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Order of Operations Worksheets

Welcome to the order of operations worksheets page at Math-Drills.com where we definitely follow orders! This page includes Order of Operations worksheets using whole numbers, integers, decimals and fractions.

Elementary and middle school students generally use the acronyms PEMDAS or BEDMAS to help them remember the order in which they complete multi-operation questions. The 'P' or 'B' in the acronym stands for parentheses or brackets. All operations within parentheses get completed first. The 'E' refers to exponents; all exponents are calculated after the parentheses. The 'M' and 'D' are interchangeable as one completes the multiplication and division in the order that they appear from left to right. The fourth and final step is to solve for the addition and subtraction in the order that they appear from left to right.

More recently, students are being taught the acronym, PEMA, for order of operations, to avoid the confusion inherent in the other acronyms. For example, in PEMDAS, multiplication comes before division which some people incorrectly assumes means that multiplication must be done before division in an order of operations question. In fact, the two operations are completed in the order that they occur from left to right in the question. This is recognized in PEMA which more correctly shows that there are four levels to complete in an order of operations question.

Unless you want your students doing something different than the rest of the world, it would be a good idea to get them to understand these rules. There is no discovery or exploration needed here. These are rules that need to be learned and practiced and have been accepted as the standard approach to solving any multi-step mathematics problem.

Most Popular Order of Operations Worksheets this Week

Order of Operations with Negative and Positive Integers (Four Steps)

Order of Operations With Whole Numbers and Integers

order of operations problem solving tes

The worksheets in this section include questions with parentheses, addition, and multiplication. Exponents, subtraction, and division are excluded. The purpose of excluding some parts of PEMDAS is to ease students into how the order of operations works. To help students see a purpose for the order of operations, try to associate the expressions with related scenarios. For example, 2 + 7 × 3 could refer to the number of days in two days and three weeks. (9 + 2) × 15 could mean the total amount earned if someone worked 9 hours yesterday and 2 hours today for $15 an hour.

  • Order of Operations With Whole Numbers (Addition and Multiplication Only) 2-Step Order of Operations with Whole Numbers ( Addition & Multiplication Only ) 3-Step Order of Operations with Whole Numbers ( Addition & Multiplication Only ) 4-Step Order of Operations with Whole Numbers ( Addition & Multiplication Only ) 5-Step Order of Operations with Whole Numbers ( Addition & Multiplication Only ) 6-Step Order of Operations with Whole Numbers ( Addition & Multiplication Only )

The worksheets in this section include questions with parentheses, addition, subtraction, and multiplication. Exponents and division are excluded. This section is similar to the previous one in that it is meant to help ease students into the order of operations without complicating things with exponents and division.

  • Order of Operations With Whole Numbers (Addition, Subtraction and Multiplication Only) 2-Step Order of Operations with Whole Numbers ( Addition, Subtraction & Multiplication Only ) 3-Step Order of Operations with Whole Numbers ( Addition, Subtraction & Multiplication Only ) 4-Step Order of Operations with Whole Numbers ( Addition, Subtraction & Multiplication Only ) 5-Step Order of Operations with Whole Numbers ( Addition, Subtraction & Multiplication Only ) 6-Step Order of Operations with Whole Numbers ( Addition, Subtraction & Multiplication Only )

One last section to help ease students into the order of operations or simply for students who haven't learned about exponents yet. The questions on the worksheets in this section include parentheses and all four operations.

  • Order of Operations With Whole Numbers (No Exponents) 2-Step Order of Operations with Whole Numbers ( No Exponents ) 3-Step Order of Operations with Whole Numbers ( No Exponents ) 4-Step Order of Operations with Whole Numbers ( No Exponents ) 5-Step Order of Operations with Whole Numbers ( No Exponents ) 6-Step Order of Operations with Whole Numbers ( No Exponents )

The worksheets in this section include questions with parentheses, exponents and all four operations.

  • Order of Operations With Whole Numbers (All Operations, Parentheses and Exponents) 2-Step Order of Operations with Whole Numbers 3-Step Order of Operations with Whole Numbers 4-Step Order of Operations with Whole Numbers 5-Step Order of Operations with Whole Numbers 6-Step Order of Operations with Whole Numbers
  • Order of Operations With Integers (No Exponents) 2-Step Order of Operations with Integers and No Exponents 3-Step Order of Operations with Integers and No Exponents 4-Step Order of Operations with Integers and No Exponents 5-Step Order of Operations with Integers and No Exponents 6-Step Order of Operations with Integers and No Exponents

The worksheets in this section include parentheses, exponents, and all four operations.

  • Order of Operations With Integers (All Operations, Parentheses and Exponents) 2-Step Order of Operations with Integers 3-Step Order of Operations with Integers 4-Step Order of Operations with Integers 5-Step Order of Operations with Integers 6-Step Order of Operations with Integers

Order of Operations With Fractions and Decimals

order of operations problem solving tes

As with other order of operation worksheets, the fractions order of operations worksheets require some prerequisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what prerequisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn't result in too much hair loss.

