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Algebra Foundations: Test Your Might!

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Lesson Plan

Algebra Foundations: Test Your Might!

Students will demonstrate mastery of the order of operations, evaluating expressions, and writing linear function rules.

This lesson is important because it solidifies fundamental algebra skills, essential for success in higher-level mathematics.

Audience

9th Grade Students

Time

65 minutes

Approach

Review, Assess, Reflect

Materials

Smartboard or projector, Whiteboard and markers, Review Guide, Unit 1 Test, Unit 1 Test Answer Key, and Pencils and scrap paper

Prep

Teacher Preparation

20 minutes

Step 1

Warm-Up & Review (15 minutes)

15 minutes

Step 2

Unit 1 Assessment (40 minutes)

40 minutes

  • Distribute the Unit 1 Test.
    - Remind students of testing procedures and expectations (e.g., no talking, clear desks, show all work).
    - Monitor students as they complete the assessment. Provide support only for clarifying instructions, not for content.
    - Collect tests upon completion. Encourage students who finish early to review their answers or begin independent reading/work.

Step 3

Reflection & Next Steps (10 minutes)

10 minutes

  • Display the reflection slide from the Algebra Foundations: Test Your Might! Slide Deck.
    - Lead a brief class discussion on the importance of demonstrating understanding and identifying areas for growth.
    - Ask students to reflect on their confidence level with the material before and after the review.
    - Briefly introduce upcoming topics or activities to transition from the assessment.
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Slide Deck

Algebra Foundations: Test Your Might!

Today, we're going to demonstrate our understanding of Unit 1 concepts: Order of Operations, Evaluating Expressions, and Linear Function Rules. Get ready to show what you know!

Welcome students to the Unit 1 Assessment. Briefly introduce the purpose of the lesson: to show what they've learned about foundational algebra.

Review: Order of Operations

Remember PEMDAS/BODMAS! 💡

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

Let's try a few problems from our Review Guide!

Guide students through a quick review of the order of operations. Use the Review Guide for examples. Ask students to share their strategies for remembering the order.

Review: Evaluating Expressions

To evaluate an expression, we substitute given values for variables and then simplify using the order of operations.

Example: If x = 3, what is 2x + 5?

Think: 2(3) + 5 = 6 + 5 = 11

Your turn! Let's practice with the Review Guide.

Move on to evaluating expressions. Emphasize substituting values carefully. Work through a couple of examples from the Review Guide together.

Review: Functions & Linear Rules

A function is like a machine: for every input, there's exactly one output!

Linear rules describe a straight-line relationship, often written as y = mx + b.

  • m is the slope (how steep the line is)
  • b is the y-intercept (where it crosses the y-axis)

Can you spot a linear pattern in your Review Guide?

Discuss the concepts of functions and linear rules. Reinforce that a function has exactly one output for each input. Highlight how to identify linear relationships and write their rules. Use examples from the Review Guide.

Time to Shine: The Assessment!

It's time for the Unit 1 Test! 🚀

  • Work independently.
  • Show all your work clearly.
  • Read each question carefully.
  • Do your best!

I'll be here to clarify instructions, but please do not ask for help with the answers. Good luck!

Clearly explain the assessment instructions. Emphasize showing work and working independently. Answer any non-content related questions.

Reflect and Grow 🌱

Now that you've completed the assessment, let's take a moment to reflect:

  • What concepts did you feel most confident about today?
  • What was challenging?
  • How can you continue to strengthen your algebra skills?

Every challenge is a chance to learn!

Facilitate a short reflection. Ask students how they felt about the review and the test. Encourage them to identify areas where they feel strong and areas where they might need more practice.

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Worksheet

Unit 1 Review Guide: Foundations of Algebra

This guide will help you refresh your memory on key algebra concepts before your test. Show all your work!

Part 1: Order of Operations (PEMDAS/BODMAS)

Remember the order: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

  1. Evaluate: 18 ÷ 3 × 2 + (7 - 4)






  2. Evaluate: 4^2 + 5 × (10 - 6)






  3. Evaluate: 30 - 2 × (3 + 5)^2 ÷ 4











Part 2: Evaluating Expressions

Substitute the given values for the variables and then use the order of operations to simplify.

For questions 4-6, evaluate each expression for a = 5, b = 2, and c = 10.

  1. a + 3b



  2. c^2 - ab






  3. (c - a) ÷ b + 4






Part 3: Functions and Linear Rules

Functions

  1. Is the following relation a function? Explain why or why not.
    {(1, 2), (2, 4), (3, 6), (1, 3)}






  2. If f(x) = 3x - 1, find f(4).





Linear Rules

  1. Write a linear function rule for the table below:

    xy
    05
    17
    29
    311







  2. A taxi charges a flat fee of $3 plus $2 per mile. Write a linear function rule to represent the cost C for m miles.





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Test

Unit 1 Test

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Answer Key

Unit 1 Test and Review Guide Answer Key

Review Guide Answer Key

Part 1: Order of Operations (PEMDAS/BODMAS)

  1. Evaluate: 18 ÷ 3 × 2 + (7 - 4)

    • First, solve inside the parentheses: 7 - 4 = 3
    • Expression becomes: 18 ÷ 3 × 2 + 3
    • Next, perform division (left to right): 18 ÷ 3 = 6
    • Expression becomes: 6 × 2 + 3
    • Next, perform multiplication: 6 × 2 = 12
    • Expression becomes: 12 + 3
    • Finally, perform addition: 12 + 3 = 15
    • Answer: 15

