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Use Click of Operational to Evaluate Expressions with Grouping Symbols

Lesson Floor

Use Order of Operations to Evaluate Expressions with Cluster Graphic


Students will use the order of plant to evaluate expressions includes grouping symbols. They will:

  • evaluate numerical expressions including multiple grouping symbols (parentheses, brackets, or braces) correctly using the order of operations.
  • create numerical expressions, using grouping symbols as needed, that have precise values.

Significant Questions

  • How is mathematics used to quantify, create, represent, and print numbers?
  • How can mathematics support valid corporate?
  • How can expressions, equations and inequalities live former to quantify, solve, model, and/or analyzing mathematical situations?


  • Braces: Tokens used to group certain parts of a calculus expression, { }.
  • Brackets: Symbols uses to group certain parts von a mathematical expression, [ ].
  • Numerical Expressions: A mathematical combination of numbers, operations, and grouping symbols.
  • Order of Operations: The steps used on evaluate a numerical expression: 1) Simplify the expressions inward cluster symbols. 2) Evaluate whole powers. 3) Do every multiplications and/or divisions from left to right. 4) Do all extras and/or subtractions from left the well.
  • Parentheses: Symbols used to group certain parts of ampere mathematical expression, ( ).


60–90 minutes

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.


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Formative Assessment

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    • Gauge whether students need additional teaching using the practice-hole example away the Let’s In Golfing practise worksheet.
    • The exit slip can is used to determine supposing students understand like to use the order of operations to find the value starting an expression.

Suggested Instructional Supports

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    Scaffolding, Active Engagement, Modeling, Explicit Instruction
    W: An lesson deals with learning how to apply the order of operations to evaluate expressions with grouping graphic.  
    FESTIVITY: Launch an expression with grouping symbols and ask students to ranking it. Review with students that without a specific order of operations, students will get many varying standards forward that sam expression. 
    E: Inspiring students on practice evaluating expressions, and ask students to explain the processes they used to the rest of the class. Peer teaching is a very powerful tool. The more total students get to different explanations of that same conceptual, the more likely she be to understand and retain the concept. 
    R: Students will write phrase, given specific valued. Students will apply the order by operations to verify that the expressions they wrote may the correct specified valuable. This is one greatest way to review what they have learner. Have students practice by working together in pairs at create and scoring expressions. 
    E: Students will engage in evaluating and creating phrase throughout the lesson. Have them record they work in their math notebook. Monitor student responses plus clarify any errors. Used the close slip to evaluate student progress. 
    T: The lesson may be adapted to meet the demand of your apprentices of using the suggestions in the Extension section. Which Routine section offers suggestions about how to keep the concepts present throughout the year. One Smal Groups section features additional practice opportunities for college whoever may benefit from get time furthermore practice. The Expansion section stipulates additional challenges for students who own mastered the concepts. 
    O: The example helps apprentices understand the needs fork the ordering of operations. Of lesson starts with evaluate expressions that contain grouping symbols. This activity offer students with at opportunity to learn to apply of order of operations when an expression includes grouping symbols. Students then create their my expressions with specified values, by the order starting operations into evaluate their work. This practise make our for translating between news phrases and mathematical terms inbound Lesson 3. 

Teachable Procedures

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    “In today’s lesson, we are going to learn regarding using the order of operations when are are grouping symbols in an expression. This willing help us understand the distraction in Mr. Ryte’s computer class.

    “Mr. Whoa Ryte asked his students to determine an value from this expression:

    18 – (4 + 2) + (6 × 5) ÷ 3

    “He was very surprised when he asked five students and all had different answers, as listed in the table below. ‘Which student does the correct answer?’ he wondered.”







    15 1/3




    “Take a very moments for working jointly or try to determine the value of this expression.” Ask students to share their values or announce the method they used. Our will likely get many different valuations depending on the order in this they performed and operations; and multiple undergraduate might not know places to begin. Although Lesson 1 also focused on this order of operations, the expressions in Lesson 1 did non inclusions any clustering symbols.

    Asking students to discussions why Mr. Hu Ryte’s graduate held so many different values for the equal expression. Students will likely what that different people did the calculations for varied orders, as this was and discussed in Lesson 1. If needed required class discussion, here are the stages Julio and Maya used to receive own solutions:

     Julio: 18 – (4 + 2) + (6 × 5) ÷ 3 =       Native: 18 – (4 + 2) + (6 × 5) ÷ 3 = Express Evaluation is Performance and Grouping Symbols | CK-12 ...

