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# Determine the Distance Between Two Rational Numbers on a Number Line

Lesson 5 of 12

## Objective: SWBAT determine 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 determine the distance between two rational numbers on a number line.

*50 minutes*

This lesson will draw upon prior knowledge for students to determine the distance between two rational numbers. 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. This lesson is intended for students to show their understanding of basic examples of rational numbers on a number line to solving real world problems involving determining distance between two rational numbers. This will come up in the next lesson. I would suggest teaching these two lessons consecutively back to back.

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#### Bell Ringer

*15 min*

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. 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 rational numbers to find the distance between them.

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#### Student Activity

*15 min*

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 in the next section to get a better understanding of these examples.

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#### Whole Group Discussion

*15 min*

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.

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#### Closing

*5 min*

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.

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- UNIT 1: Introduction to Mathematical Investigations
- UNIT 2: Integers
- UNIT 3: Proportional Reasoning with Percents
- UNIT 4: Proportional Relationships
- UNIT 5: Proportional Reasoning
- UNIT 6: Rational Numbers
- UNIT 7: Number Sense Vocabulary 5 day mini unit
- UNIT 8: Expressions and Equations
- UNIT 9: Expressions and Equations 5 Day Application of Vocabulary Mini Unit

- LESSON 1: Pre-Assessment Adding and Subtracting Signed Rational Numbers
- LESSON 2: Post Assessment Adding and Subtracting Rational Numbers
- LESSON 3: Determining situations in which opposite quantities make A FUN LESSON!
- LESSON 4: Now let's Demonstrate! Can I prove mastery of additive inverse on a number line?
- LESSON 5: Determine the Distance Between Two Rational Numbers on a Number Line
- LESSON 6: Now Let's Apply the Knowledge Gained! Determining the distance between two rational numbers on a number line.
- LESSON 7: Am I Terminating or Repeating?
- LESSON 8: A Concrete Look at Long Division!
- LESSON 9: Does McDonald's Serve Burgers? Long Division Algorithm Day 2
- LESSON 10: The World Of Inverse Operations!
- LESSON 11: Pre-Assessment Multiplying and Dividing Rational Numbers
- LESSON 12: Post Assessment Multiplying and Dividing Rational Numbers