Understanding Proportional Relationships
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to have students discuss which features of a graph are necessary for communicating information. While students may notice and wonder many things about these graphs, the missing labels on the second graph is an important discussion point.
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).
Launch
Arrange students in groups of 2. Display both graphs for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The axes on the second graph are not labeled.
- If the first graph is about speed, then f is twice as fast as g.
- Line g is something going a speed of 2 cm every sec.
- Line f is something going at a pace of about 0.25 sec per 1 cm.
Students may wonder:
- What do the two points mean?
- Why does one image show two lines while the other only has one?
- What do lines g and f represent?
- What does the line in the second graph represent?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the graphs. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the fact that the second graph is missing labels does not come up during the conversation, ask students to discuss this idea.
Standards
- 8.EE.5·Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. <em>For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.</em>
- 8.EE.B.5·Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. <span>For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.</span>
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Understanding Proportional Relationships
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to have students discuss which features of a graph are necessary for communicating information. While students may notice and wonder many things about these graphs, the missing labels on the second graph is an important discussion point.
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).
Launch
Arrange students in groups of 2. Display both graphs for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The axes on the second graph are not labeled.
- If the first graph is about speed, then f is twice as fast as g.
- Line g is something going a speed of 2 cm every sec.
- Line f is something going at a pace of about 0.25 sec per 1 cm.
Students may wonder:
- What do the two points mean?
- Why does one image show two lines while the other only has one?
- What do lines g and f represent?
- What does the line in the second graph represent?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the graphs. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If the fact that the second graph is missing labels does not come up during the conversation, ask students to discuss this idea.
Standards
- 8.EE.5·Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. <em>For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.</em>
- 8.EE.B.5·Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. <span>For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.</span>