have each student write one paragraph (which can include drawings) about what s/he did that day in class and what was learned.  [IS.6 - All Students] This should be a brief summary of the lesson. There is a 3 minute time limit on this, to be collected immediately.

Extension:

• Routine: [IS.7 - Struggling Learners] To help students remember what they learned about triangles, have students redo the lesson activity by drawing more triangles. Begin by handing out blank papers and saying, “Please divide the sheet of paper into four quadrants like so.” On the board draw a rectangle to represent the paper and then a horizontal and vertical line through the middle (creating quadrants). Then say, “Now number them one through four in the upper left hand corner of each quadrant. In the first quadrant please draw a triangle that is both a RIGHT and SCALENE triangle.” Give students under a minute to do this. Then say, “In the second quadrant draw a triangle that is EQUILATERAL, but NOT obtuse.” Give them under a minute to do this. Then say, “In the third quadrant draw a triangle that is OBTUSE and EQUIANGULAR.” Give them under a minute to do this. Then say, “In the last quadrant, 4, draw a triangle that is ACUTE and ISOSCELES.” Once students have finished their drawings go through each one, and have two to three students come up and draw their triangles on the board. Be sure to point out that there are many different possible correct answers. When at the second quadrant ask how the triangles that fit these stipulations can vary (only in size). Also ask if the stipulation of “NOT obtuse” was necessary, and why not (since it is equilateral all of the angles must equal 60 degrees and therefore acute, which is not obtuse; point out that right is also not obtuse). For the third one, ask students for their drawings of triangles that fit the parameters given. Afterwards show them that since the triangle is equiangular then all of the angles equal 60 degrees and therefore can never be obtuse. It is impossible. Then go through the last one, as the first.
• Small Group: Students who don’t understand the concepts immediately may benefit from additional practice in a small group. Have groups create classroom posters of each type of triangle. Each group will be in charge of designing a “Type of Triangle” poster. Each poster must be titled with the type of triangle, include the written definition (in their own words), and display a “large” drawing of the triangle to model the definition. On the drawing, students must give the measurement of each side length (to the nearest tenth of a centimeter) and each angle. Then on the bottom of the poster they should include a “Disclaimer” that includes the other categories under which the triangle could be classified. After they have finished, have each group present its triangle poster orally to explain each type of triangle.
• Expansion: Finding Area Activity. [IS.8 - Struggling Learners] Students who are looking for a challenge may try this activity. Have each student trace or draw three different triangles (using a meter stick) onto chart paper. They will need to measure the lengths of each of the three sides as well as the angles, and then classify the triangle according to the side lengths and angle measures. They must also record the sum of the angle measures as well as the perimeter of the triangle. Then they will need to find the height of each triangle (remembering that it “drops down” from the top of the triangle to the base at a 90 degree angle. They can choose which side they would like to be the base then draw the altitude accordingly. From there they will need to measure the height and use it to find the area of the triangle (A =  bh). This same process should be completed for all three triangles.
• Technology: If computers are available for students, have them do the small-group activity on the computer, creating a PowerPoint of their type of triangle, or use another program (e.g., Notebook, Microsoft Publisher, Adobe) to create their posters to present to the class. Students may find the following Web site helpful in the design of a triangle with dimensions on it (to take a screen shot, SnagIt, or Ctrl+F4 on a Mac) to insert into their poster or presentation:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=142