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, âNow 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, âWhen you solve math equations, you work the problem from left to right.

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

Students say, âWhen you solve math equations, you work the problem from left to right.â

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

### Task 2 â The Steps In Order Rule

Say to the students, âNew 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.â Signal.

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

Say to the students, âSay that rule with me again. Ready.â Signal.

Teacher and students say, âWhen we do a math problem, we do each of the steps in the correct order.â

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

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

The students say, âWhen we do a math problem, we do each of the steps in the correct order.â

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, âHere 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, âBEDMASâ

Say to the students, âB.E.D.M.A.S. is an acronym that tells us the order of the steps to solve a math problem. Listen again. âB.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, âMy 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, âEach letter stands for one of the steps in the problem.â

Say to the students, âMy 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, âBrackets.â

Say to the students, âThatâs 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, âDo the brackets first.â

Say to the students, âNext 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, âExponents.â

Say to the students, âThatâs 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, âWe work with the brackets.â

Say to the students, âThatâs correct. After the brackets, what do we do next? Ready.â Signal.

The students say, âWe work with the exponentsâ

Say to the students, âYou got it. First, we do brackets, then we do exponents. Here is the next letters. Listen. âDâ. âMâ. âDâ stands for

Division. âMâ 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, âWe work with the division and multiplication.â

Say to the students, âThatâs right. After the brackets and the exponents we work with any division and multiplication. Now we have âBâ, âEâ, âDâ and âMâ. Tell me what each letter stands for. âBâ. Ready.â Signal.

Students say, âBracketsâ

Say to the students, â Good remembering. Next letter âEâ. Ready.â Signal.

Students say, âExponentsâ

Say to the students, â Great. Next letter âDâ. Ready.â Signal.

Students say, âDivision.â

Say to the students, âYou got it. Last letter âMâ. Ready.â Signal.

Students say, âMultiplication.â

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

The students say, âA and S.â

Say to the students, âYes. âAâ stands for addition. âSâ stands for subtraction. Listen again. âAâ stands for addition. âSâ stands for subtraction. Your turn. What does âAâ stand for? Ready. Signal.

The students say, âA stands for addition.â

Say to the students, âCorrect. âAâ stands for addition. What does âSâ stand for? Ready. Signal.

The students say, âS stands for subtraction.â

Say to the students, âThatâs right. Now you know what each of the letters in B.E.D.M.A.S. stands for. Letâs review

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

The students say, âBrackets.â

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

The students say, âExponents.â

Say to the students, âThatâs correct. Exponents. What do we do after the exponents? Ready. Signal.

The students say, âDivision and Multiplication.â

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

The students say, âAddition and Subtraction.â

Say to the students, âYes. âAddition and Subtraction. Nice work. Now we know the order in which we will do the steps in the problem. Letâs look at some problems and see how we solve them.

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

Write on the board.

5 + 7 â 4 =

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

Students say, âFive plus seven minus four equals some number.â

Say to the students, âGood 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, âWe work the problem from left to right.â

Say to the students, âGood 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.â Signal.

Students say, âBrackets.â

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

Students say, âNo.â

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

Students say, âExponents.â

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

Students say, âNo.â

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

Students say, âDivision and Multiplication.â

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

Students say, âNo.â

Say to the students, âThatâs 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.â Signal.

Students say, âAddition and subtraction.â

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

Students say, âYes.â

Say to the students, âRead the problem. Ready.â Signal.

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

Say to the students, âWhat do we do first?â

Students say, â Add 5 +7â

Say to the students, âThatâs right. What is 5 + 7? Ready.â Signal.

Students say, âTwelve.â

Say to the students, âRight. What do we do next?â

Students say, â We subtract 4 from 12.â

Say to the students, âWhat is 12 minus 4? Ready?â

Students answer, â8â

Say to the students, âAre there any steps left to do?â

Students say, âNo.â

Say to the students, âGood working that problem. Letâs look at another one.

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

Write on the board. 6 + 9 x 3 â 12 =

Say to the students, âRead this problem. Ready. Signal.

Students read, âSix plus nine times three minus twelve equals some numberâ

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

The students say, âBrackets.â

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

Students say, âNo.â

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

Students say, âExponents.â

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

Students say, âNo.â

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

Students say, âDivision and Multiplication.â

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

Students say, âYes.â

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

The students say, âPass over it to the multiplication.â

Say to the students, âWhat do we do first? Ready.â Signal.

Students say, âWe multiply 9 x 3.â

Say to the students, âThatâs right. What does 9 x 3 equal?â

Students say, â27.â

Say to the students, âPerfect. 9 x 3 is 27. What do you do next? Ready.â Signal.

