This is an Internet lesson that I developed for an Algebra 1 class. It shows the students how to use a spreadsheet, requires critical thinking, developing a formula for the function, and explains proof by contradiction.
It addresses CA Common Core Standards for Algebra 1:
A.A.CED.11 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems in and out of context, including equations arising from linear functions.
A.A.CED.12 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales (limit to linear and quadratic).(Common Core Standard A-CED-2)
A.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
A.F.BF.10. Write a function that describes a relationship between two quantities.
(Common Core Standard F-BF-1)
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(Common Core Standard F-BF-1a)
A.CVA.1 Use and know simple aspects of a logical argument.
(California Algebra I, Standard 24.0)
a. Use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.
(California Algebra I, Standard 24.3)
A.CVA.2. Use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:
(California Algebra I, Standard 25.0)
a. Use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.
(California Algebra I, Standard 25.1)
This lesson could be adapted to use calculators instead of a spreadsheet. If this was done, it would address CA Common Core Standard for Algebra 1: A.EE.2 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.