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21 st Century Lessons Distributive Property 1 Primary Lesson Designers: Kristie Conners Sean Moran

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

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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.

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4 Lesson ObjectiveStudents will be able to apply the distributive property to write equivalent expressions. Students will be able explain how to use the distributive property verbally and in writing. Lesson DescriptionThis lesson is the second lesson for the standard 6.EE.3. The Distributive Property is a crucial concept in mathematics. The warm up in the lesson is a multiplication problem where the Distributive Property was used. This will trigger students to start to think about multiplication this way to prep them for the Distributive Property. The Launch uses a basketball court to introduce finding the area, which can be solved using two methods, one being the Distributive Property. Students then continue in their groups using divided rectangles to find their areas. Again, students will be asked to use both methods to later connect them as being equivalent; one method being the Distributive Property. The Summary part of the lesson is where students will be given the definition and explanation of the Distributive Property. Students are asked to finish the activity with challenging problems. The lesson finishes with an Exit Slip that contains three terms inside the parentheses. This was designed to push students to think about the process of the Distributive Property. Lesson Overview (1 of 4).

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5 Lesson VocabularyDistributive Property: an mathematical property which helps to multiply a single term and two or more terms inside parenthesis. Expression: numbers and symbols grouped together that show the value of something. Commutative Property: changing the order of numbers does not change the sum or product. MaterialsCopies of the class work assignment, Exit Slip, and homework. Common Core State Standard 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Lesson Overview (2 of 4)

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6 ScaffoldingThis lesson is designed around using area models as supposed to an algebraic way to show Distributive Property. Therefore, this lesson tailors to ELL students and students with learning disabilities providing visuals throughout the lesson to access this relatively abstract algebraic concept. EnrichmentIn the Activity portion of this lesson, there is an opportunity provided for students who seem to have grasped the Distributive Property relatively quickly. These questions challenge students a bit more by writing equivalent expressions using Distributive Property. Online Resources for Absent Students Tutorial: http://learnzillion.com/lessons/372-apply-the-distributive-property- using-area-models http://flash.learning.com/ahamath-demo/The-Distributive-Property- Lesson/SCORMDriver/indexAPI.html http://coolmath.com/prealgebra/06-properties/05-properties- distributive-01.htm Practice: http://www.ixl.com/math/grade-6/distributive-property Lesson Overview (3 of 4)

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7 Lesson Overview (4 of 4) Before and After Expressions and Equations is a crucial topic for students to become successful in a future Algebra course. This content standard concepts and processes are a critical part in students’ career in mathematics. Thus far in this unit, students have been exposed to writing, reading and evaluating numerical and algebraic expressions. The lessons for this standard continue working on those topics, but taking their understanding of expressions to the next level. The first lesson for this standard deals with the properties of mathematics, where this lesson strictly focuses on the Distributive Property. It is advised that both lessons be used consecutively. With a strong background of the properties and the Distributive Property, students will be successful in continuing their wok in this standard; where students are expected to prove equivalent expressions and then solve equations. Topic Background The link below is a quick reference to the properties in mathematics. This link is a also a helpful resource for students. http://mathforum.org/dr.math/faq/faq.property.glossary.html The link below is an article, “I See It: The Power of Visualization”. This supports the basic idea behind the lesson of using the idea of visuals as means to the lesson. http://www.mathrecap.com/category/conferences/nctm/page/3/

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Warm Up Objective: Students will be able to apply the distributive property to write equivalent expressions. Agenda 8 Ricardo and Keyla are arguing whether the answer to can be found by doing the following work. Do you think this is correct? Explain. Language Objective: Students will be able explain how to use the distributive property verbally and in writing.

