This lesson begins with the essential question: How can we use inverse operations to solve addition and subtraction equations. This builds on the work from the previous day - Solve Addition and Subtraction Equations using Models. So I will show a model for each of the examples. I will ask students how we solve this example. They should know from the previous lesson that I will need to add +7 to both sides in order to isolate the variable.
Some students may like to have whiteboards to draw the models while solving the problems today. I will allow this, but I want students to begin relying less on the model - especially on paper. The models are convenient for relatively low magnitude integers, but don't work quite as well with other rational numbers. I think it is important that students begin to solve these equations in the more abstract manner. This would be an application of MP8.
The first 3 guided problem solving problems are similar to the examples. I will give the students about 2 minutes to solve these first 3 problems. I will walk around doing check for understandings here. Some common errors to look out for are students not using the inverse operation to solve. Another error to look out for are students who choose the "wrong" value to undo first. Using GP1 as an example, some students may try to add 4 or subtract -4 from both sides as opposed to removing the 7. Problem GP4 and GP5 can be solved in two ways. Some students may find it easier to use the additive inverse; others may choose to subtract away the negative. I will make sure to bring these two methods to the attention of students as we review the problems. The last two problems involve non-integer rational numbers. The problems today emphasize integers, but I have included a few "simple" non-integer equations as well.
Students will work on the independent section alone. Students will be reminded to refer to their examples and GPS problems when stuck. I will not be answering questions on the first set of problems. I will gently tell students taht we will go over problems in a few minutes. That being said, I may have identified students who still need lots of support. They may not be ready to be successful with independent practice problems. I (or possibly a T.A.) will work with these individuals on additional problems similar to those in the GPS section before having them work independently.
In this section, there are 13 problems. The first 8 are most critical to this lesson, but I do want students to solve problem 9-13. These are problems where students must translate verbal descriptions into equations and then solve.
Before beginning the exit ticket, I will call on students to summarize how to solve addition and subtraction equations. I may cold call students or give them a chance to turn-and-talk before sharing out.
Students then have 5 problems to solve. Each problem is similar to the types of problems seen before.
Students will know they are successful if they are able to answer at least 4 problems correctly.