 Nov
29

# Teaching Order of Operations – Whole and Complete Lesson

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After students reach fluency in math facts, fact families, fractions and multi-step math problems, the next steps involve order of operations.

Here is a whole and complete lesson for you to use for free.

This lesson uses Direct Instruction scripting to reduce frustration and confusion for the student. It also uses behavior objectives and precision teaching methods so that the student can quickly achieve fluency and mastery in the application of order of operations problems.

You can deliver each task in the lesson as a separate activity, and repeat as necessary with students. A link to a downloadable pdf with all tasks and worksheets can be found at the bottom.

## Order of Operations

Order of Operations can be confusing for students. It is much more effectively taught if we use a formula known as B.E.D.M.A.S. B.E.D.M.A.S. outlines the order in which the various steps in an order of operations math problem must be solved. The following script outlines the concepts in a step-by-step lesson.

### Task 1 The Left-to-Right Rule

Say to the students, “Now I am going to teach you some rules about the order of operations. The order of operations tells you the steps you must use to solve math equations. Here is the first rule. When you solve math equations, you work the problem from left to right. Listen again. When you solve math equations, you work the problem from left to right. Say that rule with me. Ready. Signal.

Students and teacher together say, “When you solve math equations, you work the problem from left to right.

Say to the students, “Say that rule all by yourselves. Ready. Signal.

Students say, “When you solve math equations, you work the problem from left to right.”

Have the students repeat the rule until they can say it quickly and accurately.

### Task 2 – The Steps In Order Rule

Say to the students, “New rule. My turn. Listen. When we do math problems we do each step in the correct order. Listen again. When we do math problems we do each step in the correct order. Say that rule with me. Ready.” Signal.

The teacher and students say, “When we do math problems we do each of the steps in the correct order.

Say to the students, “Say that rule with me again. Ready.” Signal.

Teacher and students say, “When we do a math problem, we do each of the steps in the correct order.”

Repeat the rule with the students until they can say it quickly and correctly.

Say to the students, “Now it is your turn to say the rule about the order of operations all by yourselves. Ready.” Signal.

The students say, “When we do a math problem, we do each of the steps in the correct order.”

Have the students repeat the rule until they can say it quickly and correctly.

Write on the board B.E.D.M.A.S. Point to the acronym and say to the students, “Here is an easy formula to remember the order of operations. Listen B.E.D.M.A.S. Listen again. B.E.D.M.A.S. Say that word. Ready. Signal.

Students say, “BEDMAS”

Say to the students, “B.E.D.M.A.S. is an acronym that tells us the order of the steps to solve a math problem. Listen again. “B.E.D.M.A.S. is an acronym that tells us the order of the steps for solving a math problem.

Say to the students, “My turn to say the rule about B.E.D.M.A.S. Listen. Each letter stands for one of the steps in the problem. Listen again. Each letter stands for one of the steps in the problem. What does each letter in B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Each letter stands for one of the steps in the problem.”

Say to the students, “My turn to say what the letters in B.E.D.M.A.S. stand for. Listen. B stands for Brackets. What does the B in B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Brackets.”

Say to the students, “That’s correct. If there are any brackets in the problem, we have to do the brackets first. What is the first step in solving the problem? Ready. Signal.

The students say, “Do the brackets first.”

Say to the students, “Next letter. The E in B.E.D.M.A.S. stands for Exponents. What does the E in B.E.D.M.A.S. stand for? Ready? Signal.

The students say, “Exponents.”

Say to the students, “That’s correct. Exponents. After we do all the brackets in the problem, we do any exponents. Listen again. After we do the brackets, then we do the exponents. What do we do first? Ready. Signal.

The students say, “We work with the brackets.”

Say to the students, “That’s correct. After the brackets, what do we do next? Ready.” Signal.

The students say, “We work with the exponents”

Say to the students, “You got it. First, we do brackets, then we do exponents. Here is the next letters. Listen. ‘D’. ‘M’. ‘D’ stands for

Division. ‘M’ stands for Multiplication. After we do the exponents, we do the division and multiplication. What do we do after the exponents? Ready. Signal.

The students say, “We work with the division and multiplication.”

Say to the students, “That’s right. After the brackets and the exponents we work with any division and multiplication. Now we have ‘B’, ‘E’, ‘D’ and ‘M’. Tell me what each letter stands for. ‘B’. Ready.” Signal.

Students say, “Brackets”

Say to the students, “ Good remembering. Next letter ‘E’. Ready.” Signal.

Students say, “Exponents”

Say to the students, “ Great. Next letter ‘D’. Ready.” Signal.

