Lesson Plan
The PEMDAS Protocol
Students will be able to apply the order of operations (PEMDAS/BODMAS) to correctly solve multi-step mathematical expressions involving integers, fractions, and decimals.
Understanding the order of operations is crucial for accurate mathematical calculations in all areas of math and science. Mastering PEMDAS/BODMAS prevents errors and builds a strong foundation for more advanced algebra.
Audience
7th Grade Class
Time
55 minutes
Approach
Direct instruction, interactive slides, collaborative activity, and individual assessment.
Materials
Whiteboard or projector, Decoding Equations, Equation Scramble, Order Up! Quiz, PEMDAS Pathfinder Solutions, Markers/Pens, and Scratch paper
Prep
Teacher Preparation
15 minutes
- Review the The PEMDAS Protocol lesson plan, Decoding Equations slide deck, Equation Scramble activity, Order Up! Quiz, and PEMDAS Pathfinder Solutions answer key.
- Ensure projector/whiteboard is ready.
- Print copies of Equation Scramble (one per small group) and Order Up! Quiz (one per student).
Step 1
Warm-Up & Introduction (10 minutes)
10 minutes
- Begin with a quick mental math problem that could be solved differently without a consistent order (e.g., 5 + 3 * 2). Ask students how they solved it and discuss different answers.
- Introduce the concept of needing a universal 'rule' for solving equations to ensure everyone gets the same answer.
- Introduce the term PEMDAS/BODMAS as the 'protocol' for solving equations. Show the Decoding Equations slide deck, starting with the title slide.
Step 2
Direct Instruction: Decoding PEMDAS (20 minutes)
20 minutes
- Use the Decoding Equations slide deck to walk through each step of PEMDAS/BODMAS.
- Explain each letter: Parentheses/Brackets, Exponents/Orders, Multiplication/Division (left to right), Addition/Subtraction (left to right).
- Provide clear examples for each step, pausing for student questions and checking for understanding.
- Emphasize the 'left to right' rule for multiplication/division and addition/subtraction. Work through several example problems together as a class, encouraging students to explain their reasoning.
Step 3
Collaborative Activity: Equation Scramble (15 minutes)
15 minutes
- Divide students into small groups (3-4 students per group).
- Distribute the Equation Scramble activity sheets to each group.
- Explain the rules: groups work together to correctly solve the scrambled equations, applying PEMDAS/BODMAS.
- Circulate among groups, providing support and clarification as needed. Encourage peer teaching and discussion within groups.
Step 4
Individual Assessment: Order Up! Quiz (8 minutes)
8 minutes
- Distribute the Order Up! Quiz to each student.
- Instruct students to complete the quiz independently to assess their understanding of the order of operations.
- Collect quizzes for grading. (Refer to PEMDAS Pathfinder Solutions for grading).
Step 5
Wrap-Up & Review (2 minutes)
2 minutes
- Briefly review the key takeaway: PEMDAS/BODMAS ensures consistent and accurate mathematical results.
- Answer any final quick questions.
- Preview what might come next (e.g., applying this to algebraic expressions).
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Slide Deck
Decoding Equations: The PEMDAS Protocol
Your Guide to Solving Math Puzzles!
Ever wonder why everyone needs to solve math problems the same way?
Today, we'll learn the secret code!
Welcome students and prepare them for a fun and engaging lesson on solving equations correctly.
Why Do We Need Rules?
Imagine building with LEGOs without instructions... chaos!
Math is the same way. We need a clear order to solve problems so everyone gets the right answer.
Otherwise, we get different answers, and that's not good for science, engineering, or even sharing pizza evenly!
Introduce the need for a standard order of operations. Ask students if they've ever gotten different answers to the same problem.
Meet PEMDAS (or BODMAS!)
It's our special protocol for solving equations:
Parentheses / Brackets
Exponents / Orders (powers and square roots)
Multiplication & Division (from left to right)
Addition & Subtraction (from left to right)
Introduce PEMDAS/BODMAS. Emphasize that these are two acronyms for the same concept.
Step 1: Parentheses (or Brackets)
P or B
What's inside comes first!
Think of them as VIP sections in a concert – those calculations get done before anything else.
Example: (7 + 3) * 2
Solve (7 + 3) first: 10 * 2 = 20
Explain Parentheses/Brackets. Provide an example.
Step 2: Exponents (or Orders)
E or O
Powers and Roots next!
These tell you to multiply a number by itself a certain number of times (like 2³ = 2 * 2 * 2).
Example: 5 + 2³
Solve 2³ first: 5 + 8 = 13
Explain Exponents/Orders. Provide an example.
Step 3: Multiplication & Division
M & D
Work from left to right!
These two are equally important! You do whichever one comes first as you read the problem from left to right.
Example: 10 - 4 ÷ 2 * 3
First, 4 ÷ 2 = 2. Then 2 * 3 = 6. So: 10 - 6 = 4
Explain Multiplication and Division. Crucially, emphasize the left-to-right rule.
Step 4: Addition & Subtraction
A & S
Work from left to right!
Just like multiplication and division, these are also equally important! You do whichever one comes first as you read from left to right.
Example: 15 - 5 + 2
First, 15 - 5 = 10. Then 10 + 2 = 12
Explain Addition and Subtraction. Crucially, emphasize the left-to-right rule.
Let's Put It All Together!
