1. 21 st Century Lessons 1 Positive & Negative Numbers as Quantities 6.NS.5 Integers in Real World Situations

2. 2 This project is funded by the American Federation of Teachers.

3. 3 *1 st Time Users of 21 st Century Lesson: Click HERE for a detailed description of our project.HERE 21 st Century Lessons – Teacher Preparation 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. Please do the following as you prepare to deliver this lesson: Feel free to customize this file to match the language and routines in your classroom.

4. 4 Lesson ObjectiveLesson Objective: Students will be able to use positive and negative numbers to represent or describe real world situations. Lesson Description Lesson Description: This lesson is designed to help students understand and use positive and negative numbers to represent quantities in real world contexts, explaining the meaning of zero in each situation. The lesson begins by asking students to represent a description with an integer. (example: 5 ft. above sea level). Then they are asked to represent situations using a number line while understanding the starting point as a relationship to zero, for example: James has 10 points on a quiz show, he gets an answer wrong and loses 15 points. Lesson Overview (1 of 3)

5. 5 Lesson Vocabulary Number line-an infinite line in which points represent the real numbers Integer- the set of whole numbers, their opposites, and 0 Quarterback-A back in football who usually lines up immediately behind the center and directs the offense of the team. Line backer- a player on defense who takes a position close behind the linemen. Yards-a common unit of linear measure in English-speaking countries, equal to 3 feet or 36 ft..and equivalent to 0.9144 meter. Sea level-the horizontal plane or level corresponding to the surface of the sea at mean level between high and low tide. Withdraw-to draw back, away, or aside; take back; remove to place for safekeeping or in trust, especially in a bank account. Profit-to make progress Materials Chart paper, markers, copies of classwork handouts and homework Online Resources for Absent Students Here is a link to practice problems who are absent or need more review http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd= 10&ved=0CGkQFjAJ&url=http%3A%2F%2Fmlots.org%2FElana%2FNum berhandouts.doc&ei=1tMzUP-nHaOj6wHnpICwCA&usg=AFQjCNEl Lesson Overview (2 of 4)

6. 6 ScaffoldingIn the classwork the first five questions are appropriate for all levels, and increase in difficulty for students who may challenge themselves. EnrichmentAn “advanced” objective for students who have already mastered or mastered quickly the standard objective would be to ask students to write a number sentence to represent each real world context. Lesson Overview (3 of 4)

7. 7 Lesson Overview (4 of 4) Common Core State Standard 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Before and AfterStudents are expected to have been introduced to the number line and understand the general properties. This lesson focuses on the language of real world context and how they can be represented as integers on a number line. This lesson should followed lessons that develop students’ understanding of rational numbers as points on the number line, extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Topic BackgroundTell the students that as much as this is a math lesson it is more of a vocabulary lesson of real world situations that can be described using integers on a number line.

8. Warm Up: Think, Pair, Share OBJECTIVE: Agenda SWBAT understand that positive and negative numbers are used together to describe quantities having opposite directions or values by using positive and negative numbers to represent quantities in real world context. 8 Hint At 8 am the temperature was -17 °F degrees. At 3:00 pm the temperature was -22 °F degrees. Was it warmer or colder at 8 am? Be prepared to explain your answer in words or with a drawing.

9. Warm Up: Think, Pair, Share OBJECTIVE: Agenda SWBAT understand that positive and negative numbers are used together to describe quantities having opposite directions or values by using positive and negative numbers to represent quantities in real world context. 9 Hint At 8 am the temperature was -17 °F degrees. At 3:00 pm the temperature was -22 °F degrees. Was it warmer or colder at 8 am? Be prepared to explain your answer in words or with a drawing. How far from zero is each integer?

10. Agenda: OBJECTIVE: 1) Warm Up – Think, Pair Share 2) Launch -Partners 3) Explore - Whole Class 4) Summary- Independent 5) Practice- Independent 6) Assessment- Independent 10 SWBAT: SWBAT understand that positive and negative numbers are used together to describe quantities having opposite directions or values by using positive and negative numbers to represent quantities in real world context.

11. Launch: Partners Agenda 11 How could you represent the following situations using numbers and symbols? a) Kate’s Grannie lost 7 lbs b) The submarine is 235ft below sea level -7 -235

12. Launch: Partners Agenda 12 Talk to your partner about what you notice about the number line.  Extends in opposite directions infinitely  Zero is the origin  All units are spaced equally  Shows a numbers position in relation to zero  Extends in opposite directions infinitely  Zero is the origin  All units are spaced equally  Shows a numbers position in relation to zero Where would you represent 2 degrees above zero on the number line? Where would you represent -5 degrees below zero on the number line?

