Scientific Notation
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Unit Objective
Convert numbers and form Scientific Notation. Solve Problems using Scientific Notation.
Background and Rationale
Scientific notation is a way to assess the order of magnitude and to visually decrease the zeros that the student sees. It also may assist students with comparing very large (or very small numbers). Most students have little intuition about scientific notation. Teaching them to recognize that scientific notation is a short hand way to better understand big and small numbers can be useful to them in all aspects of their academic career.
Place value will be reviewed prior to implementation of this lesson. Vocabulary will be pre-taught and reviewed. Students in this class have extreme difficulty with simple commutations, terminology and mathematical reasoning. This lesson may take three plus days depending on how students are grasping scientific notation.
In my past experiences teaching scientific notation I have found that students often move the decimal in the wrong direction when dealing with positive and negative powers. Also, students forget to the move the decimal past the first non-zero digit (or count it) for very small numbers. Accordingly, I will emphasize the importance of these steps throughout the lesson. This lesson will build the foundation for upcoming lessons in which students will multiply and divide numbers in scientific notation.
This lesson will be differentiated based on the varying learning needs in the class. Students will be provided with visuals for ESL learners and simplified terminology. The Think-Pair-Share activity will include problem solving and matching activity. Students’ notes will be simplified with explicit rules and skeletal notes to assist in organization and understanding. Power point presentation (visible notes and pictures); Worksheet (homework and practice); Questions, cues (elicit information, draw in student attention) ; Note taking skills and instruction; and Technology to create a Glogster to reinforce understanding of the Scientific Method. Students with IEPS modifications and adaptations will be met based on preferential seating, extended time, repeated directions, modified homework and prompting strategies. Higher-level students will be given challenge problems based on how they grasp the information.
Lesson Objectives
Objective |
Bloom’s Verb |
---|---|
Convert numbers from scientific notation to standard form with 90% accuracy. | Convert |
Use the internet resources independently to find three (3) facts which must have a number of 1,000 or greater associated with them; and Two (2) facts must have a number less than 1 associated with it. Students will convert number facts it into Scientific notation with 85% accuracy. | Use |
Compile data and create a scientific notation presentation using Glogster with 100% accuracy. | Compile, Create |
Self-assess scientific notation Glogster using a rubric with 100% accuracy. | Assess |
Bloom’s Taxonomy
Creating (highest level)
Common Core / State and District Standards
- Cluster: 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.
- Mathematical Shifts: Focus, Coherence, and Application.
- 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.
- 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 (ex. Use millimeters per year for seafloor spreading).
- The Common Core Standards for Mathematical Practices MP4: Model with mathematics: MP6: Attend to precision. MP7; Look for and make use of structure; MP8: Look for and express regularity in repeated reasoning.
Technology Integration (ISTE) Standards
- 1.a. Apply existing knowledge to generate new ideas, products, or processes
- 4.c. Collect and analyze data to identify solutions and/or make informed decisionsUse various types of reasoning (inductive, deductive, etc. as appropriate to the situation (Reason Effectively)
- Utilize multiple media and technologies and know how to judge their effectiveness a priori as well as assess their impact
- Incorporate feedback effectively (Flexibility and Adaptability)
- Utilize time and manage workload efficiently (Initiative and Self-Direction)
- Monitor, define, prioritize and complete tasks without direct oversight (Initiative and Self-Direction)
- Conduct themselves in a respectable professional manner (Social and Cross-Cultural Skills)
- Prioritize, plan and manage work to achieve the intended result (Productivity and Accountability)
- Access information efficiently (time) and effectively (sources) (Access and Evaluate Information)
- Use information accurately and creatively for the issue or problem at hand (Use and Manage Information)
Lesson – Introduction
Students will view a short rap video clip to gain background knowledge about scientific notation. A class discussion will take place about where, when and why Scientific Notation is implemented and applied in real-world settings/examples.
[iframe src=”https://www.youtube.com/embed/HtXTKrigYqk” width=”100%” height=”500″]
Lesson Activities and Procedures
This lesson will be taught through explicit instruction, Making Thinking Visible, Think-Pair -Share and differentiation. The lesson will focus on directing student attention towards writing scientific and standard notation. Explicit instruction begins with setting the stage for learning; followed by a clear explanation of what to do (telling); followed by modeling of the process (showing/ Teacher Think Aloud); followed by multiple opportunities for practice (guiding); until independence is attained. Explicit instruction moves systematically from extensive teacher input and initially reduced student responsibility to total student responsibility and minimal teacher involvement at the conclusion of the learning cycle.
Student Procedure |
Teacher Procedure |
Materials |
---|---|---|
Warm-Up Discussion: After students have had time to use short-hand/text-lingo to shorten the text message, discuss why we shorten words, phrases, and names (Example: We don’t say American Football League- we say the “AFC”). | Tell students that mathematicians and scientists have thought this way long before texting came to be. Sometimes numbers are too long (large or small) to say and/or write. We have developed ways to efficiently write very large or very small numbers.Give students real-life examples of numbers. The age of the Earth is about 4,540,000,000 years old The mass of a helium atom is 0.000000000000000000000007 grams. The distance from the sun to the earth is 149, 597, 870.7 kilometers (92,955,887.6 miles.) | |
Think Pair Share: Students will work out scientific notation problems through a matching activity. They will then discuss answers with a partner and share out. Matching Exercise (5 min) | One teacher has primary instructional responsibility while the other assists students’ with their work, monitors behaviors, scaffold, uses prompts and corrects assignments. Teacher 2 will assist students throughout the lesson while I teach. Teachers will work with small groups of students. These particular students struggle in mathematical computations, reasoning and problem solving skills. We will scaffold, prompt and use guided questioning strategies to increase student’s understanding scientific notation.Modeling: {I do; We do; You do} Direct instruction on writing numbers in scientific notation (See Flip Chart.) Teacher 1 will model how to set up a problem, the rules, and solve Teacher1 will do a Think Aloud so students can visually see and hear thinking. (10 min) | flip chart, student notes sheet |
Independent Practice: Once students are confident with the process they will work on the problems independently. (10-15 min) |
Lesson – Closure
To end the class, Teacher 2 will briefly go over the main points of the lesson and explain homework expectations. Standard vs. scientific notation moving decimals points’ form right to left etc.
Exit Card: Students will all be required to solve standard notation and 1 scientific notation problems. They can also ask any questions they have about scientific notation to be addressed in the proceeding lesson. (5 Mins)
Student Work Example
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Heidi Gruber