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Algebra Ascent!

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Lesson Plan

Algebra Ascent!

Students will correctly solve 7th-grade level math problems involving factoring, distributing, solving for x, and identifying equivalent expressions, demonstrating a solid understanding of foundational algebraic concepts.

Mastering these foundational algebraic skills (factoring, distributing, solving for x, and equivalent expressions) is essential for building a strong base in mathematics and preparing students for more complex algebraic concepts in the future.

Audience

7th Grade Students

Time

30 minutes

Approach

Direct instruction, guided practice, and independent problem-solving.

Materials

Our Slide Deck: Algebra Ascent!, Our Worksheet: Problem Practice Patrol, and Our Answer Key: Solution Seeker's Guide

Prep

Review Materials

10 minutes

Step 1

Introduction & Warm-up (5 minutes)

5 minutes

  • Begin by displaying the first slide of the Slide Deck: Algebra Ascent! and greeting students.
    * Introduce the day's topic: strengthening our algebra skills.
    * Quickly review the concepts students will encounter (factoring, distributing, solving for x, equivalent expressions) as shown on the slides.

Step 2

Direct Instruction & Guided Practice (10 minutes)

10 minutes

  • Go through slides 2-5 of the Slide Deck: Algebra Ascent!, explaining each concept with an example.
    * For each concept, work through one or two problems together as a class, encouraging student participation and questions.
    * Emphasize key vocabulary and common pitfalls.

Step 3

Independent Practice (10 minutes)

10 minutes

  • Distribute the Worksheet: Problem Practice Patrol to each student.
    * Instruct students to work independently on the problems provided.
    * Circulate around the room to offer support and answer individual questions.
    * Remind students to show their work where applicable.

Step 4

Wrap-up & Review (5 minutes)

5 minutes

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Slide Deck

Algebra Ascent!

Ready to conquer some algebraic peaks?

Welcome students and introduce the exciting journey into algebra. Briefly explain that today they will sharpen skills in factoring, distributing, solving for x, and equivalent expressions.

Factoring Fundamentals

What is Factoring?

  • Breaking down an expression into simpler terms.
  • Finding common factors.

Example:
Factor: 3x + 9

Solution: 3(x + 3)

Explain what factoring means (breaking down an expression into simpler parts that multiply to give the original). Provide a clear example and walk through the steps.

Distributing & Solving Dash

What is Distributing?

  • Multiplying a number by each term inside parentheses.

Example:
Distribute and Solve: 2(x + 4) = 14

Solution:
2x + 8 = 14
2x = 6
x = 3

Introduce distributing (multiplying a number by each term inside parentheses) and then solving the resulting equation. Provide an example.

Solve for X Quest

What does 'Solve for X' mean?

  • Finding the value of the unknown variable.
  • Using inverse operations.

Example:
Solve for x: 5x - 7 = 18

Solution:
5x = 25
x = 5

Explain the goal of solving for 'x' (isolating the variable). Show an example with inverse operations.

Equivalent Expression Expedition

What are Equivalent Expressions?

  • Expressions that have the same value.
  • They might look different, but they simplify to be the same.

Example:
Which is equivalent to 4(x + 2)?

A) 4x + 2
B) 4x + 8
C) x + 8

Solution: B) 4x + 8

Define equivalent expressions (expressions that have the same value, even if they look different). Give an example of simplifying to find an equivalent expression.

Your Turn! Problem Practice

Time to put your skills to the test!

Encourage students to now tackle the worksheet independently, applying what they've learned. Remind them to ask questions if they get stuck.

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Worksheet

Problem Practice Patrol

Sharpen your algebra skills by working through these problems! Show your work where possible.

Part 1: Factoring

  1. Factor the expression: 5x + 10


  2. Factor the expression: 9y - 27


  3. Factor the expression: 4x + 16y


  4. Factor the expression: 12a - 8


  5. Factor the expression: 7x + 7


  6. Factor the expression: 10m - 25n


Part 2: Distributing and Solving

  1. Distribute and solve for x: 3(x + 2) = 15


  2. Distribute and solve for y: 4(y - 5) = 12


  3. Distribute and solve for m: 2(m + 7) = 20


  4. Distribute and solve for a: 5(a - 3) = 10


  5. Distribute and solve for x: 6(x + 1) = 30


  6. Distribute and solve for n: 7(n - 2) = 21


Part 3: Solve for X

  1. Solve for x: x + 9 = 23


  2. Solve for x: x - 14 = 8


  3. Solve for x: 3x = 36


  4. Solve for x: x / 5 = 7


  5. Solve for x: 2x + 5 = 19


  6. Solve for x: 4x - 10 = 26


  7. Solve for x: (x / 3) - 2 = 4


Part 4: Equivalent Expressions

  1. Which expression is equivalent to 6(y + 3)?
    A) 6y + 3
    B) y + 18
    C) 6y + 18


  2. Which expression is equivalent to 2x + 3x + 4?
    A) 9x
    B) 5x + 4
    C) 5x - 4


  3. Which expression is equivalent to (8 + a) + 7?
    A) 15a
    B) 8a + 7
    C) a + 15


  4. Which expression is equivalent to 9c - 4c?
    A) 5c
    B) 13c
    C) 5


  5. Which expression is equivalent to 3(x + 5) - 2x?
    A) x + 5
    B) x + 15
    C) 5x + 15


  6. Which expression is equivalent to 10 - (2m + 5)?
    A) 5 - 2m
    B) 15 - 2m
    C) 3 - 2m
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Answer Key

Solution Seeker's Guide

Here are the solutions and explanations for the problems on the Worksheet: Problem Practice Patrol.

