This is the first Notice and Wonder activity in the course. Students dilate a triangle from a center of dilation and are then asked: “What do you notice? What do you wonder?”

Students are given time to write down what they notice and wonder about their completed drawings and then time to share their thoughts. Their responses are recorded for all to see. Often, the goal is to elicit observations and curiosities about a mathematical idea that students are about to explore. Pondering the two open questions allows students to build interest about and gain entry into an upcoming task.

The purpose of the activity is to elicit the idea that the triangle and its dilation can be viewed as representations of the cross-sections of a three-dimensional pyramid. This will help prepare students for the next activity, in which they create a representation of a pyramid by suspending several dilations of a rectangle. While students may notice and wonder many things about the figures they draw, the three-dimensional visualization is the most important discussion point.

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.

Choose a student’s drawing, and display it for all to see. Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the displayed drawing. Next, ask students, “Is there anything on the 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 the drawing resembles a pyramid does not come up during the conversation, ask students to discuss this idea. Remind students that pyramids, like prisms, are named for their bases, so this pyramid should be called a “triangular” pyramid.

Math Community

After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “Doing Math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.