## Objective

Order integers and rational numbers. Explain reasoning behind order using a number line.

## Common Core Standards

### Core Standards

The core standards covered in this lesson

6.NS.C.6.C— Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

### The Number System

6.NS.C.6.C— Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.C.7.A— Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

*For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.*### The Number System

6.NS.C.7.A— Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

*For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.*

## Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

- Know that if a number $$a$$is to the right of number $$b$$, then $$a$$will always be bigger than $$b$$; if a number$$b$$is to the left of number $$a$$, then $$b$$will always be smaller than $$a$$.
- Understand that opposites of numbers have opposite orders of the original numbers; if a positive number $$a$$is less than a positive number $$b$$, then the opposites of $$a$$and $$b$$have the opposite order, or $$-a$$is greater than $$-b$$(e.g., $$3$$is less than $$5$$, but$$-3$$is greater than $$-5$$).
- Order rational numbers from least to greatest or greatest to least.

## Tips for Teachers

Suggestions for teachers to help them teach this lesson

- Lesson 6 and Lesson 7 are related; In Lesson 6, students determine the order for rational numbers when given a set of numbers and explain their thinking using a number line. In Lesson 7, students extend this understanding to compare rational numbers and interpret their order as it relates to real-world situations.
- Encourage students to use or draw a number line when one is not provided in the problem (see lesson notes for Lesson 1). This will continue to be a great tool for students to work precisely and accurately and avoiding common misconceptions.

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## Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

### Problem 1

Consider the set of numbers $$6$$, $${4 \frac{1}{2}}$$, $$2$$, and $$5$$, and answer the questions that follow.

a.Graph the numbers on the number line and list the numbers in order from least to greatest.

b.Write the opposites of each number and graph them on the number line.

c.Order the opposites from least to greatest.

d.Is −5 greater than −2? Explain using your number line.

#### Guiding Questions

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### Problem 2

Order therational numbers below from least to greatest.

$${5, -4, -\frac{1}{3}, \frac{10}{3}, 3, 0, -4\frac{1}{4}, -4\frac{3}{4}}$$

What strategies didyou use to determine the correct order?

#### Guiding Questions

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### Problem 3

A student orders three rational numbers from least to greatest as: $${{{{{{{{{-5}}}}}}}}}$$, $${{{{{{{{{-5}}}}}}}}} \frac {1}{3}$$,$$6$$

Are the numbers ordered correctly? Choose the best statement below.

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#### Guiding Questions

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## Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

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## Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Tram knows that $$1\frac{1}{6}$$ is less than $$1\frac{2}{3}$$. He wonders if this means that $$-1\frac{1}{6}$$ is also less than $$-1\frac{2}{3}$$.

Help Tram determine and understand the correct order of $$-1\frac{1}{6}$$ and $$-1\frac{2}{3}$$, from least to greatest.

### Student Response

An example response to the Target Task at the level of detail expected of the students.

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## Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

- Multiple-choice questions where students select the correct order of a set of numbers
- Multiple-choice questions where students select true statements about a set of numbers, similar to Anchor Problem 3

- EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic B > Lesson 8—Problem Set
- Open Up Resources
*Grade 6 Unit 7 Practice Problems*—Lesson 4, Problems 1-3 - EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic B > Lesson 7—Problem Set

Lesson 5

Lesson 7