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

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

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

4. Lesson Overview (1 of 3) 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.

5. Lesson Overview (2 of 3) Lesson Vocabulary
Exponent- shows you how many times to multiply the number by itself.
Expression- numbers and symbols grouped together that show the value of something.
Evaluate- to calculate the value.
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
Video clip
Online practice

6. Lesson Overview (3 of 3) Common Core State Standard
Expressions and Equations
6.EE.1 Write 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 Background
Note: 3 minutes into the video is the connection to the order of operations.

7. 34 1 5 3 13 1) 2) 3) 4) 5) Warm Up/Do Now Evaluate:
OBJECTIVE: SWBAT indentify and begin to follow the order of operations when evaluating expressions.
Evaluate: 1) 34 2) 1 3) 5 4) 3
(Time on this slide - 5 min) Time passed 5 min
In-Class Notes
Encourage students to answer these problems quickly.
Remember to provide #4 and #5 with the correct answer.
Scaffolding button shows correct steps to evaluate expression if you want to show
Preparation Notes
This warm up will give you an idea what prior knowledge students have based on the order of operations. Students by default should obtain the correct answer for #1-3 as they will answer the problem from left to right. #4 and #5, students may come up with different answers. At this time the correct answer should be given. Note: some students may think of 3 squared as 3 times 2. A quick discussion explaining that mathematics has a “special order” to evaluate expressions is actually what the students will be doing today-determining that order. Call on students to give their answer to each problem. Be sure to have students explain, in order, the operations in which they used. The scaffold button will show the class the steps in which were taken to evaluate the expression. This may be needed for lower level students or visual learners. 13 5)
Scaffolding
Agenda

8. Agenda: 1) Warm Up 2) Launch 3) Explore Lesson- Discussion- Notes-
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.
1) Warm Up
Independent
2) Launch
Marvin’s Trick- Independent
3) Explore
Lesson-
The Four Students Problem- Partners
Discussion-
Whole class
Notes-
Recourses for Your Notebook- Independent
(Time on this slide - min) Time passed
In-Class Notes
Preparation Notes
Quickly go over agenda. Great chance to review objective and language objective with students.
4) Practice
Partners
5) Assessment/Exit Slip
Independent
Agenda

9. Launch- Marvin’s Trick
Marvin the “Amazing Math Magician”
has a challenge for you!
Hey class, bet you can’t make 75 with the numbers: 3 7 10 15
You can use any operation you like addition, subtraction, multiplication or division, more than once, and in any order you choose.
(Time on this slide – 12 min) Time passed 17 min
In-Class Notes
Give students 5 minutes to attempt the problem. Use the online stopwatch.
NOTE: If students have not come up with a solution after 5 minutes, give them a hint, for example 15 ÷ 3.
Preparation Notes
This slide is just an introduction for students to use multiple operations. Students may complete work in their notebook. The way students write their expression does not matter here. Students will most likely write their solution as three different equations, which is acceptable for now. Use one of the student’s responses to show the “proper” way to write the expression. For example: 15 ÷ x 10.
The next slide will give you the opportunity have a class discussion.
But, you must use all 4 numbers only once.
Agenda

10. 3 7 10 15 How did you make 75 with the 4 numbers?
Launch- Marvin’s Trick 3 7 10 15
How did you make 75 with the 4 numbers?
(Time on this slide - 3 min) Time passed 20 min
In-Class Notes
This slide is optional if want students to write their process on the board.
Preparation Notes:
This slide may or may not be needed depending on how you want to run the discussion. Students can come to the board or verbally explain what they did as teachers write their responses.
Agenda

11. 75 Launch- Marvin’s Trick 3 7 10 15 A way to make using
This is a way to write the work you did as one math expression.
Expression??????
(Time on this slide - 4 min) Time passed 24 min
In-Class Notes
Read slide as it appears.
Emphasize the importance of showing how one evaluates expressions by working down.
The definition does not necessarily need to be mastered at this time.
Preparation Notes
This slide is designed to show visually how expressions are written. Be sure to explain that the process in evaluating expressions to show your work by working down without an equal sign. Some catch phrases: “walk it down”, “bring down everything”. As each operation comes up, emphasize the fact that these were done in a certain order. You should point out the yellow box as the way to write the work students did as one expression. You could ask if anyone notices a difference in the way it is written and the order in which the math was done. Another chance to lead into the idea that is an order to math.
The vocabulary word expression is there for students to become familiar with. It is not necessary at this point that students master this language as it will be enforced throughout the unit.
Numbers and symbols grouped together that show the value of something.
Agenda