  • Order of Operations with Positive Fractions (No Exponents) 2-Step Order of Operations with Positive Fractions (No Exponents) 3-Step Order of Operations with Positive Fractions (No Exponents) 4-Step Order of Operations with Positive Fractions (No Exponents) 5-Step Order of Operations with Positive Fractions (No Exponents) 6-Step Order of Operations with Positive Fractions (No Exponents)
  • Order of Operations with Positive Fractions 2-Step Order of Operations with Positive Fractions 3-Step Order of Operations with Positive Fractions 4-Step Order of Operations with Positive Fractions 5-Step Order of Operations with Positive Fractions 6-Step Order of Operations with Positive Fractions
  • Order of Operations with Positive and Negative Fractions 2-Step Order of Operations with Positive & Negative Fractions 3-Step Order of Operations with Positive & Negative Fractions 4-Step Order of Operations with Positive & Negative Fractions 5-Step Order of Operations with Positive & Negative Fractions 6-Step Order of Operations with Positive & Negative Fractions
  • Order of Operations With Positive Decimals 2-Step Order of Operations with Positive Decimals 3-Step Order of Operations with Positive Decimals 4-Step Order of Operations with Positive Decimals 5-Step Order of Operations with Positive Decimals 6-Step Order of Operations with Positive Decimals
  • Order of Operations With Positive and Negative Decimals 2-Step Order of Operations with Positive & Negative Decimals 3-Step Order of Operations with Positive & Negative Decimals 4-Step Order of Operations with Positive & Negative Decimals 5-Step Order of Operations with Positive & Negative Decimals 6-Step Order of Operations with Positive & Negative Decimals
  • Order of Operations With Positive Decimals (European Format: Comma Decimal) 2-Step Order of Operations with Positive Decimals (Comma Decimal) 3-Step Order of Operations with Positive Decimals (Comma Decimal) 4-Step Order of Operations with Positive Decimals (Comma Decimal) 5-Step Order of Operations with Positive Decimals (Comma Decimal) 6-Step Order of Operations with Positive Decimals (Comma Decimal)
  • Order of Operations With Positive and Negative Decimals (European Format: Comma Decimal) 2-Step Order of Operations with Positive & Negative Decimals (Comma Decimal) 3-Step Order of Operations with Positive & Negative Decimals (Comma Decimal) 4-Step Order of Operations with Positive & Negative Decimals (Comma Decimal) 5-Step Order of Operations with Positive & Negative Decimals (Comma Decimal) 6-Step Order of Operations with Positive & Negative Decimals (Comma Decimal)
  • Order of Operations With Fractions and Decimals Mixed Order of Operations with Fractions & Decimals Mixed Order of Operations with Fractions & Decimals Mixed with some Negative Values

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Practice With Order of Operations Problems and Answers

I see it happen all the time in my math classroom: students attempt math problems and get the wrong answer even though they are performing each math operation correctly. How can this be!? Isn’t math supposed to have a single correct answer?

Well, as it turns out, there is a set of rules that tells us the right order and wrong order that operations can be performed in a mathematical expression. And without knowing this very important set of rules, you can’t   be sure that you will always get the correct answer! Let’s take a look at this set of rules and dig into some practice with order of operations problems and answers so that you can make sure this doesn’t happen to you!

What is the Correct Order of Operations?

In math and algebra, the order of operations is an important set of rules that tell us the correct order that arithmetic operations should be performed in when working with a numerical expression. Performing operations in the right order using a standard method makes it so that two people will always get the same correct answer when solving a given problem.

In order to help remember the standard order of operations, we can use the acronym PEMDAS. 

PEMDAS acronym explained

The PEMDAS rule (sometimes known as BEDMAS or the BODMAS rule) works by matching the first letter of each operation to each of the mathematical operations. 

  • P (Parentheses) – We start by performing the operations inside any set of parentheses first. It is important to start with any expressions within innermost parentheses and work outward.
  • E (Exponents) – The next step is to evaluate or simplify any expressions involving exponents or powers. It is important to remember that this step also includes any square root.
  • MD (Multiplication and Division) – It is important to perform multiplication and division from left to right in the order that they appear in the expression. This is a common place where students make mistakes!
  • AS (Addition and Subtraction) – Finally, we perform addition and subtraction from left to right as they appear in the expression. Like multiplication and division, these operations have the same priority and are performed from left to right.

To help my students, I have told them to think of the acronym PEMDAS as standing for “Please Excuse My Dear Aunt Sally”. There are many different ways to remember the PEMDAS acronym, but I have found that this mnemonic device is a great way to help my students remember the order of the PEMDAS acronym.

If you follow the rules of the order of operations, you should find that arriving at the correct answer isn’t as hard as you once thought!

order of operations symbols pixel art

Why Does Order of Operations Matter?

In order to understand when order of operations matters, take a look at this simple 2-step order of operations problem. Consider the following expression:

$$2 + 4 \times 3$$

There are two approaches that you could take here, and only one of them will give you the correct answer! Which one do you think is correct?

two order of operations problems solved two different ways

As you can see, each strategy results in different answers. The strategy on the left adds 2 + 4 first, while the strategy on the right multiplies 4 x 3 first. Remember that we use the PEMDAS rule to help us identify the right order.

