Lesson 3: Scientific Notation
Duration of Days: 2
Lesson Objective
Students will be able to express, interpret, and manipulate very large and very small numbers using scientific notation, apply it to real scientific data, and use it to compare scales, perform calculations, and analyze patterns in scientific measurements.
-Why do scientists use scientific notation to represent extremely large and small numbers?
-How does scientific notation make data easier to compare and interpret?
-How do powers of ten represent scale in scientific measurements?
-How can scientific notation be used to perform calculations with real scientific data?
-How does scale affect our understanding of natural phenomena in science?
Scientific notation
Base
Exponent
Power of ten
Standard form
Coefficient
Order of magnitude
Scale
Conversion
Magnitude
HS-PS3-1 – Use quantitative reasoning to analyze data in systems
HS-ETS1-1 – Use mathematical representations to analyze and solve problems
NGSS Crosscutting Concepts
-Scale, Proportion, and Quantity
-Patterns
Students will interpret scientific notation in quantitative reasoning problems.
Students will compare values expressed in different formats and convert between standard and scientific notation.
Students will apply order-of-magnitude reasoning in multi-step data analysis questions.
Students will work with real scientific data involving extremely large (astronomical distances) and extremely small (atomic-scale) values. They will convert between standard form and scientific notation, perform calculations using powers of ten, and interpret how scale impacts scientific understanding.
Students will also analyze how scientific notation allows scientists to communicate efficiently across disciplines such as astronomy, chemistry, and physics.
DOK Level: 3 (Strategic Quantitative Reasoning and Application)
Scientific notation is essential in fields such as astronomy (distances between stars), medicine (cell sizes and dosages), engineering, and computing.
Students will explore how scale differences affect interpretation of data in real-world scientific research and technology development.
Students may think scientific notation changes the value of a number rather than representing it differently.
Students may confuse positive and negative exponents.
Students may struggle to interpret scale differences between very large and very small numbers.
Students may incorrectly apply rules of exponents in calculations.
-Scaffolded practice converting between standard form and scientific notation
-Visual number line models showing powers of ten
-Step-by-step exponent operation guides
-Real-world data sets at varying complexity levels
-Partner problem-solving for multi-step calculations
-Technology-based practice with interactive number scaling tools
-Quiz on conversion between scientific notation and standard form
-Multi-step calculation problems using scientific notation
-Data interpretation task using astronomical or microscopic scale values
-CER explanation of why scientific notation is necessary in science
-Formative checks during practice with exponent operations
Scientific notation reference sheets
Calculator tools (for exponent operations where appropriate)
Real-world data sets (astronomy, microbiology, physics scales)
Number line and scale visualization tools
Practice worksheets with increasing complexity