Polygons
5 min
Narrative
This Warm-up prompts students to carefully analyze and compare features of triangles. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear how students talk about characteristics of triangles and their area.
Students may describe the differences in the triangles in terms of:
- The angles (acute, right, or obtuse).
- The orientation of sides (vertical, horizontal).
- The side likely to be chosen as a base.
- The length of base or height.
- The area.
Launch
Arrange students in groups of 2–4. Display the triangles for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three triangles that go together and can explain why. Next, tell each student to share their response with their group and then together find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
A ,B, and C go together because:
- They have a base or a height that is 6 units long.
- They have a side that slants down from left to right.
A, B, and D go together because:
- All their sides have different lengths.
- All their angles have different measures.
A, C, and D go together because:
- They all have a side that is vertical.
- We could find their area by choosing the vertical side as a base.
B, C, and D go together because:
- They are not right triangles (or have no right angle).
- They all have an area of 12 square units.
- They have just one side that would be easy to use as the base (where we can tell the corresponding height from the grid).
Synthesis
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Because there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, ask students to explain the meaning of any terminology they use (such as "vertical," "horizontal," "right angle," "base," and "height") and to clarify their reasoning. Consider asking:
- “How do you know . . . ?”
- “What do you mean by . . . ?”
- “Can you say that in another way?”
Math Community
After the Warm-up, display the revisions to the class Math Community Chart that were made from student suggestions in an earlier exercise. Tell students that over the next few exercises, this chart will help the class decide on community norms—how they as a class hope to work and interact together over the year. To get ready for making those decisions, students are invited at the end of today’s lesson to share which “Doing Math” action on the chart is most important to them personally.
Standards
- 4.G.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)
- 4.G.A.2·Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
- 5.G.B·Classify two-dimensional figures into categories based on their properties.
- 5.G.B·Classify two-dimensional figures into categories based on their properties.