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Unlock The Math Code: PEMDAS!

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Lesson Plan

Unlock The Math Code: PEMDAS! Lesson Plan

Students will be able to apply the correct order of operations (PEMDAS) to accurately solve multi-step numerical expressions.

Mastering PEMDAS is crucial for accuracy in algebra and beyond, preventing common errors and building a strong mathematical foundation. This lesson provides a fundamental skill essential for success in all higher-level mathematics.

Audience

9th Grade Students

Time

65 minutes

Approach

Direct instruction, guided practice, and independent application.

Materials

Smartboard or Projector, Markers or Whiteboard Pens, Slide Deck: PEMDAS Power-Up!, Worksheet: Order of Operations Maze, and Quiz: PEMDAS Exit Ticket

Prep

Teacher Preparation

15 minutes

Step 1

Introduction & Hook: What's the Order?

10 minutes

  1. Engage: Begin by projecting a simple, ambiguous mathematical expression (e.g., 2 + 3 * 4) and ask students to solve it individually.
  2. Discuss: Ask students to share their answers. Expect different results. Lead a brief discussion about why different answers might occur.
  3. Introduce: Explain that to avoid confusion and ensure consistent results, mathematicians developed a specific 'order' for operations. Introduce PEMDAS as the tool for this order. Use Slide Deck: PEMDAS Power-Up! slides 1-2.

Step 2

Direct Instruction: Decoding PEMDAS

20 minutes

  1. Explain PEMDAS: Go through each letter of PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), explaining what each operation means and its priority. Emphasize that Multiplication/Division and Addition/Subtraction are done from left to right. Use Slide Deck: PEMDAS Power-Up! slides 3-7.
  2. Examples: Work through 2-3 clear examples step-by-step on the board, verbalizing each decision based on PEMDAS. Encourage students to take notes.
  3. Check for Understanding: Ask targeted questions after each step of an example. "Why did I do multiplication before addition here?" or "What's the first step according to PEMDAS?"

Step 3

Guided Practice: Solving Together

15 minutes

  1. Collaborative Problems: Display 2-3 new multi-step expressions on Slide Deck: PEMDAS Power-Up! slides 8-10. Work through these problems as a class.
  2. Think-Pair-Share: For one problem, have students solve the first step individually, then pair with a neighbor to compare, and finally share their reasoning with the class.
  3. Teacher Support: Circulate the room, providing immediate feedback and clarification as students work through the problems. Address common misconceptions.

Step 4

Independent Practice: PEMDAS Maze Challenge

15 minutes

  1. Distribute: Hand out the Worksheet: Order of Operations Maze.
  2. Explain Activity: Students will solve expressions and follow the correct answer through a maze to reach the finish. Explain that this allows them to practice PEMDAS in a fun, self-checking way.
  3. Individual Work: Students work independently on the maze. Provide support to students who are struggling, while encouraging those who finish early to recheck their work or create their own maze-like problems.

Step 5

Wrap-up & Assessment: Exit Ticket Reflection

5 minutes

  1. Collect Worksheets: Collect the completed Worksheet: Order of Operations Maze.
  2. Distribute Quiz: Hand out the Quiz: PEMDAS Exit Ticket.
  3. Assess: Students complete the exit ticket independently. This will serve as a quick check of individual understanding of PEMDAS. Collect the exit tickets before students leave.
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Slide Deck

What's The Order?

Can we all get the same answer?

2 + 3 * 4 = ?


### Why do we need rules in math?

Display the expression. Ask students to solve it individually and share their answers. Discuss why different answers arise.

Math's Golden Rule

To keep math fair and consistent, we follow a special order for solving problems. This order helps us get the right answer, every time!


### Welcome to PEMDAS!

Explain that to ensure everyone gets the same answer, mathematicians created a set of rules: The Order of Operations.

P is for Parentheses (and Brackets!)

Always solve whatever is inside parentheses or brackets FIRST.


### ( ) or [ ]


Example: (5 + 3) * 2


What do we do first?