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Agenda: 1) Warm Up 2) Launch 3) Explore 4) Summary 5) Explore 6) Assessment 9 Objective: Students will be able to apply the distributive property to write equivalent expressions. Individual High School Vs. College B-ball- Whole Class, Pairs Splitting Athletic Fields– Groups Exit Slip- Individual Splitting Athletic Fields- Groups The Distributive Property- Whole Class Language Objective: Students will be able explain how to use the distributive property verbally and in writing. 4 minutes 13 minutes 17 minutes 10 minutes 4 minutes 12 minutes

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Launch- High School Vs. College B-ball Agenda 10 84 ft 50 ft To find the area of the court you can use the formula of A=l w A standard size high school basketball court is 84ft long and 50ft wide in the shape of a rectangle. A = 84 ft 50ft A = 4200

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11 Agenda Can you think of a method to find the area of the college basketball court? Did you know that a college basketball court is usually 10ft longer than a high school basketball court? 84 ft 50 ft 10 ft College Basketball Court Launch- High School Vs. College B-ball

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12 Agenda Can you think of a method to find the area of the college basketball court? 84 ft 50 ft 10 ft 84+10 9450 A = 4700 4200 A = 4700 500+ +50(84+10) What can we say about these two expressions? Why parenthesis? Launch- High School Vs. College B-ball 84 50 10 50 Method 1Method 2

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Explore- Splitting Athletic Fields 13 Agenda 50 yds 120 yds 50 yds 80 yds40 yds Allison lives in a neighborhood with three rectangular fields that all have the same area. The fields are split into different sections for different sports. 20 yds 120 yds 30 yds

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14 Agenda 50 yds 120 yds 20 yds 120 yds 30 yds 1. Find the area of this field near Allison’s house. 2. This field is divided into two parts. a. Find the area of each part and record your steps as you go. Prove the area is the same as in the first field? + Explore- Splitting Athletic Fields 20 120=2400 30 120=3600

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15 Agenda b. Write one numerical expression that will calculate the area based on the work you did in part a. c. Find a different way to calculate the area of the entire field and write it as one numerical expression. 20 yds 120 yds 30 yds Explore- Splitting Athletic Fields 20 120=2400 30 120=3600 20 120 30 120 20 yds 120 yds 30 yds +

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16 Agenda 3. The field is divided into two parts. 40 yds 80 yds 50 yds a. Write 2 different numerical expressions that will calculate the area of the entire field. 4. The field below is split into two parts but are missing the dimensions. a. Fill in the missing dimensions of the rectangular field whose area can be calculated using the expression. b. Write a different numerical expression to calculate the area of the field. _______________ ______ 50 100 20 Explore- Splitting Athletic Fields

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Summary- The Distributive Property 17 Agenda 20 yds 120 yds 30 yds 50 yds 80 yds40 yds Let’s look at the two equivalent ways of finding the area and connect it to an important property in math. The Distributive Property

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18 Agenda 50 8040 The Distributive Property 50 8040 50 120 + 50 80 40 50 80 40 50 Summary- The Distributive Property 50 yds 80 yds40 yds

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19 Agenda The Distributive Property The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis. Lets use the distributive property to write an equal expression. 2 35+ 2 Check it out! Examples Summary- The Distributive Property Formal definition

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20 Agenda The Distributive Property The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis. Summary- The Distributive Property States that the product of a number and a sum is equal to the sum of the individual products of addends and the number. example

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21 Agenda 8 x 5 x 2 3 x 4 a. Write two different expressions to represent the area of each rectangle below. 5. An algebraic expression to represent the area of the rectangle below is. Explore- Splitting Athletic Fields

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22 Agenda 6. Use the distributive property to re-write each expression. You may want to draw a rectangle to represent the area. Explore- Splitting Athletic Fields a) 10( a + 7) = ___________ c) x( 3 + 10)= ___________ b) 7(x + 3)=________________ d) a(10 + 9)= _______________ e) -2(x + 10)=_______f) 3x(x + 10)= ______________

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Assessment- Exit Slip 23 Agenda Who correctly used the distributive property to write an equivalent expression? Provide evidence to support your answer. Riley Michael Michael did because he correctly distributed the 7 to all terms inside the parenthesis.

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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

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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: Standards for This Unit Back to OverviewNext Slide

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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

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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

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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

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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

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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

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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

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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

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21 st Century Lessons Writing Algebraic Expressions Primary Lesson Designer(s): Kristie Conners Sean Moran 1.

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