1. 21 st Century Lessons Evaluating Expressions The Order of Operations 1 Primary Lesson Designers: Kristie Conners Sean Moran

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 Objective Lesson Objective: Students will be able to evaluate numerical expressions. Students will explore the same expression in four different ways to help determine the order of operations. Student- Friendly Objective: Students will be able to identify and begin to follow the order of operations when evaluating expressions. Language Objective: Students will be able to discuss and interpret why the order of operations are important and identify the words expression and evaluate. Lesson Description This lesson is designed over two days. The lesson in this PowerPoint only covers Lesson 1. Lesson 1 is an exploration around the order of operations with practice. The goal for Lesson 1 is for students to gain an understanding that evaluating expressions has a particular order. Lesson 2 will cover all aspects of the order of operations, where majority of the lesson is an activity for the students to practice the order of operations. The goal for Lesson 2 is for students know and apply the order of operations. This lesson is the first lesson in the unit. As the unit progresses, students will be required to apply the order of operations, therefore, fitting to be introduced at this time. Lesson Overview (1 of 3)

5. 5 Lesson Vocabulary 1)Exponent- shows you how many times to multiply the number by itself. 2)Expression- numbers and symbols grouped together that show the value of something. 3)Evaluate- to calculate the value. 4)Operations- a mathematical process: the most common are addition, subtraction, multiplication and division. Materials Required: All students will need a notebook and pencil or pen. Board space may be needed if want to visually show students responses. Copies of the explore problem, class work assignment, exit slip, and homework. Optional: (Time permitting) Teacher may want to have students put their findings of the four students on chart paper to show the class. Therefore, chart paper and markers are needed. Scaffolding There are several opportunities throughout the lesson to give student support. In the warm up and practice section, support is available to show more details in the lesson if needed. This will benefit students who are more visual learners and English Language Learners. Enrichment During the class work assignment, teachers have the opportunity to assign a set of rigorous problems for students who may require the extra challenge. Online Resources for Absent Students Tutorial http://www.mahalo.com/order-of-operations/ Video clip http://www.youtube.com/watch?v=JgQiCSgamU8 Online practice http://www.ixl.com/math/grade-5/simplify-expressions-using-order-of-operations-and- parentheses Lesson Overview (2 of 3)

6. 6 Lesson Overview (3 of 3) Common Core State Standard Expressions and Equations 6.EE.1Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Before and After Students will rely on their basic skills to better understand the topic of order of operations. Having a strong background of the four basic operations will benefit the students in fully gaining this concept. This lesson is the first lesson in the unit which builds student’s understanding of order of operations. Students will gain an understanding that all math problems need to follow a certain order. Through exploring the different methods one can approach to evaluate expressions, students will be able to explore the common mistakes and gain a true understanding of the order of operations. After this lesson, students will have a foundation to start evaluating expressions. They will continue using the order of operations, making this lesson a very crucial part of their learning and understanding of mathematics. Topic Backgroundhttp://www.youtube.com/watch?v=w0XkQ-Q8aDg Note: 3 minutes into the video is the connection to the order of operations.

7. Warm Up/Do Now OBJECTIVE: SWBAT indentify and begin to follow the order of operations when evaluating expressions. Agenda 7 Evaluate: 1)2) 3)4) 5) 341 5 3 13 Scaffolding

8. Warm Up/Do Now OBJECTIVE: SWBAT indentify and begin to follow the order of operations when evaluating expressions. Agenda 8 Evaluate: 1)2) 3)4) 5) 341 5 3 13 Scaffolding

9. Agenda: 1) Warm Up 2) Launch 3) Explore 4) Practice 5) Assessment/Exit Slip 9 Marvin’s Trick- Independent Agenda The Four Students Problem- Partners Whole class Partners Independent OBJECTIVE: SWBAT indentify and begin to follow the order of operations when evaluating expressions. LANGUAGE OBJECTIVE: SWBAT to discuss and interpret why the order of operations are important and identify the words expression and evaluate. Independent Discussion- Lesson- Notes- Recourses for Your Notebook- Independent

10. Launch- Marvin’s Trick Agenda 10 has a challenge for you! Marvin the “Amazing Math Magician” Hey class, bet you can’t make 75 with the numbers: 3 71015 But, you must use all 4 numbers only once. You can use any operation you like addition, subtraction, multiplication or division, more than once, and in any order you choose.