Students say, “Division.”

Say to the students, “You got it. Last letter ‘M’. Ready.” Signal.

Students say, “Multiplication.”

Say to the students, “Right again. Now lets add the last two letters of B.E.D.M.A.S. Listen. The last two letters are ‘A’ and ‘S’. What are the last two letters of B.E.D.M.A.S.? Ready. Signal.

The students say, “A and S.”

Say to the students, “Yes. ‘A’ stands for addition. ‘S’ stands for subtraction. Listen again. ‘A’ stands for addition. ‘S’ stands for subtraction. Your turn. What does ‘A’ stand for? Ready. Signal.

The students say, “A stands for addition.”

Say to the students, “Correct. ‘A’ stands for addition. What does ‘S’ stand for? Ready. Signal.

The students say, “S stands for subtraction.”

Say to the students, “That’s right. Now you know what each of the letters in B.E.D.M.A.S. stands for. Let’s review

What does the B in B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Brackets.”

Say to the students, “Next letter. The E in B.E.D.M.A.S. stands for Exponents. What does the ‘E’ in B.E.D.M.A.S. stand for? Ready? Signal.

The students say, “Exponents.”

Say to the students, “That’s correct. Exponents. What do we do after the exponents? Ready. Signal.

The students say, “Division and Multiplication.”

Say to the students, “ Good remembering. What do the last two letters of B.E.D.M.A.S. stand for? Ready. Signal.

The students say, “Addition and Subtraction.”

Say to the students, “Yes. ‘Addition and Subtraction. Nice work. Now we know the order in which we will do the steps in the problem. Let’s look at some problems and see how we solve them.

### Step 3 – Simple Problem Example (Addition & Subtraction)

Write on the board.

5 + 7 – 4 =

Say to the students, “My turn to read the problem. Listen, Five plus seven minus four equals some number. Your turn to read the problem. Ready. Signal.

Students say, “Five plus seven minus four equals some number.”

Say to the students, “Good reading the problem. Remember the first rule about working the problem. When we work this problem do we go from right to left or from left to right. Ready.

Signal.

The students respond, “We work the problem from left to right.”

Say to the students, “Good remembering that rule. We work the problem from left to right. Look at the acronym for B.E.D.M.A.S. What is the first thing we look for in the problem?” Ready.” Signal.

Students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right again. There are no exponents in this problem. Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “That’s right. There are no division or multiplication signs in this problem. Look at the last part of the formula. What do we look for next? Ready.” Signal.

Say to the students, “Are there any addition and subtraction signs in this problem? Ready. Signal.

Students say, “Yes.”

Students say, “Five plus seven minus four equals some number.”

Say to the students, “What do we do first?”

Students say, “ Add 5 +7”

Say to the students, “That’s right. What is 5 + 7? Ready.” Signal.

Students say, “Twelve.”

Say to the students, “Right. What do we do next?”

Students say, “ We subtract 4 from 12.”

Say to the students, “What is 12 minus 4? Ready?”

Say to the students, “Are there any steps left to do?”

Students say, “No.”

Say to the students, “Good working that problem. Let’s look at another one.

### Task 4 – More Difficult Problem (Multiplication)

Write on the board. 6 + 9 x 3 – 12 =

Students read, “Six plus nine times three minus twelve equals some number”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right again. There are no exponents in this problem. Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do with the 6? Ready. Signal.

The students say, “Pass over it to the multiplication.”

Say to the students, “What do we do first? Ready.” Signal.

Students say, “We multiply 9 x 3.”

Say to the students, “That’s right. What does 9 x 3 equal?”

Students say, “27.”

Say to the students, “Perfect. 9 x 3 is 27. What do you do next? Ready.” Signal.

Students say, “Add 6 and 27.”

Say to the students, “Good remembering to work from the left to the right. What is 6 + 27?

Students say, “6 + 27 = 33.”

Say to the students, “Good work. What is the next step in this problem? Ready.” Signal.

Students say, “Subtract 12 from 33.”

Say to the students, “Absolutely. What is thirty-three minus twelve? Ready.” Signal.

Say to the students, “ Have we done all of the steps? Ready.” Signal.

Students say, “Yes.”

Say to the students, “Yes. You did all of the steps. Let’s look at another problem.”

### Task 5 – Second More Difficult Problem (Multiplication and Division)

Write on the board 10 x 3 – 16 ÷ 4

Students read, “Six plus nine times three minus twelve equals some number”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right again. There are no exponents in this problem. Check your formula. What do we look for next? Ready.” Signal.

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do first? Ready. Signal.

Students say, “Divide 16 by 4.”

