Lesson Plan
Operation Order: Solve It!
Students will be able to identify and apply the correct order of operations (PEMDAS/GEMS) to solve mathematical expressions with multiple operations.
Understanding the order of operations is a foundational skill in mathematics, ensuring consistent and accurate solutions to problems encountered in algebra, science, and everyday life.
Audience
6th Grade Students
Time
30 minutes
Approach
Direct instruction, guided practice, and independent application.
Prep
Teacher Preparation
15 minutes
- Review the Operation Order Slide Deck and familiarize yourself with the content.
- Print or prepare to display the Order Up! Warm-Up.
- Print or prepare to distribute the Exit Ticket: PEMDAS Power!.
- Review the Teacher Script to ensure smooth delivery.
Step 1
Warm-Up: Order Up!
5 minutes
- Distribute or display the Order Up! Warm-Up.
- Instruct students to solve the short expression individually.
- Briefly discuss student approaches and introduce the need for a standard order of operations.
Step 2
Introduction to Order of Operations (PEMDAS/GEMS)
10 minutes
- Present the Operation Order Slide Deck, using the Teacher Script for guidance.
- Introduce PEMDAS/GEMS acronym and explain each step with examples.
- Emphasize the
Step 3
Guided Practice
10 minutes
- Work through 2-3 additional example expressions as a class, encouraging student participation.
- Use the Operation Order Slide Deck to display problems and solutions step-by-step.
- Address any misconceptions and reinforce the importance of showing work.
Step 4
Cool-Down: PEMDAS Power!
5 minutes
- Distribute the Exit Ticket: PEMDAS Power!.
- Instruct students to solve the expression independently.
- Collect exit tickets to assess individual understanding and progress monitor for future instruction.
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Slide Deck
Operation Order: Solve It!
Getting Our Math in Order!
Today, we're going to unlock the secret to solving tricky math problems with lots of operations. Get ready to become a math detective!
Welcome students and prepare them for a fun and important math lesson!
Order Up! Warm-Up
Solve the following expression:
10 + 2 * 3
What answer did you get? Why did you solve it that way?
Introduce the warm-up. Give students about 3-4 minutes to solve it independently. Discuss their approaches afterwards.
Why an Order?
Imagine if everyone solved problems differently!
- 10 + 2 * 3
- Some might do 10 + 2 = 12, then 12 * 3 = 36.
- Others might do 2 * 3 = 6, then 10 + 6 = 16.
Which is correct? We need rules!
Explain why a consistent order is needed. Use the example from the warm-up to highlight potential confusion.
Meet PEMDAS (or GEMS)!
To make sure everyone gets the SAME answer, we follow a special order:
Parentheses (or Grouping Symbols)
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Introduce PEMDAS/GEMS. Explain the acronym clearly. Spend a moment on the 'left to right' rule for multiplication/division and addition/subtraction.
Let's Practice! Example 1
Solve: 5 + (8 - 3) * 2
- Parentheses: (8 - 3) = 5
- Exponents: (None)
- Multiplication: 5 * 2 = 10
- Addition: 5 + 10 = 15
Result: 15
Walk through a simple example, emphasizing each step. Point to the order as you go.
Guided Practice! Example 2
Solve: 18 / 3 + 4 * 2 - 5
- What's first? (Multiplication/Division from left to right)
- Then what? (Addition/Subtraction from left to right)
Introduce a slightly more complex example for guided practice. Encourage students to call out steps.
Solution: Example 2
Solve: 18 / 3 + 4 * 2 - 5
- 18 / 3 = 6
- 4 * 2 = 8
- Now we have: 6 + 8 - 5
- 6 + 8 = 14
- 14 - 5 = 9
Result: 9
Provide the solution for Guided Practice Example 2. Have students check their work.
Guided Practice! Example 3
Solve: (7 + 1)^2 - 10 / 5
- Don't forget the exponents!
Introduce the final guided practice problem. Again, prompt students for the steps.
Solution: Example 3
Solve: (7 + 1)^2 - 10 / 5
- Parentheses: (7 + 1) = 8
- Exponents: 8^2 = 64
- Multiplication/Division: 10 / 5 = 2
- Addition/Subtraction: 64 - 2 = 62
Result: 62
Provide the solution for Guided Practice Example 3.
Exit Ticket: PEMDAS Power!
Show what you know!
Solve the expression on your exit ticket. Remember to show your steps!
Introduce the cool-down. Emphasize that this is an individual assessment.
Great Job, Math Detectives!
You now have the power to solve expressions with confidence! Keep practicing PEMDAS/GEMS!
Remind students what they learned today and to keep practicing!
Script
Teacher Script: Operation Order: Solve It!
Warm-Up: Order Up! (5 minutes)
(Display Order Up! Warm-Up / Slide 2: "Order Up! Warm-Up")
"Good morning, future math detectives! Today, we're going to uncover a super important secret to solving math problems. To start us off, I have a quick challenge for you. On your screens or on the handout I'm passing around, you'll see a simple math expression."
"Your task is to solve it: 10 + 2 * 3. Take about two to three minutes to solve it on your own. Don't worry about being right or wrong, just try your best and think about how you approached the problem."
(After 2-3 minutes, call on a few students to share their answers and methods.)
