Michael Salas
Order of Operations
1.
Purple Math- the order of operations
Website- http://www.purplemath.com/modules/orderops.htm
Hosted by Elizabeth Stapel
This website is a very good resource for students and even teachers. This website directly explains the steps of order of operations. It clarifies on what not to do in the process of order of operations. This website gives you the techniques on how to approach a problem regarding the order of operations.
2.
Math- The Order of Operations
Website- http://www.math.com/school/subject2/lessons/S2U1L2GL.html
Hosted by math.com, (The World of Math online)
This website is a very useful resource for students. This website first explains the basics of order of operations. Next, the website goes more in depth on the rules of PEMDAS or order of operations. The next step of this website is that it shows examples of how solve problems regarding the order of operations. Finally, you can work out the problems that are given to you and then find out if you are correct or incorrect.
3.
Math Goodies- Order of Operations
Website- http://www.mathgoodies.com/lessons/vol7/order_operations.html
Hosted by Mrs. Glosser’s Math Goodies
This website is another useful tool for students. This website carefully explains the wrong and right way to do a problem. By telling you the wrong way to do it, it helps the student understand that is not the way to do it. It explains how PEMDAS operates.
This website goes step by step on how to approach a problem.
4.
Classroom.jc-schools- Order of Operations
Software- Math Order of Operation http://classroom.jc-schools.net/basic/math-order.html
Hosted is not clarified

Michael Salas
This software is a very useful reference for students. This software allows students to play games involving the order of operations.
You can play a basketball game or building a snowman game while learning the order of operations. I believe students would love to play this software.
5.
A to Z Teacher Stuff- Order of Operations
Internet Project- An Educator’s Desk Lesson Plan- http://atozteacherstuff.com/go/search.cgi?query=order+of+operatio ns&grade=&bool=OR
Written by Bambi Exum
This is a great reference for students and teachers. There are many links to help you teach the order of operations. You are able to create your own lesson plan and submit it on this internet project.

Michael Salas
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If you are asked to simplify something like " 4 + 2×3 ", the question that naturally arises is "Which way do I do this? Because there are two options!":
Choice 1: 4 + 2×3 = (4 + 2)×3 = 6×3 = 18
Choice 2: 4 + 2×3 = 4 + (2×3) = 4 + 6 = 10
It seems as though the answer depends on which way you look at the problem. But we can't have this kind of flexibility in mathematics; math won't work if you can't be sure of the answer, or if the exact same problem can calculate to two or more different answers. To eliminate this confusion, we have some rules of precedence, established at least as far back as the 1500s, called the
"order of operations". The "operations" are addition, subtraction, multiplication, division, exponentiation, and grouping; the "order" of these operations states which operations take precedence (are taken care of) before which other operations.
A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please
Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ 12 , but is rather
5 × 4 , because, going from left to right, you get to the division first. If you're not sure of this, test it in your calculator, which has been programmed with the Order of Operations hierarchy. For instance, typesetting this into a graphing calculator, you will get:
Using the above hierarchy, we see that, in the " 4 + 2×3 " question at the beginning of this article, Choice 2 was the correct answer, because we have to do the multiplication before the addition.
(Note: Speakers of British English often instead use "BODMAS", which stands for "Brackets, Orders, Division and Multiplication, and
Addition and Subtraction". Since "brackets" are the same as parentheses and "orders" are the same as exponents, the two acronyms mean the same thing.)
The order of operations was settled on in order to prevent miscommunication, but PEMDAS can generate its own confusion; some students sometimes tend to apply the hierarchy as though all the operations in a problem are on the same "level", but often those operations are not "equal". Many times it helps to work problems from the inside out, rather than left-to-right, because often some parts of the problem are "deeper down" than other parts. The best way to explain this is to do some examples:

Michael Salas

Simplify 4 + 3
2
.
I need to simplify the term with the exponent before trying to add in the 4 :
4 + 3
2
= 4 + 9 = 13

Simplify 4 + (2 + 1)
2
.
I have to simplify inside the parentheses before I can take the exponent through. Only then can I do the addition of the 4 .
4 + (2 + 1)
2
= 4 + (3)
2
= 4 + 9 = 13

Simplify 4 + [–1(–2 – 1)]
2
.
I shouldn't try to do these nested parentheses from left to right; that method is simply too error-prone. Instead, I'll try to work from the inside out. First I'll simplify inside the curvy parentheses, then simplify inside the square brackets, and only then take care of the squaring. After that is done, then I can finally add in the 4 :
4 + [–1(–2 – 1)]
2
= 4 + [–1(–3)]
2
= 4 + [3]
2
= 4 + 9
= 13
There is no particular significance in the use of square brackets (the "[" and "]" above) instead of parentheses. Brackets and curlybraces (the "{" and "}" characters) are used when there are nested parentheses, as an aid to keeping track of which parentheses go with which. The different grouping characters are used for convenience only. This is similar to what happens in an Excel spreadsheet when you enter a formula using parentheses: each set of parentheses is color-coded, so you can tell the pairs:
Copyright © Elizabeth Stapel
2000-2011 All Rights Reserved

