The goal of this activity is for students to solve an equation in a real-world context while previewing some future work solving systems of equations. Here, students first make sense of the situation using a table of values describing the water heights of two tanks and then use the table to estimate when the water heights are equal. A key point in this activity is the next step: taking two expressions representing the water heights in two different tanks for a given time and recognizing that the equation created by setting the two expressions equal to one another has a solution that is the value for time, , when the water heights are equal.

The purpose of this discussion is to elicit student thinking about why setting the two expressions in the task statement equal to one another is both possible and a way to solve the final problem.

Direct students’ attention to the reference created using Collect and Display. Ask students to explain how the expressions in the third question are related to what they noticed was happening. Invite students to borrow language from the display as needed, and update the reference to include additional phrases as they respond.

Consider asking:

• “What does represent in the first expression? The second?” (In each expression, is the time in minutes since the tank’s water level started being recorded.)
• “After we substitute a time in for and simplify one of the expressions to be a single number, what does that number represent? What units does it have?” (The number represents the amount of liters in the water tank.)
• “How accurate was your estimate about the water heights using the table?” (My estimate was within a few minutes of the actual answer.)
• “How do you know from the expressions that there is only 1 value for   that makes true?” (The coefficients of on each side are different.)
• “If you didn’t know which expression in the last problem belonged to which tank, how could you figure it out?” (One of the expressions is increasing as increased, which means it must be Tank 1. The other is decreasing as increases, so it must be Tank 2.)
• “How did you find the time at which the two water heights were equal using the expressions?” (Because each expression gives the height for a specific time, t, and we want to know when the heights are equal, I set the two expressions equal to each other and then solved for the t-value that made the new equation true.)

In this activity, students work with two expressions that represent the travel time of an elevator to a specific height. As with the previous activity, the goal is for students to work within a real-world context to understand taking two separate expressions and setting them equal to one another as a way to determine more information about the context (MP2).

This discussion should focus on the act of setting the two expressions equal and what that means in the context of the situation.

Consider asking:

• “If someone thought that the height of Elevator A before we started timing was 16 meters because they substituted 0 for the variable of the expression and got 16, how would you help them correct their answer?” (I would remind them that is height and is the time, so when we start timing at 0 that means  , not that .)
• “Which of the elevators in the image is A and which is B? How do you know?” (A is the elevator on the right since at time 0 the height is negative, while B is the elevator on the left since at time 0 the height is positive.)
• “How did you know there would be only 1 time when the elevators are at the same height?” (After setting up the equation, the coefficients on each side of the equation are different.)
• “Describe a situation in which the 2 elevators are never at the same height at the same time. What would their equations look like?” (If Elevator B is a little higher than Elevator A and they both move at the same rate. For example and .)