PEMDAS tells us that multiplication must be performed before addition. This tells us that the second solution is correct!

Order of Operations Problems and Answers

Let’s take a look at a few more examples of order of operations problems and answers! I’ll start by introducing you to some simpler problems with two basic operations, and we’ll work our way up to more complex 4-step order of operations problems! Just be sure to review the answer key for each problem to make sure you get the same answer!

2-Step Order of Operations Problems

Example #1:  \(5 – 3 \times 2\)

In this first example, following order of operations tells us to perform multiplication before subtraction. Taking a look at the given values, we know that this will result in:

\begin{split} &5 – 3 \times 2 \\ \\ =&5 – 6 \\ \\ =& -1 \end{split}

Remember, performing subtraction first is a common mistake that will prevent you from obtaining the correct answer!

Example #2:  \((4 \div 2) + 7\)

The first step of the PEMDAS rule is to tackle any math expressions inside parentheses. After that, we can add 7 to the result.

\begin{split} &(4 \div 2) + 7 \\ \\ =&2 + 7 \\ \\ =& 9 \end{split}

Example #3:  \(3^3 – 4\)

The first step in this example is to work out our exponent. After that, we can subtract 4 from the result.

\begin{split} &3^3 – 4 \\ \\ =&27 – 4 \\ \\ =&23 \end{split}

3-Step Order of Operations Problems

Example #4:  \(\sqrt{4} \times 3 – 5\)

Remember that the ‘E’ in the PEMDAS acronym also includes the square root operation. As such, we need to evaluate the square root of 4 before multiplying by 3 and subtracting 5.

\begin{split} &\sqrt{4} \times 3 – 5 \\ \\ =&2 \times 3 – 5 \\ \\ =&6 – 5 \\ \\ =&1 \end{split}

Example #5:  \((6 ÷ 2) + 3 × 2\)

In this example we must remember to tackle the parentheses first. While your instinct may be to add the 3 next, remember that you need to multiply 3 times 2 first!

\begin{split} &(6 ÷ 2) + 3 × 2 \\ \\ =&3 + 3 × 2 \\ \\ =&3 + 6\\ \\ =&9 \end{split}

Example #6:  \(7 – 2 × 3 ÷ 2\)

In this example, we multiply 2 by 3 first, then divide the result by 2. Remember that multiplication and division operations are performed in the order in which they appear from left to right.

\begin{split} &7 – 2 × 3 ÷ 2 \\ \\ =&7 – 6 ÷ 2 \\ \\ =&7 – 3  \\ \\ =&4 \end{split}

4-Step Order of Operations Problems

Example #7:  \(2 + 4 × 3 – 4 ÷ 2\)

\begin{split} &2 + 4 × 3 – 4 ÷ 2 \\ \\ =&2 + 12 – 4 ÷ 2 \\ \\ =&2 + 12 – 2  \\ \\ =&12 \end{split}

Example #8:  \(2^3 + (4 × 3) – 6 ÷ 2\)

\begin{split} &2^3 + (4 × 3) – 6 ÷ 2 \\ \\ =&2^3 + 12 – 6 ÷ 2 \\ \\ =&8 + 12 – 6 ÷ 2  \\ \\ =&8 + 12 – 3 \\ \\ =&17  \end{split}

Using Order of Operations to Solve Math Problems

When I teach order of operations in my classes, I always encourage my students to keep the PEMDAS rule handy for every problem. Sometimes these problems can seem very simple, but may actually require more thinking. In particular, problems with both multiplication and division operations tend to confuse students! 

Take the time that you need to fully understand this very important concept. You will find it comes up often in your studies of math, particularly when working with algebraic formulas !

Like all math concepts, mastering the use of order of operations takes practice and critical thinking. I am hopeful that these order of operations problems and answers have helped you feel more comfortable with this very important algebra skill!

Did you find these order of operations problems and answers helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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order of operations problem solving tes

Teaching Order of Operations: No-fail Strategies that Work!

order of operations problem solving tes

Order of operations can be frustrating to teach, but it doesn’t have to be. There’s no question that this is an extremely challenging topic for elementary students. Fortunately, there are loads of strategies for teaching order of operations that are both fun and effective.

One reason kids struggle with this concept is that there are so many rules to learn and follow. Even worse, rules that appear to be simple often prove to be deceptively complex.

For example, most kids can easily remember that multiplication and division are always performed before addition and subtraction, especially after they learn to follow the order described by “PEMDAS.”

However, they tend to get stuck when an equation includes both multiplication AND division. Most kids automatically multiply before dividing, but order of operations tells us to perform the operation that comes first when reading the problem from left to right. No wonder kids find order of operations to be super confusing!

