Unit 5, Lesson 1
Describing Graphs
Extra Support Materials for Algebra 1
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The purpose of this Warm-up is to elicit the idea that graphs can be interpreted to have meaning in situations, which will be useful when students interpret similar graphs in a later activity. While students may notice and wonder many things about this graph, connections between the graph and the real situation are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Arrange students in groups of 2. Display the graph for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder.
A rocket is shot into the air, and some aspects of its flight are shown in the graph.
What do you notice? What do you wonder?
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the graph. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If specific connections to height and time do not come up during the conversation, ask students to discuss these ideas.
In this partner activity, students take turns matching descriptions of situations to graphs of those situations. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and to critique the reasoning of others (MP3).
Arrange students in groups of 2. Display the task. Tell students that for each description, there is a matching graph. If time allows, choose a student as a partner and demonstrate how to set up and do the activity. Otherwise, share these steps:
Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to connect the representations. Display words and phrases, such as “constant,” “faster,” “slower,” “start,” “closer,” “intercept,” and “slope.”
Take turns with your partner to match a description with a graph. Be prepared to explain your reasoning.
For each match that your partner finds, listen carefully to the explanation. If you disagree, discuss your thinking and work to reach an agreement.
Mai begins at home and walks away from her home at a constant rate.
Jada begins at a neighbor’s house and walks away from home at a constant rate.
Clare begins her walk at school and walks home at a constant rate.
Elena begins at home and runs away from her home at a constant rate.
Lin begins at home and walks away from home for a while, then walks back home.
Priya begins at home and runs away from home, then walks for a while.
A
B
C
D
E
F
Much discussion takes place between partners. Invite students to share how they connected the description of a real situation to a graphical representation of the situation.
Direct students’ attention to the reference created using Collect and Display. Ask students to share the features they looked for to connect the representations. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.
Here are some additional questions for discussion:
In this activity, students practice interpreting graphs of situations by describing the graphs in their own words. As students interpret the context of the graphs, they reason abstractly and quantitatively (MP2). The contexts are similar to the ones from the matching activity, so students can draw on that understanding to write their descriptions.
In your own words, describe these graphs.
Graph of a line, origin O. Horizontal axis, 0 to 250, by 50s, time, seconds. Vertical axis, 0 to 450, by 50s, distance from home, meters. Line begins at 0 comma 200, passes through 100 comma 75, and intersects the x axis around 160. Line then changes direction and passes through points 200 comma 100, 250 comma 225, and 300 comma 350.
Graph of a line, origin O. Horizontal axis, 0 to 250, by 50s, time, seconds. Vertical axis, 0 to 450, by 50s, distance from home, meters. Line starts at 0 comma 150 and stays level through 300 comma 150.
horizontal axis, time in seconds. vertical axis, distance from home in meters. increase gradual for 60 seconds, steep next 30 seconds, gradual next 60 seconds. Decrease steep for 30 seconds, gradual for 60 seconds, steep for 30 seconds.
The purpose of the discussion is to clarify language to connect graphs to the situations they represent. Select students to share their descriptions. After each description, ask if other students have different ways to describe the situation. Encourage students to be creative in their descriptions. For example, the last graph could be described as a rocket taking off from its “home planet.”