This is the first Notice and Wonder activity in the course. Students are shown four sequences. The prompt to students is “What do you notice? What do you wonder?” Students are given a few minutes to write down things they notice and things they wonder. After students have had a chance to write down their responses, ask several students to share things they noticed and things they wondered. Record these for all to see. Often, the goal is to steer the conversation to wondering about something mathematical that the class is about to focus on. The purpose is to make a mathematical task accessible to all students with these two approachable questions. By thinking about them and responding, students gain entry into the context and might get their curiosity piqued.

The purpose of this task is to re-introduce growth factor. (Students likely encountered it in an earlier course when they studied exponential functions.) Students notice and describe that each sequence is characterized by the same type of relationship between consecutive terms.

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 precise language, and then restate their observation with more precise language in order to communicate more clearly.

The last two sequences may present a challenge since the growth factor is less than 1. The purpose of including these sequences is to encourage students to notice and make use of structure (MP7). If they notice that in the first two sequences, each pair of consecutive terms has the same quotient, they could inspect the quotients in the last sequence. These two sequences also give opportunity to point out that we still use "growth factor" even when the terms are decreasing.