Another reason kids struggle is that even when they understand how to use order of operations correctly, they don’t apply the rules systematically. Because the problems look easy, students try to rely on mental math alone to solve them. This may work with the easy problems, but mental math isn’t effective with more complex problems that include multiple operations, parentheses, exponents.

order of operations problem solving tes

Order of Operations Lesson

The lesson begins with a quick activity to get students thinking about why we need rules for solving equations. This lesson “hook” is followed by an order of operations mini-lesson, a guided practice session, and a fast-paced game that doubles as a formative assessment activity.

To get the most from the activities, each student will need a dry erase board or tablet where they can work out the problems. You’ll also need at least one calculator for the class that uses order of operations correctly. A physical calculator is fine if displayed under a document camera, or you can use an online calculator. Be sure to test the calculator prior to the lesson to be sure it can handle order of operations problems. To find out, enter 1 + 2 x 3 and press the = sign. The correct answer is 7, so if your calculator displays 9 as the answer, it does NOT use order of operations correctly.

order of operations problem solving tes

Before you teach PEMDAS or any other strategy, challenge your students to solve a simple equation such as this one: 3 + 8 x 2 = ?  Ask your students to write the equation on a dry erase board or tablet, and then solve it and show you the answer.

You’re likely to see two different answers, but resist the urge to reveal the correct answer at this point. Most students will say the answer is 22 because they added 3 and 8 and then multiplied the sum by 2. However, who have studied order of operations in the past will say the answer is 19 because they multiplied 8 times 2 and added 3 to the product. Your students might be a bit confused when they notice that some of their classmates have different answers, but they are about to become even more confused!

order of operations problem solving tes

Tell your students that you’re going to use a calculator to check the answer, and as they watch, enter the problem above. When the calculator displays 19 as the answer, act surprised and say you must have entered the problem wrong. Enter it carefully again, and when you get the same answer, try a different calculator. When you get the same answer yet again, ask your students to pair up with a partner to discuss why the calculator keeps giving the “wrong” answer. After they talk it over for a few minutes, tell them that 19 is actually the correct answer, and that you’re going to teach them some important rules for solving problems that involve more than one operation.

This activity is a great way to start your order of operations lesson because it creates a feeling of “cognitive dissonance,” a state of mind in which we struggle to assimilate new facts that don’t match what we thought we knew about a topic. When students experience cognitive dissonance, they become eager to learn and open to new ideas, so it’s the perfect time to start the actual instruction.

2. Direct Instruction: Introduce Order of Operations

How you introduce order of operations will depend on your students’ readiness and their prior experiences with algebraic concepts. You might want to start by teaching your students how to use parentheses to indicate which part of an equation should be solved first. Write an equation two different ways, keeping the numbers the same but placing the parentheses around different pairs of numbers like this: (5 + 3) x 2 = ? and 5 + (3 x 2) = ?

order of operations problem solving tes

Show your students how to solve both problems, and point out that even though the numbers used in the equations are the same, the solutions are different. Give your students several more pairs of problems that have the same numbers and the parentheses in different locations. Stop after each problem to discuss the solution and clear up misunderstandings.

Next, display an equation that doesn’t have parentheses, like 15 – 5 x 2 = x. Point out that it’s not clear which part of the problem should be solved first, and as they’ve seen with the previous example, the order in which you perform the operations DOES matter.

Tell your students that mathematicians have agreed upon a set of rules called the “order of operations” that must be followed when solving problems. If your students have already studied exponents, you can teach the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. The phrase “Please Excuse My Dear Aunt Sally” will help them remember the order of those letters. If your students haven’t studied exponents, you can substitute the acronym PMDAS and the phrase “Pass My Dad a Sandwich.”

order of operations problem solving tes

3. Guided Practice: Teaching the Step-by-Step Method for Solving Problems

For the next part of the lesson, you’ll need to download the  Order of Operations Freebie  shown above. This freebie consists of three pages from  Order of Operations Bingo Level 1 . Exponents are not mentioned on these pages, and the acronym PMDAS is used instead of PEMDAS.

After using the Order of Operations Review to explain the PMDAS acronym, display a copy of the practice page or give each student a paper copy. Introduce the step-by-step method for evaluating algebraic expressions by explaining the example at the top of the page. Using this strategy, each step is written on a separate line.

order of operations problem solving tes

Guide your students through the process of solving the 6 practice problems one at a time. Check and discuss the solutions after each problem, and be sure to have them show you their work. If needed, refer to the answer key on page 3  of the freebie for step-by-step solutions.

If you have not taught this step-by step-method of solving order of operations problems, you might be tempted to skip it and let your students use mental math. Most of the problems are so easy that your students may be able to solve them without writing out each step.

However, relying on mental math to solve more challenging problems results in a lot of careless mistakes, so I recommending teaching your students to follow this step-by-step strategy with EVERY problem. If they get in the habit of using this systematic approach, they will be able to solve more complex problems with ease later. Trust me on this!

4. Play an Order of Operations Game

After your students understand how to solve order of operations problems, they’ll need lots of practice while the concepts are fresh in their minds. Games are far more effective for practice than worksheets because they are fast-pace and fun, motivating students to solve dozens of problems in a short time.

