Evaluating Expressions The Order of Operations

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Evaluating Expressions The Order of Operations
21st Century Lessons Evaluating Expressions The Order of Operations

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

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 In-Class Notes Hidden slide to show the answers. 13 5) Scaffolding Agenda

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

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

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

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

Explore- The Four Students Problem

Explore- The Four Students Problem
Marvin challenged four students to evaluate this problem Evaluate: to calculate the value. Click to Return (Time on this slide – 15 min) Time passed 36 min In-Class Notes This is a hidden slide. Preparation Notes Agenda

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

CALCULATOR How can we test it? PC Version- Discussion
Marvin challenged four students to evaluate this problem. Melinda’s Work Ashley’s Work Shawn’s Work Juan’s Work Ashley’s Work Melinda’s Work Juan’s Work Shawn’s Work Click names Ashley How can we test it? Melinda CALCULATOR Juan Shawn All students 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 click the mouse for each step to appear and before clicking to another student’s name, you must click once more to clear all the work. To advance to the next slide, you must click on the slide itself where prompted. The button “all students” will show all fours students work simultaneously. Clicking on “summary” 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 NOTE: This slide is best view in in Slide Show Mode. 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 on 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. Ask the class how we can “test” to see who is correct. This is prompted by clicking on the “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 Agenda

Marvin challenged four students to evaluate this problem.
Discussion Marvin challenged four students to evaluate this problem. Ashley’s Work Click names Ashley Melinda Juan Shawn All students and summary In-Class Notes This is a hidden slide, showing Ashley's work. Preparation Notes Online Calculator Agenda

Marvin challenged four students to evaluate this problem.
Discussion Marvin challenged four students to evaluate this problem. Melinda’s Work Click names Ashley Melinda Juan Shawn All students and summary In-Class Notes This is a hidden slide, showing Melinda’s work. Preparation Notes Online Calculator Agenda

Marvin challenged four students to evaluate this problem.
Discussion Marvin challenged four students to evaluate this problem. Juan’s Work Click names Ashley Melinda Juan Shawn All students and summary In-Class Notes This is a hidden slide, showing Juan’s work. Preparation Notes Online Calculator Agenda

Marvin challenged four students to evaluate this problem.
Discussion Marvin challenged four students to evaluate this problem. Shawn’s Work Click names Ashley Melinda Juan Shawn All students and summary In-Class Notes This is a hidden slide, showing Shawn’s work. Preparation Notes Online Calculator Agenda

CALCULATOR How can we test it? Discussion
Marvin challenged four students to evaluate this problem. Melinda’s Work Ashley’s Work Shawn’s Work Juan’s Work Click names Ashley How can we test it? Melinda CALCULATOR Juan Shawn All students and summary (Time on this slide – 7 min) Time passed 43 min In-Class Notes NOTE: PC USESERS ONLY Click on a student’s name for their results. NOTE: you must click the mouse for each step to appear and before clicking to another student’s name, you must click once more to clear all the work. To advance to the next slide, you must click on the slide itself where prompted. The button “all students” will show all fours students work simultaneously. Clicking on “summary” will prompt the next set of 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 NOTE: This slide is best view in in Slide Show Mode. 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 on 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. Ask the class how we can “test” to see who is correct. This is prompted by clicking on the “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 Agenda

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

34 1 5 3 13 1) 2) 3) 4) 5) Click to Return 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 In-Class Notes This is a hidden slide to access the Warm Up. Preparation Notes 13 5) Click to Return Agenda

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

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

Practice Directions: Using the Order of Operations, evaluate the following expressions. 1) 2) Exponents 3) Multiplication/Division 4) Addition/Subtraction Parentheses or Grouping Symbols 1) Orders of Operations In-Class Notes This is a hidden slide to show the order of operations. Agenda

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

Practice Directions: Using the Order of Operations, evaluate the following expressions. 2) 2) Exponents 3) Multiplication/Division 4) Addition/Subtraction Parentheses or Grouping Symbols 1) Orders of Operations In-Class Notes Hidden slide used to provide the steps to evaluate the expression. Preparation Notes Agenda

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

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