12. Explore- The Four Students Problem
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.
(Time on this slide – 15 min) Time passed 36 min
In-Class Notes
Read the slide as it appears.
Assign each group either TWO students or all FOUR students to complete the class work.
Click on the button “evaluate” for the definition. This does not necessarily need to be mastered at this time.
You can click evaluate at anytime during this slide. When you click on “click to return” it will bring back to where you left off.
Preparation Notes
Students may find this challenging, especially Melinda’s problem, but encourage them to work through the problem as they may discover it on their own. Read the task to the class. Be sure to explicitly explain that each group must write the order in which the students evaluated the expressions. Ask students what evaluate means. The definition of evaluate is explained, by clicking on the button “evaluate”. However, it does not need to be mastered. It can also be explain at any point throughout this slide. Clicking “click to return” will bring you back to where you left off.
Hand out the class work assignment assigning TWO problems to each group. This will keep students focused and not feel rushed to solve all four. However, depending on the rigor of your class, you may want to assign all four. Encourage them to be ready to share their findings. As you circulate the room, make sure students are listing the order in which the students answered the problem.
Your group is responsible for 2 or 4 students.
Evaluate?
Agenda

13. Marvin challenged four students to evaluate this problem.
Discussion
Marvin challenged four students to evaluate this problem.
Click names
Ashley
Melinda
Juan
Shawn
All students
and summary
(Time on this slide – 7 min) Time passed 43 min
In-Class Notes
Click on a student’s name for their results. NOTE: you must be “off” the student’s name to show the student’s work.
The button “all students and summary” will show all fours students work simultaneously and will prompt the summary questions.
Emphasize again that each students is working down as they show their steps.
Use the calculator to prove which student is correct. Remember: focus on top of the calculator as it is written to proper way as on their worksheet.
Preparation Notes
MAC USESRS: Follow the directions below.
PC USERS: Click at the bottom of the slide and follow directions there.
MAC USERS: Have different groups share one of their solutions out loud. At this point, click on the slide for the work of that student to appear so the whole class can see. You must click one last time to clear the work before clicking on another student’s work. Show the work for all four students and ask the class which student is correct. Why do they think the student they chose is correct? This is great way to explain that only one person is correct based on the Order of Operations. Click again to clear all students’ work.
Ask the class how we can “test” to see who is correct. This is prompted by clicking on the “all students and summary”. This will also prompt you to click on the calculator. Type in the expression for the students to see the correct answer. Be sure to explain that higher functioning calculators evaluate expressions in the correct order. Focus on top of the calculator as it is written to proper way as on their worksheet (not how it is typed into the calculator).
Online
Calculator
Next slide
PC Users
Agenda

14. Resources for Your Notebook
The Order of Operations
Shawn’s Work
1) Parentheses or
Grouping Symbols 1)
2) Exponents
3) Multiplication/Division
(Left to Right)
4) Addition/Subtraction
(Left to Right)
Think back to the warm up. Is there a problem that contained any symbol Shawn didn’t use?
(Time on this slide - 5 min) Time passed 48 min
In-Class Notes
Remember students have not used parenthesis or any other grouping symbols.
Read the slide as it appears. Note the colors match the operation that is being used.
Preparation Notes
Have students take notes on this slide giving it the title Order of Operations numbering underneath 1-4. We will use this as a resource. Say to students, “Now that Shawn did it correct, let’s capture the steps that he did.” Ask a student what operation was used first for Shawn’s correct answer. Click on the button for exponents to appear. Notice this is numbered 2 since parenthesis has not been used. Have students copy this into their notebook. Continue this process until all the operations Shawn used are finished. When the multiplication/division pops up, quickly explain that multiplication and division are performed left to right and further discussion will be held tomorrow. Give the same explanation for the addition and subtraction part.
Ask the class to think back to the warm up (they can look in their notebook) or click the button provided that will take you right the warm up. Was anything in the warm up different than what Shawn and the others did? Then click the button for parenthesis and grouping symbols to appear. Explain again that more practice will be given tomorrow.
This is also a great opportunity to explain to the class that this is “the” way to evaluate expressions. This order is the order in which all mathematics, adults, kids, the whole entire world, etc. uses. You can make it a very special thing learning the correct order. The tutorial provided in the online resources may help with suggestions.
Click to
open warm up.
Agenda

