Curriculum / Math / 8th Grade / Unit 1: Exponents and Scientific Notation / Lesson 15
Math
Unit 1
8th Grade
Lesson 15 of 15
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Solve multi-step applications using scientific notation and properties of exponents.
The core standards covered in this lesson
8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.
8.EE.A.3 — Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10<sup>8</sup> and the population of the world as 7 × 10<sup>9</sup>, and determine that the world population is more than 20 times larger.
8.EE.A.4 — Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A penny is about 0.0625 of an inch thick.
a. In 2021 there were approximately 8 billion pennies minted. If all these pennies were placed in a single stack, how many miles high would that stack be?
b. In the past 100 years, nearly 550 billion pennies have been minted. If all these pennies were placed in a single stack, how many miles high would that stack be?
c. The distance from the moon to the earth is about 239,000 miles. How many pennies would need to be in a stack in order to reach the moon?
Pennies to heaven, accessed on Aug. 4, 2017, 2:17 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
This headline appeared in a newspaper.
Decide whether this headline is true using the following information:
Explain your reasoning and show clearly how you figured it out.
Giantburgers, accessed on Aug. 4, 2017, 2:20 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
The average mass of an adult human is about 65 kilograms, while the average mass of an ant is approximately $${4\times10^{-3}}$$ grams. In 2010, the total human population in the world was approximately 6.84 billion, and it was estimated there were about 10,000 trillion ants alive. Based on these values, how did the total mass of all living ants compare to the total mass of all living humans?
Ants versus Humans, accessed on Aug. 4, 2017, 2:22 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
There are approximately seven billion $${(7\times10^9)}$$ people in the world.
In the 1990’s researchers calculated that if there were just 100 people in the world:
a. What fraction of people in the world did not have food and shelter? How many people in the world did not have food and shelter?
b. How many more people in the world spoke Chinese than English?
c. Approximately $${3\times10^8}$$ people lived in the USA at the time of this comparison. In the world of 100 people, how many would live in the USA?
100 People from the Summative Assessment Tasks for Middle School is made available through the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Aug. 4, 2017, 2:24 p.m..
a. A computer has $$128$$ gigabytes of memory. One gigabyte is $${1\times10^9}$$ bytes. A floppy disk, used for storage by computers in the 1970's, holds about $$80$$ kilobytes. There are $$1,000$$ bytes in a kilobyte. How many kilobytes of memory does a modern computer have? How many gigabytes of memory does a floppy disk have? Express your answers both as decimals and using scientific notation.
b. George told his teacher that he spent over 21,000 seconds working on his homework. Express this amount using scientific notation. What would be a more appropriate unit of time for George to use? Explain and convert to your new units.
c. A certain swimming pool contains about $${3\times10^7}$$ teaspoons of water. Choose a more appropriate unit for reporting the volume of water in this swimming pool and convert from teaspoons to your chosen units.
d. A helium atom has a diameter of about 62 picometers. There are one trillion picometers in a meter. The diameter of the sun is about 1,400,000 km. Express the diameter of a helium atom and of the sun in meters using scientific notation. About many times larger is the diameter of the sun than the diameter of a helium atom?
Choosing Appropriate Units, accessed on Aug. 4, 2017, 2:28 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
A new movie is being released and it is expected to be a blockbuster. Use the information below to predict how much money the movie will make in ticket prices over the opening weekend.
Write your answer in scientific notation and standard form.
An example response to the Target Task at the level of detail expected of the students.
Lesson 14
Topic A: Review of Exponents
Review exponent notation and identify equivalent exponential expressions.
8.EE.A.1
Evaluate numerical and algebraic expressions with exponents using the order of operations.
Investigate patterns of exponents with positive/negative bases and even/odd bases.
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Topic B: Properties of Exponents
Investigate exponent patterns to write equivalent expressions.
Apply the product of powers rule and the quotient of powers rule to write equivalent, simplified exponential expressions.
Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.
Reason with zero exponents to write equivalent, simplified exponential expressions.
Reason with negative exponents to write equivalent, simplified exponential expressions.
Simplify and write equivalent exponential expressions using all exponent rules.
Topic C: Scientific Notation
Write large and small numbers as powers of 10.
8.EE.A.3 8.EE.A.4
Define and write numbers in scientific notation.
8.EE.A.3
Compare numbers written in scientific notation.
Multiply and divide with numbers in scientific notation. Interpret scientific notation on calculators.
8.EE.A.4
Add and subtract with numbers in scientific notation.
8.EE.A.1 8.EE.A.3 8.EE.A.4
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