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# Adding and Subtracting Positive and Negative Decimals on a Numberline

Lesson 17 of 27

## Objective: SWBAT add and subtract signed decimals using a number line

#### Introduction

*10 min*

In this part of the lesson I will ask students the essential question: How does adding and subtracting positive and negative decimals compare with adding and subtracting integers? We will explore this more in the problem solving section of the lesson. After posing the question, we will then review how to add and subtract values on a number line. Students will be given the pointers that we used with adding and subtracting integers. Using a number line and pointers is **MP5**.

A number line divided into tenths has been provided. Before we begin moving around on the number line, I will ask students some prerequisite questions about tenths. For example: How many tenths equals 1 whole? Or moving 2 whole is the same as moving how many tenths? I will also give a value like 2.7 and say what is 1,2, or 3 whole steps greater? This should make it easier for students to move 3.8 steps as they will not have to count 38 individual tenths.

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#### Problem Solving

*15 min*

In this section we will quickly review some of the essential questions that we explored with integers. The point here is to lead students to seeing that all rational numbers behave in the same manner. As students answer these questions they are engaging with **MP3 **and **MP7**.

For each of the 6 questions, I will most likely have the students go through each question in a series of **turn-and-talks**. Students should be prepared to provide an example as evidence to support their claim. As students share out or listen to others, they are practicing **MP3**. I say most likely because sometimes, based on the energy of the class, I may find it better to have them work through the questions silently first. I prefer doing turn-and-talks because they help me keep the pace of the class moving.

Finally students solve 10 addition and subtraction problems. They match these problems to the conclusions made at the beginning of this lesson section.

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The first 6 problems in independent practice are designed to see if students can reason about the quantities (**MP2**).

Problems 7-14 are straight ahead addition and subtraction problems. Students may use the given number line and pointers to solve. I hope that many students, especially those who have mastered adding and subtracting integers, go straight to their most efficient procedure.

Problem 15 presents an addition problem and 3 common errors and one correct answer. Students are challenged with the task of figuring out and explaining what mistakes were made by the students in the problem (**MP3**).

The extension has one-step addition and subtraction equations for the students to solve in any manner they find workable.

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#### Exit Ticket

*5 min*

The first problem asks students to create the sum of -1.7 using a positive and a negative number. A number line has been provided on the exit ticket. I will read the question out loud and make sure students know they are to use a positive and a negative integer.

Problem 2 requires a difference of 2.4 using two negative numbers.

Problem 3 requires the additive inverse.

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- LESSON 1: Fractions as Quotients - Using Long Division to Convert a Fraction to a Decimal
- LESSON 2: Finding the Distance Between Integers On a Number Line
- LESSON 3: Where Do We Go From Here? Adding Integers on the Number Line
- LESSON 4: What is the Sign of the Sum?
- LESSON 5: Algorithms for Adding Integers
- LESSON 6: How Addition and Subtraction are Related (Part 1 of 3)
- LESSON 7: Subtracting for More or Less. Subtracting Integers on a Number Line
- LESSON 8: How Addition and Subtraction are Related (Part 2 of 3)
- LESSON 9: How Addition and Subtraction are Related (Part 3 of 3)
- LESSON 10: Algorithms for Subtracting Integers
- LESSON 11: Assessment - Fluency and Concepts of Integer Sums and Differences
- LESSON 12: Integer Product Signs - Using Counters to Discover Signs of Products
- LESSON 13: Integer Quotients
- LESSON 14: Expand Expressions Using the Distributive Property
- LESSON 15: Integers Assessment
- LESSON 16: Finding the Distance Between Signed Decimals on a Number Line
- LESSON 17: Adding and Subtracting Positive and Negative Decimals on a Numberline
- LESSON 18: Adding and Subtracting Signed Decimals Using a Procedure
- LESSON 19: Multiplying Signed Decimals
- LESSON 20: Dividing Signed Decimals
- LESSON 21: Finding the Distance Between Signed Fractions on a Number Line
- LESSON 22: Adding and Subtracting Positive and Negative Fractions on a Numberline
- LESSON 23: Adding and Subtracting Positive and Negative Fractions Using Counters
- LESSON 24: Adding and Subtracting Signed Fractions Using a Procedure
- LESSON 25: Multiplying Signed Fractions
- LESSON 26: Dividing Signed Fractions
- LESSON 27: Rational Numbers Operations - Final Unit Assessment