Order of

Created Feb. 7, 2024 by Itzhak Feygelman

Lesson Title:

Order of Operations Made Easy! - Remix

Abstract

This lesson is about evaluating numerical expressions, and it was designed for adult learners who are preparing to take their High School Equivalency tests. This course will help the students evaluate numerical expressions correctly by following the correct order of operations, which includes the four basic arithmetical operations and the use of exponents and grouping symbols.

Learner Audience / Primary Users

This lesson was designed for adult learners that are preparing to take their High School Equivalency tests, and instructors as well.

Educational Use

  • Curriculum / Instruction

College & Career Readiness Standards (CCRS) Alignment

  • Level: Adult Education
  • Grade Level: Grade Level C
  • Subject: Mathematics
  • Domain: Operations and Algebraic Thinking
  • Standard: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (5.OA.1) 
  • Domain: Equations and expressions
  • Standard Description:  Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1)

Language

English

Material Type

  • Instructional Material
  • Homework and Assignments
  • Images and Videos
  • Diagnostic, formative and final assessments

Learning Goals

The purpose of this lesson is for learners to:

  • Identify which operations have priority when calculating prices for groceries before checkout
  • Apply the order of operations correctly when evaluating 3 out of 5 grocery carts before checkout
  • Simplify 3 out of 5 grocery prices before checkout

Keywords

  • Designers for Learning
  • Adult Education
  • Exponents
  • Grouping symbols
  • Numerical expressions
  • Order of operations
  • PEMDAS

Time Required for Lesson

45 minutes

Prior Knowledge

Students should be able to:

  • Work with the basic arithmetic operations.
  • Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.

Required Resources

Depending on the resources available, this course can be delivered as a fully online course, a face-to-face course, or a hybrid course.

  • Access to an electronic device which includes: computers, smartphones and tablets
  • Access to the internet
  • Whiteboard and whiteboard markers
  • Printer (to print out grocery item cards) or Projector/ Screen Clone Display (to show learners grocery item cards)
  • Paper
  • Pencil
  • Eraser

Lesson Author & License

  • Itzhak Feygelman
  • License: Creative Commons CC BY  4.0 license

Learning Objectives

By the end of this lesson, the learner should be able to:

  • Identify which operations have priority when calculating prices for groceries before checkout
  • Apply the order of operations correctly when evaluating 3 out of 5 grocery carts before checkout
  • Simplify 3 out of 5 grocery prices before checkout

Lesson Topics

Key topics covered in this lesson include:

  • Evaluating numerical expressions
  • Order of operations
  • Grouping symbols and exponents

Context Summary

This course will engage students to one of the fundamental skills in Arithmetic, which is the order of operations. By learning the correct order in which a numerical expression should be solved, the students will be able to apply this knowledge in future courses in Algebra, Geometry and Precalculus.

Relevance to Practice

When given a mathematical problem, why do different people get different answers? The answer may lie in the order in which we solved the problem. Many people are not conscious that there are conventions applied to solve numerical problems involving more than two operations. This lesson aims to provide the students with the knowledge to apply this conventions when solving numerical expressions.

Key Terms and Concepts

  • Numerical expression
  • Evaluating numerical expressions
  • Grouping symbols
  • Order of operations
  • PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction)
  • Simplifying expressions

Instructional Strategies and Activities

Warm-Up

Time: 5 minutes

The teacher will talk about a recent grocery trip and write on the board the prices of groceries that they selected during the trip. The teacher will say and write out what they bought: 2 lbs of bananas at .99 cents per lb and 2 dozen eggs at $1.99 each. The teacher will then say they checked their pocket and found out they forgot their credit card and phone, and only have 5 dollars on them. The teacher will then ask the learners: Can they buy everything they picked up?

Learners will try to answer and even write out the problem on their notebook/piece of paper. The teacher will call out learners or even ask them to come write on board. The equation will be written out as: 2x.99+2x1.99. The teacher will then ask if any student knows where to start first in the equation. The teacher will take any answers and will segue into the next activity. 

Introduction

Time: 1 minute

The teacher explains the goals of this lesson, which are: 

  • Identify which operations have priority when calculating prices for groceries before checkout
  • Apply the order of operations correctly when evaluating 3 out of 5 grocery carts before checkout
  • Simplify 3 out of 5 grocery prices before checkout

Presentation / Modeling / Demonstration

Time: 12 minutes

  • The teacher will begin a simulation of a grocery store trip
  • The teacher will pull up on the screen or handout the GroceryCart_POV_1.jpg picture that is included here
  • The teacher will tell a story of how a family relative, Aunt Sally burps in front of everyone in the grocery store, and family members always have to say: “Please Excuse My Dear Aunt Sally”
  • The teacher/ will then also explains that this is how you can remember the acronym for order of operations – PEMDAS
  • The teacher will then present images of grocery store items and will show the quantity times the price as an equation, e.g., 1 lb of bananas at $.99 a lb + 2 dozen eggs at 1.99 each + 2 bottles of soda at a price of 4 for 5. The teacher will display the image located here while working on this problem. 
  • Or 1 x .99 + 2 x 1.99 + 2 x (4 / 5) =
  • The teacher will ask if anyone can tell them the price of the grocery
  • The teacher will then say “Please Excuse My Dear Aunt Sally” and use the first letter of each word to see which operation should be used first in the equation above

