1. Additional Algebra Skills Needed to Solve Equations 1

2. 2 *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.

3. 3 Lesson Objective OBJECTIVE: Students will be able to efficiently solve equations by thoughtful selection of first moves, eliminating fractional coefficients and distributing negative signs. LANGUAGE OBJECTIVE: Students will discuss with a partner potential solution moves in order to better understand the reasoning for selecting a particular first move. Lesson DescriptionThis is the second in a series on basics of solving equations. This lesson covers some more sophisticated ideas involved in solving equations. Students explore selecting a first move where they come to understand the value in scanning and assessing options before taking action to find the most efficient means of solving. They will develop skill in distributing a negative sign using distributive property and in eliminating fractional coefficients by multiplying by the denominator of the fraction. These skills enable students to add sophistication to their equation solving skills. Lesson Overview (1 of 4)

4. 4 Lesson VocabularyDistributive property, negative, coefficient, constant, denominator Materialsindependent class work, homework, exit slip, powerpoint, calling sticks Common Core State Standard 8EEc7b - Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. http://www.corestandards.org/ http://www.corestandards.org/ Lesson Overview (2 of 4)

5. 5 ScaffoldingThe frequent turn-and-talk strategy used throughout the lesson is a method utilized to aid student understanding by giving them time to think and to hear the thinking of others besides the teacher. This is a great strategy for both ELL students and for students with learning differences. The work is scaffolded with many opportunities for guided practice and color coding for each new move. EnrichmentStudents seeking additional challenges will find challenging work on both the class work and homework worksheets. Here is some challenging online practice: http://www.algebralab.org/practice/practice.aspx?file=algebra1_3- 3.xml http://www.algebralab.org/practice/practice.aspx?file=algebra1_3- 3.xml Online Resources for Absent Students http://www.algebra-class.com/solving-algebra-equations.html Good LearnZillion lessons on this topic: https://learnzillion.com/lessonsets/560-solve-linear-equations-in- one-variable https://learnzillion.com/lessonsets/560-solve-linear-equations-in- one-variable Lesson Overview (3 of 4)

6. 6 Lesson Overview (4 of 4) Before and AfterThe work of solving equations has been built upon through previous grades and also the ratios and proportions 8 th grade unit. In 6 th grade for example students have solved basic equations and they have created equivalent expressions using the distributive property and combining like terms. The work is solidified in 7 th grade using numbers in any form (decimals, fractions, and negative numbers) and relying more heavily on the properties of the operations. This lesson follows algebra work looking at expressions and graphs and the previous lesson titled Introduction to Solving Equations covers basics of solving equations. Later lessons will move into solving systems of equations and reasoning about the shape and characteristics of the graph of a line by looking at an equation, often requiring manipulations first – manipulations that this lesson provides the skills for. Topic BackgroundA nice history of solving equations can be found here: http://faculty.etsu.edu/gardnerr/Galois/history-of-equations.htm

7. Warm Up Agenda 7 Answers    5(n + 6 + 2p) = -3(2x + 4) = Evaluate.Simplify. OBJECTIVE: Students will be able to efficiently solve equations by thoughtful selection of first moves, eliminating fractional coefficients and distributing negative signs. LANGUAGE OBJECTIVE: Students will discuss with a partner potential solution moves in order to better understand the reasoning for selecting a particular first move.

8. Warm Up Answers Agenda 8    5(n + 6 + 2p) = -3(2x + 4) = Evaluate.Simplify. = 4 5n + 30 + 10p -6x – 12 OBJECTIVE: Students will be able to efficiently solve equations by thoughtful selection of first moves, eliminating fractional coefficients and distributing negative signs. LANGUAGE OBJECTIVE: Students will discuss with a partner potential solution moves in order to better understand the reasoning for selecting a particular first move.