13. Guided Practice Agenda 13 Write the integer that represents each real life description, and place them on the number line.. 7 degrees below zero 7 degrees below zero $6.00 profit starting from zero dollars 8 feet below sea level 8 feet below sea level Deposit of $4.00 starting from zero Deposit of $4.00 starting from zero Withdrawal of $5.00 starting from zero. Withdrawal of $5.00 starting from zero. The climber was at an elevation of 10 km Loss of $3.00 starting from zero 2 degrees above zero 2 degrees above zero Loss of $3.00 starting from zero Withdrawal of $5.00 starting from zero. Withdrawal of $5.00 starting from zero. $6.00 profit starting from zero dollars 2 degrees above zero 2 degrees above zero Deposit of $4.00 starting from zero Deposit of $4.00 starting from zero 8 feet below sea level 8 feet below sea level The climber was at an elevation of 10 km 7 degrees below zero 7 degrees below zero

14. Launch: Partner Work Agenda 14 6 6 15 10 -5-5 -5-5 -2 -9 -15 -14 -12 9 9 ab g j i h f e d c

15. Launch: Continued Kate had $10 in her bank account and then she withdrew $12 The temperature was -15º F at 6am and then rose 25º F 15 Let’s look at different situations. Read each question carefully. Discuss with your partner what you notice? How are these situations different or similar from the previous ones? How can we represent these situations in a drawing? Can you draw a picture of each situation using a vertical or horizontal number line?

16. Launch: Continued Kate had $10 in her bank account and then she withdrew $12 16 In this situation we are starting at______ on the number line, which is different from the last examples because we are not starting at _____ on the number line. -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 10 + (-12)= -2 start endend

17. The temperature was -15º F at 6am and then rose 25º F In this situation we are starting at______ on the number line… Create a number line to represent this situation… Can you write an numerical equation to represent this situation. -15 + 25 = 10

18. Explore: Poster Activity Jack was on a quiz show. He had a score of 10 points. He got the next question wrong and lost 15 points. The elevator started on the 3 rd floor, and rose up 5 floors then came down 7 floors. 18 Directions: You and your partner are going to make drawings to represent the following real life situations involving positive and negative quantities. - Read each problem carefully looking for key words - Using a number line, draw a picture to represent the situation, be sure to show the starting and ending places - Be sure your posters are labeled and neat. The quarterback was standing on the 5 yard line. He gained 6 yards and then lost 8 yards. Jose had $8 in his pocket. His uncle gave him another $5 and then he spent $10 on a new shirt.

19. Explore: Classwork Challenge 19 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 end start (+3) (-5) (+3) + (-5) = -2

20. Summary: 3 Independent and share 20 Agenda Your friend had an orthodontist appointment and missed class. Write a note to your friend in your math journal explaining how integers are used in the real world and how we can determine whether an integer is a positive or negative quantity. Be sure to include several examples from your practice. Dear Suzy Q, Today we learned about using integers in the real world. We see integers when we look at…______________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ ______________________ Dear Suzy Q, Today we learned about using integers in the real world. We see integers when we look at…______________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ ______________________ Be prepared to share what you wrote with another person. Hint

21. Summary: 3 Independent and share 21 Agenda Your friend had an orthodontist appointment and missed class. Write a note to your friend in your math journal explaining how integers are used in the real world and how we can determine whether an integer is a positive or negative quantity. Be sure to include several examples from your practice. Dear Suzy Q, Today we learned about using integers in the real world. We see integers when we look at…______________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ ______________________ Dear Suzy Q, Today we learned about using integers in the real world. We see integers when we look at…______________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ ______________________ Be prepared to share what you wrote with another person. WORD BANK above below ascending descending withdrawal gain loss before profit steps forward Hint

22. Assessment: Exit Ticket 22 Agenda

23. Assessment: Homework 23 Agenda Homework

24. Back to Overview 24 1 st Time Users of 21 st Century Lessons Welcome to 21 st 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. 21 st 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. Description of 21 st Century Lessons: Next Slide

25. 25 1 st Time Users of 21 st Century Lessons The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Standards for This Unit Back to OverviewNext Slide

26. 26 1 st Time Users of 21 st Century Lessons In order to properly use 21 st 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 Requirements to teach 21 st Century Lessons: Back to OverviewNext Slide

27. 27 1 st Time Users of 21 st 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. Strongly Suggested to teach 21 st Century Lessons: Back to OverviewNext Slide

28. 28 1 st Time Users of 21 st Century Lessons 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. Lesson Preparation (Slide 1 of 2) Back to OverviewNext Slide

29. 29 1 st Time Users of 21 st Century Lessons 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. Lesson Preparation (Slide 2 of 2) Back to OverviewNext Slide

30. 30 1 st Time Users of 21 st Century Lessons 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 Features built into each PowerPoint lesson Back to OverviewNext Slide

31. The goal of 21 st 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. 21 st Century Lessons The goal… 31

32. 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 21 st Century Lessons Brian Connor – Technology Coordinator 21 st Century Lessons The people… 32