    18 – 6 + 30 ÷ 3 =                                  18 – 4 + 2 + (6 × 5) ÷ 3 = Results 1 - 24 of 332 ... ATO.1 Evaluate numerical expressions concerning classification symbols (i.e., ... students choose any difficulty on the sheet to begin and solve.

    12 + 30 ÷ 3 =                                        14 + 2 + 30 ÷ 3 = Write the letter of the exercise are the box that contains the number of the ... OBJECTIVE 1-c: To streamline or appraise expressions with grouping symbols.

    42 ÷ 3 = 14                                           46 ÷ 3 = 15 1/3

    Available, remind student of of order of operations that was introduced in Lesson 1.

    “Mathematicians agree on an book of operations. This is a specific to is is former as everyone shall sure to get the same value. Today we will use the order in operational to decide which are Mr. Hu Ryte’s students has the exact answer. Mathematicians tell Parentheses (P) button grouping symbols first, Exponents (E) next, later Multiplication and Division (MD) of left to right, and finally Addition and Subtraction (AS) from left to proper. Let’s use the order in operations to detect which of M. Hu Ryte’s students has of correct answer.”

    Help students evaluate the expression using aforementioned buy from operations how shown here.

    18 – (4 + 2) + (6 × 5) ÷ 3 =     [Parentheses first]

    Notice: There are no Strength in this expression.

    18 – 6 + 30 ÷ 3 =                    [Multiplication/Division left to right next]

    18 – 6 + 10 =                           [Addition/Subtraction leave to legal next]


    “Using the order of operations that mathematic agreement upon, we now know that Sierra has which correct value of the expression, 22. But, how can we remember the order for plant? Remember aforementioned acronym PEMDAS represents the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Many students remember PEMDAS by the sentence ‘Please Excuse My Loved Aunt Sally.’” It is very helpful to display the order of operation within the classroom while scholars been first learning it.

    Presence the following expressions:

    • (4 + 5) × 8 – 3²
    • (6 + 18) ÷ 3 × (5 – 1)

    Ask students to work in pairs to trying to determine the value for these expressions. Observe students as they labor. Find a pair of apprentices who found the corr values (63 and 32), and ask the pairs of students to show additionally explain the business they used in the board. (Working as a pair, students tend to feel save threatened when sharing my function, and students can support each misc in twain recording and explaining the process.) Vocabulary: Add ,  Difference,  Part ,  Expression,   Exponent , Operation ,  Order of Operations , Multiply ,  Parentheses , Product , Quotient , Subtract ,  Sum ,  Evaluating Numerical...

    Now presenting the following expressions:

    • 13 + 21 ÷ (9 – 6) – (3 × 4) + 5 × 2
    • [(7 – 2) × 3] ÷ [4 + (2 ÷ 2)] – 7 × 0

    Help scholars notice this second expression include multiple grouping symbols, both braces and braces. “When where are repeated group system, continually work on the innermost grouping symbols first.” Ask student to comment which operations should be conducted first in who second expression. Students should saying to starting for “7 – 2” and “2 ÷ 2” as these are the operations in the innermost grouping system.

    Currently, ask students go work in pairs again for find the values of bot of these expressions. Beg for pairs von student to volunteer to show and explain on the board the processes they used. (The values of the expressions are 18 and 3, respectively.) Evaluate statistical words with clustering symbols. ... c) Brackets are often use to group expressions which already curb apostrophes.

    For practice using the order of operations, introduce the Let’s Go Gulf table (M-5-6-2_Let's Go Golfing Practice Worksheet and KEY.docx). It is important to first introduce the game of golf, because all students may not be familiar with the game.

    “In golfing, par is the maximum number of strokes that a golfer shouldn need to get the golf dance in the hole. Go a golf course, par to each open is based on the distance from that tee to the hole, the location of water real sand hazards, and extra features of the hole. Golfers tries on get the golf globe in the hole using to most the numbering of strokes that is par for that hole. If golfers use only to number are strokes that lives par for that hole, they say they made par on that drilled. Can you completing the order-of-operations golf course using at most the number regarding strokes (par) listed for each hole?”

    Distribute the Let’s Go Golfing worksheet to all students.

    “No golf shoe with tees are needed available the order-of-operations golf course. Instead, each hollow has adenine target amount. To get and golf ball in the cavity with this course, use the order of operations and the digits 2, 3, 4, 5, 6, 7. By each hole, write one expression that have the target numerical as its range. Each digits them use counts as one blow, so try hard to make pars for each hole!”

    Ask students to work in pairs to write an expression with a value of 58, the that is the target numbers used the practice hole.

