The purpose of this Warm-up is for students to think about points on the axes. In previous lessons, students plotted points with non-zero coordinates. Thinking about the points with zero prepares them for plotting points on the horizontal and vertical axes which they will do in this lesson.
“How can we describe the location of the point?” (It is at the bottom left of the grid.)
“The coordinates of this point are . What would be the coordinates of the point if we moved it up 2 units?” (0, 2)
Activity 1
Standards Alignment
Building On
Addressing
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.,-axis and -coordinate, -axis and -coordinate).
The purpose of this activity is for students to plot several points with the same vertical or horizontal coordinate and observe that they lie on a horizontal or vertical line respectively (MP7). Students also plot points on the axes for the first time. Before plotting the points on a grid with grid lines, students first estimate the location of the points. This encourages them to think about the coordinates as distances (from the vertical axis for the first coordinate and from the horizontal axis for the second coordinate).
MLR8 Discussion Supports. Display sentence frames to support partner discussion: “First, I _____ because . . .” and “I noticed _____ so I . . . .” Advances: Conversing, Representing
Action and Expression: Internalize Executive Functions. Invite students to verbalize their strategy for estimating and plotting points before they begin. Students can speak quietly to themselves, or share with a partner. Supports accessibility for: Organization, Conceptual Processing, Language
Launch
Groups of 2
“You and your partner will each complete a different set of 4 problems independently. After you’re done, discuss your work with your partner.”
Activity
5–7 minutes: independent work time
5 minutes: partner discussion
Monitor for students who:
Use the halfway point on each axis as a benchmark for the coordinate grid without grid lines.
Start at zero and count spaces along each axis for the marked coordinate grid with grid lines.
Recognize the points should be aligned because they share a common horizontal or vertical coordinate.
Partner A
Estimate to plot and label the location of each point.
point
coordinates
Plot and label the same points on the coordinate grid.
What do the points have in common?
Plot the point with coordinates on the coordinate grid.
Partner B
Estimate to plot and label the location of each point.
point
coordinates
Plot and label the same points on the coordinate grid.
What do the points have in common?
Plot the point with coordinates on the coordinate grid.
Student Response
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Advancing Student Thinking
Activity Synthesis
Ask previously identified students to share their thinking.
“What can we say about a set of points when they share the same first coordinate?” (They will be on the same vertical line.)
Display the image from the student solution showing points with the first coordinate 5.
“How did you know where to put the point with coordinates ?” (I put it on the horizontal axis. I went over 5 but did not go up at all.)
“What happens when a set of points share the same second coordinate?” (They will be on the same horizontal line.)
Display the image from the student solution showing points with the second coordinate 3.
“What does the zero in (0,3) tell us?” (It means the point will be on line zero of the horizontal axis, which is the vertical axis.)
“ is an important point because it's where we start when we plot a point on the coordinate grid. Find on the grid you have been working with.”
Activity 2
Standards Alignment
Building On
Addressing
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.,-axis and -coordinate, -axis and -coordinate).
In the previous activity, students noticed that points with the same vertical coordinate lie on a horizontal line and points with the same horizontal coordinate lie on a vertical line. The purpose of this activity is to reinforce this idea by asking students to plot points on a blank coordinate grid given a single point. Using this point, students can plot other points with the same horizontal or vertical coordinate. Some students may keep one coordinate the same and double or halve the other as is shown in the student solution. Other students may label points on the axes. The given point, for example, allows students to identify 4,0 and 0,2. An advantage to working with points on the axes is that these are essentially number lines with which students have been working for several years. The Activity Synthesis highlights the special nature of the points 1,0 and 0,1. All of the points where the grid lines meet can be measured off exactly after 1,0 and 0,1 are plotted.
Launch
Groups of 2
Activity
3–5 minutes: independent work time
5 minutes: partner discussion
The grid lines are removed from this coordinate grid and a point is plotted and labeled. Plot and label some other points. Explain or show your reasoning.
Can you plot and accurately? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students only plot one other point, consider asking:
“What do you know about the point that is plotted?”
“How can you use the one of the coordinates of the point that is plotted to plot a different point with one of the same coordinates?”
Activity Synthesis
Invite students to share the points that they plotted and their reasoning.
Plot the points as they discuss their reasoning.
“How did you plot 1,0?” (I know where 2,0 is on the vertical axis because it has the same horizontal coordinate as 2,4. Then I halved the distance to the vertical axis and that's 1,0.)
“Once you know where is, what other points can you locate on the vertical axis?” ((2,0), (3,0), (4,0),... I can just keep marking off that distance like I do when I am on a number line.)
Lesson Synthesis
“Today we plotted points that lie on the same horizontal or vertical line, including the horizontal and vertical axes.”
Display the first image from the Partner A solution in the first activity.
“Do these points have the same horizontal coordinate or vertical coordinate? How do you know?” (They all sit over the same place on the horizontal axis. That tells you the horizontal coordinate and it’s the same for all of the points.)
“Do any of the points have vertical coordinate 0? How do you know?” (No, if the vertical coordinate were 0, the points would be on the horizontal axis.)
“In the next section, we will be exploring rectangles and other quadrilaterals and sometimes we’ll put them on the coordinate grid.”
Student Section Summary
We learned about the coordinate grid. We saw that the grid is formed by 2 perpendicular number lines called axes. We also saw that the 2 axes intersect at 0.
The horizontal axis runs left to right.
The vertical axis runs up and down.
We used coordinates to plot and describe points on the coordinate grid. The coordinates are 2 numbers that tell a point’s exact location on a coordinate grid.
The first coordinate tells the point’s horizontal position—how far it is from 0 along the horizontal axis.
The second coordinate tells the point’s vertical position—how far it is from 0 along the vertical axis.
The coordinates of point P are . This means point P is located 4 units from 0 along the horizontal axis and 2 units from 0 along the vertical axis. So, to get to point P, start at 0 and go 4 units right and 2 units up.
The coordinates of point Q are . This means point Q is located 0 units from 0 along the horizontal axis and 7 units from 0 along the vertical axis. So, to get to point Q, start at 0 and go 0 units right and 7 units up
Standards Alignment
Building On
Addressing
Building Toward
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.,-axis and -coordinate, -axis and -coordinate).
