Worksheet Grade 8 Engineering & Design
Brackwater Bay's Desalination Pilot: A Scientific Notation Worksheet
A grade 8 worksheet using scientific notation to size a fictional desalination pilot, compare it to a real large plant, and test it against a capacity criterion.
Objectives
- Students will express large water-volume and energy quantities in scientific notation.
- Students will compare two quantities expressed in scientific notation to find how many times larger one is than the other.
- Students will evaluate a design's production capacity against a stated engineering criterion.
Vocabulary
- Desalination
- Turning salty water, like ocean water, into fresh water people can use. It works, but it takes a lot of energy and leaves behind very salty water that must be handled carefully.
- Reverse osmosis
- Reverse osmosis cleans water by pushing it through a membrane with holes so tiny that salt and most other dissolved things cannot fit through. It can even turn seawater into fresh water.
Also: scientific notation, capacity, criterion
Teacher overview
The fictional coastal town of Brackwater Bay is facing drought and is evaluating a small-scale seawater reverse-osmosis desalination pilot plant to supplement its water supply. This worksheet has students size the pilot plant's output in scientific notation, compare it to the real Carlsbad, California desalination plant, the nation's largest, and check whether the pilot meets the town's stated production criterion.
Student Worksheet
Desalination takes the salt out of seawater. Brackwater Bay's fictional engineering office has proposed a pilot desalination plant. Its capacity is 500,000 gallons per day.
- Express Brackwater Bay's pilot plant capacity, 500,000 gallons per day, in scientific notation.
- The real Carlsbad, California desalination plant is the nation's largest. It produces about 50 million gallons per day. Express this capacity in scientific notation.
- Use your answers from items 1 and 2. How many times larger is the Carlsbad plant's daily capacity than Brackwater Bay's proposed pilot plant?
- The two plants would serve communities of very different sizes. Even so, comparing a small pilot plant like Brackwater Bay's to a large plant like Carlsbad's is useful for planning. Explain why, in one or two sentences.
- Suppose Brackwater Bay's pilot plant ran at full capacity every day for one year (365 days). How many total gallons would it produce? Express your answer in scientific notation.
- Seawater reverse osmosis uses roughly 11 to 15 kWh of energy for every 1,000 gallons treated. Use 13 kWh per 1,000 gallons as a working estimate. How much energy would the pilot plant use in one day at full capacity?
- Use your answer from item 6. Calculate the pilot plant's energy use over one year (365 days). Express your answer in scientific notation, rounded to three significant figures.
- Brackwater Bay's town council set a criterion for any proposed system. It must produce at least 400,000 gallons per day. Does the 500,000-gallon-per-day pilot plant meet this criterion? By how many gallons per day does it exceed or fall short?
- Challenge. Suppose Brackwater Bay later scaled up its plant to match exactly one-tenth of Carlsbad's daily capacity. How many gallons per day would that be? How many times larger is that scaled-up capacity than the original 500,000-gallon pilot plant?
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 5 × 10^5 gallons per day.
500,000 = 5 × 100,000 = 5 × 10^5.Answer: 5 × 10^7 gallons per day.
50 million = 50,000,000 = 5 × 10,000,000 = 5 × 10^7.Answer: 100 times larger.
(5 × 10^7) ÷ (5 × 10^5) = (5 ÷ 5) × 10^(7−5) = 1 × 10^2 = 100.Answer: Accept any well-reasoned response. A strong answer notes that comparing a small proposal to a proven large-scale plant lets engineers see whether the pilot's design and technology are realistic and tested at a bigger scale, even though Brackwater Bay does not need nearly as much capacity as Carlsbad provides.
Answer: 1.825 × 10^8 gallons.
500,000 × 365 = 182,500,000 gallons. In scientific notation: 182,500,000 = 1.825 × 10^8.Answer: 6,500 kWh per day.
500,000 gallons ÷ 1,000 = 500. 500 × 13 kWh = 6,500 kWh.Answer: About 2.37 × 10^6 kWh.
6,500 kWh/day × 365 days = 2,372,500 kWh. In scientific notation, rounded to three significant figures: 2,372,500 ≈ 2.37 × 10^6.Answer: Yes, it meets the criterion, exceeding it by 100,000 gallons per day.
500,000 gallons per day is greater than the 400,000-gallon-per-day minimum. 500,000 − 400,000 = 100,000 gallons per day above the criterion.Answer: 5,000,000 gallons per day, which is 10 times larger than the original pilot.
10% of Carlsbad's 50,000,000 gallons per day is 0.10 × 50,000,000 = 5,000,000 gallons per day. 5,000,000 ÷ 500,000 = 10.
Differentiation
Support
Provide a worked example converting 300,000 to scientific notation (3 × 10^5) alongside item 1, and give students a printed reference card showing the pattern "move the decimal point left, count the places, that count becomes the exponent of 10."
Extension
Ask students to calculate how many days it would take Brackwater Bay's pilot plant, running at full capacity, to produce the same total volume Carlsbad produces in a single day, using their answers from items 1 and 2.
ELL supports
Provide a simple visual scale showing a small pitcher (Brackwater Bay's pilot) next to a large water tank (Carlsbad's plant) labeled with their respective capacities, to make the "100 times larger" comparison in item 3 concrete before students work with the scientific notation symbols. Allow item 4's explanation to be written as a single sentence using a provided sentence frame: "Comparing the two plants helps because ___."
Extensions
Have students calculate, using only the figures given in this worksheet, how many pilot-plant-sized facilities like Brackwater Bay's would need to operate at once to match Carlsbad's daily output, using their answer from item 3 as a starting point for the calculation.