Primary Lesson Designer(s): 21st Century Lessons Additive Opposites Primary Lesson Designer(s): Corey Cheever 6.NS.6a

This project is funded by the American Federation of Teachers.

21st Century Lessons – Teacher Preparation Please do the following as you prepare to deliver this lesson: Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets. Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly. Feel free to customize this file to match the language and routines in your classroom. *1st Time Users of 21st Century Lesson: Click HERE for a detailed description of our project.

Lesson Overview (1 of 4) Lesson Objective SWBAT identify additive inverses as reflections about zero on a number line. Language Objective: Students will be familiar with the words additive identity, and opposite, and understand the properties of these words. Lesson Description The lesson begins with a review on number lines as a do now. After, it goes right into defining additive identity and opposite. There are a few practice problems to make sure students understand these vocabulary words. The heart of the lesson is in the exploration. Students will be guided to understanding where the name opposite comes from, and why they are important in math. Following the exploration, a summary of what students found will take place, proceeded by practice and an individual exit ticket. Homework is also provided to further enhance students understanding.

Lesson Overview (2 of 4) Lesson Vocabulary Additive identity - When any number is added to the additive identity, that number remains unchanged. Zero is the additive identity in the real number system. Opposite – Also known as additive inverse, two opposites are on reverse sides of zero on a number line. Materials Handouts Paper Scissors (Optional) Ruler (Optional) Common Core State Standard 6.NS.6a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

Lesson Overview (3 of 4) Scaffolding There are handouts available for the practice at the beginning of the lesson which includes space to write vocabulary if the student is in need for this extra handout. Enrichment There is a challenging bonus question on the exit slip, as well as optional questions on the homework for students who have mastered the standard objective. In class, it would be wise for these students to lead the discussions when prompting students to think about opposites on a number line. Online Resources for Absent Students http://www.flaslet.com/math/practice/7087/additive-inverse-of-a-rational-number This website provides an interactive “Quiz” on additive opposites. It gives an explanation to students when problems are answered incorrectly.

Lesson Overview (4 of 4) Before and After Before: Students will need to have a clear idea of how to plot rational numbers on a number line. After: Students will be familiar with the additive identity, and the relative positions of opposites in regards to the additive identity. Students will begin to practice with the idea of adding integers. Topic Background Include any or all of these: a) interesting historical facts related to the day’s objective, b) how the lesson’s mathematics is used in the real world, and c) a brief description of the research supporting the practices used in the lesson (sometimes with a link to the source).

Warm Up OBJECTIVE: SWBAT identify opposites as reflections about zero on a number line. Language Objective: Students will be able to perform operations with opposites, and identify the additive identity. Quick Review: You are a carpenter, and need to make some cuts! Place each measurement on the ruler as accurately as possible. 7/8’’ 1 15/16’’ 3 1/2’’ 4’’ 1) 4’’ 2) 3 1/2’’ 3) 7/8’’ 4) 1 15/16’’ (5 - min) 0-5 In-Class Notes This problem is designed to make sure all the students are familiar with a number line, and can place rational numbers on a number line. Now would be a great time to make sure all the students are up to speed. good strategies for students to apply is to imagine evenly spaces lines in between the two whole numbers for each fraction. For example, on 3 ½ imagine two spaces in between 3 and 4, and for 1 15/16, imagine 16 even spaces between 1 and 2. Preparation Notes Be prepared to spend a little extra time on the warm up, just in case some people haven't mastered this skill yet. Agenda

Agenda: 1) Warm Up – Quick Review OBJECTIVE: SWBAT identify opposites as reflections about zero on a number line. Language Objective: Students will be able to perform operations with opposites, and identify the additive identity. 1) Warm Up – Quick Review 2) Launch – Additive identity and opposites 3) Explore – Opposites on the number line 4) Summary – Opposites and Reflections 5) Practice – Putting everything together! 6) Assessment – Exit Slip (1- min) 5-6

Launch What do you think of when you think of the word identity? In plain English, identity means: Being who or what a person or thing is. In Mathematics, we have something called an additive identity. When you add any number to the additive identity, you get back what that thing is. In this case, the thing is a number! (2- min) 6-8 In-Class Notes have students copy these notes into a notebook. If students are having trouble, they can request the scaffolding vocabulary worksheet. Preparation Notes Make sure you have some of the scaffolding vocabulary worksheets printed out in case some students need them. Agenda