Students say, âAdd 6 and 27.â

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

Students say, â6 + 27 = 33.â

Say to the students, âGood work. What is the next step in this problem? Ready.â Signal.

Students say, âSubtract 12 from 33.â

Say to the students, âAbsolutely. What is thirty-three minus twelve? Ready.â Signal.

Students reply, â 21â

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

Students say, âYes.â

Say to the students, âYes. You did all of the steps. Letâs look at another problem.â

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

Write on the board 10 x 3 â 16 Ã· 4

Say to the students, âRead this problem. Ready. Signal.

Students read, âSix plus nine times three minus twelve equals some numberâ

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

The students say, âBrackets.â

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

Students say, âNo.â

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

Students say, âExponents.â

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

Students say, âNo.â

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

Students say, âDivision and Multiplication.â

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

Students say, âYes.â

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

Students say, âDivide 16 by 4.â

Say to the students, âGood work. What is 16 divided by 4? Ready.â Signal.

Students say, â16 Ã· 4 = 4â

Write on the board 10 x 3 â 4 =

Say to the students, âNice work. 16 Ã· 4 does equal 4. What do you do next? Ready.â Signal.

Students say, âMultiply 10 x 3.â

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

Students say, â10 x 3 = 30.â

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

Write on the board, 30 â 4 =

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

The students say, âWe subtract 4 from 30.â

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

Students say, â26â

Say to the students, âDid we finish all of the steps? Ready.â Signal.

Students say, âYes.â

Say to the students, âGood work. Here is a more difficult question.â

### Task 6 â More Advanced Problem (Exponents)

Write on the board. 100 â 7Â² + 12 Ã· 3 =

Say to the students, âRead this problem. Ready. Signal.

Students read, âOne hundred minus seven squared plus twelve divided by three equals some number.â

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

The students say, âBrackets.â

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

Students say, âNo.â

Students say, âExponents.â

Students say, âYes.â

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

The students say, â Seven squaredâ

Say to the students, âLetâs work this part of the problem. What is seven squared? Ready.â Signal.

The students say, â7Â² = 49â

Say to the students, âThatâs right.â

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

Check your formula. What do we look for next? Ready.â Signal.

Students say, âDivision and Multiplication.â

Students say, âYes.â

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

Students say, âDivide 12 by 3.â

Say to the students, âGood work. What is 12 divided by 3? Ready.â Signal.

Students say, â12 Ã· 3 = 4â

Write on the board 100 – 49 + 4 =

Say to the students, âNice work. 12 Ã· 3 does equal 4. What do you do next? Ready.â Signal.

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

The students say, âWe subtract 49 from 100.â

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

Students say, âOne hundred minus forty nine is fifty-oneâ

Write on the board. 51 + 4

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

Ready.â Signal.

Students say, âNo.â

Say to the students, âWhat do we still have to do?â

Students say, âAdd fifty-one plus four.â

Say to the students, âDo that. How much is fifty-one plus four?â

The students say, âFifty-one plus four is fifty-fiveâ

Write on the board 55

Say to the students, âHave we done all of the steps. Ready.â Signal.

Students say, âYes.â

Say to the students, âSo what is 100 – 7Â² + 12 Ã· 3? Ready.â Signal.

Students say, âFifty-five.â

### Task Seven â More Advanced Problem (Brackets)

Write on the board 36 Ã· 12 + 2(5 â 2) =

Say to the students, âThis problem is more difficult. Letâs see if you can solve this one. Read this problem. Ready.â Signal.

Students read, âThirty-six divided by twelve plus two bracket five minus two bracket equals some number.â

The students say, âBrackets.â

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

Students say, âYes.â

Say to the students, âRight. There are brackets. What numbers are in the brackets. Ready.â Signal.

Students say, âFive minus two.â

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

Students say, âFive minus two equals three.â

Say to the students, âThatâs 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.â Signal.

The students say, âTwoâ.

Say to the students. âThatâs right. So what numbers do we multiply? Ready.â

The students say, âTwo times three.â

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

Students say, âTwo times three equals six.â

Say to the students, âYou got it. Now you have removed the brackets.â

Write on the board. 36 Ã· 12 + 6 =

Say to the students, âWhat is the next step?â

Students say, âDivide twelve into thirty-six.â

Say to the students, âThatâs correct. How many times does twelve divide into thirty-six? Ready.â Signal.

