# Order of Operations Made Easy!

## 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

• 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)

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 evaluating a numerical expression.
• Apply the order of operations correctly when evaluating numerical expressions.
• Simplify their answers as much as possible when evaluating numerical expressions.

## Keywords

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

35 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
• Whiteboard and whiteboard markers
• Paper
• Pencil
• Eraser

• Andres Chan

## Learning Objectives

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

• Identify which operations have priority when evaluating a numerical expression.
• Apply the order of operations correctly when evaluating numerical expressions.
• Simplify their answers as much as possible when evaluating numerical expressions.

## 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: 1 minutes

The teacher will give the students 20 seconds to solve the following problem:

In the remaining time, the class will reflect on which was the correct answer and why.

The correct answer is 9. If the students applied the wrong order of operations, they would probably get answers like: 8, 3, etc. Their wrong answers may also include fractions.

This warm-up will serve as a diagnostic test to see how much the students know about the order of operations.

### Introduction

Time: 1 minute

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

• Identify which operations have priority when evaluating a numerical expression.
• Apply the order of operations correctly when evaluating numerical expressions.
• Simplify their answers as much as possible when evaluating numerical expressions.

### Presentation / Modeling / Demonstration

Time: 12 minutes

• The students will watch the following video:

• After watching the video, the students will reflect on the order of operations by analyzing the acronym PEMDAS: Parentheses/Brackets, Exponents, Multiplication, Division, Addition, and Subtraction.
• The teacher should make sure that the students understand that multiplication and division have the same priority, and when they face a problem with both multiplication and division or division and multiplication one next to the other, they should solve the problem from left to right. For example:   12 / 4 x 3 =  12 / 4 x 3 = 3 x 3 = 9
• The same rule applies when there is an addition and subtraction, one next to the other. You should solve the problem from left to right. For example: 16 - 4 + 12 = 16 - 4 + 12 = 12 + 12 = 24

### Guided Practice

Time: 5 minutes

The students will play an interactive game to test their mastery of the order of operations. The game has different levels, and if the student has difficulty getting the right answers, there is an option for hints about PEMDAS.

When a student makes a mistake, the game gives an instant feedback on what was wrong.

Exploring Order of Operations - Use It! (link to the interactive game)

### Evaluation

Time: 10 minutes

On a piece of paper solve the 12 problems presented in the following quiz. To see the answer, just click the 'Answer' link next to each problem, and a complete step-to-step solution of the problem will be shown on screen.

Order of Operations QUIZ (link to the quiz)

### Application

Time: 6 minutes

In order to apply all the concepts learned on this lesson, the student will pick two problems from the worksheet presented below. He/she will solve those two problems on a piece of paper, and will check the answers on the answer key at the end of the worksheet. The answer key includes a detailed step-by-step explanation for each problem.