We'll begin with the essential question: How can we use inverse operations to solve one-step equations? We have already solved addition and subtraction equations using models and inverse operations. This lesson includes addition and subtraction equations and multiplication and division equations.
This lesson will be treated as a direct instruction lesson, though I may have students guide me through the first four problems since we have already solved these types. Students should now be able to apply MP8 to equations through the previous work with models.
Each example has a check for understanding problem. They may also serve as an additional example, if students do not understand the first example.
On example 3, it will be important for students to realize that x/4 "x over 4" is a division equation. Therefore we use multiplication. When multiplying both sides by 4, I will tell students that they may want to write 4 as 4/1 and place any other integer values over 1. Using example 3, they would have 4/1 and -32/1. I think this at least helps students see the "canceling" affect on the variable side of the equation.
Now students work with partners on the first 8 problems. The last two problems haven't been addressed formally: they have fractional coefficients. I have included them to see if students can apply the same reasoning to solve these problems: either divide by the coefficient or multiply by the reciprocal. From past experience, I know that equations with fraction coefficients can warrant an exclusive lesson. Therefore, my focus will be on the first 6 problems.
Students should be warned to make sure they use the correct signs in their solutions. I notice students can be especially lax on this when solving multiplication and division equations. Some students may still be confusing signs of rational products and quotients, but others just may think it is not necessary to show the correct sign.
Students will now work independently and silently. The first 8 problems mirror the guided problem solving problems. Students should be able to refer to the GPS problems if they are stuck. The last 5 problems require students to translate verbal statements into equations and then solve.
Before students take the exit ticket, I will ask them to summarize how to solve the one-step equations seen today. After a quick discussion, students will take the exit ticket. To show success, I will tell students they need to at least answer 4 problems correctly.