15. Practice- Partners
Directions: Using the Order of Operations, evaluate the following expressions.
Let’s do number 1 and 2 together!! 1)
2) 20 ÷ (6 – 1)
3) – 5
4) ÷ 3
5) ÷ 2 – 1
(Time on this slide - 1 min) Time passed 49 min
In-Class Notes
Hand out the work sheet.
Model the first the example with them. (Shown on the next slide).
Preparation Notes
Hand out the work sheet and read the directions with the class. The idea behind this assignment is to have students work on some examples with a partner. However, the first one is to be done as you model the process and steps. (The next slide gives the opportunity for the work.) The second problem is more the students work off your model and is quickly discussed before they start working with partner. (Slide 15 is provided to have a discussion).
Be sure to circulate the room as students are working. The order of operations is listed on the class work, but students should also have their notebooks open.
6) x 6 ÷ 2
Agenda

16. Practice
Directions: Using the Order of Operations, evaluate the following expressions. 1)
(Time on this slide - 2 min) Time passed 50 min
In-Class Notes
Click for the proper steps to appear. Model for the students how you would evaluate this expression.
The scaffold button will reveal the order of operations.
Be sure to continue the language of working down to show your steps.
Preparation Notes
The first question of the class work is designed to be modeled on how to evaluate an expression using the order of operations. Depending on the level of the class, the scaffold button provides the list of the order of operations for students to see while you are working through this problem. Ask the class which operation should be used first and why. Be sure to emphasize that numbers that were not used need to be brought down, “walk it down”. Ask the class which operation should come next and why. Again, repeating the process of brining the work down.
Scaffolding
Agenda

17. Practice
Directions: Using the Order of Operations, evaluate the following expressions. 2)
(Time on this slide - 9 min) Time passed 59 min
In-Class Notes
Give students about 2 minutes to answer this question on their own.
Click for the proper steps to appear to see if students calculated the problem correctly.
The scaffold button will reveal the order of operations.
Be sure to continue the language of working down to show your steps.
Preparation Notes
This question of the class work is designed to have students practice on their own and then quickly discussed to see if the students obtained a correct answer. Depending on the level of the class, the scaffold button provides the list of the order of operations for students to see while they are working through this problem. Give the students about 2 minutes to answer this question. Ask students for their results. Click the slide for the correct process to appear. Be sure to emphasize numbers that are not used need to be brought down, “walk it down”. Be sure to clear up any misunderstandings of the problem.
Have students now work with a partner for about 7 minutes to finish the class work. Additional problems were provided for more challenging problems depending on the level of your class.
Scaffolding
Agenda

18. Practice
Directions: Using the Order of Operations, evaluate the following expressions. 1) 8
2) 20 ÷ (6 – 1) 4
3) – 5 13
4) ÷ 3 15
5) ÷ 2 – 1 10
(Time on this slide - 2 min) Time passed 61 min
In-Class Notes
Click for the remaining answers to appear.
The depth of the discussion is teacher’s discretion.
Preparation Notes
This slide just provides the answers to the class work assignment. A suggestion to go over the class work without each problem being show on the board is to have students switch their work with another group’s work to see if there are similarities.
6) x 6 ÷ 2 17
Agenda

19. 1) 2) 3) Evaluate : 14 3 Who is correct? Amy Jamal
Assessment/Exit Slip
Evaluate : 1) 2) 14 3 3)
Who is correct?
Woops!! Amy added first
Amy
Jamal
(Time on this slide - 5 min) Time passed 66 min
In-Class Notes
Hand out copies of the exit slip to each student.
Teacher discretion on how to conduct the exit slip.
Preparation Notes
This assessment is an exit slip. The purpose behind this is to see if students were able to grasp a understanding that there is an order to follow to evaluate expressions. Since the explore part of the lesson was based around ‘who is correct’, asking this question again here connects the whole lesson together. By clicking the mouse, the answers will appear. This is the teacher’s discretion whether or not to provide the answers before the end of the class. Homework is provided.
Agenda

20. 21st Century Lessons The goal…
The goal of 21st 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. 21st Century Lessons The people…
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 21st Century Lessons
Brian Connor – Technology Coordinator