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Big Ideas:
Solving an equation is a process of mathematical reasoning whose goal is to find the value which makes an equation true.
The equation in the form p(x +q)=r is a form of the equation where p and (x + q) are two factors of r.
This lesson builds on students' prior work in solving equations; using inverse operations to solve for the value of the variable in 6.EE.B.7. In this lesson, students continue to write and solve equations as they model real world scenarios. Students will write and solve multi-step equations in the form p(x + q) = r. This form of an equation is open to two solution methods; with the use of the distributive property and without the use of the distributive property. Students will quickly discover that it is quite efficient to solve this form of the equation without distributing at all. The fitness studio scenario provides the context through which students will write the equations in the form p(x+q) = r to solve for the missing prices for the various fitness classes. Students will also be asked to model their thinking in tape diagrams. 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. The mathematical concepts in this lesson build towards students future work in writing and solving equations and inequalities fluently in grade 7 and in grade 8 linear equations.
Vocabulary: distributive property, inverse operations
Special Materials:
Calculators optional