9. Agenda: 1) Warm Up – basic skills review - YOU 2) Mini-Lesson #1 – Picking a First Move - ME 3) Mini-Lesson #2 – Shortcut for a Fractional Coefficient – ME 4) Guided Practice – practice solving equations – US 5) Mini-Lesson #3 – Distributing a Negative Sign – ME 8) Assessment – Exit Ticket - YOU 9 OBJECTIVE: Students will be able to efficiently solve equations by thoughtful selection of first moves, eliminating fractional coefficients and distributing negative signs. LANGUAGE OBJECTIVE: Students will discuss with a partner potential solution moves in order to better understand the reasoning for selecting a particular first move. 6) Guided Practice – practice solving equations – US 7) Independent Practice – practice solving equations – YOU

10. Agenda 10 Mini-lesson #1: Picking a First Move Launch Ex. 1 3m + 13 = 5m + 6 Did you get m = 7/2 or 3½ for a solution? What was your first move? Turn and Talk: Take turns speaking with a partner to share your first move. Was it the same? If not, ask your partner why he or she chose that move first. Turn and Talk: Take turns speaking with a partner to share your first move. Was it the same? If not, ask your partner why he or she chose that move first. Solve using the symbolic method.

11. Agenda 11 There is more than 1 first move from which to choose. Launch Ex. 1 3m + 13 = 5m + 6 13 = 2m + 6 - 3m OR - 5m -2m + 13 = 6 Will there be 2 different solutions? Let’s find out! - 6 22 7 = 2m 7/2 = m - 13 -2m = -7 -2 m = 7/2 Either 1 st move can be used to get the same result. Either 1 st move can be used to get the same result.

12. Agenda 12 There is more than 1 first move from which to choose. Launch Ex. 1 3m + 13 = 5m + 6 13 = 2m + 6 - 3m OR - 5m -2m + 13 = 6 Are there any other first moves? Turn and Talk: Discuss with your partner. See if you can work together to find all the possible first moves.

13. Agenda 13 Launch 3m + 13 = 5m + 6 13 = 2m + 6 - 3m 3m + 13 = 5m + 6 - 5m -2m + 13 = 6 These are all the possible first steps. Do they all result in the same solution? These are all the possible first steps. Do they all result in the same solution? 3m + 13 = 5m + 6 - 13 3m = 5m + -7 - 6 3m + 7 = 5m Turn and Talk: Is there one first move that is better to use? Why do you think that one is better than the others?

14. Agenda 14 Launch 3m + 13 = 5m + 6 13 = 2m + 6 - 3m 3m + 13 = 5m + 6 - 5m -2m + 13 = 6 3m + 13 = 5m + 6 - 13 3m = 5m + -7 - 6 3m + 7 = 5m Some people might say that the calculations are easier if you do not have to divide by a negative. - 6 22 7 = 2m 7/2 = m - 13 -2m = -7 m = 7/2 -2 - 5m -2m = -7 -2 m = 7/2 7 = 2m - 3m 2 7/2 = m 2 Some people might say that the calculations are easier if you do not have to divide by a negative. You can avoid this if you do not create a negative with your first move. These two first moves are similar.

15. Agenda 15 Launch 2 7/2 = m 2 - 6 13 = 2m + 6 3m + 13 = 5m + 6 - 3m - 6 7 = 2m This order of moves is the way most solutions will be presented in examples. Although it is important to realize that there are many possible first moves. In general, a preferable order of moves would minimize the need to calculate with negative numbers, fractions, or decimals.

16. Agenda 16 Mini-lesson #2: Shortcut for a fractional coefficient. Launch Ex. 2 8 + ¼b = 5 Solve for b. Check your answer. – 8 ¼b = -3 – 8 Why is subtracting 8 a better first move than subtracting ¼b? ¼¼ We know that ¼ is attached to the b by multiplication and the way to undo a coefficient is to divide by the coefficient. But there is a faster way to undo this coefficient because it is a fraction.

