Composing Figures
10 min
Narrative
The purpose of this Warm-up is to connect prior student knowledge about triangles with rigid transformations, which will be useful when students perform rigid transformations on triangles in a later activity. While students may notice and wonder many things about this image, properties of triangles under rigid transformations are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that since triangle ABC has two side lengths of the same length, triangle ABD must as well.
Launch
Arrange students in groups of 2. Display the image for all to see. Tell students that triangle ABD is the image of triangle ABC under a rigid transformation. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- Triangle ABC and triangle ABD share a side.
- Triangle ABC is an isosceles triangle.
- BD must be 2 units, and AD must be 3 units.
Students may wonder:
- Is triangle ABD a reflection or a rotation of triangle ABC?
- Is triangle ABC congruent to triangle ABD?
- How many copies of triangle ABC would it take to go all the way around point A?
Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the idea that triangle ABD could be a reflection or a rotation of triangle ABC does not come up during the conversation, ask students to discuss this idea.
Standards
- 8.G.1.b·Angles are taken to angles of the same measure.
- 8.G.A.1.b·Angles are taken to angles of the same measure.