The purpose of this Warm-up is to elicit the idea that a single function can have many representations, which will be useful when students connect the representations in a later activity. While students may notice and wonder many things about these representations, that they all represent the same function 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.

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 representations. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the idea that all the representations are connected to the same function does not come up during the conversation, ask students to discuss this idea.

In this activity, students use equations to find values and complete tables. In the associated Algebra 1 lesson, students examine functions in different representations including equations and tables such as these. As students use the equations to build the tables they look for and make use of structure (MP7).

In this activity, students use values given in a table to draw and write other representations, then invent a function for their partner to guess the rule. Students look for and express regularity in repeated reasoning when they use the patterns in the table and graph to write an equation (MP8). In the associated Algebra 1 lesson, students connect different representations of functions. This activity supports students by strengthening their understanding of the connection between table representations and equations.