Part 1: Factoring

  1. Factor the expression: 5x + 10
    • Identify the greatest common factor (GCF) of 5x and 10, which is 5.
    • Divide each term by the GCF: 5x/5 = x and 10/5 = 2.
    • Write the GCF outside the parentheses and the results inside: 5(x + 2).
    • Answer: 5(x + 2)
  2. Factor the expression: 9y - 27
    • The GCF of 9y and 27 is 9.
    • Divide each term by 9: 9y/9 = y and 27/9 = 3.
    • Answer: 9(y - 3)
  3. Factor the expression: 4x + 16y
    • The GCF of 4x and 16y is 4.
    • Divide each term by 4: 4x/4 = x and 16y/4 = 4y.
    • Answer: 4(x + 4y)
  4. Factor the expression: 12a - 8
    • The GCF of 12a and 8 is 4.
    • Divide each term by 4: 12a/4 = 3a and 8/4 = 2.
    • Answer: 4(3a - 2)
  5. Factor the expression: 7x + 7
    • The GCF of 7x and 7 is 7.
    • Divide each term by 7: 7x/7 = x and 7/7 = 1.
    • Answer: 7(x + 1)
  6. Factor the expression: 10m - 25n
    • The GCF of 10m and 25n is 5.
    • Divide each term by 5: 10m/5 = 2m and 25n/5 = 5n.
    • Answer: 5(2m - 5n)

Part 2: Distributing and Solving

  1. Distribute and solve for x: 3(x + 2) = 15
    • Distribute the 3: 3x + 6 = 15.
    • Subtract 6 from both sides: 3x = 9.
    • Divide by 3: x = 3.
    • Answer: x = 3
  2. Distribute and solve for y: 4(y - 5) = 12
    • Distribute the 4: 4y - 20 = 12.
    • Add 20 to both sides: 4y = 32.
    • Divide by 4: y = 8.
    • Answer: y = 8
  3. Distribute and solve for m: 2(m + 7) = 20
    • Distribute the 2: 2m + 14 = 20.
    • Subtract 14 from both sides: 2m = 6.
    • Divide by 2: m = 3.
    • Answer: m = 3
  4. Distribute and solve for a: 5(a - 3) = 10
    • Distribute the 5: 5a - 15 = 10.
    • Add 15 to both sides: 5a = 25.
    • Divide by 5: a = 5.
    • Answer: a = 5
  5. Distribute and solve for x: 6(x + 1) = 30
    • Distribute the 6: 6x + 6 = 30.
    • Subtract 6 from both sides: 6x = 24.
    • Divide by 6: x = 4.
    • Answer: x = 4
  6. Distribute and solve for n: 7(n - 2) = 21
    • Distribute the 7: 7n - 14 = 21.
    • Add 14 to both sides: 7n = 35.
    • Divide by 7: n = 5.
    • Answer: n = 5

Part 3: Solve for X

  1. Solve for x: x + 9 = 23
    • Subtract 9 from both sides: x = 23 - 9.
    • Answer: x = 14
  2. Solve for x: x - 14 = 8
    • Add 14 to both sides: x = 8 + 14.
    • Answer: x = 22
  3. Solve for x: 3x = 36
    • Divide both sides by 3: x = 36 / 3.
    • Answer: x = 12
  4. Solve for x: x / 5 = 7
    • Multiply both sides by 5: x = 7 * 5.
    • Answer: x = 35
  5. Solve for x: 2x + 5 = 19
    • Subtract 5 from both sides: 2x = 14.
    • Divide both sides by 2: x = 7.
    • Answer: x = 7
  6. Solve for x: 4x - 10 = 26
    • Add 10 to both sides: 4x = 36.
    • Divide both sides by 4: x = 9.
    • Answer: x = 9
  7. Solve for x: (x / 3) - 2 = 4
    • Add 2 to both sides: x / 3 = 6.
    • Multiply both sides by 3: x = 18.
    • Answer: x = 18