Launch – Additive Identity Example Example of additive identities: What number can we add to 5 to get back 5? 5 + = 5 ? Zero is the Additive Identity! When you add zero to ANY number, you get back that number! (2 - min) 8-10 In-Class Notes have students copy these notes into a notebook. If students are having trouble, they can request the scaffolding vocabulary worksheet. Have the students discuss out loud other examples for addition with the additive identity. Preparation Notes Make sure you have some of the scaffolding vocabulary worksheets printed out in case some students need them. Can you think of another example of addition with the additive identity? Agenda

Launch What do you think of when you think of the word opposite? In plain English, opposite means: Having a position on the reverse side of something or someone. In Mathematics, every number has an opposite. Two numbers that are the same with opposite signs are known as opposites. For example, 5 and -5 are opposites. (2- min) 10-12 In-Class Notes have students copy these notes into a notebook. If students are having trouble, they can request the scaffolding vocabulary worksheet. Preparation Notes Make sure you have some of the scaffolding vocabulary worksheets printed out in case some students need them. Opposites in math are also referred to as Additive Inverses. For example, 5 and -5 are Additive Inverses. Agenda

5 +(-5)= ? Launch *Remember!* Zero is the additive identity! What do we get when we add two opposites or additive inverses? 5 +(-5)= ? *Remember!* Zero is the additive identity! When you add two opposites, you get the additive identity! (2 - min) 12-14 In-Class Notes have students copy these notes into a notebook. If students are having trouble, they can request the scaffolding vocabulary worksheet. Have the students discuss out loud other examples for opposites. Remind the students from slide 11 that zero IS the additive identity. Preparation Notes Make sure you have some of the scaffolding vocabulary worksheets printed out in case some students need them. Can you think of two other numbers that are opposites? Agenda

Launch 1) 12 and ____ -12 2) -3 and ____ 3 -3 + 3 = 0 12 + (-12) = 0 Find the opposites for the following numbers, so they add up to the additive identity: 1) 12 and ____ -12 2) -3 and ____ 3 -3 + 3 = 0 12 + (-12) = 0 3) ¾ and ____ - ¾ 4) 0 and ____ Remember! -0 = 0 ¾ + (- ¾ ) = 0 0 + 0 = 0 5) Bonus – What is the opposite of an opposite? (For example -(-5)?) (5 - min) 14-19 In-Class Notes have students copy these notes into a notebook. If students are having trouble, they can request the scaffolding vocabulary worksheet. Preparation Notes Make sure you have some of the scaffolding vocabulary worksheets printed out in case some students need them. You end up back with the original number! -(-5) = 5! Agenda

Where does the name opposite come from? Launch Where does the name opposite come from? We are going to explore this question with a partner, and try to come up with the answer on our own! (1- min) 19-20 In-Class Notes This is the launch for the exploration. Let the students try to answer the question, then suggest everyone works on this problem through a set of questions that you hand out. Preparation Notes You should pay attention to answers such as “opposites are on exact different locations,” or “opposites have reverse locations,” etc. Let the students who answer in such a manner know they are on the right track, but try not to spend to much time on this question – it is more rhetorical to lead into the exploration. Agenda

In 10 minutes you will be asked to stop and present! Explore Work with your partner. You will see five examples of opposites. Plot them on the number lines given. You will get a worksheet a ruler and some number lines. You should: Read each scenario Plot the points on the number line Answer the questions! Click on the timer! 1-Partners 2-Share Out 3-Discussion Online timer link on slide – (10 min) (20-30) In-Class Notes Pass out “Explore” Classwork, Calculator. Focus on strategies and help struggling pairs recall previous techniques click the timer to give a 10 minute countdown. In 10 minutes you will be asked to stop and present! Agenda

Explore Example: You have $10. You owe the pizza delivery boy $10. a) Plot 10 and -10 on a number line. b) Draw a line from 10 to 0, and a line from -10 to 0. (2- min) 30-32 In-Class Notes This example is provided to guide the students through the rest of the exploration. Take this time to answer any questions and clarify any uncertainties about directions. Preparation Notes This slide should be shown once the explore worksheet is passed out, before the students start working. c) Fold the number line at 0 to compare the length of each line. Agenda

Explore – Student Share Out Discussion - (5 Min) Students share out work. Make sure to ask questions for anything you are unsure about! (1 min) 32-33 In-Class Notes The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. Classwork Questions Agenda

