Curriculum / Math / 8th Grade / Unit 1: Exponents and Scientific Notation / Lesson 14
Math
Unit 1
8th Grade
Lesson 14 of 15
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Add and subtract with numbers in scientific notation.
The core standards covered in this lesson
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Two students are presented with the challenge of adding $${2.5\times10^3}$$ and $${1.3\times10^4}$$. They have just learned how to multiply numbers in scientific notation, and they try out using similar strategies. They get two possible answers:
$${3.8\times10^4}$$ OR $${3.8\times10^7}$$
a. Explain or show to the students how both of the answers are incorrect.
b. Why will the strategies used when multiplying numbers in scientific notation not work when adding?
c. What are some strategies that can be used to solve this problem? Find the sum.
The Great Lakes are a series of freshwater lakes located on the US and Canadian border. Lake Superior has the greatest volume of water with $${3.12\times10^{15}}$$ gallons of water. The smallest lake, by volume of water, is Lake Ontario with $${4.26\times10^{14}}$$ gallons of water.
How many more gallons of water are in Lake Superior than in Lake Ontario?
A water molecule is made up of 2 hydrogen atoms and 1 oxygen atom, represented as H2O. One hydrogen atom has a mass of $${1.7\times10^{-27}}$$ kg, and one oxygen atom has a mass of $${2.7\times10^{-26}}$$ kg.
What is the total mass of a single water molecule?
Grade 8 Mathematics > Module 1 > Topic B > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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A 2020 survey of personal income compared median incomes in different countries. All the data is in US dollars.
a. Luxembourg had the highest median income per person at $$$1.8\times 10^4$$. Ghana had the smallest median income at $$$4.7\times 10^1$$. How much more is the median income in Luxembourg than in Ghana?
b. In 2020, Luxembourg had a population of $$6.3\times 10^5$$ while Ghana had a population of $$3.1\times 10^7$$. How many more people are in Ghana than in Luxembourg?
c. Using the median as a measure of center, on average, which country had a higher total income? Show your reasoning.
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Lesson 13
Lesson 15
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
Solve multi-step applications using scientific notation and properties of exponents.
8.EE.A.1 8.EE.A.3 8.EE.A.4
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