If you play the game as a class and discuss the answers after each problem, your students will know within a few round of the game if they are solving the problems correctly. If they aren’t, they will be motivated to ask questions and seek help to improve. Furthermore, many games can serve as formative assessment activities if you walk around while students are solving each problem to observe their work. Without having to administer a formal test, you’ll be able to see who understands the concepts and who needs more help.

order of operations problem solving tes

Order of Operations Bingo  is my favorite activity for practicing this skill because players can’t win without using order of operations correctly. To foster math skill development, ask your students to work out each problem on a dry erase board or tablet, using the step-by-step method. Stop after each problem to discuss each solution before presenting the next task card. Remind your students that they can only cover the answer on their Bingo boards with a chip if they had the correct answer BEFORE you revealed the solution to the class. If you enforce this rule, I can guarantee a huge drop in careless errors after the first round of the game!

5. Review and Practice with Order of Operations Task Cards or digital Boom Cards  

The first four strategies are extremely effective for teaching kids how to use order of operations correctly. However, in order to retain what they’ve learned, your students will need opportunities for more review and practice throughout the year.

Whether you’re teaching students remotely or in the classroom, the Order of Operations Boom Cards below will meet this need perfectly! Boom Cards are self-checking, interactive, digital task cards that can be played on almost any device with Internet access. They are hosted on the Boom Learning platform, but free accounts are available. My Boom Cards also include optional audio directions; students can click the sound icon in the corner of each card to hear the words on the card read aloud! Kids love these interactive task cards because they’re fun, and teachers love them because they’re so effective!

order of operations problem solving tes

If you prefer printable task cards, the Order of Operations Task Cards below will make it easy for your students keep these skills fresh. You can use the task cards shown below in math centers and with cooperative learning activities like Showdown  or  Team Scoot .

Order of Operations Task Cards Bundle from Laura Candler

Differentiating Instruction is Easy

Differentiating instruction is easy because there are two levels of instructional materials, including the task cards, bingo game, and assessments. Level 1 includes basic problems like the ones used in the freebie. The materials for Level 2 have more complex problems and some of the problems include exponents. Both sets of bingo games, the printable task cards, and the assessments are included in one cost-saving bundle. If your curriculum includes exponents, the Order of Operations Games and Tests Bundle is your best option. If you use both levels in your classroom, you might want to print the task cards and game materials for each level on different colored card stock to keep them separate. (Boom Cards must be purchased separately.)

Order of Operations Games, Task Cards, and Tests Bundle

Classroom-Tested: Teacher and Student Approved

I love having teachers field test my products with their students. Several teachers tested Order of Operations Bingo with their students, and two of them sent pictures of their students playing the game. I love to see photos of kids using my lessons and activities, and I couldn’t resist sharing a few of them with you!

Fourth grade teacher Christina Ashburn tested Order of Operations Bingo and had her students solve the problems on dry erase boards as described in the lesson. She didn’t have bingo chips, so she laminated the game boards and had her students color over the answers with dry erase markers. I honestly never thought of doing that, but it’s a brilliant idea! For one thing, if kids are solving problems on dry erase boards, their markers should be handy. Also, you don’t have to worry about plastic Bingo chips ending up all over the classroom floor!

Order of Operation Bingo is a fun and effective math game for practicing order of operations skills. #orderofoperations

Fifth grade teacher Sheryl Nicholas also tested the game in her class. After observing her students play Order of Operations Bingo , she discovered an unexpected benefit. Sheryl explained, “My favorite part was how my non-English speakers immediately felt involved in the review. So much lately is ‘drill and test,’ but this made it a lot more interesting for the students. All were engaged in the activity and there was quite a bit of math talk as well as individual practicing of skills.”

order of operations problem solving tes

After they played the game, Sheryl interviewed her students to get their feedback and shared some of their comments with me. I especially loved reading two comments about having to write out the steps of each problem. One student said, “I liked that you wouldn’t let me do them in my head but made me write the problems on the iPad and do them.” Another student wasn’t quite as enthusiastic about that part of the lesson, stating, “I wish you would have let me do these problems in my head. But then again, I always work too fast so I probably did better since I had to write them down.”

I just laughed when I read that last comment because it’s exactly the sort of thing some of my students would have said! This “no-fail” order of operations lesson is fun for students, and the step-by-step strategies make it highly effective, too. After playing the game, even kids recognize the importance of writing out the steps when solving order of operations problems, whether they like it or not!

order of operations problem solving tes

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Algebra 01/31 Order of Operations

Algebra 01/31 Order of Operations

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Mammathematicians

Last updated

25 June 2021

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order of operations problem solving tes

This lesson titled ‘The Order of Operations’ is fully differentiated, and uses whiteboard questions as a scaffolding and Assessment for Learning method. These whiteboard questions are also particularly useful for reducing students’ maths anxiety by providing them with multiple answer they can choose from. All of the whiteboard questions have diagnostic-style wrong answers, obtained from common misconceptions The title of the lesson is throughout the PowerPoint. This provides consistency throughout, allows students to catch up if they missed it, and takes late-comers into consideration. The date is also throughout the PowerPoint and updates automatically. This is done so that the students know exactly where it is each lesson, and to make it easier on the class teacher.

