Energy Flow

20 min

Narrative

This activity prompts students to apply what they know about equivalent ratios to solve problems about water consumption. Some numbers in the problems are non-whole numbers. Students may decide to use one or more representations previously learned, or reason only numerically, without the use of double number line diagrams or tables. As students compute and compare the different flow rates and interpret the rates in terms of water usage at each house, they reason abstractly and quantitatively (MP2).

This activity uses the Three Reads math language routine to advance reading and representing as students make sense of what is happening in the text.

Launch

Arrange students in groups of 2–4. Use Three Reads to support reading comprehension and sense-making about this problem. Display only the first two paragraphs, without revealing Andre’s, Lin’s, and Kiran’s data or the questions.

  • For the first read, read the problem aloud and then ask, “What is this situation about?” (Three students are trying to find out the flow of their shower heads for a science project.). Listen for and clarify any questions about the context.
  • After the second read, ask students to list any quantities that can be counted or measured. (The volume of containers and how much time it takes to fill them).
  • After the third read, reveal the first question about the shower head with the highest flow rate and ask, “What are some ways we might get started on this?” Invite students to name some possible starting points, referring to quantities from the second read. (Compare flow rates in the same time period, create a table, create a double number line)

Give students time to complete the rest of the activity, and follow that with a whole-class discussion.

Action and Expression: Provide Access for Physical Action. Activate or supply background knowledge. Provide students with access to a blank table or blank double number line diagram to support information processing.
Supports accessibility for: Visual-Spatial Processing, Organization

Student Task

Andre, Lin, and Kiran are studying their water usage from showers. They need to find the flow rate of their shower heads, which measures how much water flows out when the shower head is turned to the maximum. Flow rate is measured in gallons per minute. 

To collect data, each student turns on the shower head to the maximum and measures the time it takes to fill a container of a known volume.  

  • Andre fills a 5-gallon container in 2 minutes.
  • Lin fills a 3-gallon container in 34\frac{3}{4} minute.
  • Kiran fills a 1.5-gallon container in 12\frac{1}{2} minute.

For each question, explain or show your reasoning.

  1. Whose shower head has the highest flow rate?

  2. If the students wish to limit their water use to no more than 10 gallons a shower, to what amount of time do they need to limit their shower?
  3. The shower head in one student's home was on for a total of 19.5 minutes and 58.5 gallons of water was used. Whose home was that?

Sample Response

  1. Lin's shower head. Sample reasoning:
    • Andre's shower head lets out 2.5 gallons per minute, because 5÷2=2.55 \div 2 = 2.5. Kiran’s shower head lets out at 3 gallons a minute, because 1.5⋅2=31.5 \boldcdot 2 = 3. Lin’s shower head lets out 3 gallons in 45 seconds, so more than 3 gallons would flow in 1 minute.
    • Andre: 
      volume of container (gallons) time to fill container (minutes)
      5 2
      2. 1
    • Lin: 
      volume of container (gallons) time to fill container (minutes)
      3 0.75
      1 0.25
      4 1
    • Kiran: 
      volume of container (gallons) time to fill container (minutes)
      1.5 0.5
      3 1
  2. 4 minutes for Andre, 2.5 minutes for Lin, and 3 minutes and 20 seconds for Kiran. Sample reasoning:
    • Andre: 10÷2.5=410 \div 2.5 = 4
    • Lin: 10÷4=2.510 \div 4 = 2.5
    • Kiran: 10÷3=31310 \div 3 = 3\frac{1}{3} and 13\frac{1}{3} of a minute is 20 seconds.
  3. Kiran’s home. Sample reasoning: (19.5)⋅3=58.5(19.5) \boldcdot 3 = 58.5.
Activity Synthesis (Teacher Notes)

Invite students who use different reasoning strategies to share their responses. Highlight connections across strategies, in particular, between those that made use of flow rate per minute and those that did not. For example, to find the maximum shower time on Andre’s shower head so as to not exceed 10 gallons, some students may double the 2 minutes in the given ratio (5 gallons of water in 2 minutes). Others may divide 10 by the flow rate of 2.5 gallons per minute. 

Here are some questions for discussion:

  • “Why does the amount of water used matter?” (Water is a limited resource.)
  • “Other than the shower, what are some ways you use water?” (drinking, cooking, brushing teeth, cleaning, doing laundry, washing dishes)
  • “What could you do to be more aware of your water usage?” (Time showers. Turn off water when not using it.)

If desired, the activity can be extended to include students’ actual water usage. Consider inviting students to collect data on the flow rate of their shower heads, the length of their showers, and the amount of water used for showers. Their results can be used to reflect on their water consumption and possible ways to conserve water.

Extension

To help conserve water, there are laws that specify the maximum flow rate of shower heads.

  1. By federal law, the flow rate of new shower heads made in 1992 or later cannot exceed 2.5 gallons per minute.

    The shower head in Lin’s home is used for about 21 minutes a day. If her family switches to a new shower head, how would their daily water use change? Explain or show your reasoning.

  2. Some state governments specify even lower flow rates than the federal law. For example, California, Hawaii, and Washington require a maximum flow rate of 1.8 gallons per minute.

    Andre’s family uses about 45 gallons of water for showers each day. How much water would they save each month by switching to a newer shower head with a flow rate of 1.8 gallons per minute? Explain or show your reasoning.

Extension Response
  1. Sample responses: 
    1. Lin’s family would save at least 31.5 gallons a day. Switching from a flow rate of 4 gallons per minute to 2.5 gallons per minute saves 1.5 gallons per minute. This means saving 21⋅(1.5)21 \boldcdot (1.5) or 31.5 gallons a day. 
    2. Lin’s family would use at most 52.5 gallons of water for showers (21⋅(2.5)=52.521 \boldcdot (2.5) = 52.5) instead of 84 gallons (21⋅4=8421 \boldcdot 4 = 84) each day.
  2. Sample response: 336 gallons a month. Andre’s family runs the shower head for 18 minutes each day (45÷2.5=1845 \div 2.5 = 18). Switching from a flow rate of 2.5 to 1.8 gallons per minute means reducing water use by 0.7 gallon per minute. 18⋅(0.7)=12.618 \boldcdot (0.7) = 12.6, so that’s a saving of 12.6 gallons a day. In a 30-day month, that’s a savings of 30⋅(12.6)30 \boldcdot (12.6) or 378 gallons.
Standards
Addressing
  • 6.RP.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • 6.RP.3.d·Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
  • 6.RP.A.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • 6.RP.A.3.d·Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

15 min