Introducing Order of Operations
Students will be able to solve math expressions using the order of operations.
- On a piece of chart paper, write '4 + 5 x 6', and ask the students to solve it in their math journals.
- Ask students to compare their answers with an elbow partner.
- Invite students to share their answer with the whole class.
- Explain on the chart paper that if you add 4 to 5 first, and get 9, then multiply 9 by 6 which equals 54, the answer is incorrect. Tell students that when you have multiple operations meaning addition, subtraction, multiplication, and/or division, in one expression, you must follow some rules about the order of operations.
- Tell students that the order of operations states that multiplication and division must be done before addition and subtraction. For the sample problem, first you would multiply 5 by 6 which is 30, then add 4, equalling 34.
Explicit Instruction/Teacher modeling(10 minutes)
- Write a few more problems on chart paper such as 8 - 4 ÷ 2 and 12 - 2 x 5 + 6. Show students how to solve these problems.
- Tell students that if we rewrite the problems as follows: (8 - 4) ÷ 2 and 12 - 2 x (5 + 6), the answers would change. Explain that a parenthesis, or the ( ) symbol, means that part of the expression should be calculated first. Solve the two problems with the parentheses, and compare the answers to the same problems but without the parentheses.
- On a separate piece of chart paper, write the acronym PEMDAS, and explain that it is a way to remember the order of operations.
- Write the meaning of the acronym and the symbols to match: P (parenthesis), E (exponents), M (multiply), D (divide), A (add), S (subtract).
- Explain that when you see an expression with multiple operations, you must calculate the answer in this specific order. If the order of operations is not followed, the calculation will be incorrect. Clarify that M & D, and A & S should be calculated from left to right.
- Inform students that many people remember the acronym PEMDAS by associating it with the following sentence: Please Excuse My Dear Aunt Sally. Tell students that they can use this sentence or create their own to remember the acronym.
Guided Practice(10 minutes)
- Show students the Order of Operations: PEMDAS video (see additional resources).
- Distribute the Parentheses First! Find the Missing Operation #1 worksheet to students and display a copy on the document camera.
- Model your thinking to find the missing operation for the first 4 problems.
- Have students work with a table partner to solve the rest of the problems on the worksheet. Remind them to use the PEMDAS chart as a reference.
- Review the answers as a whole class.
Independent working time(10 minutes)
- Hand out the Parentheses First! Find the Missing Operation #2 worksheets to students, and instruct them to complete it independently.
- Circulate the room, and offer assistance as needed.
- Students who do not know all their multiplication facts may use a multiplication chart as they solve the problems in the independent work section.
- Have students write their own problems with multiple operations for their peers to solve.
- Hand out a whiteboard and marker to each student.
- Write the following problems on the board, and have students write the answer on their whiteboards . 50 - 20 + 10 x 2 21 ÷ 7 + (4 - 1)
- Tell students to hold up their answers so you can assess their understanding of the order or operations.
Review and closing(5 minutes)
- Ask students to discuss how they plan on remembering the acronym PEMDAS.