A dyslexic-friendly font (Verdana) is used throughout the PowerPoint and any worksheets. Worksheets are embedded in the PowerPoint on the slides to which they relate.

Animated answers to all questions are provided where possible.

The learning objectives are designed to be as short sentences as possible to allow students to read them and write them down (if necessary) as quickly as possible. They also use a mixture of simplistic and specialised words to engages students’ thinking about definitions whilst allowing them to access the meaning of the sentences. These objectives are reviewed at the end of the lesson as a self-evaluation of learning technique. Students are awarded ‘brain’ medals depending on how well they have done.

These are kept as simple as possible and broken down carefully. This is to encourage students to access the material whilst giving them the confidence by achieving something in the lesson. B) Review BIDMAS. S) Use BIDMAS to calculate sums and products G) Correct calculations in line with BIDMAS.

If you like the resource, please leave a review. If you didn’t please leave one anyway with any suggestions on how I could improve it.

Whilst this lesson is part of a larger bundle, and does link nicely with some of the other lessons, it can certainly be used independently as well.

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Algebra Course Part 1 - 10 Full Lessons

A huge 40% discount on these 10 lessons with this bundle! A great collection of 10 lessons to introduce students to algebra. Part 2 of this course is available here: https://www.tes.com/teaching-resource/resource-12443957 Parts 1 and 2 are available, at a further discount, here: https://www.tes.com/teaching-resource/resource-12443955 Starting with the basics with the Order of Operations, working through Notation and how to simplify algebraic terms, moving towards Indices and their rules, ending with composite and inverse functions. The lessons all follow a simple theme with dyslexic-friendly font (Verdana). There are whiteboard diagnostic questions throughout and fully scaffolded practice questions and worksheets.

Algebra Course Parts 1 and 2 - 20 Full Lessons

A massive 45% discount on these 20 lessons with this bundle! A great collection of 20 lessons to introduce students to algebra. Part 1, on its own, is also available here: https://www.tes.com/teaching-resource/resource-12434912 Part 2, on its own, is also available here: https://www.tes.com/teaching-resource/resource-12443957 Starting with the basics with the Order of Operations, working through Notation and how to simplify algebraic terms, Rearranging Formulae, and ending with Inequalities and Factorising Expressions. The lessons all follow a simple theme with dyslexic-friendly font (Verdana). There are whiteboard diagnostic questions throughout and fully scaffolded practice questions and worksheets.

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order of operations problem solving tes

What is the Order of Operations in Math (PEMDAS)?

Does the order in which we solve math problems matter? Yes! Let’s learn about the order of operations in math, aka PEMDAS, to solve multi-step expressions.

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Author Amber Watkins

order of operations problem solving tes

Published November 7, 2023

order of operations problem solving tes

Published Nov 7, 2023

  • Key takeaways
  • The order of operations teaches the order in which to solve multi-operational expressions.
  • The order of operations can easily be remembered using the acronym PEMDAS .
  • As your child successfully masters the order of operations , they will be able to solve more advanced problems with ease.

Table of contents

  • What is the order of operations?
  • Order of operations rules

order of operations problem solving tes

When reading a math problem, we usually start from left to right. So it is natural to want to solve problems in the same way. Does this method get us the right answer for every problem?

Let’s solve the following problem in two ways to see how order makes a difference: 3 – 2 x 5 =

1. You can solve this problem by subtracting first.

3 – 2 x 5

2. Or you can solve it by multiplying first.

3 – 10

In both examples, we took the same actions: we multiplied and subtracted , but switched the order. As a result, we found two very different answers. How can we know which is the right answer? By following the math order of operations .

What is the Order of Operations in Math?

Operations are the actions we take in math. The most common math operations are adding , subtracting, multiplying, dividing , simplifying exponents, and finding square roots .

Some math problems have more than one kind of operation in the problem. How can we solve those types of problems? We follow the order of operations ! What is the order of operations? The order of operations tells us the order in which to perform operations when the problem contains more than one kind of operation.

Order of Operations Rules

Many times you will see the order of operations called PEMDAS. What is Pemdas? Pemdas is an acronym that helps us remember the order in which to solve multi-operational problems. What does Pemdas stand for? PEMDAS is an acronym that stands for Parenthesis, Exponents, Multiplication or Division, Adding or Subtracting.

pemdas

Now that we know the Pemdas meaning , let’s discuss the Pemdas Rule . #1 PEMDAS Rule – When solving order of operation problems in math, you must follow the order of the acronym.