Explore 1) You go to the store and want three apples. The store has three apples that you plan to buy! a) Plot the points 3 and -3 on the number line b) Draw a line from 3 to 0, and a line from -3 to 0. (1 min) 33-34 In-Class Notes The purpose of these questions is just to get the students to see opposites plotted on a number line. Any observations they make about the opposites will be useful. The final goal is to realize that all opposites are the same distance from zero (Have the same absolute value). This will prepare them for math classes in the future that will have a strong emphasis on absolute value. The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. c) Fold the number line at 0 to compare the length of each line. Agenda

Explore 2) You stand on a diving board that is 6.5 feet high. When you dive off, you go down 6.5 feet under water. a) Plot the points -6.5 and 6.5 on the number line b) Draw a line from -6.5 to 0, and a line from 6.5 to 0. (1 min) 34-35 In-Class Notes The purpose of these questions is just to get the students to see opposites plotted on a number line. Any observations they make about the opposites will be useful. The final goal is to realize that all opposites are the same distance from zero (Have the same absolute value). This will prepare them for math classes in the future that will have a strong emphasis on absolute value. The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. c) Fold the number line at 0 to compare the length of each line. Agenda

Explore 3) You need 3 ¼ cups of flour to bake a cake. Your neighbor has 3 ¼ cups that you can borrow. a) Plot the points 3 ¼ and -3 ¼ on the number line b) Draw a line from 3 ¼ to 0, and a line from -3 ¼ to 0. (1 min) 35-36 In-Class Notes The purpose of these questions is just to get the students to see opposites plotted on a number line. Any observations they make about the opposites will be useful. The final goal is to realize that all opposites are the same distance from zero (Have the same absolute value). This will prepare them for math classes in the future that will have a strong emphasis on absolute value. The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. c) Fold the number line at 0 to compare the length of each line. Agenda

Explore 4) You ride your bike 3.75 miles to a friend’s house. You ride your bike 3.75 miles in the opposite direction to get back home. a) Plot the points 3.75 and -3.75 on the number line b) Draw a line from 3.75 to 0, and a line from -3.75 to 0. (1 min) 36-37 In-Class Notes The purpose of these questions is just to get the students to see opposites plotted on a number line. Any observations they make about the opposites will be useful. The final goal is to realize that all opposites are the same distance from zero (Have the same absolute value). This will prepare them for math classes in the future that will have a strong emphasis on absolute value. The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. c) Fold the number line at 0 to compare the length of each line. Agenda

Explore 5) A friend let’s you borrow $7.50. You pay her back all $7.50 a week later. a) Plot the points -7.50 and 7.50 on the number line b) Draw a line from -7.50 to 0, and a line from 7.50 to 0. (1 min) 37-38 In-Class Notes The purpose of these questions is just to get the students to see opposites plotted on a number line. Any observations they make about the opposites will be useful. The final goal is to realize that all opposites are the same distance from zero (Have the same absolute value). This will prepare them for math classes in the future that will have a strong emphasis on absolute value. The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. c) Fold the number line at 0 to compare the length of each line. Agenda

Summary 6a) Name two things that each pair of opposites have in common. They are both the same distance from zero! The negative ones are always to the left of zero! The positive ones are always to the right of zero! Did anyone come up with any others? (1 min) 38-39 In-Class Notes The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. Agenda

Summary 6b) What do you notice about the length of the lines from each opposite to 0? They “have a position on the reverse side of zero.” Remember the definition of opposite from earlier? – “Having a position on the reverse side of something or someone.” (1 min) 39-40 In-Class Notes If students are confused about “reverse side,” give them a visual example such as people lined up on a football field, or someone looking in to a mirror. The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. This is where the name opposite comes from! Agenda

Summary 6b) What do you notice about the length of the lines from each opposite to 0? Imagine a mirror right down the line at zero. Then, two opposites would be reflections of each other! (1 min) 40-41 In-Class Notes Students should definitely write down the bullet points on this slide! The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. In math language, we say that opposites are: Reflections about zero. Agenda

Summary 6c) How are opposites and the additive identity related? Opposites are always the same distance from the additive identity, but on reverse sides. Additive opposites add up to the additive identity. (1 min) 41-42 In-Class Notes The summary goes over what everyone just explored on the last worksheet. Try to have a student based discussion during the next slides, especially once you get to question 6. Use question 6 to prompt students to answer what they have learned about opposites by answering these questions. Preparation Notes If students are a little shy about answering, go over the problems together, and have them just discuss problem six as a class. 5 +(-5)= For any number a, a + (-a) = 0 Agenda

