Curriculum / Math / 8th Grade / Unit 1: Exponents and Scientific Notation / Lesson 10
Math
Unit 1
8th Grade
Lesson 10 of 15
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Lesson Notes
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Write large and small numbers as powers of 10.
The core standards covered in this lesson
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 foundational standards covered in this lesson
5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
There are about one million people living in Austin, Texas. There are about ten times as many people living in New York City, NY. Phil says that means there are one billion people living in New York City.
Explain why Phil is incorrect.
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Read the following sentences to a peer:
Represent the following numbers as powers of 10 or multiples of powers of 10.
a. One billion
b. 10,000
c. 0.001
d. 0.00000001
e. 0.00000005
f. 100,000,000
g. 500,000,000
h. How many times bigger is one billion than 10,000?
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A large construction crane weighs one million pounds. A large truck weighs 10,000 pounds. How many times greater is the weight of the crane than the weight of the truck?
Complete the chart below. The first row has been completed for you as an example.
Example of something
measured in this quantity
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Define and write numbers in scientific notation.
Topic A: Review of Exponents
Review exponent notation and identify equivalent exponential expressions.
Standards
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
8.EE.A.38.EE.A.4
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.
Solve multi-step applications using scientific notation and properties of exponents.
8.EE.A.18.EE.A.38.EE.A.4
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