"Who would like to share their answer and, more importantly, how they got that answer? Don't be shy, there's no wrong way to think about it at this stage!"
(Acknowledge different answers, if any. Transition to Slide 3.)
Introduction to Order of Operations (PEMDAS/GEMS) (10 minutes)
(Slide 3: "Why an Order?")
"That was interesting! As you can see, some of us might have gotten 36, while others might have gotten 16. This shows us exactly why we need a special set of rules in mathematics. Just like in a game, if everyone follows different rules, the outcome will be different every time! In math, we need to make sure everyone gets the same correct answer."
(Slide 4: "Meet PEMDAS (or GEMS)!")
"To keep things fair and consistent, mathematicians around the world follow something called the Order of Operations. You might have heard of it before as PEMDAS or GEMS. It's an acronym that helps us remember the steps."
"Let's break it down:
- P stands for Parentheses. These are the first things we look for. Any calculations inside parentheses or other grouping symbols (like brackets) must be done first."
- "E stands for Exponents. After parentheses, we tackle any exponents. Remember, an exponent tells you how many times to multiply a base number by itself."
- "Next comes Multiplication and Division. This is important: you do multiplication and division together, from left to right in the expression. It's like reading a book – you go from left to right. Whichever one comes first as you read from left to right, you do it first."
- "Finally, we have Addition and Subtraction. Just like multiplication and division, you do these together, from left to right. Whichever one appears first as you read from left to right, you perform that operation first."
"So, if we go back to our warm-up problem: 10 + 2 * 3. According to PEMDAS, what operation should we do first? (Pause for answers) That's right, multiplication! 2 * 3 equals 6. Then we do the addition: 10 + 6 equals 16. So, the correct answer is 16!"
Guided Practice (10 minutes)
(Slide 5: "Let's Practice! Example 1")
"Let's try another one together to really get the hang of it. We're going to solve: 5 + (8 - 3) * 2."
"What's the very first step according to PEMDAS? (Parentheses) Exactly! What's inside the parentheses? (8 - 3) And what does that equal? (5) So, now our expression looks like 5 + 5 * 2."
"Are there any exponents? (No) Okay, what's next? (Multiplication and Division) Do we have any multiplication or division? (Yes, 5 * 2) What does 5 * 2 equal? (10) Now our expression is 5 + 10."
"And finally, what's our last step? (Addition) What is 5 + 10? (15) Great job! The answer is 15."
(Slide 6: "Guided Practice! Example 2")
"You're doing great! Let's try a slightly longer one. Here's our next problem: 18 / 3 + 4 * 2 - 5."
"Remember the rule for multiplication and division, and addition and subtraction: left to right! Take a moment to think about what you would do first."
(Allow a moment for students to think or try it on scratch paper.)
"Okay, what operation should we perform first as we read from left to right? (Division: 18 / 3) Yes! What is 18 divided by 3? (6) Now we have 6 + 4 * 2 - 5."
"What's next? (Multiplication: 4 * 2) Correct! And 4 times 2 is? (8) Our expression is now 6 + 8 - 5."
"Now we're down to addition and subtraction, from left to right. What do we do first? (Addition: 6 + 8) That's 14. So we have 14 - 5."
"And finally, 14 minus 5 is? (9) Excellent! The answer is 9."
(Slide 7: "Solution: Example 2")
"Here's a quick look at all the steps. Does that match what you got?"
(Slide 8: "Guided Practice! Example 3")
"Let's challenge ourselves with one more. This one includes an exponent! Solve: (7 + 1)^2 - 10 / 5."
"Think carefully about each step of PEMDAS. Work it out on your paper."
(Allow students to work for about 2-3 minutes.)
"Alright, who can tell me the first step? (Parentheses: 7 + 1 = 8) Perfect! So we have 8^2 - 10 / 5."
"What comes after parentheses? (Exponents: 8^2) And what is 8 squared? (64) Now we have 64 - 10 / 5."
"What's next? (Division: 10 / 5) And what does that equal? (2) So, our expression is now 64 - 2."
"And the final step? (Subtraction: 64 - 2 = 62) Fantastic! The answer is 62."
(Slide 9: "Solution: Example 3")
"Take a look at the solution steps. Great work everyone, you're becoming pros at this!"
Cool-Down: PEMDAS Power! (5 minutes)
(Slide 10: "Exit Ticket: PEMDAS Power!")
"To wrap up our lesson today, I want to see how much you've mastered the order of operations. I'm going to hand out an exit ticket, or you'll see it on your screen. Your task is to solve the expression provided on your own. This is your chance to show me what you know! Please make sure to show your steps so I can see your mathematical thinking."
(Distribute Exit Ticket: PEMDAS Power! and collect them when students are finished.)
(Slide 11: "Great Job, Math Detectives!")
"Excellent work today, math detectives! You've learned a vital skill that will help you solve countless problems in the future. Remember to keep practicing PEMDAS/GEMS, and you'll always find the correct solution. Have a great day!"
Warm Up
Order Up! Warm-Up
Directions: Solve the expression below. Show your work!
10 + 2 * 3
Bonus Question: Why do you think it's important to have a specific order for solving problems like this?
Cool Down
Exit Ticket: PEMDAS Power!
Directions: Solve the expression below, showing all your steps clearly. This will help me understand what you've learned today!
24 / (6 - 2) + 5 * 3