Practice 1. Identify the additive opposite of the number, and then plot them both on a number line: a) 9 and _____   b) -7.5 and _____ c) 4.25 and ____ -9 7.5 -4.25 (3 - min) 42-45 In-Class Notes You can choose to have the students answer the questions individually, or with a partner, and then go over the answers, or you can work on the practice as a class. The slides directly reflect the class work. Preparation Notes Print out enough class work practice worksheets for everyone in the class to have one. Agenda

Practice 14.6 13 3.2 -17 ½ 3 ¼ 2. Evaluate the following: a) 8 + (-8) = b) 14.6 + 0 =   c) -4 + 4 = d) - (-13) = e) 9.6 + (-9.6) = f) 0 + (-3.2) = g) -17 ½ + 0 = h) – (-3 ¼ ) = 14.6 13 3.2 (3 - min) 45-48 In-Class Notes You can choose to have the students answer the questions individually, or with a partner, and then go over the answers, or you can work on the practice as a class. The slides directly reflect the class work. Preparation Notes Print out enough class work practice worksheets for everyone in the class to have one. -17 ½ 3 ¼ Agenda

b a w y z Practice Remember! -(-y) = y Remember! -0 = 0 a) What letter represents the opposite of d?_________________________________   b) What letter represents the opposite of x?_________________________________ c) What letter represents the opposite of c?_________________________________ d) What letter represents the opposite of –y?________________________________ (Careful! –y is not shown on the number line.) e) What letter represents the opposite of z?__________________________________ a w Remember! -(-y) = y y (3 - min) 48-51 In-Class Notes You can choose to have the students answer the questions individually, or with a partner, and then go over the answers, or you can work on the practice as a class. The slides directly reflect the class work. Preparation Notes Print out enough class work practice worksheets for everyone in the class to have one. Remember! -0 = 0 z Agenda

Assessment – Exit Ticket (2- min) 51-53 In-Class Notes This should be an individual exit ticket. Encourage students who have mastered the standard to attempt the bonus question. Preparation Notes Print out a copy of the exit ticket for each student to hand out at this time. Agenda

Opposites Homework Agenda (2- min) 53-55 In-Class Notes Pass out the homework, and encourage all students to try the bonus questions, especially if they have mastered the material in class. This homework is designed to make sure the students understand the concept of reflection in regards to an opposite. It shouldn’t take two long, and hopefully it gives them confidence moving forward with negative numbers in the future. Preparation Notes Print out a copy of the homework for each student to hand out at this time. Agenda

1st Time Users of 21st Century Lessons Description of 21st Century Lessons: Welcome to 21st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Next Slide Back to Overview

1st Time Users of 21st Century Lessons Standards for This Unit The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: 6.NS.6a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.   Next Slide Back to Overview

1st Time Users of 21st Century Lessons Requirements to teach 21st Century Lessons:  In order to properly use 21st Century Lessons you will need to possess or arrange the following things:   Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Scissors – at least 1 for every pair Next Slide Back to Overview

1st Time Users of 21st Century Lessons Strongly Suggested to teach 21st Century Lessons: Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with a student’s name on each one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students’ attention. (“hands- up”, Count from “5” to “0” etc.) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Next Slide Back to Overview

1st Time Users of 21st Century Lessons Lesson Preparation (Slide 1 of 2) We suggest spending 30-45 minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you.    Note: All of our lessons are designed to be taught during a 45-55 minute class. If your class is shorter than this you will have to decide which sections to condense/remove. If your class is longer we suggest incorporating some of the “challenge” questions if available. Next Slide Back to Overview

1st Time Users of 21st Century Lessons Lesson Preparation (Slide 2 of 2)  After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for the lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the content, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Next Slide Back to Overview

1st Time Users of 21st Century Lessons Features built into each PowerPoint lesson There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include:   Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Click the agenda button on any slide to return to the agenda. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Next Slide Back to Overview

21st Century Lessons The goal… The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons.  These lessons are intended to:   Support an increase in student achievement; Engage teachers and students; Align to the National Common Core Standards and the Massachusetts curriculum frameworks; Embed best teaching practices, such as differentiated instruction; Incorporate high-quality multi-media and design (e.g., PowerPoint); Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; Be available, along with videos and supporting materials, to teachers free of charge via the Internet. Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers.

21st Century Lessons The people… Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21st Century Lessons Brian Connor – Technology Coordinator