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Order of Operations Competition
Students will be able to analyze a math expression, and use the order of operations to determine if a parenthesis is needed.
- Write PEMDAS in large print on the board, along with the definitions and symbols: P (parentheses), E (exponents), M (multiply), D (divide), A (add), S (subtract).
- Tell students that it is important to know the proper order of operations so that we are all consistent with our answers.
- Show students 'The Order Of Operations Song' by Silly School Songs on a video projector or tablet.
Explicit Instruction/Teacher modeling(10 minutes)
- Write '10 x 4 - (6 + 6)' on the board, and model how you use PEMDAS to solve.
- Tell students that any operations inside parentheses must be done first, then exponents (indicate that there are none in this problem), followed by multiplication and division from left to right, whichever comes first, and finally addition and subtraction also from left to right.
- Demonstrate how to solve the following problems on the board, using PEMDAS. Make sure to show each step of the process and model your thinking aloud.
Solve: 16 + 8 ÷ (10 - 6) x 2 Determine if a parenthesis is needed, and place it correctly: 6 + 9 - 18 ÷ 2 + 4 = 12 ('I notice that if I divide 18 by 2 first, I get 9. Six plus 9 minus 9 equals 6, and when I add 4, my answer is 10. That's not right. Let's see, where could I put the parenthesis? If I put it around 2 + 4, the equation amounts to 12!')
Guided Practice(15 minutes)
- Divide students into two groups.
- Have each group take turns sending two students at a time to the board to solve a math expression, showing each step of their work, in competition with representatives from the other group. Whichever group solves the expression correctly first, gets a point. Use a variety of problems such as the following:
5 x (6 + 2) - 6
(12 - 3) x (13 + 5) - 4 3 + 5 x 6 + (24 ÷ 4) 60 - 20 + 5 ÷ (3 x 3) Determine if a parenthesis is needed, and place it correctly: 17 - 5 + 8 ÷ 2 = 2 20 x 2 - 30 + 5 = 15 30 - 9 + 12 ÷ 3 + 10 = 33 100 x 2 - 100 ÷ 2 + 2 = 175
- If the two groups arrive to different answers, instruct them to show evidence of how they solved the expression. Review any mistakes or misconceptions.
- Once each student has had a turn, tally the scores and announce the winning team.
Independent working time(15 minutes)
- Distribute the Order of Operations Puzzle worksheet to students, and explain the directions.
- Go over the sample problem, and instruct students to complete the page independently.
- Circulate the room, and offer assistance as needed.
- Students may use a multiplication chart as they solve the problems in the independent work section.
- Provide struggling students with simple order of operations problems, without division or parentheses, to solve at first.
- Have students work on a computer or tablet to complete more difficult exercises on order of operations (see additional resources).
- Show the following problems on the board, and ask students to discuss with a partner what went wrong in the calculations.
5 + 10 x 2 = 30 (Addition was done before multiplication) 2 × 6 + 11 × (5 + 2) = 117 (Parenthesis was not done first)
- Have students share out their answers, and gauge students understanding of the order of operations.
Review and closing(5 minutes)
- Have students stand in a circle in the classroom. Tell students that they will review the acronym PEMDAS.
- Go around the circle and have each student chant out the word for each letter (Parentheses! Exponents! Multiply! Divide! Add! Subtract!). See how fast students can go around chanting the acronym.