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Plugging In!

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Lesson Plan

Plugging In: The Art of Evaluating Expressions

Students will be able to substitute given values for variables to evaluate algebraic expressions correctly.

Understanding how to evaluate expressions is a fundamental skill in algebra. It helps us solve problems by using formulas and understanding how different quantities relate to each other in real-world situations.

Audience

9th Grade Students

Time

65 minutes

Approach

Direct instruction, guided practice, independent practice, and an exit ticket assessment.

Materials

Plugging In Slide Deck, Variable Substitution Practice Worksheet, Real-World Formulas Activity, and Exit Ticket Quiz

Prep

Teacher Preparation

20 minutes

Step 1

Introduction & Hook: What's Your Number?

10 minutes

  • Begin by displaying a simple algebraic expression (e.g., "2x + 5") on the board or Plugging In Slide Deck (Slide 2).
    - Ask students: "If I told you 'x' was a secret number, and I wanted you to tell me the value of '2x + 5', what would you need to know?" (Wait for responses like 'what x is').
    - Introduce the concept of a variable as a 'mystery number' and evaluating an expression as 'plugging in' the secret number.
    - Present the objective for the day: "Today, we're going to become experts at 'plugging in' values to find out exactly what an expression is worth!"

Step 2

Direct Instruction: The Art of Evaluation

15 minutes

  • Use the Plugging In Slide Deck (Slides 3-7) to guide students through the key concepts:
    - Variables: What they are and how they're represented.
    - Substitution: The act of replacing a variable with its given numerical value.
    - Order of Operations (PEMDAS/BODMAS): Emphasize its importance when evaluating after substitution.
    - Algebraic Notation: Discuss how multiplication is implied (e.g., 3x means 3 * x).
    - Model 2-3 examples on the board, thinking aloud as you substitute and simplify. Examples should include positive/negative numbers and basic fractions/decimals if appropriate for the class level.

Step 3

Guided Practice: We Plug, You Solve!

15 minutes

  • Distribute the Variable Substitution Practice Worksheet.
    - Work through the first 2-3 problems on the worksheet together as a class, using the Plugging In Slide Deck (Slide 8) as a guide or projecting the worksheet.
    - Encourage students to share their steps and reasoning. Address common misconceptions immediately.
    - Circulate the room, providing individual support and checking for understanding as students begin working on their own.

Step 4

Independent Practice: Real-World Formulas Activity

15 minutes

  • Introduce the Real-World Formulas Activity. Explain that many real-world situations use expressions or formulas to calculate things.
    - Students will work individually or in pairs to solve problems using various formulas (e.g., Area = length * width, Simple Interest = Principal * Rate * Time, Celsius to Fahrenheit conversion).
    - Provide different formulas and values to substitute. Ensure a mix of complexity.
    - Circulate to offer help and check progress.

Step 5

Wrap-up & Assessment: Exit Ticket

10 minutes

  • Bring the class back together.
    - Briefly review one or two challenging problems from the activity or worksheet.
    - Distribute the Exit Ticket Quiz.
    - Students complete the quiz independently as a formative assessment to gauge their understanding of evaluating expressions.
    - Collect the exit tickets before students leave.
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Slide Deck

Plugging In: The Art of Evaluating Expressions

Unlocking the secrets of algebra!

Welcome students and introduce the lesson's exciting topic! Ask them to think about 'secret codes' or 'mystery numbers' that they might encounter in daily life (like a secret ingredient in a recipe).

What's Your Number?

Imagine you have this secret code:

2x + 5

What would you need to know to find out its value?

Use this slide to pose the hook question. Emphasize that 'x' is just a placeholder for any number. This sets up the idea of needing to know the value of 'x' to 'evaluate' the expression.

Meet the Variables!

  • A variable is a letter or symbol that represents an unknown number or a quantity that can change.
  • Think of it as a placeholder, like an empty box waiting for a number!
  • Common variables: x, y, a, b

Define variables and provide simple examples. Connect them to placeholders or unknown quantities. Ask students for examples where something changes or is unknown (e.g., number of friends coming to a party).

Substitution: The Big Switch!

  • Substitution is when you replace a variable with a specific number.
  • It's like finding the secret number for your 'x' and putting it in!

Example: If x = 3, then x + 7 becomes 3 + 7

Explain substitution clearly. Emphasize that we are replacing the variable. Show a very simple substitution example.

Evaluating Expressions: Finding the Value

  • To evaluate an expression means to find its numerical value by substituting given numbers for the variables and then simplifying.

Example: Evaluate 5 + y when y = 4

Step 1: Substitute y with 4
5 + 4

Step 2: Simplify
9

This is the core concept. Define evaluating and tie it directly to finding the numerical value. Give a straightforward example.

Don't Forget PEMDAS!

  • Once you substitute the numbers, you MUST follow the Order of Operations (PEMDAS/BODMAS) to simplify correctly.

Parentheses / Brackets
Exponents / Orders
Multiplication & Division (from left to right)
Addition & Subtraction (from left to right)

Crucial reminder! Review PEMDAS/BODMAS as needed. Provide an example where order of operations is vital after substitution.

Algebraic Notation Secrets

  • When a number is next to a variable (e.g., 3x), it means multiplication (3 * x).
  • When parentheses are next to a number or another parenthesis, it also means multiplication (e.g., 2(x+1) or (4)(5)).

