In this activity, students use a step function to determine the price of tickets for groups composed of people in different age groups. In the associated Algebra 1 lesson, students examine piecewise functions and their graphs. Although this activity does not mention piecewise functions, understanding how to compute the ticket price for the group will help students think about this kind of function. As students interpret this function in the context of ages, they reason abstractly and quantitatively (MP2).

The purpose of the discussion is to get students thinking about functions for which there are different rules for different domains. Select students to share their solutions. Here are some questions for discussion:

• “Is there an equation for the function that connects the input and output?” (There is not a single, nice equation that works for all of the ages.)
• “Are there people for whom the price of a ticket would be confusing or unknown?” (No. The convention for ages is that if someone is turning 14 tomorrow, they will still be charged the $4 price since they are still currently 13. So, everyone should fit into one of the categories listed.)
• “If we graphed the information in the table, what would that graph look like?” (There would be horizontal lines for each range of ages to look a little like steps.)

The purpose of the discussion is to recognize that using the domain is important when describing graphs of situations where different things may be happening. Select students to share their solutions. If students describe the domain for the light levels in words (like “between 9 a.m. and 4 p.m..”), ask students how they might write that as an inequality. Here are some questions for discussion:

• “In Noah’s story, we know that sometimes he is walking and sometimes he is running. How can you use the graph to tell when he is walking and when he is running?” (The increasing lines showing Noah moving away from home have two different slopes. The steeper slope is when he is running, and the less steep slope is when he is walking.)
• “When Noah was going home, was he walking or running? How do you know?” (He was walking because the slope is the same, but opposite, as when he was walking away from home.)
• “In the graph about the level of light in a room, how would the graph change if there were a thunderstorm around 1 p.m.?” (In a thunderstorm it usually gets cloudy and dark, so the amount of light might decrease. The amount of decrease would depend on if it is dark enough that someone turns on a light in the room.)