Simplify 4(
–2
/
3
+
4
/
3
) .
I will simplify inside the parentheses first:

Michael Salas
Then I get 4(
–2
/
3
+
4
/
3
) =
8
/
3
The next page has more worked examples examples....
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Michael Salas
When expressions have more than one operation, we have to follow rules for the order of operations:
1.
First do all operations that lie inside parentheses.
2.
Next, do any work with exponents or radicals.
3.
Working from left to right, do all multiplication and division.
4.
Finally, working from left to right, do all addition and subtraction.
Click Show Me to see the correct order to solve the expression below:
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Unit
7
Puzzles Calculators
Problem
:
Evaluate the following arithmetic expression:
3 + 4 x 2
Solution
:
Studen t 1
Studen t 2
3 + 4 x
2
3 + 4 x
2
= 7 x 2 = 3 + 8
= 14 = 11

Michael Salas
It seems that each student interpreted the problem differently, resulting in two different answers. Student 1 performed the operation of addition first, then multiplication; whereas student
2 performed multiplication first, then addition. When performing arithmetic operations there can be only one correct answer.
We need a set of rules in order to avoid this kind of confusion.
Mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.
Rule 1:
Rule 2:
Rule 3:
First perform any calculations inside parentheses.
Next perform all multiplications and divisions, working from left to right.
Lastly, perform all additions and subtractions, working from left to right.
The above problem was solved correctly by Student 2 since she followed Rules 2 and 3. Let's look at some examples of solving arithmetic expressions using these rules.
Example 1: Evaluate each expression using the rules for order of operations.
Solution:
Order of Operations
Expression Evaluation Operation
6 + 7 x 8 = 6 + 7 x 8 Multiplication
= 6 + 56 Addition
= 62
16 ÷ 8 - 2 = 16 ÷ 8 - 2 Division

Michael Salas
= 2 - 2
= 0
Subtraction
(25 - 11) x 3 = (25 - 11) x 3 Parentheses
= 14 x 3 Multiplication
= 42
In Example 1, each problem involved only 2 operations. Let's look at some examples that involve more than two operations.
Example
2:
Evaluate 3 + 6 x (5 + 4) ÷ 3 - 7 using the order of operations.
Solution: Step
1:
3 + 6 x (5 + 4) ÷ 3
- 7
= 3 + 6 x 9 ÷ 3
- 7
Parenthes es
Step
2:
3 + 6 x 9 ÷ 3 - 7 = 3 + 54 ÷ 3 - 7 Multiplicati on
Step
3:
3 + 54 ÷ 3 - 7 = 3 + 18 - 7 Division
Addition Step
4:
3 + 18 - 7
Step
5:
21 - 7
= 21 - 7
= 14 Subtractio n

Michael Salas

Operation Order
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Michael Salas
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Information
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Subject
Areas
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Practice
Math Order of Operation
Math
6 th
-8 th
Works properly basketball
Yes
Yes
Useful in lessons snowman
Easy to understand
Math Frog
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The directions are clear and easy to follow for the intended age group. Strongly Agree
Useful directions are available via a written manual or on-screen help. Agree
It is easy for the students to exit the program. Strongly Agree

Students may start up where they left off in the program. Disagree
Searching for certain items is simple and complex searches may be done. Agree
The program functions well on the computer and it is free on bugs. Strongly Agree
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Michael Salas
Included graphics and animations are meaningful. Agree
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The program automatically branches based on student responses. Disagree
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The software contains a useful management tool for the teacher. Disagree
The software covers a wide range of skill levels. Agree
Other thoughts: These games make math fun to do instead of hearing a teacher lecturing the whole class. These games are enjoyable to play and I hope to use these games for my future students.

