ALEX Classroom Resource

  

Comparing Powers of 10

  Classroom Resource Information  

Title:

 Comparing Powers of 10

URL:

 https://aptv.pbslearningmedia.org/resource/mgbh-math-ee-compow/comparing-powers-of-10/

Content Source:

 PBS
Type: Interactive/Game

Overview:

Use powers of 10 to investigate scientific notation. This interactive exercise focuses on determining which of a series of numbers written in scientific notation is larger and by what magnitude then you need to use your critical thinking skills to determine methods for general cases.

This resource is part of the Math at the Core: Middle School collection.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
16. Express and compare very large or very small numbers in scientific notation. [Grade 8, 5]

a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used, expressing answers in scientific notation. [Grade 8, 6]

b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. [Grade 8, 6a]

c. Interpret scientific notation that has been generated by technology. [Grade 8, 6b]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Rewrite numbers using scientific notation.
  • Use use numbers in scientific notation to estimate measurements and values.
  • Use the laws of exponents to multiply and divide expressions containing numbers written in scientific and decimal notation to solve real-world problems.
  • Compare numbers written in scientific notation and express the multiplicative relationship between the numbers.
Teacher Vocabulary:
  • Multiplicative relationship
  • Scientific Notation
Knowledge:
Students know:
  • That scientific notation is formed using base ten system and is the reason a 10 is used as the base number.
  • Raising or lowering an exponent is has an effect on the place value of the decimal expansion.
  • That scientific notation is formed using a base ten system.
  • how to apply laws for multiplying and dividing exponents
Skills:
Students are able to:
  • Write numbers in standard notation in scientific notation.
  • Convert numbers from scientific notation back to standard form.
  • Use information given in scientific notation to estimate very large or small quantities given in real-world contexts.
  • Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both scientific and decimal notation are used.
  • Choose between appropriate units of measure when determining solutions or estimating
Understanding:
Students understand that:
  • The movement of decimals in converting between scientific and standard notation is a function of an exponent.
  • Every decimal place represents a power of ten (this is a connection many students have not made yet when thinking about place value).
  • Scientific notation has real-world applications for very large and very small quantities found in many disciplines.
  • performing scientific notation operations are another application of integer exponent operations.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 8
5. Estimate and compare very large or very small numbers in scientific notation.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Rewrite numbers using scientific notation.
  • Use numbers in scientific notation to estimate measurements and values.
Teacher Vocabulary:
  • Scientific Notation
Knowledge:
Students know:
  • that scientific notation is formed using the base ten system and is the reason a 10 is used as the base number.
  • Raising or lowering an exponent has an effect on the place value of the decimal expansion.
Skills:
Students are able to:
  • write numbers in standard form in scientific notation.
  • Convert numbers from scientific notation back to standard form.
  • Use information given in scientific notation to estimate very large or small quantities given in real-world contexts.
Understanding:
Students understand that:
  • the movement of decimals in converting between scientific and standard notation is a function of an exponent.
  • Every decimal place represents a power of ten (this is a connection many students have not made yet when thinking about place value).
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.5.1: Recognize a fraction as division of the denominator into the numerator.
M.8.5.2: Demonstrate that when multiplying powers of like bases; add the exponents (Property of products of powers).
M.8.5.3: Demonstrate that when dividing powers of like bases; subtract the exponents (Property of quotient of powers).
M.8.5.4 : Demonstrate how to convert fractions to a decimal, with or without a calculator.
M.8.5.5: Recall how to write numbers in scientific notation.
M.8.5.6: Recall estimation strategies.

Prior Knowledge Skills:
  • Define the parts of a division problem including divisor, dividend, and quotient.
  • Write a division equation.
  • Apply the signs ÷ and = to the action of separating sets.
  • Recognize division as either repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.
  • Model grouping with basic division facts partitioned equally (e.g. 8/2).
  • Apply properties of operations as strategies to subtract.
  • Subtract within 20.
  • Represent equal groups using manipulatives.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.5 Find the square root of the perfect squares up to 100.
Mathematics
MA2019 (2019)
Grade: 8
6. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

a. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

b. Interpret scientific notation that has been generated by technology.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use the laws of exponents to multiply and divide expressions containing numbers written in scientific and decimal notation to solve real-world problems.
  • Compare numbers written in scientific notation and express the multiplicative relationship between the numbers.
Teacher Vocabulary:
  • Multiplicative Relationship
  • Scientific Notation
Knowledge:
Students know:
  • that scientific notation is formed using a base ten system.
  • how to apply laws for multiplying and dividing exponents.
Skills:
Students are able to:
  • perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both scientific and decimal notation are used.
  • Choose between appropriate units of measure when determining solutions or estimating
Understanding:
Students understand that:
  • scientific notation has real-world applications for very large and very small quantities found in many disciplines.
  • performing scientific notation operations are another application of integer exponent operations.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.6.1: Define scientific notation.
M.8.6.2: Calculate multiplication and division of scientific notation, with or without a calculator.
M.8.6.3: Recall properties of exponents.
M.8.6.4: Recall how to write a number using scientific notation.
M.8.6.5: Restate exponents as repeated multiplication.
M.8.6.6: Discuss the real-world application of scientific notation (very large or very small quantities).
M.8.6.7: Demonstrate difference of scientific notation symbol between paper and calculator.

Prior Knowledge Skills:
  • Recall that exponents are repeated multiplication.
  • Demonstrate the ability to multiply and divide a number by a power of ten.
  • Recognize the place value changes when multiplying/dividing by powers of ten.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.6 Identify irrational numbers as non perfect squares (e.g. discriminate between perfect and non perfect squares).
Tags: critical thinking skills, larger, magnitude, powers of ten, scientific notation
License Type: Custom Permission Type
See Terms: https://aptv.pbslearningmedia.org/help/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
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AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource includes a teacher activity reference and student practice problem worksheet entitled "How Far is the Moon".

  This resource provided by:  
Author: Kristy Lacks
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