Explain implied multiplication. Give examples like 3x and 2(5). This avoids common errors.

Guided Practice: Let's Plug In Together!

Work through these problems on your worksheet with the class:

  1. Evaluate x - 8 when x = 15
  2. Evaluate 3y + 2 when y = -4
  3. Evaluate a^2 + b when a = 5 and b = 10

Use this slide for the guided practice portion. Work through a couple of problems from the worksheet together. Encourage student participation.

Independent Practice: Real-World Formulas!

Many real-world situations use formulas, which are just special types of expressions!

Your task: Use different formulas and given values to solve practical problems. Show your work!

Introduce the independent activity. Explain the concept of formulas being expressions. Students will apply their skills to real-world scenarios.

Time for Your Exit Ticket!

A quick check to see how well you've mastered 'Plugging In'!

Complete the quiz independently.

Explain the exit ticket as a quick check for understanding. Reassure them it's to see what they've learned.

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Worksheet

Variable Substitution Practice: Plugging It In!

Name: ____________________________

Instructions: For each problem, substitute the given value(s) for the variable(s) and then evaluate the expression. Show all your work!

  1. Evaluate x + 12 when x = 7






  2. Evaluate 25 - y when y = 9






  3. Evaluate 4a when a = 6






  4. Evaluate b / 3 when b = 27






  5. Evaluate 3m + 5 when m = 4






  6. Evaluate 10 - 2k when k = -3






  7. Evaluate p^2 + 1 when p = 8






  8. Evaluate (n + 3) * 2 when n = 5






  9. Evaluate x - y when x = 10 and y = 3






  10. Evaluate 2ab + 7 when a = 2 and b = 5






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Activity

Real-World Formulas Activity: What's the Value?

Name: ____________________________

Instructions: Below are some common formulas used in real life. Substitute the given values into each formula and calculate the result. Show your work clearly!

Part 1: Geometry

  1. Area of a Rectangle (A = l * w)

    • Find the area of a rectangle if l = 8 feet and w = 5 feet.






  2. Perimeter of a Square (P = 4s)

    • Find the perimeter of a square if s = 7 inches.






Part 2: Temperature Conversion

  1. Celsius to Fahrenheit (F = (9/5)C + 32)
    • Convert C = 20 degrees Celsius to Fahrenheit.






Part 3: Simple Interest

  1. Simple Interest (I = P * r * t)
    • Calculate the simple interest if P = $500 (principal), r = 0.05 (rate), and t = 2 years (time).






Part 4: Distance, Rate, Time

  1. Distance (d = r * t)
    • How far does a car travel if its r = 60 miles per hour for t = 3.5 hours?






Part 5: Challenge!

  1. Volume of a Rectangular Prism (V = l * w * h)
    • Find the volume of a box with l = 4 cm, w = 3 cm, and h = 10 cm.






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Quiz

Exit Ticket

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Answer Key

Variable Substitution Practice: Plugging It In! - Answer Key

Instructions: Review the step-by-step solutions for each problem.

  1. Evaluate x + 12 when x = 7

    • Thought Process: Substitute 7 for x, then add.
    • 7 + 12 = 19
    • Answer: 19

  2. Evaluate 25 - y when y = 9

    • Thought Process: Substitute 9 for y, then subtract.
    • 25 - 9 = 16
    • Answer: 16

  3. Evaluate 4a when a = 6

    • Thought Process: Remember 4a means 4 * a. Substitute 6 for a, then multiply.
    • 4 * 6 = 24
    • Answer: 24

  4. Evaluate b / 3 when b = 27

    • Thought Process: Substitute 27 for b, then divide.
    • 27 / 3 = 9
    • Answer: 9

  5. Evaluate 3m + 5 when m = 4

    • Thought Process: Substitute 4 for m. Following order of operations, multiply first, then add.
    • 3 * 4 + 5 = 12 + 5 = 17
    • Answer: 17

  6. Evaluate 10 - 2k when k = -3

    • Thought Process: Substitute -3 for k. Following order of operations, multiply 2 * -3 first, which is -6. Then subtract -6 from 10, which is the same as adding 6.
    • 10 - (2 * -3) = 10 - (-6) = 10 + 6 = 16
    • Answer: 16

  7. Evaluate p^2 + 1 when p = 8

    • Thought Process: Substitute 8 for p. Following order of operations, calculate the exponent first, then add.
    • 8^2 + 1 = 64 + 1 = 65
    • Answer: 65

  8. Evaluate (n + 3) * 2 when n = 5

    • Thought Process: Substitute 5 for n. Following order of operations, calculate inside the parentheses first, then multiply.
    • (5 + 3) * 2 = 8 * 2 = 16
    • Answer: 16

  9. Evaluate x - y when x = 10 and y = 3

    • Thought Process: Substitute 10 for x and 3 for y, then subtract.
    • 10 - 3 = 7
    • Answer: 7

  10. Evaluate 2ab + 7 when a = 2 and b = 5

    • Thought Process: Remember 2ab means 2 * a * b. Substitute 2 for a and 5 for b. Following order of operations, multiply first, then add.
    • 2 * 2 * 5 + 7 = 4 * 5 + 7 = 20 + 7 = 27
    • Answer: 27
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