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Lesson Plans : Mathematics : Grades 6-8 : Operations
Resources:
Order of Operations Lesson Plan
A lesson teaching the order of operations that must be followed when solving equations. Exercise and answer key attached. http://www.lessontutor.com/eesA4.html

FIND MORE
Grade Level(s): 912 • Rating: 6 Votes: 10 Rate It
Dr. Seuss Activities Lesson Plan
Cross-curricular activities for 15 Dr. Seuss books, including The Foot
Book, Dr. Seuss' ABC, If I Ran the Zoo, The Lorax, and more! http://www.atozteacherstuff.com/pages/250.shtml
Grade Level(s): K, 1-2 Rate It
Lunch Count and Attendance All-In-One Teacher Tip
Since I use a racing theme in my class room, I have a race car with the kid's names on them. Each car has a small piece of magnet on the back and they hang on the file cabinet. Each day, the kids come in the room and they move their race car underneath their lunch choices
(choice 1, choice 2 or lunch from home). It's a three-fold tool-I know who is at school, I know what they want for lunch, and it's a great way for them to show responsibility. After the first month or so, if a student is present and they don't move their race car, I order their lunch for them. I usually only have to do that once because they like to order their own lunch. This would work for any theme in a classroom... just change the race car to whatever cut-out you want. http://www.atozteacherstuff.com/pages/819.shtml
Grade Level(s): K, 1-2, 3-5 Rate It
How to make sure everyone has turned in their paper
Teacher Tip
During the first week of school I assign everyone a number. I usually just go down the roll book and assign the numbers in alphabetical order . I instruct the students that each time they turn in a paper the number should be in the right hand corner of the paper. When all papers are collected I put the in order and I can quickly check and see if anyone has not turned a paper in. This works great and is fast. http://www.atozteacherstuff.com/pages/1744.shtml
Grade Level(s): Rate It
April Fool's Day Printables Printable
Worksheets for April Fool's: ABC order , vocabulary word jumble, word searches http://www.apples4theteacher.com/holidays/april-fools-day/printables/
Michael Salas

Grade Level(s): 1-2, 3-5 Rate It
Earth Day Printables and Worksheets Printable
Word search, ABC order , word jumble, and acrostic poem for Earth
Day. http://www.apples4theteacher.com/holidays/earth-day/printables/
Grade Level(s): K, 1-2, 3-5 Rate It
Color Patterns Lesson Plan
To be able to make a pattern of three colors and then repeat the pattern on paper. http://www.atozteacherstuff.com/pages/365.shtml
Grade Level(s): Preschool, K Rate It
Numbers Teacher Tip
To emliminate always having to write new studnets names on small pieces of paper or whatever I was using at the time, I simply numbered my students and gave them each a clothes pin. Then I chose 5 needed jobs. I wrote the titles on sentence strips and placed them in a small apple pocket chart (any pocket chart will do- small is the key). I clipped the clothes pin next to the title and then I move them each week in number order . All students not working that week are 'on vacation.' Any unused clothes pins go on top at the leaf. No more need to remember who did what last week or what about the new student. http://www.atozteacherstuff.com/pages/1648.shtml
Grade Level(s): Rate It
Sentence Strip Unscramble Teacher Tip
This activity is great to use the first day kids walk in, while you greet new students and their parents. Type a short letter attached to an envelope inviting students to unscramble the sentence you have placed in their envelope. Sentences like: Welcome to 3rd grade! It's going to be a great year! I'm glad you are here!
Be sure to cut between the words like a puzzle. The students job is to place the sentence in order . http://www.atozteacherstuff.com/pages/5069.shtml
Grade Level(s): 1-2, 3-5 Rate It
Michael Salas

Counting by 2: Fill in the Blank (Random) Printable
Counting by 2s - Fill in the blank 2 to 100 (5 problems in random order ) math/countingby2s_2.pdf
Grade Level(s): 1-2 Rate It
Everyone gets a turn Teacher Tip
In order to make sure all students are given an opportunity to answer, read or respond in my classroom, I purchased an inexpensive deck of playing cards and wrote a student's name on each card, making sure to use each name an equal number of times. Before each class, I shuffle the cards. I hold them, name up, and use them to call on students. It adds ramdomness and keeps students alert because they do not know when they will be called on. http://www.atozteacherstuff.com/pages/4481.shtml
Grade Level(s): 5-7 Special Education Rate It
Storing Sentence Strips Teacher Tip
I use a lot of sentence strips in my classroom and have found that shower curtain hooks used in a hole punched hole keep all for a particular subject in order . These can be stored in a wallpaper trough, or I hang them on a line. http://www.atozteacherstuff.com/pages/1771.shtml
Grade Level(s): Rate It
Subject/Verb Agreement and Pronoun/Antecedent
Agreement
Lesson Plan
This lesson is designed to of fer a hands on approach to learning pronoun/antecedent agreement--analyzing sentences and identifying pronouns and their antecedents in order to verify their agreement. http://www.atozteacherstuff.com/pages/336.shtml
Grade Level(s): 68 • Rating: 4 Votes: 6 Rate It
Campaign 2004: Classroom Electorate Lesson Plan
Students take on the role of a political analyst, forecasting the electoral vote count for the 2004 presidential election. In order to
Michael Salas