Part 4: Equivalent Expressions

  1. Which expression is equivalent to 6(y + 3)?
    • Distribute the 6 into the parentheses: 6 * y = 6y and 6 * 3 = 18.
    • So, 6(y + 3) is equivalent to 6y + 18.
    • Answer: C) 6y + 18
  2. Which expression is equivalent to 2x + 3x + 4?
    • Combine like terms: 2x + 3x = 5x.
    • So, 2x + 3x + 4 is equivalent to 5x + 4.
    • Answer: B) 5x + 4
  3. Which expression is equivalent to (8 + a) + 7?
    • Use the associative property to rearrange and combine the numbers: 8 + 7 + a = 15 + a.
    • So, (8 + a) + 7 is equivalent to a + 15.
    • Answer: C) a + 15
  4. Which expression is equivalent to 9c - 4c?
    • Combine like terms: 9c - 4c = 5c.
    • Answer: A) 5c
  5. Which expression is equivalent to 3(x + 5) - 2x?
    • Distribute the 3: 3x + 15 - 2x.
    • Combine like terms (3x - 2x): x + 15.
    • Answer: B) x + 15
  6. Which expression is equivalent to 10 - (2m + 5)?
    • Distribute the negative sign to both terms inside the parentheses: 10 - 2m - 5.
    • Combine the constant terms: 10 - 5 = 5.
    • So, the expression simplifies to 5 - 2m.
    • Answer: A) 5 - 2m
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Activity

Time Travel Tally: Algebraic Adventures!

Embark on a journey through time! For each correct answer, you'll leap forward, but an incorrect answer might send you backward through the ages. Keep track of your progress!

Jurassic Era Journeys

  1. If Correct: A friendly Pterodactyl swoops down, carrying you 3 spaces forward on your prehistoric path!
    If Incorrect: A grumpy Triceratops blocks your way, sending you 2 spaces backward in time.

  2. If Correct: You cleverly solve the equation, and a lush fern forest grows, granting you passage 4 spaces forward.
    If Incorrect: Your answer awakens a sleeping T-Rex, and you scramble 3 spaces backward to safety.

  3. If Correct: You accurately factor the expression, causing a geyser to erupt, propelling you 5 spaces forward!
    If Incorrect: An incorrect solution causes a tar pit to appear, trapping you and forcing you 4 spaces backward.

Ice Age Expeditions

  1. If Correct: Your distribution skills are sharp! A woolly mammoth guides you safely 3 spaces forward across the icy plains.
    If Incorrect: You slip on a glacier, losing your footing and sliding 2 spaces backward.

  2. If Correct: You correctly solve for x, and a warm cave is discovered, allowing you to advance 4 spaces forward.
    If Incorrect: A sabre-tooth tiger spots you, forcing a hasty retreat 3 spaces backward.

  3. If Correct: Your equivalent expression is spot on! A frozen river thaws just enough for you to cross, moving 5 spaces forward.
    If Incorrect: A sudden blizzard kicks up, and you get disoriented, moving 4 spaces backward.

  4. If Correct: Your algebraic insight helps you find an ancient artifact, granting you 3 spaces forward.
    If Incorrect: You accidentally wake a hibernating cave bear, leading to a quick scramble 2 spaces backward.

Modern Era Marvels

  1. If Correct: Your phone gets excellent signal, and you navigate 2 spaces forward with ease.
    If Incorrect: Your Wi-Fi cuts out, and you are stuck, moving 1 space backward.

  2. If Correct: You find the exact ingredient you need at the store, moving you 3 spaces forward.
    If Incorrect: You realize you forgot your wallet, sending you 2 spaces backward to retrieve it.

  3. If Correct: Your smart home device understands your command perfectly, granting you 1 space forward.
    If Incorrect: It misunderstands completely, causing a minor inconvenience and moving you 1 space backward.

  4. If Correct: You catch your bus just in time, moving 4 spaces forward on your journey.
    If Incorrect: You miss your bus and have to wait, moving 2 spaces backward.

  5. If Correct: Your creative solution helps a friend, and you both advance 3 spaces forward.
    If Incorrect: A typo in your message causes confusion, setting you back 1 space backward.

  6. If Correct: You successfully parallel park on the first try, earning you 2 spaces forward.
    If Incorrect: You have to circle the block multiple times, losing 2 spaces backward.

  7. If Correct: Your online order arrives a day early, bringing you 3 spaces forward.
    If Incorrect: Your package is delayed, holding you up 1 space backward.

  8. If Correct: You master a new video game level, propelling you 4 spaces forward.
    If Incorrect: You lose a life in the game, forcing you 2 spaces backward.

  9. If Correct: You remember your friend's birthday and send a thoughtful message, moving 2 spaces forward.
    If Incorrect: You accidentally double-book yourself, causing you to cancel plans and move 1 space backward.

  10. If Correct: Your meal delivery arrives hot and fresh, advancing you 3 spaces forward.
    If Incorrect: The order is incorrect, and you have to wait for a replacement, moving 2 spaces backward.

  11. If Correct: You find a great deal on something you needed, moving you 2 spaces forward.
    If Incorrect: You accidentally subscribe to something you didn't want, costing you 1 space backward.

  12. If Correct: Your presentation goes smoothly and is well-received, moving you 4 spaces forward.
    If Incorrect: Technical difficulties interrupt your flow, setting you back 3 spaces backward.

  13. If Correct: You learn a new skill that will benefit you in the future, moving you 5 spaces forward.
    If Incorrect: You spend too much time on social media, wasting valuable time and moving 2 spaces backward.

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