Say to the students, “Good work. What is 16 divided by 4? Ready.” Signal.

Students say, “16 ÷ 4 = 4”

Write on the board 10 x 3 – 4 =

Say to the students, “Nice work. 16 ÷ 4 does equal 4. What do you do next? Ready.” Signal.

Students say, “Multiply 10 x 3.”

Say to the students, “Yes indeed. What is 10 x 3?” Ready.” Signal.

Students say, “10 x 3 = 30.”

Say to the students, “You got it 10 x 3 equals 30.

Write on the board, 30 – 4 =

Say to the students, “What is the next step?” Ready.” Signal.

The students say, “We subtract 4 from 30.”

Say to the students, “ Yes. “What is 30 minus 4?”

Students say, “26”

Say to the students, “Did we finish all of the steps? Ready.” Signal.

Students say, “Yes.”

Say to the students, “Good work. Here is a more difficult question.”

Write on the board. 100 – 7² + 12 ÷ 3 =

Students read, “One hundred minus seven squared plus twelve divided by three equals some number.”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “No.”

Say to the students, “Right. There are no brackets. Look at the formula. What do we look for next? Ready. Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right again. There are exponents in this problem. What is the exponent in this problem? Ready. Signal.

The students say, “ Seven squared”

Say to the students, “Let’s work this part of the problem. What is seven squared? Ready.” Signal.

The students say, “7² = 49”

Say to the students, “That’s right.”

Write on the board. 100 – 49 + 12 ÷ 3 =

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do next. Ready. Signal.

Students say, “Divide 12 by 3.”

Say to the students, “Good work. What is 12 divided by 3? Ready.” Signal.

Students say, “12 ÷ 3 = 4”

Write on the board 100 – 49 + 4 =

Say to the students, “Nice work. 12 ÷ 3 does equal 4. What do you do next? Ready.” Signal.

Say to the students, What is the next step? Ready.” Signal.

The students say, “We subtract 49 from 100.”

Say to the students, “ Yes. What does 100 minus 49 equal?”

Students say, “One hundred minus forty nine is fifty-one”

Write on the board. 51 + 4

Say to the students, “Correct again. Did we finish all of the steps?

Students say, “No.”

Say to the students, “What do we still have to do?”

Students say, “Add fifty-one plus four.”

Say to the students, “Do that. How much is fifty-one plus four?”

The students say, “Fifty-one plus four is fifty-five”

Write on the board 55

Say to the students, “Have we done all of the steps. Ready.” Signal.

Students say, “Yes.”

Say to the students, “So what is 100 – 7² + 12 ÷ 3? Ready.” Signal.

Students say, “Fifty-five.”

Write on the board 36 ÷ 12 + 2(5 – 2) =

Say to the students, “This problem is more difficult. Let’s see if you can solve this one. Read this problem. Ready.” Signal.

Students read, “Thirty-six divided by twelve plus two bracket five minus two bracket equals some number.”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right. There are brackets. What numbers are in the brackets. Ready.” Signal.

Students say, “Five minus two.”

Say to the students, “Right. First we work with the numbers inside the bracket. What is five minus two? Ready.” Signal.

Students say, “Five minus two equals three.”

Say to the students, “That’s correct. Now we have a three inside the brackets. To get rid of the brackets we have to multiply the

number outside the bracket by the number inside the bracket. What number is outside the brackets. Ready.” Signal.

The students say, “Two”.

Say to the students. “That’s right. So what numbers do we multiply? Ready.”

The students say, “Two times three.”

Say to the students, “ How much is two times three? Ready.” Signal.

Students say, “Two times three equals six.”

Say to the students, “You got it. Now you have removed the brackets.”

Write on the board. 36 ÷ 12 + 6 =

Say to the students, “What is the next step?”

Students say, “Divide twelve into thirty-six.”

Say to the students, “That’s correct. How many times does twelve divide into thirty-six? Ready.” Signal.

The students say “Three times.”

Say to the students, “Yes, three times.”

Write on the board. 3 + 6 =

Say to the students, “What does 3 + 6 equal?”

Students say, “Three plus six equals nine.”

Say to the students, “So what does thirty-six divided by twelve plus two times five minus two equal? Ready.” Signal

Students say, “Nine.”

Write on the board. 6³ – 3(4) + 90 ÷ 10

Students read, “Six cubed minus three bracket four bracket plus ninety divided by ten equals some number.”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right. There are brackets.

What do we look for next? Ready. Signal.

Students say, “We multiply the number in the bracket by the number outside of the bracket.”

Say to the students, “What numbers do we multiply? Ready.” Signal.

