21 st Century Lessons Combining Like Terms Primary Lesson Designer(s): Kristie Conners 1

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

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 Lesson ObjectiveStudents will be able to determine if expressions are equivalent. Language Objective: Students will be able to explain in words how to combine like terms Lesson DescriptionThis lesson is designed around the fact that students have prior knowledge around the properties of math. The Launch of this lesson is based around the notion that students are familiar with the Distributive Property. (The previous lesson in this unit of Expression and Equations focuses on the distributive Property.) In this lesson, students are shown, through the use of tiles/cards, how expressions that look different really are equivalent. Students are given the opportunity to explore with several expressions and prove why two expressions are equivalent. To end the lesson students are given an exit slip for a quick assessment pertaining to this concept. Lesson Overview (1 of 4)

5 Lesson VocabularyCommutative Property: changing the order of numbers does not change the sum or product. Expression: numbers and symbols grouped together that show the value of something. Terms: a single number, variable, or numbers and variables multiplied together. Like Terms: terms that have the same variable of power. MaterialsTiles or chips (two different colors) or some other form of manipulatives; a template is provided that can be copied and cut. Copies of the class work, homework, and exit slip. Common Core State Standard 6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Lesson Overview (2 of 4)

6 ScaffoldingThrough out this lesson, students are asked to use manipulatives to understand the concept of combining like terms. At one point in the lesson, students are not asked to use their tiles, but think more conceptually on the problem. However, a step by step process is provided for students. This is a gradual release from practicing using tiles to making the mathematical connection where the tiles are no longer needed. EnrichmentDuring the practice activity, there are few problems for students who quickly grasped this concept. The challenge problems, located at the end of the activity, consist of using the Distributive Property within an expression. Students are expected to write an equivalent expression, but first must use the Distributive Property and then use the concepts from this lesson to combine like terms to write an equivalent expression. Online Resources for Absent Students Tutorial: combining-like-termshttp://learnzillion.com/lessons/654-write-equivalent-expressions-by- combining-like-terms Practice: using-propertieshttp:// using-properties Practice and Tutorials: expressions-common-core-standard-6-ee-4 Lesson Overview (3 of 4)

7 Lesson Overview (4 of 4) Before and AfterThis lesson is best used with the previous lesson in this unit. The previous lesson focuses on students mathematical reasoning and algebraic skills in proving whether two expressions are equivalent. This lesson continues with writing equivalent expressions, however using a process of combining like terms. With this foundation, students will be successful in up coming lessons involving solving equations and inequalities. Topic BackgroundThe standard Expressions and Equations is a crucial concept for students to understand. In sixth grade, The Common Core focuses making a bridge from fifth grade mathematics into seventh grade mathematics. By using their prior knowledge, these concepts start to become more abstract algebraically, and in turn, prepare students for their mathematics learning in seventh grade. The link listed below explains in great detail about these connections in the Expression and Equations content. Select Progressions for the Common Core, then Draft Progression 6-8 Expressions and Equations.

Warm Up OBJECTIVE: Students will be able to determine if expressions are equivalent by combining like terms. Language Objective: Students will be able to explain in words how to combine like terms. Agenda 8 True or False? Explain your answer. a. b. c. d. True False

Agenda: 1) Warm Up 2) Launch 3) Explore 4) Summary 5) Practice 6) Assessment 9 True or False?- Individual What is the Area?- Whole Class No Tiles, Vocabulary, Process, Quick Check- Partners, Whole Class Using Tiles- Partners Exit Slip- Individual Partners OBJECTIVE: Students will be able to determine if expressions are equivalent by combining like terms. Language Objective: Students will be able to explain in words how to combine like terms. 5 minutes 17 minutes 18 minutes 15 minutes

Launch- What is the Area? Agenda 10 What is the area of the rectangle? x 43 x 43 x 7 x 43 x 4x3x Area = 4x + 3x + 7x Area = 7x

Explore- Using Tiles Agenda 11 Think back to the warm up. xx x Can we represent 3x another way using tiles? So, how many tiles would we need? + Let each x represent a red tile. x x x We just combined all the x’s! Definition

Explore- Using Tiles Agenda 12 Think back to the warm up. xx x So, how many tiles would we need? Let each x represent a red tile. We just combined all the x’s! Click to go back

13 Explore- Using Tiles Using your tiles, what would you get Agenda x x xxxx + xxxxxx if you combined 2x + 4x? Is this the only way to show 6x? Now combine!

14 Explore- Using Tiles Agenda x x x xxx + xxxxxx Is this the only way to show 6x? + 3x + 5xx1 + More Practice

Explore- Using Tiles Agenda 15 What if we use a different variable, say y? We would need a different color to represent the y. Combine 4y + 3y using tiles. y y y + y y y y 4y 3y +

16 Explore- Using Tiles What would you get if you combined Agenda 5x + 3y + 2x + y? Use your tiles. xxxxx xx yyy y y + ++ xxxxx yyy + xx + y y +

17 Summary- No Tiles Agenda Commutative Property How can we combine without using tiles? 5x + 3y + 2x + y 5x + 3y2x + y + Identify variables that are the same Now Combine! +

18 Agenda Summary- Vocabulary Term: a single number, variable, or number and variables multiplied together. Example are terms in this expression. Like Terms: terms that have the same variable or power. and

19 Agenda 1. Copy the expression 3. Rewrite using the Commutative Property 4. Combine the variables that are the same 2. Identify the like terms Summary- Process 5x + 3y2x + y +

Summary- Quick Check Agenda 20 With your partner, write an equivalent expression for the following: #1. 4a + 6b + 3a + 9b #2. 15x – 4x + 12 #3. y + y + y #4. 5y + 7z 7a + 15b 11x y 5y + 7z Click for definition

Summary- Process Agenda 21 With your partner, write an equivalent expression for the following: Definition: two expressions that are equal Press to go back

Practice- Partners 22 Agenda I. Model the following expression by drawing squares. Let = x = y a. b

Practice- Partners 23 Agenda II. Explain why the following statement is true. 2x and 4y are not like terms, therefore, you cannot combine them. Another Explanation

Practice- Partners 24 Agenda II. Explain why the following statement is true. If x = 3 and y = 5

Practice- Partners 25 Agenda III. Write an equivalent expression for the following expressions

Practice- Partners 26 Agenda IV. Explain Yvonne’s mistake in the following problem. Yvonne just added all the numbers together. She can add numbers that are the like terms, 8x and 6x, but not 2 since it does not have an x.

Assessment- Exit Slip 27 Agenda Jose and Amy were asked to combine 7x + 2y + 6y + 3x. Decide who is correct. Explain. Jose 7x + 2y + 6y + 3x Jose’s work 7x + 3x + 2y + 6y 10x + 8y 18xy 7x + 2y + 6y + 3x = 18xy Amy 7x + 2y + 6y + 3x Amy’s work 7x + 3x + 2y + 6y 10x + 8y 7x + 2y + 6y + 3x = 10x + 8y

Back to Overview 28 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

29 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: Standards for This Unit Back to OverviewNext Slide

30 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

31 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

32 1 st Time Users of 21 st Century Lessons We suggest spending 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 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

33 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

34 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

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… 35

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… 36