# Operations with Rational Numbers

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## Objective

SWBAT use order of operations to simplify numerical expressions with rational numbers.

#### Big Idea

Students formalize their understanding of order of operations and apply this understanding to develop their skill at rewriting numerical expressions in simpler form

## Launch

10 minutes

The learning objective for this lesson is that students are able to apply the order of operations to determine the answer to problems. The learning objective will be on the board when students enter the room. As I review the plan for the day with the class, I will discuss the objective.

To assess my students’ prior knowledge, I will give this problem as the Problem of the Day:

Mr. Thomas wrote the expression 5(x +1/3) on the board, he asked his class to write the expression in another form. Mr. Thomas sent Tonya and Eric to the board to write their answers. Tonya wrote 5x +1 2/3  and Eric wrote 5x +1/3 . Which student had the correct answer? Explain your thinking.

After giving them a few minutes to work on the problem, we will discuss their responses and I will ask students to volunteer to demonstrate how to solve the problem at the board.  If a student doesn't agree they can explain their reasoing and we will have a discussion on who is correct (MP3).

## Explore

20 minutes

To begin this section of the lesson, students will take notes from the board as part of the classroom discussion on applying properties of operations. We will start with listing the order of operations as a chart with headers, and inserting symbols and examples into the chart for students to use as a reference. We will include words like plus, add, and times in the chart. I also want to include phrases my students use like "subtracted from" in the chart. This phrase is consistently used but there is no consistency in its use. Does 7-3 mean 3 subtracted from 7 or 7 subtracted from 3? Depending on which students I ask, I will usually hear that it means both. Including this phrase in the table ensures that it will be part of the discussion and we can decide on the terminology we will use to express what students want to say. I also want to reinforce the ideas of the order to multiply and divide as well as the order in which to add and subtract. We will complete the problems on the Operations sheet as a whole class. Students can come up and demonstrate how to solve a problem or I can solve the problem under the document camera using student input to provide my steps toward the solution. Usually, students will do all of the multiplication in order from left to right then the division. The distinction that they need to perform the multiplication and division in order from left to right is not always clear. To stress this point, there will be examples while we work on the concept in class.

After the class notes and the Operations with Rational Numbers sheet are finished, students will individually create two problems that are solved with at least one step in the process done out of order to share with the class.  I will ask for volunteers to display their problems under the document camera and we will analyze the steps included and make a judgment on the error.

## Summary

3 minutes

To end the class, students will put operation signs into the problem to get the answer given.

32  4  8  2  3  5  = 128.5