Lesson 8

This warm-up prompts students to estimate the measure of an angle in a triangle. This will be important as they classify triangles in this lesson so will need to distinguish acute, right, and obtuse angles. They will not need to measure angles explicitly but recalling angle measure will help them distinguish the different types of triangles. 

• Groups of 2
• Display the image.
• “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “How do we know the angle is more than 90 degrees?” (90 degrees is a right angle and this angle is obtuse. It's more than a right angle.)
• “How do we know the angle is less than 180 degrees?” (180 degrees is a straight line and this bends inward so it’s less than 180 degrees.)

The purpose of this activity is to sort triangles according to their angle measures and side lengths. When they finish sorting, students will notice that two of the possible categories will not have any matching triangles, namely if all 3 sides of a triangle have the same length then the triangle will not have a right angle or an obtuse angle. Students think about whether or not such a triangle could exist and present informal arguments to explain their reasoning (MP3). The activity synthesis formally introduces the category of right triangles.

• Create a set of cards from the blackline master for each group of 2. 

• Groups of 2
• Give each pair of students a set of triangle cards from the blackline master. 

• 5 minutes: independent work time
• 5 minutes: partner work time

If a student needs an entry point into the task, cover the criteria listed in the top row of the table prompt them to find triangles that fit in the criteria listed in the first column. Then, reveal one criteria at a time from the top view and ask, “Which triangle also fits this description?”

• Display a set of triangle cards and a blank table from the workbook. Place the cards in the correct location in the table as you discuss the questions in the synthesis.
• “How did you determine which triangles have 90 degree angles?” (I used the corner of a sheet of paper, measured it using a protractor, or used the grids.)
• “Triangles with a 90 degree angle are called right triangles.”
• “How can we be certain that a triangle is a right triangle?” (We can measure the angles or use the grid.)
• Display shape F.
• “What do you notice about the angles of this triangle?” (One is a 90 degree angle and the other two are equal to each other. The other two are half of a 90 degree angle.)
• “What do you notice about the sides of this triangle?” (Two of them are the same length.)

The purpose of this activity is for students to sort triangles in a way that makes sense to them and then make observations about right triangles. Students make statements about the right triangle shape cards using the quantifiers all, some, or none. The main shape characteristics students will likely use in their statements are the angle measures, particularly for the two angles that are not right angles, and the side lengths. Students might also choose other characteristics like the orientation of the triangles.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• Gather materials from previous activity:
  • Triangle Cards

• Groups of 2 or 4 (if doing a gallery walk)

• 5 minutes: independent work time
• 5 minutes: small-group work time

MLR7 Compare and Connect

• “Create a visual display that shows your thinking about the problems. You may want to include details such as notes, diagrams, or drawings to help others understand your thinking.”
• 2–5 minutes: independent or group work
• 5–7 minutes: gallery walk 

• Invite students to share how they sorted the cards, including
  • triangles with a right angle
  • triangles with an obtuse angle
  • triangles with acute angles
  • triangles with no sides equal
  • triangles with 2 or more sides equal
• “How did you know which triangle cards have right triangles?” (I used the grid lines. I measured with a protractor. I used the corner of a card.)
• Invite students to share their responses for properties all of the right triangles share.
• Record their responses.