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Big Ideas:
Algebraic solutions are a generalized form of arithmetic solutions.
Solving complex equations algebraically is more efficient than solving arithmetically.
Fluency in solving equations in the form px + q = r and p(x+q) = r is achieved through examining scenarios that afford practice with positive, negative and rational numbers.
This lesson builds on students' prior work in solving equations and using inverse operations to solve for equations in the forms px+q=r and p(x+q)=r. In this lesson, students write and solve equations as they work to piece together word problems that have been 'shredded' by a malfunctioning copy machine. Students will use the solutions to the equations as well as cues from the wording of the verbal problems to construct the equations. Students will discover that it is more efficient to solve equations algebraically when rational and negative numbers are involved. The task supports and extends students’ understanding of the 7.EE.B.4a standards by engaging them in the essentials of writing and solving equations that include rational and negative numbers and asks them to compare an arithmetic solution to the algebraic solution. The mathematical concepts in this lesson build towards students' fluency in solving equations and their future work with solving inequalities in 7th grade and linear equations in 8th grade.
Vocabulary: algebraic solution, arithmetic solution
Special Materials:
Supplementary handout