Plugging In Lesson Plan Plugging In
The Art of Evaluating Expressions
65 Minutes
9th Grade Algebra
Why This Lesson?
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.
Teacher Preparation
Review the Plugging In Slide Deck .
Print copies of the Variable Substitution Practice Worksheet (one per student).
Prepare materials for the Real-World Formulas Activity .
Print copies of the Exit Ticket Quiz (one per student).
Ensure projector/smartboard is ready for the slide deck.
Estimated Prep Time: 20 minutes
Objective
Students will be able to substitute given values for variables to evaluate algebraic expressions correctly.
Approach
Direct instruction, guided practice, independent practice, and a formative exit ticket assessment.
Instructional Flow
10 min
Introduction & Hook: What's Your Number?
Display a simple expression like \(2x + 5\). Ask: "If I told you 'x' was a secret number, what would you need to know to find the total value?"
Introduce the variable as a "mystery number" and evaluation as "plugging in" the secret value.
15 min
Direct Instruction: The Art of Evaluation
Use the Slide Deck to define:
Variables: Symbols for unknowns.Substitution: Replacing the symbol with a number.PEMDAS: Crucial for simplifying after substitution.Algebraic Notation: Implied multiplication (e.g., \(3x\)).
Model 2-3 examples aloud, focusing on the "replace then simplify" sequence.
15 min
Guided Practice: We Plug, You Solve!
Distribute the Practice Worksheet . Work through the first 3 problems together.
Circulate to catch misconceptions—especially with negative numbers or exponents.
15 min
Independent Practice: Real-World Formulas
Transition to the Real-World Formulas Activity . Explain that engineers and scientists "plug in" data to these formulas daily.
Students work in pairs. Formulas include Area, Interest, and Temperature.
10 min
Wrap-up & Assessment: Exit Ticket
Review one challenging real-world formula as a class.
Distribute the Exit Ticket Quiz for students to complete independently.
Plugging In Slide Deck Plugging In
The Art of Evaluating Expressions
9th Grade Algebra • Lesson 1.2
What's Your Number?
Imagine you have this secret code:
2x + 5
What would you need to know to find out its value?
Meet the Variables!
A variable is a letter or symbol that represents an unknown number.
Think of it as a placeholder , like an empty box waiting for a value!
Common variables: x, y, a, b
?
Placeholder
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!
Variable
x + 7
If x = 3
3 + 7
Evaluating Expressions
To evaluate means to find the numerical value of an expression.
1
Substitute variables with numbers.
2
Simplify the result.
EXAMPLE: Evaluate \(5 + y\) when \(y = 4\)
Step 1: 5 + (4)
Step 2: 9
Don't Forget PEMDAS!
Once you substitute, you MUST follow the correct order to simplify.
P
Parentheses
E
Exponents
M
Mult.
D
Div.
A
Add.
S
Subt.
Simplify multiplication/division and addition/subtraction from LEFT to RIGHT.
Algebraic Notation Secrets
Hidden Multiplication
A number next to a variable always means multiplication .
3x = 3 * x
Parentheses Power
Numbers next to parentheses also mean multiplication .
2(x+1) → 2 * (x+1) (4)(5) → 4 * 5
Guided Practice: Let's Plug In!
Grab your worksheets! Let's solve these together:
1. Evaluate x - 8 when
Variable Substitution Practice Worksheet Variable Substitution Practice
Plugging It In!
Name:
Date:
Instructions: For each problem, substitute the given value(s) for the variable(s) and then evaluate the expression. Show all your work in the space provided!
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 p² + 1 when p = 8
8
Evaluate (n + 3) * 2 when n = 5
9
Evaluate x - y when x = 10, y = 3
10
Evaluate 2ab + 7 when a = 2, b = 5
Real-World Formulas Activity Real-World Formulas Activity
What's the Value?
Name:
Date:
Instructions: Many professionals—from engineers to bankers—use formulas every day. Substitute the given values into each formula and calculate the result. Show your work clearly to get full credit!
Part 1: Geometry
1. Area of a Rectangle (\(A = l \times w\))
Find the area if \(l = 8\) feet and \(w = 5\) feet.
2. Perimeter of a Square (\(P = 4s\))
Find the perimeter if \(s = 7\) inches.
Part 2: Temperature Conversion
3. Celsius to Fahrenheit (\(F = \frac{9}{5}C + 32\))
Convert \(C = 20\) degrees Celsius to Fahrenheit.
Part 3: Simple Interest
4. Simple Interest (\(I = P \times r \times t\))
Calculate the simple interest if \(P = \$500\) (principal), \(r = 0.05\) (rate), and \(t = 2\) years (time).
Part 4: Distance, Rate, Time
5. Distance (\(d = r \times t\))
How far does a car travel if its \(r = 60\) miles per hour for \(t = 3.5\) hours?
Part 5: Challenge!
6. Volume of a Rectangular Prism (\(V = l \times w \times h\))
Find the volume of a box with \(l = 4\) cm, \(w = 3\) cm, and \(h = 10\) cm.
Exit Ticket Quiz Exit Ticket: Evaluating Expressions
Final Check
Name:
Date:
1
What does the 'x' represent in the expression 3x + 7?
The number 3
An unknown value
The answer to the problem
A multiplication sign
2
Evaluate the expression y - 5 when y = 12.
5
7
12
17
3
Evaluate the expression 2a + 3 when a = 4.
9
10
11
14
4
Explain in your own words what it means to "evaluate an expression."
5
Evaluate the expression m² - 2n when m = 5 and n = 3.
Excellent work! Please turn this in before leaving.
Variable Substitution Practice Answer Key Variable Substitution: Answer Key
Teacher Resource
Step-by-step solutions and simplified answers for the Variable Substitution Practice Worksheet.
1
\(x + 12\) when \(x = 7\)
Substitute 7 for x:
\(7 + 12 = \mathbf{19}\)
2
\(25 - y\) when \(y = 9\)
Substitute 9 for y:
\(25 - 9 = \mathbf{16}\)
3
\(4a\) when \(a = 6\)
Multiply 4 by 6:
\(4(6) = \mathbf{24}\)
4
\(b / 3\) when \(b = 27\)
Divide 27 by 3:
\(27 \div 3 = \mathbf{9}\)
5
\(3m + 5\) when \(m = 4\)
PEMDAS: Multiply first
\(3(4) + 5 = 12 + 5 = \mathbf{17}\)
6
\(10 - 2k\) when \(k = -3\)
Subtracting a negative:
\(10 - 2(-3) = 10 - (-6) = \mathbf{16}\)
7
\(p^2 + 1\) when \(p = 8\)
Exponents first:
\(8^2 + 1 = 64 + 1 = \mathbf{65}\)
8
\((n + 3) \times 2\) when \(n = 5\)
Parentheses first:
\((5 + 3) \times 2 = 8 \times 2 = \mathbf{16}\)
9
\(x - y\) when \(x = 10, y = 3\)
Double substitution:
\(10 - 3 = \mathbf{7}\)
10
\(2ab + 7\) when \(a = 2, b = 5\)
Multiply all first:
\(2(2)(5) + 7 = 20 + 7 = \mathbf{27}\)
Common Student Errors
Notation confusion: Students may see \(4a\) as \(46\) instead of \(4 \times 6\).Order of Operations: Forgetting to multiply before adding (Problem 5).Integers: Errors with negative signs when multiplying or subtracting (Problem 6). 
