Small Groups
Activities teach students a mnemonic device to remember the order of operations and help them see how order of operation applies to nearly everything they do during the day.
Invitation to Learn
Socks and Shoes
Before beginning this lesson, teachers must have a sound understanding of why the process of order of operations is important in math and how to correctly perform it. Order of operations is important in math because it helps assure us that math works the same way for everyone, regardless if they are students in Utah or professors in Japan. Through this understanding; we can safely say that an addition or multiplication problem solved correctly will always result in the same answer. As educators we need to help our students understand that they will always get the right answer if they follow the process correctly.
A common misconception is that multiplication must be performed before division. When we use the mnemonic Please Excuse My Dear Aunt Sally, it is often assumed that because we say My (multiplication) before Dear (division) that we need to multiply first. However, multiplication and division are on the same level and should be performed based on their position in the order of operations problem. This same principle applies with addition and subtraction. The correct order of operations starts with working in parentheses, then looking for exponents, and then returning to the left or beginning of the equation and working your way towards the right as you solve. Once you have performed the multiplication or division steps, you return the beginning of the problem and work your way left to right, performing addition or subtraction in the proper order. This will allow you to answer the problem correctly.
For these activities, we are going to focus on order of operations problems that deal with addition, subtraction, multiplication, and division. Students need to be familiar with basic multiplication and division facts and need to be taught about parentheses. Exponents are not found in the Utah State Math core until the 5th grade and so we are not going to be working with problems that have exponents in them.
2. Become effective problem solvers by selecting appropriate methods, employing a variety of strategies, and exploring alternative approaches to solve problems.
4. Communicate mathematical ideas and arguments coherently to peers, teachers, and others using the precise language and notations of mathematics.
Invitation to Learn
The most commonly used mnemonic for order of operations is Please Excuse My Dear Aunt Sally. Instead of teaching this mnemonic to the class, the purpose of this invitation to learn is to help students develop ownership for their learning as they work together to develop a unique classroom mnemonic of their own liking.
The first step in this process is to say, "Today we are going to create a mnemonic that is going to help us as we learn about order of operations. Does anyone know what a mnemonic is? A mnemonic is a phrase or saying that makes information easier to remember. Has anyone ever heard of "righty-tighty, lefty-loosey"? How about "Every Good Boy Does Fine"? These are mnemonics that help us remember how to tighten or loosen a bolt and the order of musical notes on a treble staff. Using these mnemonics makes it easier to remember these things."
Go to the board and write order of operations at the top of the board. Explain that there are five steps in solving order of operation problems. (Don't worry about explaining the steps in detail. We will do that in greater detail later.) As you introduce the steps, write the steps on the board. The steps are Parentheses, Multiplication, Division, Addition, and Subtraction. Remember that our students are not going to be using exponents in 4th grade and so we do not need to include exponents in our mnemonic.
Next say, "Now we need to come up with a mnemonic phrase that will help us remember the steps when solving order of operations problems. Do you remember what a mnemonic phrase is? It is a phrase or saying that helps us remember. The most common mnemonic for order of operations is Pardon My Dear Aunt Sally (The mnemonic changes when the E for exponents is taken out), but that's no fun. Let's come up with a fun mnemonic. For example, we could say "Pink Monkeys Dance Around Santa" or "Pretty Muffins Dream About Snickerdoodles."
The next step can be done either as a whole class process or as a think-pair-share activity. We will focus on the think-pair-share activity because it gives every student an opportunity to participate. Begin by saying, "We are going to do this by doing a think-pair-share. First, you are going to use your math journals and write down a fun mnemonic phrase. Then, you are going to share your mnemonic phrase with your neighbor."
While the students are thinking and sharing, go around the room and put the class into groups of six. Then say, "Now that you have had a chance to share with your neighbor, you are going to get into your groups and share again. When you have all had a chance to share, you need to pick one mnemonic phrase from your group that you feel would be the most successful as our class saying."
When the students have decided, have each group share the mnemonic phrase. Write each mnemonic on the board and then have the class vote on which mnemonic phrase they would like to use. Once the mnemonic phrase is decided, have the students write down the phrase in their math journals.
Instructional Procedures
Socks and Shoes
The purpose of this activity is to bring students' background knowledge into the lesson and to allow them to see how order of operation applies to nearly everything they do during the day.
Curriculum Extensions/Adaptations/ Integration
Family Connections
Research Basis
Millis, B.J. (2002). Enhancing learning-and more! through cooperative learning. Idea Paper # 38. The Idea Center, 211 South Seth Child Road Manhattan.
In this article, Millis explains the power and effectiveness of cooperative learning. Not only is cooperative learning an effective teaching strategy, it "promotes a shared sense of community" in the classroom because "learning, like living, is inherently social." As students learn to work together through cooperative learning, they develop trust with each other and are given an opportunity to develop self-efficacy. As teachers come to understand how to implement cooperative learning, "student learning can be deepened, students will enjoy attending classes, and they will come to respect and value the contributions of their fellow classmates."
Willis, J. (2007). Cooperative learning is a brain turn-on. Middle School Journal. March pgs. 4-13
Judy Willis states in her article that research has shown that "in math collaboration, students learn to test one another's conjectures and identify valid or invalid solutions." This happens because cooperative learning provides students with the most opportunities to ask questions, express ideas and opinions, and come to conclusions that they might not otherwise have through whole group instruction. Teachers can increase student understanding and involvement by increasing the amount of cooperative learning in their classrooms.