Introduce P for Parentheses. Explain that any operation inside parentheses (or brackets) must be done first.

E is for Exponents

After parentheses, tackle any exponents.


### x² or 5³


Example: 4² + (2 * 3)


What's next after the parentheses?

Introduce E for Exponents. Explain that after parentheses, exponents are next.

MD is for Multiplication & Division

These two are a team! Do them from left to right in the order they appear.


### × or ÷


Example: 10 - 2 × 3 + 6 ÷ 2


Which operation comes first, multiplication or division?

Introduce MD for Multiplication and Division. Emphasize that these are done from left to right.

AS is for Addition & Subtraction

Another team! Do them from left to right in the order they appear.


### + or -


Example: 7 + 8 - 4 + 2


Which operation should we do first?

Introduce AS for Addition and Subtraction. Emphasize that these are also done from left to right.

Putting it All Together: PEMDAS!

Parentheses

Exponents

Multiplication & Division (left to right)

Addition & Subtraction (left to right)


### Mnemonic: Please Excuse My Dear Aunt Sally

Review the full PEMDAS order with a mnemonic device. Ask students if they know any other mnemonics.

Guided Practice: Problem 1

Let's solve this together!


### 18 ÷ 3 × 2 + (4 - 1)²

Guided Practice problem 1. Work through this problem step-by-step with the class, asking students for each next step.

Guided Practice: Problem 2

Your turn to start!

Solve the first step, then share with a partner.


### (7 + 2) × 5 - 3² + 1

Guided Practice problem 2. Have students try the first step individually, then discuss with a partner, then share with the class.

Guided Practice: Problem 3

One more together!


### 24 - 4 × 3 + (10 ÷ 2)

Guided Practice problem 3. Work through as a class, focusing on common pitfalls or tricky parts.

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Worksheet

Order of Operations Maze

Instructions: Solve each problem using the order of operations (PEMDAS). Follow the path of your correct answer to navigate through the maze from START to FINISH.

START

1. 8 + 2 × 3

A) 30

B) 14

C) 24

D) 10


(If your answer is B, go to #2. If your answer is A, go to #3.)

2. (5 + 3) × 2 - 1

A) 15

B) 10

C) 16

D) 9


(If your answer is A, go to #4. If your answer is C, go to #5.)

3. 6 × 4 ÷ 2 + 5

A) 17

B) 12

C) 29

D) 19


(If your answer is A, go to #5. If your answer is D, go to #6.)

4. 12 - 2² + (7 - 3)

A) 10

B) 12

C) 16

D) 8


(If your answer is D, go to #7. If your answer is B, go to #8.)

5. 30 ÷ (2 × 3) + 5

A) 10

B) 15

C) 11

D) 20


(If your answer is A, go to #8. If your answer is C, go to #9.)

6. 5 × (4 + 1) - 3²

A) 16

B) 25

C) 20

D) 18


(If your answer is A, go to #9. If your answer is D, go to #10.)

7. (15 - 5) ÷ 2 + 4²

A) 21

B) 26

C) 11

D) 20


(If your answer is A, go to FINISH! If your answer is B, check your work and try again.)

8. 7 + 3 × (6 ÷ 2) - 5

A) 11

B) 25

C) 15

D) 18


(If your answer is A, go to #7. If your answer is C, go to #10.)

9. 4² + 20 ÷ 5 - 3

A) 17

B) 19

C) 15

D) 13


(If your answer is A, go to #7. If your answer is D, go to #8.)

10. 25 - (3 × 4) + 2²

A) 17

B) 12

C) 10

D) 21


(If your answer is A, go to #7. If your answer is B, go to #9.)

FINISH!

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Quiz

PEMDAS Exit Ticket

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Answer Key

Order of Operations Maze Answer Key

Path:

START -> 1 (B) -> 2 (A) -> 4 (D) -> 7 (A) -> FINISH!

