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Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.
Sarah can use the expression 5(2j + 3 + j) to represent the amount of money she can earn.
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Part 1: Writing Expressions
Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.
Translate the algebraic expression you created in Question 1 to a verbal expression.
Part 2: Writing Equivalent Expressions
Use your knowledge of the mathematical properties to create two equivalent algebraic expressions for the algebraic expression you created in Question 1. Explain how you arrived at the equivalent expressions by showing all your steps and stating which properties you used.
Use substitution to prove your algebraic expressions are equivalent. You may substitute any number for the variables you choose. Show all your work for complete credit.
Part 3: Finish the Story
Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did Sarah earn?
Choose a method to present your assignment. You may submit your work in a Word Document or you may choose to develop a PowerPoint presentation or video recording of yourself. Use your creativity! Make sure to include the information from all three parts in your Word Document or presentation.