Students hone their skills of solving multi-step equations and inequalities, redefining their definition of "solution" to include results such as 4 = 5, and interpreting solutions in context.
In Unit 2, eighth-grade students hone their skills of solving equations and inequalities. They encounter complex-looking, multi-step equations, and they discover that by using properties of operations and combining like terms, these equations boil down to simple one- and two-step equations. Students also discover that there are many different ways to approach solving a multi-step equation, and they spend time closely looking at their own work and the work of their peers. When solving an equation with variables on both sides of the equal sign, students are challenged with results such as 4=5, and they refine their definition of “solution” to include such examples. Throughout this unit, students use equations as models to capture real-world applications. They reason abstractly and quantitatively as they de-contextualize situations to represent them with symbols and then re-contextualize the numbers to make sense in context (MP.2).
In sixth grade, students developed the conceptual understanding of how the components of expressions and equations work. They learned how the distributive property can create equivalent forms of an expression and how combining like terms can turn an expression with three terms into an expression with one term. By the end of seventh grade, students fluently solved one- and two-step equations with rational numbers and used equations and inequalities to represent and solve word problems.
Students’ ability to manipulate and transform equations will be required again in Unit 5: Linear Relationships and Unit 6: Systems of Linear Equations. Furthermore, these skills will be needed throughout high school as students are introduced to new types of equations involving radicals, exponents, multiple variables, and more.
Pacing: 16 instructional days (12 lessons, 3 flex days, 1 assessment day)
This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
combine like terms
distribute a negative
properties of operations
Write equivalent expressions using properties of operations and verify equivalence using substitution.
Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.
Justify each step in solving a multi-step equation with variables on one side of the equation.
Write and solve multi-step equations to represent situations, with variables on one side of the equation.
Model with equations using a three-act task.
Solve equations with variables on both sides of the equal sign.
Write and solve multi-step equations to represent situations, including variables on both sides of the equation.
Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.
Solve and reason with equations with three types of solutions.
Use equations to model a business plan and determine the break-even point.
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