  2. Evaluate: 4^2 + 5 × (10 - 6)

    • First, solve inside the parentheses: 10 - 6 = 4
    • Expression becomes: 4^2 + 5 × 4
    • Next, evaluate the exponent: 4^2 = 16
    • Expression becomes: 16 + 5 × 4
    • Next, perform multiplication: 5 × 4 = 20
    • Expression becomes: 16 + 20
    • Finally, perform addition: 16 + 20 = 36
    • Answer: 36

  3. Evaluate: 30 - 2 × (3 + 5)^2 ÷ 4

    • First, solve inside the parentheses: 3 + 5 = 8
    • Expression becomes: 30 - 2 × 8^2 ÷ 4
    • Next, evaluate the exponent: 8^2 = 64
    • Expression becomes: 30 - 2 × 64 ÷ 4
    • Next, perform multiplication (left to right): 2 × 64 = 128
    • Expression becomes: 30 - 128 ÷ 4
    • Next, perform division: 128 ÷ 4 = 32
    • Expression becomes: 30 - 32
    • Finally, perform subtraction: 30 - 32 = -2
    • Answer: -2

Part 2: Evaluating Expressions

For a = 5, b = 2, and c = 10.

  1. a + 3b

    • Substitute the values: 5 + 3(2)
    • Perform multiplication: 5 + 6
    • Perform addition: 11
    • Answer: 11

  2. c^2 - ab

    • Substitute the values: 10^2 - (5)(2)
    • Evaluate exponent: 100 - (5)(2)
    • Perform multiplication: 100 - 10
    • Perform subtraction: 90
    • Answer: 90

  3. (c - a) ÷ b + 4

    • Substitute the values: (10 - 5) ÷ 2 + 4
    • Perform parentheses: 5 ÷ 2 + 4
    • Perform division: 2.5 + 4
    • Perform addition: 6.5
    • Answer: 6.5

Part 3: Functions and Linear Rules

  1. Is the following relation a function? Explain why or why not. {(1, 2), (2, 4), (3, 6), (1, 3)}

    • Answer: No. A relation is a function if each input (x-value) has exactly one output (y-value). In this relation, the input 1 is paired with two different outputs (2 and 3).

  2. If f(x) = 3x - 1, find f(4).

    • Substitute x = 4 into the function: f(4) = 3(4) - 1
    • Perform multiplication: f(4) = 12 - 1
    • Perform subtraction: f(4) = 11
    • Answer: 11

  3. Write a linear function rule for the table below:

    xy
    05
    17
    29
    311
    • Find the slope (m): The y-values increase by 2 for every increase of 1 in x. So, m = 2/1 = 2.
    • Find the y-intercept (b): When x = 0, y = 5. So, b = 5.
    • Write the rule: y = 2x + 5
    • Answer: y = 2x + 5

  4. A taxi charges a flat fee of $3 plus $2 per mile. Write a linear function rule to represent the cost C for m miles.

    • The flat fee is the y-intercept (b): b = 3
    • The cost per mile is the slope (m): m = 2
    • Write the rule: C = 2m + 3
    • Answer: C = 2m + 3

Unit 1 Test Answer Key

  1. Evaluate: 24 ÷ 4 + 2 × (10 - 7)

    • 10 - 7 = 3
    • 24 ÷ 4 + 2 × 3
    • 6 + 2 × 3
    • 6 + 6
    • 12
    • Answer: 12

  2. Evaluate: 5^2 - (12 + 3) ÷ 5

    • 12 + 3 = 15
    • 5^2 - 15 ÷ 5
    • 25 - 15 ÷ 5
    • 25 - 3
    • 22
    • Answer: 22

  3. Which of the following expressions has a value of 15?

    • a) 3 + 2 × 5 = 3 + 10 = 13
    • b) (3 + 2) × 5 = 5 × 5 = 25
    • c) 10 ÷ 2 + 10 = 5 + 10 = 15
    • d) 4 × 3 + 1 = 12 + 1 = 13
    • Answer: c) 10 ÷ 2 + 10

  4. Evaluate 4x + 7 when x = 3.

    • 4(3) + 7
    • 12 + 7
    • 19
    • Answer: 19

  5. Evaluate y^2 - 2z when y = 5 and z = 8.

    • 5^2 - 2(8)
    • 25 - 16
    • 9
    • Answer: 9

  6. If a = 4 and b = 1, what is the value of (a - b) × b + a?

    • (4 - 1) × 1 + 4
    • 3 × 1 + 4
    • 3 + 4
    • 7
    • Answer: b) 7

  7. Does the set of ordered pairs {(0, 1), (1, 3), (2, 5), (0, 4)} represent a function? Explain why or why not.

    • Answer: No. The input 0 has two different outputs (1 and 4). For a relation to be a function, each input must have only one output.

  8. If g(x) = x^2 - 5, find g(3).

    • g(3) = 3^2 - 5
    • g(3) = 9 - 5
    • g(3) = 4
    • Answer: 4

  9. Write a linear function rule y = mx + b for the data in the table.

    xy
    02
    16
    210
    314
    • The change in y is 4 for every 1 change in x, so m = 4.
    • When x = 0, y = 2, so b = 2.
    • Answer: y = 4x + 2

  10. A gym membership costs $20 to sign up, plus $15 per month. Write a linear function rule to represent the total cost C for m months of membership.

    • The initial sign-up fee is the y-intercept (b): b = 20.
    • The monthly cost is the slope (m): m = 15.
    • Answer: C = 15m + 20
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Algebra Foundations: Test Your Might! • Lenny Learning