Guided Practice

Time: 7 minutes

    • The learner will go through a shopping trip where they are only allowed to spend 10 dollars.
    • The teacher will handout images of grocery store items (with the price included) in the form of 1 banana card, 2 soda cards, 1 egg carton card and 1 bread card
    • The teacher will give guided practice as the learners write out the groceries they have in the form of an equation: 1.99 + 2 x .99 + 1.99 + 1.99.
    • The teacher will again mention Aunt Sally and her story of how she burps in front of everyone in the grocery store, and family members always have to say: “Please Excuse My Dear Aunt Sally”
    • The teacher/ will then again explain that this is how you can remember the acronym for order of operations – PEMDAS
    • The teacher will then refer them again to their playing cards and simplify the equation further: 1.99+1.98+1.99+1.99 and then finally 7.95. 
    • The teacher will give immediate feedback
    • Link to download banana card is here
    • Link to download soda card is here
    • Link to download egg carton card is here
    • Link to download bread card is here
    • Link to download cheese card is here

Evaluation

  • Time: 10 minutes
    • The learner will go through a five different scenarios of a shopping trip where they are only allowed to spend 10 dollars in each scenario
    • The teacher will hand out a set of cards for each scenario and then collect the cards at the end of each scenario. The teacher will use the links for cards in the guided practice above. 
    • The learner cannot use a calculator in any form (stand-alone, smart phone, computer)
    • The teacher will give immediate feedback after each scneario

      Scenario 1:
    • The teacher will hand out 2 banana cards, 1 egg carton card, 1 soda card and 2 bread cards
    • The equation will look like this: 2 x .99 + 1 x 1.99 + 1 x .99 + 2 x 1.99
    • The final answer is $8.94 and the answer is yes, the learner can afford the groceries in this scenario. 

      Scenario 2:
    • The teacher will hand out 1 banana card, 2 egg carton cards, 3 soda cards and 1 bread card
    • The equation will look like this: 1 x .99 + 2 x 1.99 + 3 x .99 + 1 x 1.99
    • The final answer is $9.93 and the answer is yes, the learner can afford the groceries in this scenario.

      Scenario 3:
    • The teacher will hand out 2 banana cards, 2 egg carton cards, 2 soda cards and 1 bread card
    • The equation will look like this: 2 x .99 + 2 x 1.99 + 2 x .99 + 1 x 1.99
    • The final answer is $9.93 and the answer is yes, the learner can afford the groceries in this scenario.

      Scenario 4:
    • The teacher will hand out 2 banana cards, 2 egg carton card, 2 soda cards, 1 bread card and 1 cheese card
    • The equation will look like this: 2 x .99 + 2 x 1.99 + 2 x .99 + 1 x 1.99 + 1 x 1.99
    • The final answer is $11.92 and the answer is no, the learner cannot afford the groceries in this scenario.

      Scenario 5:
    • The teacher will hand out 2 banana cards, 2 egg carton card, 2 soda cards, 2 bread cards and 1 cheese card
    • The equation will look like this: 2 x .99 + 2 x 1.99 + 2 x .99 + 2 x 1.99 + 1 x 1.99
    • The final answer is $13.91 and the answer is no, the learner cannot afford the groceries in this scenario.

Application

Time: 10 minutes

Anchored instruction activity: The learner is now a grocery store checker/cashier and has to check out different customers with a variety of different items. The twist is that the cash register is broken and the learner must calculate the groceries themselves. The learner cannot use a calculator in any form (stand-alone, smart phone, computer).

Customer 1:

For simulating the first customer, the teacher will give the learner 2 banana cards, 2 egg carton card, 2 soda cards, 1 bread card and 1 cheese card. The equation will look like this: 2 x .99 + 2 x 1.99 + 2 x .99 + 1 x 1.99 + 1 x 1.99. The final answer is $11.92. 

Customer 2:

For simulating the second customer, the teacher will give the learner 1 banana card, 2 egg carton cards, 3 soda cards and 1 bread card. The equation will look like this: 1 x .99 + 2 x 1.99 + 3 x .99 + 1 x 1.99. The final answer is $9.93.

Customer 3:

For simulating the third customer, the teacher will give the learner 2 banana cards, 2 egg carton card, 2 soda cards, 2 bread cards and 1 cheese card. The equation will look like this: 2 x .99 + 2 x 1.99 + 2 x .99 + 2 x 1.99 + 1 x 1.99. The final answer is $13.91.

Customer 4:

For simulating the fourth customer, the teacher will give the learner 2 banana cards, 2 egg carton cards, 2 soda cards and 1 bread card. The equation will look like this: 2 x .99 + 2 x 1.99 + 2 x .99 + 1 x 1.99. The final answer is $9.93.

Customer 5: 

For the fifth customer, the teacher will give the learner 2 banana cards, 1 egg carton card, 1 soda card and 2 bread cards. The equation will look like this: 2 x .99 + 1 x 1.99 + 1 x .99 + 2 x 1.99. The final answer is $8.94. 

Part 3: Supplementary Resources & References

Supplementary Resources

Khan Academy videos:

References

  • Chan, A. (2017, January 17). Order of Operations Made Easy! Retrieved April 01, 2017, from https://www.oercommons.org/authoring/13476-order-of-operations-made-easy/view

Attribution Statement

The images of grocery items and baseball cards were distributed by iStock for licensed use and published at https://www.istockphoto.com. These images are copyrighted and are not licensed under an open license. Embedded as permitted by terms outlined in the Getty Images contract. 

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