## Describe the Graph

• Lesson
3-5,6-8
2

In this lesson students will review plotting points and labeling axis.  Students generate a set of random points all located within the first quadrant.  Students will plot and connect the points and then create a short story that could describe the graph.  Students must ensure that the graph is labeled correctly and that someone could recreate their graph from their story.

Each student will need a Describe the Graph Activity Sheet and a graphing calculator or some other tool(s) to generate random numbers between 0 and 10 such as cards, number cubes, etc.

Students will each student generate 12 random numbers between 0 and 10 and write them in the order they are generated in the spaces provided on the activity sheet. One thing to be careful of is having duplicate domain values. If this happens just have the student generate an additional number for that spot.

Each student will then plot their unique points and connect them in order from left to right with line segments on the graph provided on their activity sheet. This is a second chance to catch any duplicate domain values as they graph. The level and knowledge of the students will guide your information here. Higher level students will need very little guidance while lower level or younger children will need a review or lesson in how the ordered pairs match up to the graph, such as the first value corresponds to the horizontal axis, etc.

Now students will need to decide what is represented by each axis of their graph and label them as such. I usually have an example to share with the class here for clarification, so this is a good place to use the Describe the Graph Overhead.

Students are then ready to write a short story that describes what is being depicted in the graph. The activity sheet provides lines for students to write their story on. If they cannot fit their entire story in the space provided, I would encourage students to use their own sheet of paper do that both the graph and the story can be displayed at one time. I emphasize that someone reading their story must be able to recreate their graph based solely on their story. This doesn’t mean that every point has to be given but that someone could get to each point from the information given. Refer to the Overhead where the point (2, 4) is specifically stated but can be gleaned from the facts given. Allow students to work in groups of 2–3 only to discuss ideas for their stories. My experience is that students are very excited to share their stories and ideas so that by allowing them to work with a partner they can narrow down their selections based on feedback from their peers. Each student should create unique labels and therefore a unique story to go along with them.

Most students will not complete their story within a 45-minute class period so allow students to complete their stories outside class. Allow time the following day for students to clarify and ask questions regarding their graphs and story. Students may exchange papers to check each other’s work. It is also a good idea to allow students to present their graph and stories to the class. I do not make this mandatory because many students are very uncomfortable in this kind of setting but I do make it available for those students who would like to share. If you decide to let students present their work make sure you allow a good portion of the period because you will be amazed at the number of students who decide to present.

Assessment Options

1. As the students are working on their points, graphs and stories, the teacher needs to circulate among them to check their progress and answer any questions they may have as they work.
2. Collect the papers and read through them for accuracy of story in relation to graph.
3. Assess them on their presentation. You can create your own rubric for this using various online resources. There are a number of criteria to chose from. Some appropriate for this lesson would be accuracy of the mathematics involved, delivery of presentation (volume, etc.), and followed directions. Make the rubric available to students beforehand so they know what your expectations are for the presentation.

Extensions

1. Once this lesson is complete you can then use is in the opposite direction. Copy the stories that were written being sure not to include names. Randomly pass them out to students along with a sheet of large graph paper. Have students create the graph from the story being sure to include a title and labels for the axis.
2. Have students draw numbers from two bags. One bag should contain the integers from 0 to 10 (possible x-values). The second bag should contain the integers from -10 to 10 (possible y-values). Have students repeat the lesson.

Questions for Students

1. How do the coordinates of the point locate that point on the coordinate grid?

[The first coordinate moves from the origin to the right because it is positive and the second coordinate move up because it is also positive.]

2. How do the coordinates of the points link to the story that you wrote?

[The coordinates of the points should directly link to a specific event in the story. In the overhead example, the point (6, 7) identifies the age of the dog as 6 years and the weight at that age as being 7 pounds.]

3. What portion of the coordinate plane are we working in?

[All of our stories take place in the first quadrant because we are only dealing with positive numbers. Make sure that students understand that the graph we created is located in the coordinate plane but that we left off the other quadrants because we have no need of them for this specific graph.]

4. What is another way of telling someone to get to the next point without naming it by its ordered pair?

[There are many examples of this in the overhead example such at "as he only managed to gain a pound during those first 2 years" or "that by the time he was 5 years old he had doubled his weight from the 2 year mark".]

Teacher Reflection

• Were students enthusiastic about telling their story?
• What were some of the ways that the students illustrated that they were actively engaged in the learning process?
• Was your lesson developmentally appropriate? If not, what was inappropriate? What would you do to change it to make it more appropriate for your students?
• How well did the students demonstrate understanding of the materials presented?
• Did you set clear expectations so that students knew what was expected of them? If not, how can you make them clearer?

### Learning Objectives

Students will:

• Plot points given its coordinate.
• Create a line plot.
• Describe the line plot in a real life context specifically hitting on the points plotted.

### NCTM Standards and Expectations

• Model and solve contextualized problems using various representations, such as graphs, tables, and equations.
• Use graphs to analyze the nature of changes in quantities in linear relationships.

### Common Core State Standards – Mathematics

• CCSS.Math.Content.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., x-axis and x-coordinate, y-axis and y-coordinate).

• CCSS.Math.Content.5.G.A.2
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

• CCSS.Math.Content.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

• CCSS.Math.Content.6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

• CCSS.Math.Content.7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ''increase by 5%'' is the same as ''multiply by 1.05.''

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.