# Now Let's Apply the Knowledge Gained! Determining the distance between two rational numbers on a number line.

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## Objective

SWBAT solve real world word problems that involve determining the distance between two rational numbers on a number line.

#### Big Idea

Students will tap into their prior knowledge of comparing rational numbers, conversion of rational numbers, and adding rational numbers to solve real world problems that involve determining the distance between two rational numbers on a number line.

## Teacher Guided Notes

This lesson is an extension off of what students learned from the lesson Determining The Distance Between Two Rational Numbers On A Number Line without word problems.  The first lesson focused on the process, this lesson will assess if students are able to apply the process in solving real world word problems.  The problems are rich in rigor, and will take students a step further in the objective.  Students will work with positive and negative fractions, positive and negative improper fractions, positive and negative mixed numbers, positive and negative decimals, and integers.  Students will need to have a strong understanding of comparing rational numbers, adding integers, absolute values, and conversion of rational numbers.  You may find it necessary to do a mini review on some or all of these objectives.  When students tackle any word problem, it is important to understand what the text is asking them to do.  Unpacking the problem is a crucial step in doing so.  This will allow students to identify the needed information to solve the problem accurately.  It is important for students to understand the process taught in the previous lesson in order to be successful with these word problems.

## Bell Ringer

15 minutes

As the students enter the room, hand them the bell ringer that will focus on the objective of the day.  Students will work independently for 10 minutes.  During this time students should practice MP 1, 2, 4, and 5.  Walking the room gauging student understanding will benefit the type of open ended questioning you will want to ask during the student activity.  This will also drive your whole group instruction. During the whole group discussion we will pull out the calculators as a tool to help us solve these problems. Just as in the previous lesson, I would suggest you not give the calculators to the students during this time.  Give them a chance to grapple through the problem, and see if they ask to use a calculator to help them through the problem.  This will be a great assessment of students knowing when to practice MP 5. If students ask to use the calculator, by all means give it to them.  This is a great gauge that they are attempting to add the absolute values of the rational numbers to find the distance between them.

## Student Activity

15 minutes

After students have had an opportunity to grapple through the problem on their own for 10 minutes, have them discuss their work with one another in their designated groups.  Mathematical practice 3 comes into play heavily during this time.  Students should also focus on solving the problem with their peers accurately during this time.  This places heavy emphasis on MP 6. Students will be given 15 minutes to discuss their findings together.  During this time you will want to visit each group to listen to their mathematical discussions, asked guided questions that will help them navigate through the problem, and gather data that will help you guide your whole group discussion.  With your lower level learners you may want to take this opportunity to give small group direct instruction so that they may offer rich discussion during the whole group instruction and to pin point what the scaffolding questions you need to ask during the whole group instruction.  The scaffolding questions should involve comparing rational numbers, converting rational numbers, and adding absolute values. Please see my teacher resource to get a better understanding of these examples.

## Whole Group Discussion

10 minutes

During this time, your goal is for students to share out what was discussed during the student activity.  This is the time in which all students are able to learn from one another at one time.  Students will share what process they used to solve the problem, what difficulties they are having with the problem, what successes they had while solving the problem, and which strategies were used to accomplish the task.  As you walked the room you were able to gauge what questions you will ask during this time.  Please use the Teacher Resource to help with addressing common mistakes, and your direct instruction.  During this time it is important for students to have the correct process to solve the problems, and good notes to refer back to as a reference for other problems that will be upcoming.

## Closing

10 minutes

During your closing summarize what has been learned in the lesson. Choose important points of emphasis that you will want to focus on in a 5 minute summary.