Unit 7, Lesson 13
Interpreting Points in a Coordinate Plane
Grade 6
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In this Warm-up, students practice skills that they have developed for plotting points in all four 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. This will be useful in following activities, when students apply these skills to answer questions in context.
Give students 3 minutes of quiet work time, and follow with a whole-class discussion.
Label each point in the coordinate plane with the letter that represents its coordinates.
Coordinate plane, horizontal axis, negative 10 to 10 by ones, vertical axis, negative 10 to 10 by ones. One point is 8 units left and 4 units up from the origin. A point is 3 point 5 left and point 2 up from the origin. A point is three units right and 2 units up from the origin. A point is 7 units right and between 5 and 6 units below the origin.
The main goal of this discussion is to 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
MLR5: Co-Craft Questions
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In this activity, students reason abstractly and quantitatively as they interpret points in the coordinate plane that correspond to the balance in a bank account (MP2). Since bank accounts may not be familiar to students in grade 6, they may need to be oriented to the context.
Arrange students in groups of 2. Introduce the context graph. Use Co-Craft Questions to orient students to the context and elicit possible mathematical questions.
The graph shows the balance in a bank account over a period of 14 days. The axis labeled
Coordinate plane, horizontal axis, d, 0 to 14 by ones, vertical axis, b, negative 150 to 400 by fifties. Points at (1 comma 350), (2 comma 350), (3 comma 350), (4 comma 275), (5 comma 275), (6 comma negative 50), (7 comma 110), (8 comma 110), (9 comma 110), (10 comma 110), (11 comma negative 90), (12 comma 25), (13 comma 25).
The purpose of the discussion is for students to share their responses when interpreting the coordinate plane in context. Begin by asking for students to explain their responses to each question. To include more students in the discussion, consider asking:
If time allows, 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.
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In this activity, students reason abstractly and quantitatively about temperatures over time graphed in a coordinate plane (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. Give students 3 minutes of quiet work time and 1–2 minutes to discuss with their partner. Follow with a whole-class discussion.
The coordinate plane shows the high (x) and low (circle) temperatures in Nome, Alaska, over a period of 8 days. The axis labeled
Coordinate plane, origin O, horizontal axis, d, 0 to 9 by ones, vertical axis, T, negative 6 to 28 by twos. Red points at (one comma 28), (2 comma 26), (3 comma 21), (4 comma 11), (5 comma 13), (6 comma 17), (7 comma 7), (8 comma 2). Blue points at (1 comma 28), (2 comma 20), (3 comma 11), (4 comma 3), (5 comma 10), (6 comma 7), (7 comma negative 3), (8 comma negative 1).
On which day(s) did the largest difference between the high and low temperatures occur? What was this difference in degrees Fahrenheit?
The goal of this discussion is for students to use inequalities to express the range of values for the low and high temperatures. Begin by inviting students to share their response for the warmest high temperature (
If time allows, ask students to share their strategies for finding the vertical distance between points. Encourage them to explain how they took the scale of the vertical axis into account
The goal of this discussion is to practice selecting and drawing an appropriate scale for axes and using them to interpret the meaning of an ordered pair in context. Begin by displaying this blank grid for all to see:
Discuss the following questions, and update the grid as necessary:
If time allows, ask students to sketch a graph to represent this situation: The high temperature on day 6 of a 10-day period is 30 degrees Celsius, and the low temperature on that same day is 12 degrees Celsius. Ask students how much warmer the high temperature is than the low temperature.
Help us improve by sharing suggestions or reporting issues.
If some students do not notice that day 7 also had a difference of 10 degrees between the high and low temperatures, consider asking:
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