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Evaluate It!

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Lesson Plan

Evaluate It!

Students will be able to evaluate algebraic expressions by substituting given values for variables and applying the order of operations.

Understanding how to evaluate expressions is a fundamental skill in algebra, crucial for solving equations, working with formulas, and understanding real-world mathematical models.

Audience

9th Grade

Time

35 minutes

Approach

Direct instruction, guided practice, and independent application.

Materials

Evaluate It! Slide Deck, Expression Warm-Up, Expression Evaluation Worksheet, Worksheet Answer Key, Discussion Questions: Real-World Expressions, and Expression Exit Ticket

Prep

Teacher Preparation

15 minutes

Step 1

Warm-Up: Math Match

5 minutes

  1. Distribute the Expression Warm-Up to students.
    2. Instruct students to complete the warm-up, matching expressions to their simplified values.
    3. Review answers as a class, addressing any immediate misconceptions.

Step 2

Introduction to Evaluating Expressions

10 minutes

  1. Use the Evaluate It! Slide Deck to introduce the concept of variables and expressions.
    2. Explain what it means to 'evaluate' an expression.
    3. Demonstrate step-by-step how to substitute values for variables.
    4. Emphasize the importance of the order of operations (PEMDAS/BODMAS) when evaluating.

Step 3

Guided Practice: Let's Evaluate!

10 minutes

  1. Present a few example expressions from the Evaluate It! Slide Deck on the board.
    2. Work through these examples with the class, encouraging student participation in each step.
    3. Pay close attention to common errors, such as incorrect order of operations or substitution mistakes.

Step 4

Independent Practice: Worksheet Challenge

5 minutes

  1. Distribute the Expression Evaluation Worksheet.
    2. Instruct students to work independently on the worksheet.
    3. Circulate the room to provide individual support and answer questions.

Step 5

Discussion & Wrap-Up

5 minutes

  1. Lead a brief discussion using the Discussion Questions: Real-World Expressions.
    2. Discuss any challenges students faced on the worksheet and clarify concepts.
    3. Distribute the Expression Exit Ticket for students to complete before leaving.
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Slide Deck

Welcome to 'Evaluate It!'

Today, we're going to become expression experts!

Greet students and introduce the day's topic: evaluating expressions. Ask them if they've ever seen letters in math problems before.

What Are Expressions & Variables?

Variables: Letters that stand for numbers (like x, y, a, b)
Expressions: Math phrases with variables, numbers, and operations (like x + 5, 2y - 3)

Explain what a variable is (a letter representing an unknown value) and what an expression is (a mathematical phrase with variables, numbers, and operations). Give simple examples like x + 5.

What Does 'Evaluate' Mean?

To 'evaluate' an expression means to find its numerical value.

How? By replacing each variable with a specific number.

Define 'evaluate.' It means to find the value of an expression. The key is to replace the variable with a given number.

Step 1: Substitute!

Replace each variable in the expression with its given numerical value.

Example: Evaluate x + 7 if x = 3
Solution: 3 + 7

Show an example of substitution. Emphasize replacing every instance of the variable. Use parentheses for clarity, especially with negative numbers or multiplication.

Step 2: Order of Operations (PEMDAS)

Once you've substituted, follow the Order of Operations to simplify:

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

Review the order of operations (PEMDAS/BODMAS). Go through each letter and explain what it stands for. This is critical for correct evaluation.

Let's Practice Together!

Evaluate 2x + 5 if x = 4

  1. Substitute x = 4: 2(4) + 5
  2. Multiply: 8 + 5
  3. Add: 13

So, 2x + 5 evaluated at x = 4 is 13.

Work through a full example. First, substitute. Then, apply PEMDAS step-by-step. Show each step clearly.

Another Example!

Evaluate y^2 - 3y + 1 if y = 2

  1. Substitute y = 2: (2)^2 - 3(2) + 1
  2. Exponents: 4 - 3(2) + 1
  3. Multiply: 4 - 6 + 1
  4. Add/Subtract (left to right): -2 + 1
  5. Final Answer: -1

Another example, perhaps with more operations or a negative number. Ask students to guide you through the steps.

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Warm Up

Expression Warm-Up: Math Match!

Instructions: Draw a line to match each expression on the left to its correct simplified value on the right, given the values below.

Given:

  • a = 2
  • b = 5
  • c = 1

Expressions

  1. a + b
  2. b - c
  3. 2a + c
  4. b * c
  5. (a + c)^2

Simplified Values














  • 9
  • 5
  • 7
  • 4
  • 5
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Discussion

Discussion Questions: Real-World Expressions

Let's connect what we've learned to the world around us!

  1. Can you think of any everyday situations where you might need to calculate a value based on different inputs? (Hint: Think about cooking, shopping, or even video games!)


  2. Why is following the order of operations so important when evaluating expressions? What might happen if you don't follow it?


  3. Imagine you're designing a simple game. How might you use variables and expressions to calculate a player's score or health?


  4. What was the most challenging part of evaluating expressions today? What strategy helped you overcome it?
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Worksheet

Expression Evaluation Practice

Instructions: Evaluate each expression for the given variable values. Remember to show your work and follow the order of operations!

Part 1: Given Values
Let x = 3, y = 5, and z = 2

  1. x + y



  2. y - z



  3. 2x + z



  4. y * z - x



  5. (x + z)^2



  6. y^2 - 4x



Part 2: New Values
Let a = 4, b = -1, and c = 10

  1. a + b + c



  2. c - 2a



  3. 3b^2 + a



  4. c / a + b



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Answer Key

Worksheet Answer Key

Part 1: Given Values
Let x = 3, y = 5, and z = 2

  1. x + y
    • Substitute: 3 + 5
    • Simplify: 8
    • Answer: 8



  2. y - z
    • Substitute: 5 - 2
    • Simplify: 3
    • Answer: 3



  3. 2x + z
    • Substitute: 2(3) + 2
    • Multiply: 6 + 2
    • Simplify: 8
    • Answer: 8



  4. y * z - x
    • Substitute: 5 * 2 - 3
    • Multiply: 10 - 3
    • Simplify: 7
    • Answer: 7



  5. (x + z)^2
    • Substitute: (3 + 2)^2
    • Parentheses: (5)^2
    • Exponents: 25
    • Answer: 25



  6. y^2 - 4x
    • Substitute: (5)^2 - 4(3)
    • Exponents: 25 - 4(3)
    • Multiply: 25 - 12
    • Simplify: 13
    • Answer: 13



Part 2: New Values
Let a = 4, b = -1, and c = 10

  1. a + b + c
    • Substitute: 4 + (-1) + 10
    • Simplify: 3 + 10
    • Simplify: 13
    • Answer: 13



  2. c - 2a
    • Substitute: 10 - 2(4)
    • Multiply: 10 - 8
    • Simplify: 2
    • Answer: 2



  3. 3b^2 + a
    • Substitute: 3(-1)^2 + 4
    • Exponents: 3(1) + 4
    • Multiply: 3 + 4
    • Simplify: 7
    • Answer: 7



  4. c / a + b
    • Substitute: 10 / 4 + (-1)
    • Divide: 2.5 + (-1)
    • Simplify: 1.5
    • Answer: 1.5



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Cool Down

Expression Exit Ticket

Instructions: Please answer the following questions to show what you learned today.

  1. In your own words, what does it mean to evaluate an expression?


  2. What is one important rule you need to remember when evaluating expressions? (Hint: Think about the order!)


  3. Evaluate the expression 3m + 7 if m = 4. Show your work!



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