Worksheet Grade 8 Art & Music
Residence Time and the Powers of Ten: A Scale-Graphic Worksheet
A grade 8 art-design worksheet where students write water residence times in scientific notation and use the exponents to plan a scaled wall graphic's bar lengths.
Objectives
- Students will write large day-counts as a single digit times a power of ten.
- Students will compare two quantities in scientific notation to find how many times as large one is.
- Students will use each value's exponent to set the bar lengths in a scaled wall graphic.
Vocabulary
- Residence time
- Residence time is how long a drop of water typically stays in one part of the water cycle before moving on. Water passes through the air quickly but can stay underground for a very long time.
Also: scientific notation, power of ten, exponent, scale
Teacher overview
Residence time is how long a water molecule tends to stay in one place before it moves on. A raindrop may spend only days in the air, but water deep underground can stay for thousands of years. Those numbers are so far apart that a designer cannot draw them to true scale without a plan. This worksheet has students write a set of residence times in scientific notation, compare their sizes, and then use each value's exponent to set the bar lengths for a fictional science-center wall graphic. Writing each number as a single digit times a power of ten turns an impossible range into a design a viewer can actually read.
Student Worksheet
A wall graphic will show how long water stays in five places. The rounded residence times for this scenario are:
- Atmosphere: about 9 days
- A river: about 20 days
- A large lake: about 3,000 days
- A shallow aquifer: about 60,000 days
- Deep groundwater: about 300,000 days
Use scientific notation, which means one digit times a power of ten, such as 3 x 10^3.
- Write 3,000 days in scientific notation.
- Write 300,000 days in scientific notation.
- Write 60,000 days in scientific notation.
- Write 20 days in scientific notation.
- Deep groundwater is 3 x 10^5 days, and the large lake is 3 x 10^3 days. How many times as long is the deep-groundwater time?
- Deep groundwater is 3 x 10^5 days, and the atmosphere is 9 days. About how many times as long is the deep-groundwater time? Write your answer as one digit times a power of ten.
- On the graphic, each bar's length is its exponent times 4 centimeters. Deep groundwater has exponent 5. How long is its bar?
- Using the same rule, how long is the large-lake bar, which has exponent 3?
- The atmosphere is 9 x 10^0 days. Using the exponent-times-4 rule, how long is its bar, and what should the designer do about that?
- Explain your reasoning: why does scientific notation make this wall graphic easier to plan than writing every number in full?
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: 3 x 10^3 days. The value 3,000 is 3 followed by three zeros, so the exponent is 3.
- Answer: 3 x 10^5 days. The value 300,000 is 3 followed by five zeros, so the exponent is 5.
- Answer: 6 x 10^4 days. The value 60,000 is 6 followed by four zeros, so the exponent is 4.
- Answer: 2 x 10^1 days. The value 20 is 2 followed by one zero, so the exponent is 1.
- Answer: 100 times. Dividing 3 x 10^5 by 3 x 10^3 leaves 10^2, which equals 100.
- Answer: About 3 x 10^4 times. 300,000 divided by 9 is about 33,000, which rounds to 3 x 10^4.
- Answer: 20 centimeters. The exponent 5 times 4 centimeters equals 20 centimeters.
- Answer: 12 centimeters. The exponent 3 times 4 centimeters equals 12 centimeters.
- Answer: 0 centimeters. The exponent 0 times 4 is 0, so there is no bar; the designer should mark this value with a dot or a small minimum tick so it is not lost.
- Answer: The times range from single days to hundreds of thousands of days. Scientific notation shows each as one digit times a power of ten, so the designer can compare sizes and set bar lengths from the exponents instead of counting long strings of zeros.
Differentiation
Support
Provide a filled example (write 500 as 5 x 10^2) and a place-value chart showing 10^1 through 10^5 with their plain-number values. Let students match each residence time to its power of ten before writing the full notation.
Extension
Ask students to add a sixth place to the graphic, ocean water at about 1,000,000 days, write it in scientific notation, and state how long its bar would be under the exponent-times-4 rule and how it compares to the deep-groundwater bar.
ELL supports
Pre-teach "exponent" and "power of ten" with a short place-value demonstration. Provide sentence frames for items 5, 6, and 10, and allow students to show comparisons with a labeled drawing of two bars of different lengths.