First, you solve whatever operations are in the parenthesis . ()

Second, you calculate any exponents . x²

Third, you multiply or divide . x  or  ÷

Fourth, you add or subtract . + or – 

BODMAS vs PEMDAS

You may also hear the order of operations called BODMAS. What is BODMAS?  BODMAS stands for Brackets, Orders (Powers or Roots), Division or Multiplication, Adding or Subtracting.

order of operations problem solving tes

Brackets are another name for parenthesis and orders are another name for exponents. Although the terms used for operations are different than Pemdas, both Bodmas and Pemdas follow the same rules of order of operations . What are those rules and how can we use them to solve PEMDAS problems ?

How to Solve Order of Operations Problems

Let’s solve this Order of Operations problem as we learn some PEMDAS rules. 4² – ( 3 x 5 ) + 9 ፥ 3 x 2 

In our example problem, we would multiply 3 x 5 first because it is in the parenthesis . P E M D A S 

4² – ( 3 x 5 ) + 9 ፥ 3 x 2

4² – 15 + 9 ፥ 3 x 2 2. Pemdas Rule for Exponents Exponents should always be simplified before moving to the next step in the order of operations. If you begin multiplying, dividing, adding, or subtracting while there is still an exponent in the problem, you may have missed this step. This is how we would simplify the exponents . P E M D A S 

4² – 15 + 9 ፥ 3 x 2 16 – 15 + 9 ፥ 3 x 2 3. Pemdas Rule for Multiplying or Dividing When using the order of operations, you may have noticed the word “or” is used when multiplying or dividing. When following the order of operations in math , you can multiply or divide in any order. Simply complete the operation that comes first. We have both multiplication and division in this problem, so we will go from left to right. First is division, then is multiplication. 

P E M D A S 

16 – 15 + 9 ፥ 3 x 2

16 – 15 + 3 x 2

16 – 15 + 6

4. Pemdas Rule for Adding or Subtraction

When using the order of operations, you may have also noticed the word “or” is used when adding or subtracting. When following the order of operations in math , you can add or subtract in any order. Simply complete the operation that comes first.

Finally, we would add or subtract depending on which operation comes first.

16 – 15 + 6 

Now that we know some of the PEMDAS rules, let’s go over some PEMDAS examples together. 

PEDMAS Examples

PEMDAS EXAMPLE 1: Solve 3 + ( 8 x 9 ) =

Explanation : First, we see parenthesis comes first in the P EMDAS acronym. So we would multiply 8 x 9 because it is in the parenthesis. Therefore, 8 x 9 is equal to 72. Then we would add 3 and 72 to get 75 as our answer.

Our Work for this PEMDAS example would look like this:         

3 + ( 8 x 9 ) 3 + 72 75 

PEMDAS EXAMPLE 2: Solve 12  ፥ 3 + 14 =

First, we see that division comes before adding in PEM D AS. So we divide 12 by 3 which is equal to 4. Next, add 4 and 14 which equals 18. Our Work for this PEMDAS example would look like this:   12 ፥ 3 + 14 4 + 14 18

PEDMAS Practice Questions

Scroll down for the answers!

order of operations problem solving tes

1. Use Pemdas to solve 2² + 12 – ( 3 x 2) =

Doodle-Blog-NumberIcons_2

2. Use Pemdas to Solve (3 x 2) + (12 ፥ 3 ) =

Doodle-Blog-NumberIcons_3

3. Use Pemdas to Solve 100  ፥  10 – (6 ፥ 2 ) =

First, multiply 3 x 2 because it is in the parenthesis. Then, simplify the exponent 2² which equals 4. Next, add 4 + 12 which equals 16. Finally, subtract 6 which equals 10. 

2² + 12 – (3 x 2) =                                                            2² + 12 – 6 = 4  + 12 – 6 = 16 – 6 = 10

First, multiply 3 x 2 because it is in the first parenthesis. Next, divide 12 by 3 because it is in the second parenthesis. Finally, add 6 + 4 which equals 10. (3 x 2) + (12 ፥ 3 ) 6 + (12 ፥ 3 ) 6 + 4   10

First, divide 6 by 2 because it is in the parenthesis. Next, divide 100 by 10. Finally, subtract 3 from 10 which equals 7. 

100  ፥  10 – (6 ፥ 2 )    100  ፥  10 – 3 10 – 3 7

FAQs About Order of Operations

Pemdas stands for Parenthesis, Exponents, Multiplication or Division, Adding or Subtracting.

In PEMDAS problems , multiplication or division can happen in any order. The Pemdas rule is to complete whichever operation comes first.

In Pemdas problems , always complete whichever operation is inside of the parenthesis first.

BODMAS stands for Brackets, Orders, Division or Multiplication, Adding or Subtracting.

Yes. PEMDAS and BODMAS are both acronyms to represent the order of operations, but they use different words to describe the same operation. For example, PEMDAS uses the terms parenthesis and exponents. BODMAS uses the terms brackets and powers. 

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Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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  1. KS3/KS4 Maths: Order of Operations (BIDMAS)

    ppt, 497.5 KB docx, 17.26 KB ppt, 822.5 KB fjsw, 15.46 KB Without Indices A PowerPoint with examples and problem solving. A Code breaker activity on order of operations (BIDMAS) With Indices A PowerPoint with examples and problem solving. A card sort activity on order of operations (BIDMAS) Creative Commons "Sharealike"

  2. Order of operations

    Order of operations Subject: Mathematics Age range: 10 - 12 Resource type: Worksheet/Activity File previews ppt, 125 KB Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch. Last updated Not quite what you were looking for?

