Lesson 13

In this warm-up, students practice skills that they have developed for plotting points in all 4 quadrants of the coordinate plane. This warm-up also gives students the opportunity to describe points that do not fall nicely on the intersection of grid lines. In the next few activities, students apply these skills to answer questions in context. 

Give students 3 minutes of quiet work time followed by whole-class discussion.

Some students may have trouble locating decimal values on a coordinate plane. (They have placed decimals on horizontal number lines before, but up to this point have mostly seen coordinates that are integers or 0.5's.) Demonstrate how point \(B\) is 4 units above the \(x\)-axis by tracing a pencil 4 units vertically to land on point \(B\). Then ask, "What if the point was only 0.2 units above the \(x\)-axis? Where would it go?"

The main goal of discussion is to review the order of ordered pairs and make sense of points that don't fall on the intersection of grid lines. Invite students to explain how they knew which points matched with which coordinates. Ask students how they would make sense of point \(D\), since it doesn't fall nicely where grid lines cross.

In this activity, students interpret points in the coordinate plane that correspond to the balance in a bank account (MP2). Since bank accounts are not likely to be familiar to students in grade 6, they will need to be oriented to the context.

Arrange students in groups of 2. Tell students that when someone opens a bank account, they have to put money into the account. The "account balance" is the amount of money in the account at any given time. For example, they might put $350 into the account when they open it, and then the account balance will be 350. However, sometimes they have to borrow money from the bank and then their account balance is a negative value. For instance, if they have no money in the account and borrow $200, then the account balance is -200. The graph they see shows the account balance for a person's account at the start of each day for two weeks.

Give students 10 minutes of work time. Encourage students to check in with their partner after each problem and work to reach agreement if they disagree. Follow with whole-class discussion.

The purpose of the discussion is to check how comfortable students are with the concept of an account balance that included negative numbers and how to interpret the coordinate plane in this context. Ask for students to explain their responses to each question. To include more students in the discussion, consider asking:

• "Do you agree or disagree? Why?"
• "Who can restate ___’s reasoning in a different way?"
• "Does anyone want to add on to _____’s reasoning?"

Bring attention to the days when the account balance changed. Ask students to come up with a story of what might have happened on those days.

Students reason abstractly and quantitatively about temperatures over time graphed on coordinate axes (MP2). The goal of this activity is for students to use inequalities to describe the location of points on a coordinate grid in one direction. This activity also introduces the idea of vertical difference on the coordinate plane using a familiar context. Students may use previous strategies such as counting squares, but are not expected to explicitly add or subtract using negative numbers.

Arrange students in groups of 2. Allow students 3–4 minutes of quiet work time and 1–2 minutes to check results with their partner. Follow with a whole-class discussion.

Because the high temperature on day 7 was positive and the low temperature was negative, some students may not notice that the difference was 10 degrees on this day as well. Consider prompting them to use tracing paper to compare the temperature differences on days 6 and 7.

This discussion should lead to two key takeaways. First, students express the range of values for the low and high temperatures using inequalities. Second, students share strategies for finding a difference between two values on the coordinate plane.

Ask students to share their inequalities for \(H\) and \(L\). It is expected that students have inequalities that describe the maximum high temperature for \(H\) and the minimum low temperature for \(L\), but the discussion should bring out that each variable has 4 statements that capture its possible values: \(L>\text-3\), \(L=\text-3\), \(L < 26\), and \(L=26\) for the variable \(L\) and \(H>2\), \(H=2\), \(H < 28\), and \(H=28\) for the variable \(H\).

Ask students to share their strategies for finding the vertical distance between points. Push them to explain how they took the scale of the vertical axis into account. Invite students to explain how they used the context to make sense of their answers.