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18.2

Activity

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR7: Compare and Connect

Materials

To Gather

Internet-enabled device

Activity Narrative

In this activity, students are presented with the question of whether baths or showers use more water. First, they brainstorm information that might help them investigate the question. Then, they determine values for the quantities of interest and complete their calculations.

As students identify relevant quantities, research or estimate necessary values, and make assumptions about a situation to solve a problem, they are engaging in aspects of mathematical modeling (MP4).

Launch

Introduce the problem context: “Some people take showers, some people take baths. There is disagreement over which one takes more water.” Ask students to think for a minute about whether a shower or a bath uses more water. (This is just to record their first instinct—they should not spend any time researching or calculating right now.) Poll the class and record the total number of students predicting each answer for all to see.

Arrange students in groups of 2–4. Either tell them that they should research relevant information (and provide access to internet enabled devices) or tell them that they can ask you for the information they need.

Values that may be useful for students:

Typical (modern) shower heads have a flow rate of 1.9 to 2.5 gallons per minute. Older shower heads (pre-1992) could have flow rates up to 5.5 gallons per minute.
Bathtubs hold approximately 120 to 180 gallons of water when completely filled to the top.
The interior of a typical bathtub has an approximate width of 30 to 32 inches, length of 55 to 60 inches, and depth of 18 to 24 inches.
There are approximately 230 cubic inches in 1 gallon of water.
1 liter is 1,000 cubic centimeters.
1 liter is approximately 0.26 gallons
1 inch is 2.54 centimeters.
Typical showers last approximately 10 minutes. During a drought, it is recommended to reduce the time to about 5 minutes. During normal circumstances, some people appreciate much longer showers.

Action and Expression: Internalize Executive Functions. To support development of organizational skills in problem-solving, chunk this task into more manageable parts. For example, check to make sure students have a valid method for comparing the water usage for a bath and a shower prior to allowing them to research typical values of measurements.
Supports accessibility for: Organization, Attention

Activity

None

Some people say that it uses more water to take a bath than a shower. Others disagree.

What information would you need in order to answer the question?
Describe how you could get the information and how you would use the information to find the answer.
Find out values for the measurements you need to use the method you described. You may ask your teacher or research them yourself.
Under what conditions does a bath use more water? Under what conditions does a shower use more water? Explain or show your reasoning.

Student Response

to access Student Response.

Building on Student Thinking

Activity Synthesis

The goal of this discussion is to show different ways that students used proportional reasoning to determine whether a bath or shower uses more water. There is no clear cut answer to this question, because it depends on the interaction of a variety of factors. As students share their reasoning with the class, highlight how their estimates and assumptions affected their final answer. For example, using a shorter average shower length in the calculations may suggest that a shower uses less water than a bath, while using a longer average shower length may give the opposite impression.

MLR7 Compare and Connect. Invite groups to prepare a visual display that shows the strategy they used to decide what conditions cause the bath or shower to use more water. Encourage students to include details that will help others interpret their thinking. Examples might include using specific language, different colors, shading, arrows, labels, notes, diagrams, or drawings. Give students time to investigate each other’s work. During the whole-class discussion, ask students:

“What did the approaches have in common? How were they different?”
“Why did some approaches lead to the same outcome? Why did some approaches lead to different outcomes?”
“What kinds of additional details or language helped you understand the displays?”

Advances: Representing, Conversing

18.3

Activity

Optional

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR1: Stronger and Clearer Each Time

Materials

To Gather

Tools for creating a visual display

Activity Narrative

This optional activity gives additional review for the material from the unit in the context of this lesson. Students build on the work they did in the previous activity and see that water used in the shower is proportional to time spent in the shower, with a constant of proportionality equal to the flow rate of the shower head.

Launch

Keep students in the same groups. Tell them they will continue considering the situation about water usage in baths and showers from the previous activity. Give students 5–6 minutes of partner work time.

MLR1 Stronger and Clearer Each Time. Give students time to meet with 2–3 partners to share and get feedback on their first draft response to the first question, about how they know the two quantities are in a proportional relationship. Invite listeners to ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing. Give students 3–5 minutes to revise their first draft based on the feedback they receive.
Advances: Writing, Speaking, Listening

Action and Expression: Internalize Executive Functions. Give students a checklist or list of steps to provide access to the tools or assistive technologies students will use, such as a graphing calculator or graphing software.
Supports accessibility for: Memory, Attention

Activity

None

Continue considering the problem from the previous activity. Name two quantities that are in a proportional relationship. Explain how you know they are in a proportional relationship.
What are two constants of proportionality for the proportional relationship? What do they tell us about the situation?
On graph paper, create a graph that shows how the two quantities are related. Make sure to label the axes.
Write two equations that relate the quantities in your graph. Make sure to record what each variable represents.

Student Response

to access Student Response.

Building on Student Thinking

Activity Synthesis

Invite students to share their equations and graphs with the class. Use their examples to review the characteristics of a proportional relationship, such as:

A constant of proportionality that relates the two quantities multiplicatively.
An equation of the form .
A graph that makes a straight line through the origin.

Consider displaying a graph representing the water usage in a bath for all to see. Ask students to interpret the graph and compare it to their graph of water usage in a shower. Consider asking “Why is this relationship not proportional?” (The water does not flow at a constant rate during the whole bath.)

If time permits, consider adding a line to the graph to represent the water usage in a shower. Ask students to interpret the meaning of the point where the two graphs cross. (It shows the amount of time in which a shower uses the same amount of water as a bath. A shower longer than that would use more water than a bath.)

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Lesson 18

Using Water Efficiently

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Standards Alignment

Building On

Addressing

7.RP.A.2

Building Toward

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Standards Alignment

Building On

Addressing

7.RP.A.2

Building Toward

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Standards Alignment

Building On

Addressing

7.RP.A.2

Building Toward