Constructing the Coordinate Plane
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students reason about the need for quadrants beyond the first quadrant in the coordinate plane when representing data within a situation’s context. When choosing an appropriate set of axes, students should also notice that the scale of the axes is important for the given data. Both of these ideas will be important for students’ reasoning in upcoming activities.
Launch
Give students 2 minutes of quiet work time, and follow with a whole-class discussion. If needed, clarify that the term “noon” refers to 12 p.m.
Student Task
The following data were collected over one December afternoon in England.
| time after noon (hours) | temperature(∘C) |
|---|---|
| 0 | 5 |
| 1 | 3 |
| 2 | 4 |
| 3 | 2 |
| 4 | 1 |
| 5 | -2 |
| 6 | -3 |
| 7 | -4 |
| 8 | -4 |
-
Which set of axes would you choose to represent these data? Explain your reasoning.
A B C - Explain why the other two sets of axes did not seem as appropriate as the one you chose.
Sample Response
- Set B. Sample reasoning: All of the data points will fit on this set of axes, and it will be easy to tell exactly where each data point goes because of the spacing of the grid lines.
- Sample explanation: Set A does not include any negative numbers, so all the data would not get represented. Set C will fit all the data, but since the grid lines are spaced 10 units apart, it would be hard to plot the data accurately.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to share their responses and reasoning. Begin by asking the class which set of axes they chose to represent the data, and record their responses for all to see. Invite students to share their reasoning.
If time allows, ask students what kind of data would make the other sets of axes appropriate choices. For example, Set A would be appropriate if the temperatures were all positive, and Set C would be appropriate if the data were collected at 10-hour intervals and happened to be close to multiples of 10.
Standards
- 5.G.1·Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- 5.G.A.1·Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g.,<span class="math">\(x\)</span>-axis and <span class="math">\(x\)</span>-coordinate, <span class="math">\(y\)</span>-axis and <span class="math">\(y\)</span>-coordinate).
- 6.NS.6·Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
- 6.NS.C.6·Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Constructing the Coordinate Plane
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students reason about the need for quadrants beyond the first quadrant in the coordinate plane when representing data within a situation’s context. When choosing an appropriate set of axes, students should also notice that the scale of the axes is important for the given data. Both of these ideas will be important for students’ reasoning in upcoming activities.
Launch
Give students 2 minutes of quiet work time, and follow with a whole-class discussion. If needed, clarify that the term “noon” refers to 12 p.m.
Student Task
The following data were collected over one December afternoon in England.
| time after noon (hours) | temperature(∘C) |
|---|---|
| 0 | 5 |
| 1 | 3 |
| 2 | 4 |
| 3 | 2 |
| 4 | 1 |
| 5 | -2 |
| 6 | -3 |
| 7 | -4 |
| 8 | -4 |
-
Which set of axes would you choose to represent these data? Explain your reasoning.
A B C - Explain why the other two sets of axes did not seem as appropriate as the one you chose.
Sample Response
- Set B. Sample reasoning: All of the data points will fit on this set of axes, and it will be easy to tell exactly where each data point goes because of the spacing of the grid lines.
- Sample explanation: Set A does not include any negative numbers, so all the data would not get represented. Set C will fit all the data, but since the grid lines are spaced 10 units apart, it would be hard to plot the data accurately.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to share their responses and reasoning. Begin by asking the class which set of axes they chose to represent the data, and record their responses for all to see. Invite students to share their reasoning.
If time allows, ask students what kind of data would make the other sets of axes appropriate choices. For example, Set A would be appropriate if the temperatures were all positive, and Set C would be appropriate if the data were collected at 10-hour intervals and happened to be close to multiples of 10.
Standards
- 5.G.1·Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- 5.G.A.1·Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g.,<span class="math">\(x\)</span>-axis and <span class="math">\(x\)</span>-coordinate, <span class="math">\(y\)</span>-axis and <span class="math">\(y\)</span>-coordinate).
- 6.NS.6·Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
- 6.NS.C.6·Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.