Secondary
Teacher Name / Date(s):
Lesson Title / Scientific Notation (using real world problems and technology)
Curriculum Area / Equations and Expression
Grade Level / 8th
School-based Initiatives / AVID______WICR______Schoolnet____X______ClassScape______
Curriculum Standard(s) / 8.EE. 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.
Technology Objective(s):
from Common Core & Essential Standards / 8.TT.1 Use technology and other resources for assigned tasks.
Essential Question(s):
What question should students be able to answer at the end of the lesson? / What type of numbers use scientific notation?
How do I interpret scientific notation that has been generated by technology?
How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?
Learning Target(s): The What-What students should know and be able to do. Students should to be able to articulate the learning target for and for others. / Students understand scientific notation as generated on various calculators or other technology. Students
enter scientific notation using E or EE (scientific notation), * (multiplication), and ^ (exponent) symbols.
Example 1:
2.45E+23 is 2.45 x 1023 and 3.5E-4 is 3.5 x 10-4 (NOTE: There are other notations for scientific notation depending
on the calculator being used.)
Students add and subtract with scientific notation.
Example 2:
In July 2010 there were approximately 500 million facebook users. In July 2011 there were approximately 750
million facebook users. How many more users were there in 2011. Write your answer in scientific notation.
Solution: Subtract the two numbers: 750,000,000 - 500,000,000 = 250,000,000 2.5 x 108
Students use laws of exponents to multiply or divide numbers written in scientific notation, writing the product or
quotient in proper scientific notation.
Example 3:
(6.45 x 1011)(3.2 x 104) = (6.45 x 3.2)(1011 x 104) Rearrange factors
= 20.64 x 1015 Add exponents when multiplying powers of 10
= 2.064 x 1016 Write in scientific notation
Example 4:
3.45 x 105 6.3 105 – (-2) Subtract exponents when dividing powers of 10
6.7 x 10-2 1.6
= 0.515 x 107 Write in scientific notation
= 5.15 x 106
Example 5:
(0.0025)(5.2 x 104) = (2.5 x 10-3)(5.2 x 105) Write factors in scientific notation
= (2.5 x 5.2)(10-3 x 105) Rearrange factors
= 13 x 10 2 Add exponents when multiplying powers of 10
= 1.3 x 103 Write in scientific notation
Higher Order Thinking (Revised Bloom’s & DOK) Connection/Extension / Music project (technology) http://showyourthinkingmath.blogspot.com/2013/11/made-4-math-monday-scientific-notation.html
Lesson Summary: Describe the strategies and the activities you will use to teach new information to students. / Complete 90 minute lesson at http://dnet01.ode.state.oh.us/ims.itemdetails/lessondetail.aspx?id=0907f84c805326da
Academic/Content Vocabulary / · base
· coefficient
· factor
· mantissa
· power
· scientific notation
Multiple Intelligence Alignment
· Verbal/Linguistic
· Musical/Rhythmic
· Visual/Spatial
· Bodily/Kinesthetic
· Intrapersonal
· Interpersonal
· Naturalist
· Existential
Circle multiple intelligence incorporated in lesson plan / · Musical/Rhythmic – music project
· Visual/Spatial –
· Bodily/Kinesthetic –
· Intrapersonal –
· Interpersonal-
Differentiation: How will you differentiate instruction to meet the needs of all students? / · This standard can be differentiated for students that are challenged by the content and those that experience success immediately by the size of numbers used and by the number of problems learners complete.
· Students that experience success early in the lesson can evaluate when scientific notation would be useful and when it would not make sense to use. Once this evaluation occurs, students research specific examples such as space explorations, exponential growth or decay to back up their evaluations.
· Students experiencing difficulties with concepts can be presented with adjusted assignments to meet their needs. Adaptations for this lesson could include a partially-completed Power of
10 table or a newspaper article with a minimal selection of numbers to be converted into scientific notation.
· Cooperative learning strategies make all students accountable and provide auditory and kinesthetic learners ways to access the content.
· Present students needing intense intervention models of numbers using base-ten blocks or visual representations of base-ten blocks. Begin by having students represent whole numbers
with the models or visual representations. Relate the size of the blocks to the exponent: a cube (1 unit), representing the zero power, a rod (10units), representing the first power, a flat (100 units), representing the second power and a large cube (1000 units), representing the third power. Scaffold understanding by having them represent numbers in scientific notation. Continue the use of models and representations with all students as the lessons progress. Although the blocks have limitations, they provide access to understanding the basis of the concept for a variety of learners.
· Provide additional computational problems for students in need of assistance.
Closure: What type of formative assessment will be used to determine level of mastery by all students? / Have each student write as a Mathematics Exit Ticket or a journal entry a step-by-step outline or flow chart demonstrating how to compare numbers written in scientific notation.
Complete the post assessment activity, Writing and Comparing Numbers in Scientific Notation – Post-Assessment, Attachment D. See the answer key and the scoring guidelines on Attachment E.
Lesson Reflection: What went well?
What would you do differently?
Resources and Materials
What resources and materials are needed to teach this lesson? / Computer
1-1 computer/laptop/tablet
headphones
Projector
SchoolNet assessment
PowerPoint
Re-teaching and Enrichment Activities
How would you extend students’ understanding of the lesson concepts through another activity or lesson? / Students create a model of the solar system. Distances from each planet to the sun and the circumference of the sun could be researched. Students could then scale those measurements and physically build the solar system with appropriate proportions. Students can also research why there is a problem with using Pluto in this model.
· Students research both the national debt and world population. Students examine the growth of each and display their conclusions graphically which could lead into a discussion about exponential growth.
Modifications
Are there any students for whom you need to make modifications? / Modify the number of assessment questions the students in the lesson, modification of the number of answer choices,
Adapted from North Carolina Teacher Academy