  3. Order of Operations Practice Problems

    Answer Part 2: Order of Operations problems involving the four arithmetic operations and parenthesis (or nested grouping symbols) Problem 4: Simplify the numerical expression below. Answer Problem 5: Simplify the numerical expression below. Answer Problem 6: Simplify the numerical expression below. Answer

  4. Order of Operations Practice Questions

    Click here for Answers. . Order of Operations Answers - Corbettmaths. BODMAS, BIDMAS, bodmas, Practice Questions. Previous: Ordering Numbers Practice Questions. Next: Cube Numbers and Cube Roots Practice Questions.

  5. Worked example: Order of operations (PEMDAS)

    The order of operations (PEMDAS) is essential for solving complex math problems. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (same level), and Addition and Subtraction (same level). By following these steps, you can simplify and accurately solve mathematical expressions, ensuring a correct final answer. Created by Sal ...

  6. Order of Operations Worksheets

    This page includes Order of Operations worksheets using whole numbers, integers, decimals and fractions. Elementary and middle school students generally use the acronyms PEMDAS or BEDMAS to help them remember the order in which they complete multi-operation questions. The 'P' or 'B' in the acronym stands for parentheses or brackets.

  7. Order Of Operations Problem Solving

    "Order Of Operations Problem Solving" teaching resources for those 'aha' moments

  8. Practice With Order of Operations Problems and Answers

    2 + 4 × 3 There are two approaches that you could take here, and only one of them will give you the correct answer! Which one do you think is correct? As you can see, each strategy results in different answers. The strategy on the left adds 2 + 4 first, while the strategy on the right multiplies 4 x 3 first.

  9. Order of Operations: No-fail strategies that really work!

    Lesson Hook: Solve a Not-so-simple Equation Before you teach PEMDAS or any other strategy, challenge your students to solve a simple equation such as this one: 3 + 8 x 2 = ? Ask your students to write the equation on a dry erase board or tablet, and then solve it and show you the answer.

  10. Algebra 01/31 Order of Operations

    Algebra 01/31 Order of Operations Subject: Mathematics Age range: 11-14 Resource type: Lesson (complete) File previews pptx, 626.71 KB This lesson titled 'The Order of Operations' is fully differentiated, and uses whiteboard questions as a scaffolding and Assessment for Learning method.

  11. Intro to order of operations (video)

    At. 5:40. Sal says that you have to do things from left to right when you have multiple operations at the same level. At this point in the video, the problem is: 10 x 4 / 2 - 5 x 6. Sal solves left to right: 40 / 2 - 5 x 6 = 20 - 30 = -10. But if I don't do it in the same order I get the same answer: 10 x 2 - 5 x 6 = 20 - 30 = -10.

  12. Order of operations with fractions and exponents

    1 3 ( 4 ⋅ 3) + 2 3 =. Stuck? Review related articles/videos or use a hint. Report a problem. Do 4 problems. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone ...

  13. Order of operations

    Course: 6th grade > Unit 4. Lesson 5: More on order of operations. Order of operations examples: exponents. Math >. Exponents and order of operations >.

  14. Order of operations example (video)

    AboutTranscript. The order of operations tells us the order to solve steps in expressions with more than one operation. First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right. Fourth, we solve all addition and subtraction from left to ...

  15. What is Order of Operations (PEMDAS)?

    Let's solve this Order of Operations problem as we learn some PEMDAS rules. 4² - ( 3 x 5 ) + 9 ፥ 3 x 2 Pemdas Rule for Parenthesis When solving order of operation problems, first complete the operations that are found inside the parenthesis or brackets.. In our example problem, we would multiply 3 x 5 first because it is in the parenthesis. P E M D A S

  16. Order of Operations (PEMDAS) Calculator

    Send us Feedback. Free Order of Operations (PEMDAS) calculator - solve algebra problems following PEMDAS order step-by-step.

  17. Order of Operations

    Understanding order of operations is essential for solving longer math equations with multiple operations. When students first look at these types of problems, they often just think they work through the operations from left to right, similar to how you read a book.

  18. Order of Operations Quiz

    This quiz will test your understanding of how to perform or apply the order of operations. This quiz contains a total of ten (10) multiple-choice questions. To pass, you must obtain a score of at least 70%. Good luck!

  19. Order Of Operations Problem Solving

    Order Of Operations Problem Solving Sort: Relevance Grades Pre-Kindergarten 17 Kindergarten 99 Grade 1 216 Grade 2 291 Grade 3 362 Grade 4 232 Grade 5 243 Grade 6 155 Grade 7 6 Teaching Resource 748 Lesson Plan 10 Blog 2 Unit Plan 1 Resource Types Price Format Free Plan Soccer Stats - Mixed Operation Problem Solving Worksheets