Students say, “Four times three.”

Say to the students, “How much is four times three. Ready.”

Students say, “Twelve”

Write on the board. 6³ – 12 + 90 ÷ 10 =

Say to the students, “What do we do next in this problem? Ready.” Signal.

Students say, “Exponents.”

Say to the students, “That’s correct. After the brackets, we look for exponents. Are there any exponents in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right again. There are exponents in this problem. What is the exponent in this problem? Ready. Signal.

The students say, “Six cubed”

Say to the students, “Let’s work this part of the problem. What is six cubed? Ready.” Signal.

The students say, “Six cubed equals eighteen.”

Say to the students, “That’s right.”

Write on the board. 18 – 12 + 90 ÷ 10 =

Students say, “Division and Multiplication.”

Say to the students, “You got that right as well. Are there any division or multiplication signs in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Remember. You work the problem from the left to the right. What do you do next? Ready. Signal.

Students say, “Divide ninety by ten.”

Say to the students, “Good work. What is 90 divided by 10? Ready.” Signal.

Students say, “Ninety divided by ten equals nine”

Write on the board 18 – 12 + 9 =

Say to the students, “Nice work. 90 ÷ 10 does equal 9. What do you do next? Ready.” Signal.

The students say, “We subtract 12 from 18.”

Say to the students, “ Yes. What is 18 minus 12?”

Students say, “Eighteen minus twelve is six”

Write on the board. 6 + 9

Say to the students, “Correct again. Did we finish all of the steps?

Students say, “No.”

Say to the students, “What do we still have to do?”

Students say, “Add six plus nine.”

Say to the students, “Do that. How much is six plus nine?”

The students say, “Six plus nine is fifteen”

Write on the board 15

Say to the students, “Have we done all of the steps. Ready.” Signal.

Students say, “Yes.”

Say to the students, “So what is 6³ – 12 + 90 ÷ 10? Ready.” Signal.

Students say, “Fifteen.”

Task 9 – Order of Operation with Fractions

Write on the board. (8² – 4)

(12 ÷ 2 + 4)

Students read, “Bracket eight squared minus four bracket over bracket twelve divided by two plus four.”

Say to the students, “Let’s use our formula to solve this problem. What do we look for first? Ready. Signal.

The students say, “Brackets.”

Say to the students, Correct. Are there any brackets in this problem? Ready. Signal.

Students say, “Yes.”

Say to the students, “Right. There are brackets. Let’s start with the brackets on the top part of the fraction. What are the numbers inside those brackets? Ready.” Signal.

Students say, “Eight squared minus four.”

Say to the students, “Can you work this problem? Ready.” Signal.

Students say, “No, we have to work the exponent first.”

Say to the students, “Good using your rule. You worked the brackets first, but you cannot do the subtraction because you have to do the exponent first. The E in B.E.D.M.A.S. comes before the S, so you have to do the Exponent before you can do the Subtraction. So let’s work the exponent. How much is 8²? Ready.” Signal.

The students say, “Eight squared equals sixty-four.”

Write on the board 60 =

(12 ÷ 2 + 4)

Say to the students, “You got that right. What do you do next? Ready.” Signal.

The students say, “ You subtract four from sixty-four.”

Say to the students, “Good job. What is sixty-four minus four? Ready.” Signal.

Students say, ” Sixty-four minus four equals sixty.”

What do we do next? Ready. Signal.

Students say, “We work with the bracket on the bottom part of the fraction.”

Say to the students, “Can we work the problem the way it is written? Ready.” Signal.

Students say, “No. We have to do the division first.”

Say to the students, “That’s correct. The D in B.E.D.M.A.S. comes before the S, so we have to do the division before we do the subtraction. What does the division problem say? Ready.”

Students say, “Twelve divided by two”

Say to the students, “How much is twelve divided by two? Ready.” Signal.

The students say, “Twelve divided by two equals six.”

Write on the board.

60

(6 + 4)

Say to the students, “What do we do next in this problem? Ready.” Signal.

Students say, “We add six plus four.”

Say to the students, “That’s correct. How much is six plus four? Ready. Signal.

The students say, “Six plus four equals ten.”

Say to the students, “Good. What do we do next?

The students say, “We divide ten into sixty.”

Say to the students, “That’s right. How much does sixty divided by ten equal?”

The students say, “Sixty divided by ten equals six.”

Say to the students, “So what does 8² – 4 equal?

(12 ÷ 2 + 4)

The students say, “Six”

Say to the students, “Nice work. That was a hard problem.

Now you are going to work the problems on the worksheet exercise. Remember to follow your formula to get each step done correctly.