Operations With Scientific Notation Introduction
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This learning activity provided by:
Author:
YVETTE AKRIDGE
System: Andalusia City School: Andalusia City Board Of Education
General Activity Information
Activity ID:
2878
Title: Operations With Scientific Notation Introduction
Digital Tool/Resource: Operations with Scientific Notation Online Math Learning
Web Address – URL:
Overview: In this learning activity, a teaching video will help students learn how to perform operations with numbers expressed in scientific notation, including problems with both decimal and scientific notation. The students will 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). Finally, they will interpret scientific notation that has been generated by technology.
This learning activity can be used as a stand-alone activity or a Before Activity. The During and After activities can be found in the Notes or Recommendations section.
Associated Standards and Objectives
Content Standard(s):
Mathematics 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 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:
Learning Objectives: Learning Targets:
I can perform operations using numbers expressed in scientific notations.
I can use scientific notation to express very large and very small quantities.
I can choose appropriate units of measure when using scientific notation.
Strategies, Preparations and Variations
Phase: Before/Engage
Activity: Procedure
1. Introduction (5 minutes, whole group)
The teacher will say, "Many mathematicians, statisticians, and other professionals who regularly work with large numbers use scientific notation to break down the numbers into more manageable amounts and for easier calculation. Scientific notification allows individuals to more easily understand the number and simplify arithmetic operations. We will explore the definition of scientific notation, why it's important, how it works, and the different ways you can write in scientific notation."
2. Watching the video (10 minutes, whole group) :
The teacher will define scientific notation as a way to express numbers that are too big or little to write in basic decimal form. Scientific notation is also referred to as standard form, scientific form, or standard index form in some settings. Most frequently used by scientists, mathematicians, and engineers, scientific notation allows professionals and others to write very long numbers in a much easier-to-understand manner. When using a scientific calculator, the scientific notation can be implemented by selecting the "SCI" display mode.
The teacher will use Using Scientific Notation video as a teaching tool.
Students will observe, take notes, use their math journals or paper, and ask questions.
3. Conclusion (10 minutes, whole group)
The teacher will review the lesson content embedded in the Using Scientific Notation video , using the Operations with Scientific Notation Introduction Practice , and answer any further questions the students may have concerning performing operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
Assessment Strategies: The student responses during the class discussion will be used as a formative assessment.
Advanced Preparation:
Variation Tips (optional):
The teacher can assign the example problems through a digital platform and have the students work on the problems first before the whole group learns together.
The teacher can have the students write their notes on plain notebook paper instead of in math journals.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
decimal, divide, multiply, operations, scientific notation