make a prediction, students are introduced to campaign issues, the
Electoral College, the role of swing states, and the importance of political participation. The lesson plan includes a fun, interactive classroom competition where students make electoral predictions and compare with the actual results following the November 2nd voting deadline. http://www.atozteacherstuff.com/pages/4533.shtml
Grade Level(s): 6-8, 9-12 Rate It
Working Together for Classroom Behavior... Teacher Tip
In order to motivate the entire class to work together for great classroom behavior, I am designing a race track with several pit rows on poster board. Whenever the class gets a compliment from the principal, a parent, an assistant, or teacher, the race car will be advanced one space. If group misbehavior continues aft... more>> http://www.atozteacherstuff.com/pages/1733.shtml
Grade Level(s): • Rating: 8 Votes: 6 Rate It
Counting by 3: Fill in the Blank (Hints) Printable
Counting by 3s (3 to 120 in order w/ HINTS) Fill in the blank math/countingby3s_2.pdf
Grade Level(s): 1-2 Rate It
TeachDelaware Resource Site
Delaware Center for Teaching Careers (TeachDelaware) was established by Delaware State Department of Education to recruit qualified individuals to the teaching pr of ession in order to alleviate the shortage of credential teachers in Delaware. TeachDelaware is a one-stop information and referral recruitment center for individuals who may be interested in a teaching career. TeachDelaware of fers a variety of informational and advisor-assisted services to prospective teachers. http://www.teachdelaware.com/
Grade Level(s): Rate It
FOCUS on Classroom Management: Week 1 -
Focus Attention on You!
Resource Site
All too of ten, the most common mistake many teachers make is
Michael Salas

starting a lesson without all of the students' attention. Eager to get into teaching, a teacher might begin the lesson while some students are visiting with their neighbor, searching through their desks, or even walking around the classroom! http://www.atozteacherstuff.com/pages/7664.shtml
Grade Level(s): K, 1-2, 3-5, 6-8, 9-12 Rate It
Counting by 3: Fill in the Blank (Random w/ Hints) Printable
Counting by 3s (3 to 102, 5 problems in random order w/ hints) Fill in the blank math/countingby3s_4.pdf
Grade Level(s): 1-2 Rate It
Lesson Plan
The purpose of this lesson is to create an awareness and understanding that important technological advances within our culture, in a variety of areas, are the result of the work done by a diverse group of people, many of whom are African Americans. To this end, students will be actively involved in discussions, research, and sharing sessions. Between six and ten class periods will be necessary for this lesson. http://www.atozteacherstuff.com/pages/252.shtml
Grade Level(s): 68 • Rating: 8 Votes: 9 Rate It
Mexican Food Lesson Plan
Following a lecture on the history of Mexican food, grade five students will be able to recognize and order Mexican cuisine, at a restaurant, with 100% accuracy. http://www.atozteacherstuff.com/pages/368.shtml
Grade Level(s): 3-5 Rate It
Using student numbers Teacher Tip
Because keeping up with papers from each student in each subject can be overwhelming, I've added onto the idea of assigning student numbers in the classroom. When students head their papers, they are required to include their personal numbers based on alphabetical order . At the end of the day, papers are collected and put in "ordinal position" by students. I have a quick record of which papers are missing. When papers are graded, student helpers file the papers in
Michael Salas

individual file folders for the students to check. The folders are kept in a basket in the back of the room and I don't waste valuable time passing papers to students. http://www.atozteacherstuff.com/pages/1750.shtml
Grade Level(s): Rate It
Filing System Teacher Tip
I have found a wonderful way to file all my papers. It really cuts down on time and desk clutter and anybody can do it. Assign each subject a color. For example, red for reading, yellow for math, green for science, etc. Buy (I hate that word too, but they are not expensive), or get a parent to donate, file folders of each color for each subject. I started out with at least 5 of each color. Then file and label the various topics for each subject in the corresponding color. This way if you need a worksheet on clocks, you know that all the math files are yellow and you go to the yellow folder labled time. If you need a reading comprehension test sheet, you would look in the red folder labled comprehension tests. It is also an ideal system to use for memos from the of fice and order forms from various companies. I hope it works for you as well as it has for me! http://www.atozteacherstuff.com/pages/1784.shtml
Grade Level(s): Rate It
Family Tree Lesson Plan
Students will examine their family history in order to create a family tree. http://www.canteach.ca/elementary/wsoccult4.html
Grade Level(s): 35 • Rating: 5 Votes: 8 Rate It
Mixed Up Sentences Lesson Plan
I mix up words using those sight words being worked on and words from our word walls. The children then put the words in order to make a sentence. http://www.atozteacherstuff.com/pages/414.shtml
Grade Level(s): K, 1-2 Rate It
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Michael Salas

Michael Salas
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