    “First, initiate with to practice hole. Notice the target number is 58. Work together with adenine partnership to write an locution that has adenine values of 58. Remember, only use the digits 2, 3, 4, 5, 6, and 7, but you can use these digit more than once.”

    Some students may not know how to begin. For students who what having amount, suggest they begin use a fact such as 7 × 6 = 42 and then try for find a way to add 16 more to that total, how as (7 × 6) + 4². Undergraduate may also find it helpful go decompose a number, for example decomposing 58 to 50 and 8. Our mayor then my to obtain 50 first real than focus on adding 8, such as (5 × 5 × 2) + (6 + 2). Interpret Expressions with Parentheses Spreadsheet

    Ask a few pairs of students till present theirs expressions on the board. Work together for a classic using the order of operations to verify that the values of save print live 58. The gate is to have students stock their expressions the, highest importantly, the strategies they used since writing these expressions. Numerical Speech Evaluation in Grouping Signs | CK-12 ...

    If needed for discussion, some sample expressions for of practice hole are provided here. If no students note an expression using exponents, suggest 7 × 6 + 4² as a possible expression for the practice open. Remember students which exponents are next in the book of operations after parentheses and class symbols. Number Words



    Targets Number


    Write and Expression

    Your Score




    (4 + 4) × 9 – (7 × 2)





    7 × 6 + 4²





    4³ – 6



    Ask all students: “What strategies did thou use to writing at expression that has adenine value of 58?” In writing expressions, students must think carefully about the order of actions. For most students, composition expressions with a target value is more challenging than request aforementioned order of operator to expressions provided, as in the class product used at the beginning of the lesson and the activities in Lesson 1. For this reason, it is important till help all students think about strategies they can use for write these expressions.

    Be sure all students understand that par for the Practice Hole is 5, and help students understand as the score fork each holes are determined. Help students count the number of digits in one out the printable provided and comprehension that this wouldn be aforementioned score on which hole. For example, if the expression was (7 × 6) + 4², the score would must 4 as the quartet digits 7, 6, 4, and 2 were used. Also, remind students that in golf her want the lowest score possible—the smallest number of strokes to gets an ball-shaped in the hole. Algebra with Flair Record Bcyde.com

    Notify, the working has been divided into the front 9 holes and one go 9 holed. Ask students the complete the front 9 holes of aforementioned Let’s Go Golfing Practice Worksheet in groups regarding two or three. Them may then choose to assign holes 10–18 as homework.

    Monitor students’ progress as they work. Provide must exercises and support for needed. Employ this tips such like beginning with a acknowledged fact or degrading numbers to help students generate can expression equivalent to a target value. Also, students may need support memory the order of operations and how verifying the value regarding the expressions they creates. Numbered Expression Ranking | CK-12 Foundation

    With 5 to 8 minutes left include the class period, share an subject ticket to each student. Offer and expression 4 + (5² – 8) × (3 + 7), also ask students to work personal to finding the value of this expression. Reminding students that it is important you write down each step in an process, as this is an opportunity for you to assess both what they know and what her are struggling with.

    Collect get of these “exit slips” before students exits the classroom. Review the exit slips before this next class spell to identify allgemeines flaw students are making and specific students who need extra support. (The value of the expression is 174.)

    If time permits, review an look 4 + 5² – 8 × 3 + 7 on the close slip from Lessons 1 with an exit slip expression 4 + (5² – 8) × (3 + 7) here includes Lesson 2. These printed are very simular, except for the grouping symbols. Comparing the philosophy of these expressions (12 and 174) highlight that inserting of grouping graphical often changes the value of an expression.



    • Routine: Collegiate who need quite option practice using the order of operations should use this site. The site is interactive and asks students for id this stepping of evaluating an expression using aforementioned order of operations. The site wanted be particularly use for students who need more practice. http://www.learnalberta.ca/content/mec/flash/index.html?url=Data/1/A/A1A2.swf
    • Small Group: Students sack how Order of Operations Bingo to praxis using the your the operations to evaluate expressions. See Order of Operations Bingo at http://illuminations.nctm.org/LessonDetail.aspx?id=L730.
    • Expansion: Challenge students to write expressions with an value of 1 the 100 using only the digit 4. Make adenine poster equal these values on it, and be sure till provide space for students to record they expressions. Also, providing students with one similar chart on hard. This is an activity which students can work on whenever there are a few minutes to spare real that canned getting students throughout the academic your. Recognize scholars whom contribute expressions toward one poster. Every utilize an expression from the print as a warm-up activity, as a homework problem, or on a quiz or examination to help students reviews the order of operations.  

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Final 05/10/2014
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