The students say âThree times.â

Say to the students, âYes, three times.â

Write on the board. 3 + 6 =

Say to the students, âWhat does 3 + 6 equal?â

Students say, âThree plus six equals nine.â

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

Students say, âNine.â

Task 8 â More Advanced Problem (Exponents and Brackets)

Write on the board. 6Â³ – 3(4) + 90 Ã· 10

Say to the students, âRead this problem. Ready.â Signal.

Students read, âSix cubed minus three bracket four bracket plus ninety divided by ten equals some number.â

The students say, âBrackets.â

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

Students say, âYes.â

Say to the students, âRight. There are brackets.

What do we look for next? Ready. Signal.

Students say, âWe multiply the number in the bracket by the number outside of the bracket.â

Say to the students, âWhat numbers do we multiply? Ready.â Signal.

Students say, âFour times three.â

Say to the students, âHow much is four times three. Ready.â

Students say, âTwelveâ

Write on the board. 6Â³ – 12 + 90 Ã· 10 =

Say to the students, âWhat do we do next in this problem? Ready.â Signal.

Students say, âExponents.â

Students say, âYes.â

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

The students say, âSix cubedâ

Say to the students, âLetâs work this part of the problem. What is six cubed? Ready.â Signal.

The students say, âSix cubed equals eighteen.â

Say to the students, âThatâs right.â

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

Check your formula. What do we look for next? Ready.â Signal.

Students say, âDivision and Multiplication.â

Students say, âYes.â

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

Students say, âDivide ninety by ten.â

Say to the students, âGood work. What is 90 divided by 10? Ready.â Signal.

Students say, âNinety divided by ten equals nineâ

Write on the board 18 – 12 + 9 =

Say to the students, âNice work. 90 Ã· 10 does equal 9. What do you do next? Ready.â Signal.

The students say, âWe subtract 12 from 18.â

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

Students say, âEighteen minus twelve is sixâ

Write on the board. 6 + 9

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

Ready.â Signal.

Students say, âNo.â

Say to the students, âWhat do we still have to do?â

Students say, âAdd six plus nine.â

Say to the students, âDo that. How much is six plus nine?â

The students say, âSix plus nine is fifteenâ

Write on the board 15

Say to the students, âHave we done all of the steps. Ready.â Signal.

Students say, âYes.â

Say to the students, âSo what is 6Â³ – 12 + 90 Ã· 10? Ready.â Signal.

Students say, âFifteen.â

Task 9 â Order of Operation with Fractions

Write on the board. (8Â² – 4)

(12 Ã· 2 + 4)

Say to the students, âRead this problem. Ready.â Signal.

Students read, âBracket eight squared minus four bracket over bracket twelve divided by two plus four.â

The students say, âBrackets.â

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

Students say, âYes.â

Say to the students, âRight. There are brackets. Letâs start with the brackets on the top part of the fraction. What are the numbers inside those brackets? Ready.â Signal.

Students say, âEight squared minus four.â

Say to the students, âCan you work this problem? Ready.â Signal.

Students say, âNo, we have to work the exponent first.â

Say to the students, âGood 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 letâs work the exponent. How much is 8Â²? Ready.â Signal.

The students say, âEight squared equals sixty-four.â

Write on the board 60 =

(12 Ã· 2 + 4)

Say to the students, âYou got that right. What do you do next? Ready.â Signal.

The students say, â You subtract four from sixty-four.â

Say to the students, âGood job. What is sixty-four minus four? Ready.â Signal.

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

What do we do next? Ready. Signal.

Students say, âWe work with the bracket on the bottom part of the fraction.â

Say to the students, âCan we work the problem the way it is written? Ready.â Signal.

Students say, âNo. We have to do the division first.â

Say to the students, âThatâs 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.â

Students say, âTwelve divided by twoâ

Say to the students, âHow much is twelve divided by two? Ready.â Signal.

The students say, âTwelve divided by two equals six.â

Write on the board.

60

(6 + 4)

Say to the students, âWhat do we do next in this problem? Ready.â Signal.

Students say, âWe add six plus four.â

Say to the students, âThatâs correct. How much is six plus four? Ready. Signal.

The students say, âSix plus four equals ten.â

Say to the students, âGood. What do we do next?

The students say, âWe divide ten into sixty.â

Say to the students, âThatâs right. How much does sixty divided by ten equal?â

The students say, âSixty divided by ten equals six.â

Say to the students, âSo what does 8Â² – 4 equal?

(12 Ã· 2 + 4)

The students say, âSixâ

Say to the students, âNice 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.

A printable pdf version of the lesson including all worksheets is available for download. Click here to download the Teaching Order of Operations Complete Lesson pdf.