Step-by-Step Solutions:

1. 8 + 2 × 3

  • Thought Process: According to PEMDAS, multiplication comes before addition.
    • 2 × 3 = 6
    • 8 + 6 = 14
  • Answer: B) 14

2. (5 + 3) × 2 - 1

  • Thought Process: First, solve inside the parentheses, then multiply, then subtract.
    • (5 + 3) = 8
    • 8 × 2 = 16
    • 16 - 1 = 15
  • Answer: A) 15

3. 6 × 4 ÷ 2 + 5

  • Thought Process: Multiplication and Division are done from left to right. Then add.
    • 6 × 4 = 24
    • 24 ÷ 2 = 12
    • 12 + 5 = 17
  • Answer: A) 17

4. 12 - 2² + (7 - 3)

  • Thought Process: Parentheses first, then exponents, then subtraction and addition from left to right.
    • (7 - 3) = 4
    • 2² = 4
    • 12 - 4 + 4 = 8 + 4 = 12
  • Answer: B) 12

5. 30 ÷ (2 × 3) + 5

  • Thought Process: Parentheses first, then division, then addition.
    • (2 × 3) = 6
    • 30 ÷ 6 = 5
    • 5 + 5 = 10
  • Answer: A) 10

6. 5 × (4 + 1) - 3²

  • Thought Process: Parentheses first, then exponents, then multiplication, then subtraction.
    • (4 + 1) = 5
    • 3² = 9
    • 5 × 5 = 25
    • 25 - 9 = 16
  • Answer: A) 16

7. (15 - 5) ÷ 2 + 4²

  • Thought Process: Parentheses first, then exponents, then division, then addition.
    • (15 - 5) = 10
    • 4² = 16
    • 10 ÷ 2 = 5
    • 5 + 16 = 21
  • Answer: A) 21

8. 7 + 3 × (6 ÷ 2) - 5

  • Thought Process: Parentheses first, then multiplication, then addition and subtraction from left to right.
    • (6 ÷ 2) = 3
    • 3 × 3 = 9
    • 7 + 9 - 5 = 16 - 5 = 11
  • Answer: A) 11

9. 4² + 20 ÷ 5 - 3

  • Thought Process: Exponents first, then division, then addition and subtraction from left to right.
    • 4² = 16
    • 20 ÷ 5 = 4
    • 16 + 4 - 3 = 20 - 3 = 17
  • Answer: A) 17

10. 25 - (3 × 4) + 2²

  • Thought Process: Parentheses first, then exponents, then subtraction and addition from left to right.
    • (3 × 4) = 12
    • 2² = 4
    • 25 - 12 + 4 = 13 + 4 = 17
  • Answer: A) 17
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Answer Key

PEMDAS Exit Ticket Answer Key

1. In the expression 5 + 3 × (8 - 2)², what is the first step you should perform?

  • Thought Process: According to PEMDAS, the operations inside parentheses come first.
  • Answer: Subtraction inside parentheses

2. Solve the following expression, showing all your steps:

10 - 2 × 3 + 12 ÷ 4

  • Thought Process:
    • First, perform multiplication and division from left to right.
      • 2 × 3 = 6
      • 12 ÷ 4 = 3
    • Then, perform addition and subtraction from left to right.
      • 10 - 6 = 4
      • 4 + 3 = 7
  • Answer: 7

3. Which operation should be performed before addition if both are present in an expression and no parentheses are involved?

  • Thought Process: According to PEMDAS, multiplication and division come before addition and subtraction.
  • Answer: Both Multiplication and Division (from left to right)

4. Solve the following expression:

(4 + 6) ÷ 2 + 3² - 5

  • Thought Process:
    • Parentheses first: (4 + 6) = 10
    • Exponents next: 3² = 9
    • Now the expression is: 10 ÷ 2 + 9 - 5
    • Division next: 10 ÷ 2 = 5
    • Now the expression is: 5 + 9 - 5
    • Addition/Subtraction from left to right: 5 + 9 = 14
    • Finally: 14 - 5 = 9
  • Answer: 9
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