11. 11 3 71015 How did you make 75 with the 4 numbers? Launch- Marvin’s Trick Agenda

12. 12 A way to make 371015 75 using Expression?????? This is a way to write the work you did as one math expression. Numbers and symbols grouped together that show the value of something. Launch- Marvin’s Trick Agenda

13. Explore- The Four Students Problem 13 Agenda Marvin challenged four students to evaluate this problem Your task with your partner is to determine how the students obtained their answer. Juan Melinda Shawn Student’s results Ashley Support your response with evidence, by listing the operations in the order in which the student did them. Your group is responsible for 2 or 4 students. Evaluate?

14. Explore- The Four Students Problem 14 Agenda Marvin challenged four students to evaluate this problem Evaluate: to calculate the value. Click to Return

15. 15 Marvin challenged four students to evaluate this problem. Juan Melinda Shawn Click names Ashley Agenda Online Calculator All students and summary PC Users Next slide Discussion

16. 16 Marvin challenged four students to evaluate this problem. Juan Melinda Shawn Click names Ashley Next slide All students Agenda Online Calculator summary Ashley’s Work PC Version- Discussion Melinda’s Work Juan’s Work Shawn’s Work Melinda’s WorkAshley’s Work Shawn’s Work Juan’s Work How can we test it?

17. 17 Marvin challenged four students to evaluate this problem. Click names Ashley’s Work Agenda Online Calculator Juan Melinda Shawn Ashley All students and summary Discussion

18. Melinda’s Work Marvin challenged four students to evaluate this problem. Click names Online Calculator Agenda Juan Melinda Shawn Ashley All students and summary Discussion

19. Marvin challenged four students to evaluate this problem. Click names Online Calculator Juan’s Work Agenda Juan Melinda Shawn Ashley All students and summary Discussion

20. 20 Marvin challenged four students to evaluate this problem. Click names Agenda Online Calculator Shawn’s Work Juan Melinda Shawn Ashley All students and summary Discussion

21. 21 Marvin challenged four students to evaluate this problem. Juan Melinda Shawn Click names Ashley Agenda Online Calculator All students and summary How can we test it? Melinda’s WorkAshley’s Work Shawn’s Work Juan’s Work Discussion

22. Resources for Your Notebook 22 Agenda The Order of Operations 1) Think back to the warm up. Is there a problem that contained any symbol Shawn didn’t use? 1) Parentheses or Grouping Symbols Click to open warm up. Shawn’s Work 2) Exponents 3) Multiplication/Division 4) Addition/Subtraction (Left to Right)

23. Warm Up/Do Now OBJECTIVE: SWBAT indentify and begin to follow the order of operations when evaluating expressions. Agenda 23 Evaluate: 1)2) 3)4) 5) 341 5 3 13 Click to Return

24. 24 Practice- Partners 1) 2) 20 ÷ (6 – 1) 3) 10 + 2 3 – 54) 9 + 3 + 9 ÷ 3 5) 6 + 10 ÷ 2 – 16) 2 + 5 x 6 ÷ 2 Directions: Using the Order of Operations, evaluate the following expressions. Agenda Let’s do number 1 and 2 together!!

25. 25 Directions: Using the Order of Operations, evaluate the following expressions. Practice Scaffolding 1) Agenda

26. 26 Directions: Using the Order of Operations, evaluate the following expressions. Practice 2) Exponents 3) Multiplication/Division 4) Addition/Subtraction Parentheses or Grouping Symbols 1) Orders of Operations 1) Agenda

27. 27 Directions: Using the Order of Operations, evaluate the following expressions. Practice 2) Agenda Scaffolding

28. 28 Directions: Using the Order of Operations, evaluate the following expressions. Practice 2) Agenda 2) Exponents 3) Multiplication/Division 4) Addition/Subtraction Parentheses or Grouping Symbols 1) Orders of Operations

29. 29 Practice 1) 2) 20 ÷ (6 – 1) 3) 10 + 2 3 – 54) 9 + 3 + 9 ÷ 3 5) 6 + 10 ÷ 2 – 16) 2 + 5 x 6 ÷ 2 Directions: Using the Order of Operations, evaluate the following expressions. 8 4 13 15 10 17 Agenda

30. Assessment/Exit Slip 30 Amy Evaluate : Who is correct? Agenda Jamal 3 14 Woops!! Amy added first

31. Back to Overview 31 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

32. 32 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 Expressions and Equations 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions. 1. Write and evaluate numerical expressions involving whole-number exponents. 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real- world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = ½. 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. 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

33. 33 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

34. 34 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

35. 35 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

36. 36 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

37. 37 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

38. 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… 38

39. 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… 39