Solve Two-Step Equations Using Inverse Operations

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SWBAT solve two-step equations using inverse operations

Big Idea

Some equations can be solved through models or mental math. All equations can be solved by using inverse operations.


10 minutes

I'll begin with the essential question:  How can we use inverse operations to solve an equation?  I will ask students to discuss in a turn-and-talk the order of inverse operations.  We learned this in the previous lesson.  We will then fill this in on the first page of the resource.

I will then do the examples.  Here is where students will see a method of showing work that is pretty common when first solving two-step equations - the operations will be written in below.  As needed, I may have some diagrams ready - or let students diagram on whiteboards - to help.  That being said, I want students to understand how to show the steps in an equations without drawing in a diagram.

When writing in the steps, make sure that students are writing the correct operation symbol and value.  Students often get confused by the division step especially.  I will constantly ask them about what the fraction bar means when undoing multiplication.  

The two examples at the bottom of the page might be skipped.  I think that these equations sometimes deserve a lesson to themselves.  I have included them here in case the students are showing ease with the first examples.

Guided Problem Solving

15 minutes

I will ask students to work on GP1, GP2, GP5, and GP6 first.  They may work with their partners.  I will be walking the room to observe their progress.  

Common Errors - I expect some students to use the "wrong" value when solving equations.  On GP1, they may try to subtract -3 or add 3 instead of subtract 12.  I expect some students to use the wrong operation too.  Instead of dividing by 3, they may multiply by 3.

Again GP3 and GP4 might not be addressed.  They may be worth discussing by paying attention to the structure (MP7).  6(x+2) = -42 can be seen as the product of 6 and a sum equals -42.  Students can then discuss what can 6 be multiplied by to get -42.  I'll need to make sure students understand that x is not -7 but x + 2 must be -7 so x must equal -9.

Independent Problem Solving

20 minutes

Now it is time for students to work independently.  The first 9 problems are similar to what students have seen, although fractions or decimals are included on problem 7-9.  Problems 10-12 are included to encourage students to simplify expression with like terms.  While that is not the only way to solve these problems, it is probably the most effective.  

Problem 13 will require students to apply everything they've learned about algebra so far.  Students will likely be confused by seeing three variables.  I may give some hints here like:  1) How could we solve the given equation to isolate y? to isolate x?  Are the equations in ii and iii equivalent?


Exit Ticket

5 minutes

Before beginning the exit ticket, I will ask students to discuss the order of inverse operations.  The conclusion should be to first undo addition and subtraction, then multiplication and division.  There are 5 problems on the exit ticket.  4 out of 5 will be a successful exit ticket.