17. Agenda 17 How to cancel the fractional coefficient : Launch 8 + b = 5 – 8 b = -3 – 8 b = -12 8 + b = 5 – 8 b = -3 Remember that when you divide by a fraction you multiply by the reciprocal. So if you multiply both sides by 4 you will cancel the. 4( ) ( )4 b = -12 -3 ÷ = -3  = -  = -12

18. Practice: Solve for the variable, substitute to check 18 Agenda 1.) -6 + x = -5 3.) 0 = 4 + 2.) x + 9 = - x + 12 n This is the same as Answers

19. Practice 1.) -6 + x = -5 3.) 0 = 4 + 2.) x + 9 = - x + 12 +6 x = 1 3( ) ( )3 4( ) x = 3 - 9 -9 x = - x + 3 + x + x x = 3 ( )4 3x = 12 x = 4 - 4 -4 -4 = 5( ) ( )5 -20 = n Check: -6 + (3) = -5 -6 + 1 = -5 -5 = -5 ✓ Check: (4) + 9 = - (4) + 12 2 + 9 = -1 + 12 11 = 11 ✓ Check: 0 = 4 + 0 = 4 + -4 0 = 0 ✓ -20 19 Agenda

20. Practice 20 Agenda Mini-lesson #3: Distributing a negative sign. Ex. 3 14 = – (p – 8) 2(x – 5) – p + 8 – 8 14 = 2 x – 10 6 = -p -6 = p Let’s review the distributive property: -(p) = -1(p) = -p -(-8) = -1(-8) = +8 Wait, what happened? Now, solve for p.

21. Practice: Solve for the variable, substitute to check 21 Agenda 4.) -8 = –(x + 4) 5.) 12 = – (-6x – 3) 6.) –(y – 2) + = 3(y + 1) Answers

22. Practice Agenda 4.) -8 = –(x + 4) 5.) 12 = – (-6x – 3)6.) –(y – 2) + = 3(y + 1) -8 = –x – 4 +4 -4 = –x 4 = x 12 = 6x + 3 -3 - 3 9 = 6x 6 9/6 = x x = 3/2 or 1½ –y + 2 + = 3y + 3 2( ) –y + 2 + = 3y + 3 ( )2 –2y + 4 + 5 = 6y + 6 –2y + 9 = 6y + 6 +2y +2y 9 = 8y + 6 -6 - 6 3 = 8y 8 Y = ⅜ Check it Check: -8 = –(4 + 4) -8 = -(8) -8 = -8 ✓ Check: 12 = – (-6( ) – 3 12 = -(-9 – 3) 12 = 12 ✓ 22

23. Practice: Independent Class work 23 Agenda 6.) –(y – 2) + = 3(y + 1) y = ⅜ Check: –( – 2) + = 3( + 1) – + 2 + = + 3 – 3 + 16 + 20 = 9 + 24 33 = 33 ✓ 8( )( )8

24. Practice: Independent Class work 24 Agenda Answers Next blank section

25. Practice: Review Class work 25 Agenda Exit Slip Next Blank Section

26. Practice: Class worksheet 26 Agenda Go to Answers Exit Slip

27. Practice: Review Class work 27 Agenda Next Blank Section Exit Slip

28. Practice: Class worksheet 28 Agenda Go to Answers Exit Slip

29. Practice: Review Class work 29 Agenda Next Blank Section Exit Slip

30. Practice: Class worksheet 30 Agenda Go to Answers Exit Slip

31. Practice: Review Class work 31 Agenda Exit Slip

32. 32 Agenda

33. Back to Overview 33 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

34. 34 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: 8EEc7b - Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. http://www.corestandards.org/ http://www.corestandards.org/ Standards for This Unit Back to OverviewNext Slide

35. 35 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

36. 36 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

37. 37 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

38. 38 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

39. 39 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

40. 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… 40

41. 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 Wendy Welch - Curriculum Director (Social Studies and English) Carla Zils – Curriculum Director (Math) Shane Ulrich– Technology Director Marcy Ostberg – Technology Evaluator 21 st Century Lessons The people… 41