Lesson 17

Adding and Subtracting Positive and Negative Decimals on a Numberline

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Objective

SWBAT add and subtract signed decimals using a number line

Big Idea

Do sums of positive and negative decimals behave the same way as integers? Students explore this question with tenths on a number line.

Introduction

10 minutes

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.

Problem Solving

15 minutes

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.  

Independent Practice & Extension

20 minutes

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.  

Exit Ticket

5 minutes

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.