Solve: 24 ÷ (2 * 3) + 5² - 10
-
Parentheses: (2 * 3) = 6
New problem: 24 ÷ 6 + 5² - 10 -
Exponents: 5² = 25
New problem: 24 ÷ 6 + 25 - 10 -
Multiplication/ Division (left to right): 24 ÷ 6 = 4
New problem: 4 + 25 - 10 -
Addition/ Subtraction (left to right): 4 + 25 = 29
New problem: 29 - 10 = 19
Answer: 19
Provide a comprehensive example that uses all steps. Work through it carefully with the students.
Practice Makes Perfect!
The more you practice using PEMDAS/BODMAS, the easier it will become.
Remember: Each step is like a clue to unlock the correct answer!
Any questions before we try an activity?
Encourage students to ask questions and reinforce the importance of practice.
Activity
Equation Scramble: PEMDAS Challenge!
Instructions: Work with your group to correctly solve each equation using the PEMDAS/BODMAS order of operations. Show all your steps! The first group to correctly solve all problems wins bragging rights!
Equation 1
Problem:
18 ÷ 6 + (5 * 3) - 7
Your Solution:
Equation 2
Problem:
4² + (12 - 3) ÷ 3
Your Solution:
Equation 3
Problem:
25 - 8 * 2 + 100 ÷ 5²
Your Solution:
Equation 4
Problem:
(1/2 + 1/4) * 8 - 3
Your Solution:
Equation 5
Problem:
7 + [ (6 * 2) - 4 ] ÷ 2
Your Solution:
Quiz
Order Up! Quiz
Answer Key
PEMDAS Pathfinder Solutions
Here are the solutions and step-by-step reasoning for the Equation Scramble activity and Order Up! Quiz.
Equation Scramble Solutions
Equation 1: 18 ÷ 6 + (5 * 3) - 7
- Parentheses: (5 * 3) = 15
Expression becomes: 18 ÷ 6 + 15 - 7 - Division: 18 ÷ 6 = 3
Expression becomes: 3 + 15 - 7 - Addition: 3 + 15 = 18
Expression becomes: 18 - 7 - Subtraction: 18 - 7 = 11
Answer: 11
Equation 2: 4² + (12 - 3) ÷ 3
- Parentheses: (12 - 3) = 9
Expression becomes: 4² + 9 ÷ 3 - Exponents: 4² = 16
Expression becomes: 16 + 9 ÷ 3 - Division: 9 ÷ 3 = 3
Expression becomes: 16 + 3 - Addition: 16 + 3 = 19
Answer: 19
Equation 3: 25 - 8 * 2 + 100 ÷ 5²
- Exponents: 5² = 25
Expression becomes: 25 - 8 * 2 + 100 ÷ 25 - Multiplication: 8 * 2 = 16
Expression becomes: 25 - 16 + 100 ÷ 25 - Division: 100 ÷ 25 = 4
Expression becomes: 25 - 16 + 4 - Subtraction: 25 - 16 = 9
Expression becomes: 9 + 4 - Addition: 9 + 4 = 13
Answer: 13
Equation 4: (1/2 + 1/4) * 8 - 3
- Parentheses: 1/2 + 1/4 = 2/4 + 1/4 = 3/4
Expression becomes: 3/4 * 8 - 3 - Multiplication: 3/4 * 8 = 6
Expression becomes: 6 - 3 - Subtraction: 6 - 3 = 3
Answer: 3
Equation 5: 7 + [ (6 * 2) - 4 ] ÷ 2
- Parentheses (innermost): (6 * 2) = 12
Expression becomes: 7 + [ 12 - 4 ] ÷ 2 - Parentheses (outermost): [ 12 - 4 ] = 8
Expression becomes: 7 + 8 ÷ 2 - Division: 8 ÷ 2 = 4
Expression becomes: 7 + 4 - Addition: 7 + 4 = 11
Answer: 11
Order Up! Quiz Solutions
Question 1: Which operation should be performed first in the expression: 10 + 4 * 2 - 6 / 3?
- Correct Answer: Multiplication
- Reasoning: According to PEMDAS/BODMAS, Multiplication and Division come before Addition and Subtraction. Between multiplication and division, you work from left to right. In this expression, multiplication
4 * 2appears before division6 / 3when reading from left to right.
Question 2: What is the first step in solving: (7 - 2) + 3² * 4?
- Correct Answer: Subtract 7 - 2
- Reasoning: The first step in PEMDAS/BODMAS is Parentheses (or Brackets). Therefore, you must perform the operation inside the parentheses
(7 - 2)first.
Question 3: Solve the following expression, showing your steps:
20 ÷ 4 + (2 * 5) - 3²
- Parentheses: (2 * 5) = 10
Expression becomes: 20 ÷ 4 + 10 - 3² - Exponents: 3² = 9
Expression becomes: 20 ÷ 4 + 10 - 9 - Division: 20 ÷ 4 = 5
Expression becomes: 5 + 10 - 9 - Addition: 5 + 10 = 15
Expression becomes: 15 - 9 - Subtraction: 15 - 9 = 6
Answer: 6
Question 4: In the expression 5 * 6 / 3, which operation do you perform first?
- Correct Answer: Multiplication
- Reasoning: Multiplication and Division are at the same level of priority in PEMDAS/BODMAS. When operations of the same priority appear, you solve them from left to right. In this case, multiplication comes before division.
Question 5: Explain in your own words why the order of operations is important in mathematics.
- Correct Answer: The order of operations is important because it ensures that everyone solves mathematical expressions in the same way, leading to a single correct answer. Without it, different people could get different results for the same problem, causing confusion and errors in various fields like science and engineering.
Note to Teacher: Look for student responses that emphasize consistency, accuracy, and avoiding ambiguity in mathematical solutions.