Each unit includes:
🎯 Objective – A quick summary of what you’ll learn
📝 Class Handouts The papers that we passed out in class 

🎥 Teacher Videos – Direct instruction from one of your teachers
📺 Supplementary Videos – Curated YouTube videos with different teaching styles (visual, fast-paced, contextual)
📝 Practice Activities – Opportunities to try problems and check your understanding

💡 Tips for Success:
▶️ Watch the teacher video first to learn the core idea
👀 Explore extra videos if you need a different explanation
✍️ Do the practice — it’s how you’ll get better and more confident
🙋 Ask your teacher if you get stuck — we’re here to help

Unit 5

🎯 Unit 5 Objective

Unit 5: Exponents & Exponential Functions

You will be able to:

• Use exponent rules to simplify expressions.

• Recognize and write exponential functions of the form f(x)=ab^(x).

• Graph exponential growth and decay and describe key features.

• Model real-world situations with exponential functions, including percent increase/decrease.

• Decide when a situation is linear vs exponential based on tables, graphs, or descriptions.

🚦 Start Here – Must Do First

Class Handouts

• Lesson 5-1

• Lesson 5-2

• Lesson 5-3

• Lesson 5-4

• Lesson 5-5

• Lesson 5-6

• Lesson 5-7

• Lesson 5-8

• Unit 5 Review 1

🎥 Teacher-created video(s)

• Lesson 5-1

• Lesson 5-2

• Lesson 5-3

• Lesson 5-4

• Lesson 5-5

• Lesson 5-6

• Lesson 5-7

• Lesson 5-8

• Unit 5 Review 1

📚 If You’re Behind – Start Here First

These review videos rebuild foundations you’ll need for Unit 5.

1. 🎥 Exponents as Repeated Multiplication (gentle intro)

   • Math Antics – Intro to Exponents – What exponents mean, why 343^434 is not 3×43\times43×4, and how to read exponent notation.

2. 🎥 Properties of Exponents (review of rules)

   • Properties of Exponents (6.1 Big Ideas Math – Algebra 1) – Product, quotient, power rules, zero and negative exponents with lots of examples.

3. 🎥 Intro to Exponential Functions & Percent Change

   • Algebra 1 – Intro to Exponential Functions (Meri Teaches Math) – Identifying exponential functions from tables and equations; basic growth vs decay.

If these still feel hard, rewatch them before doing anything else in the unit.

🔍 Need More Help? Try One of These

Organized by subtopic, with beginner / visual / challenge options.

1️⃣ Exponent Basics & Laws of Exponents

Beginner Video

• 🎥 Intro & Meaning of Exponents
  Math Antics – Intro to Exponents – Focuses on what exponents mean and connects to repeated multiplication. Great if you’re shaky on basics.

Visual / Conceptual Video

• 🎥 Properties of Exponents in an Algebra 1 Lesson
  Properties of Exponents (6.1 Big Ideas Math – Algebra 1) – Walks through rules with clear worked examples and visual structure.

Challenge / Deep Dive

• 🎥 Exponent Rules – Formulas and Equations
  Exponent Rules – The Organic Chemistry Tutor – Long, thorough review including negatives, fractions, and multiple variables. Use this to master complex exponent expressions.

2️⃣ Exponential Functions & Graphs f(x)=abxf(x)=ab^xf(x)=abx

Beginner Video

• 🎥 What Is an Exponential Function?
  Intro to Exponential Functions (MATH TEACHER GON) – Introduces the form f(x)=abxf(x)=ab^xf(x)=abx, growth vs decay, and simple graphs.

Visual / Graph-Focused Video

• 🎥 Graphing Exponential Functions (Algebra 1)
  Graphing Exponential Functions – Big Ideas Math 6.3 (Mr. G Math) – How to make tables, plot points, and describe the shape of exponential graphs.

• 🎥 Graphing Exponential Functions (Khan Academy)
  Graphing Exponential Functions – Another take on graphs, asymptotes, and intercepts.

Challenge / Conceptual

• 🎥 Why Exponentials Grow So Fast
  How Bad is Exponential Growth? – Computerphile – Uses computer science and doubling ideas to show how quickly exponential growth explodes. Great for big-picture understanding.

3️⃣ Exponential Growth & Decay Word Problems (Percent Change)

Beginner Video

• 🎥 Word Problems: Growth & Decay with Percent
  Word Problem Solving – Exponential Growth and Decay (Khan Academy) – Step-by-step modeling using a(1±r)ta(1\pm r)^ta(1±r)t for percent increase or decrease.

Visual / Contextual

• 🎥 Zombie Exponential Growth Story
  Practice Using the Exponential Growth Formula – with Zombies! (MashUp Math) – Uses a zombie outbreak to practice growth and decay formulas in a fun story context.

Challenge / Mixed Problems

• 🎥 Exponential Growth and Decay Word Problems (Full Review)
  Exponential Growth and Decay Word Problems & Functions – The Organic Chemistry Tutor – Many examples with population, half-life, and finance; great if you want to feel test-ready.

4️⃣ Linear vs Exponential & Writing Equations from Data

Beginner Video

• 🎥 Comparing Exponential and Linear Functions
  Comparing Exponential and Linear Function – Khan Academy – Classic “plan A vs plan B” comparison to see how exponential growth eventually beats linear growth.

Visual / From Data

• 🎥 Linear vs Exponential Growth from Data
  Linear vs Exponential Growth from Data – Khan Man Math – Uses tables of values to decide whether a function is linear or exponential.

Challenge / Conceptual Models

• 🎥 Understanding Linear and Exponential Models (PBS / Khan-based)
  Understanding Linear and Exponential Models – PBS LearningMedia – Big-picture video on when to choose linear vs exponential models in real situations.

These support questions like:

• “Is this table linear or exponential?”

• “Write an exponential equation that passes through these points.”

✏️ Practice Activities

Each link gives you ready-to-use practice. You can pick by subtopic.

A. Exponent Rules Practice

1. 📄 Exponent Rules Worksheets (Mixed Difficulty)

   • Exponent Rules Worksheets – MashUp Math – Printable sheets practicing product, quotient, power, zero, and negative exponents.

2. 📄 Laws of Exponents Worksheet

   • Worksheet: Laws of Exponents – Third Space Learning – Structured worksheet with guided examples and questions.

B. Exponential Functions & Graphs

3. 🌐 Intro to Exponential Functions (Notes + Examples)

   • Introduction to Exponential Functions – MathBitsNotebook (A1) – Notes with examples, graphs, and explanations of f(x)=abxf(x)=ab^xf(x)=abx.

4. 🌐 Simple Exponential Function Practice (Multiple Choice)

   • Simple Exponential Function Practice – MathBitsNotebook (A1) – Online practice identifying growth/decay, intercepts, domains, etc.

5. 🎮 Desmos Activity: Marbleslides – Exponentials

   • Marbleslides: Exponentials – Desmos – Move graphs of exponentials to make marbles hit stars; great for understanding shifts and growth/decay shape.

C. Exponential Growth & Decay / Percent Problems

6. 🌐 Percent Increase/Decrease with Exponential Functions

   • Percent of Increase/Decrease & Exponential Growth/Decay – MathBitsNotebook (A1) – Guided notes and examples for turning percent stories into exponential functions.

7. 📄 Exponential Growth & Decay Worksheets

   • Exponential Growth and Decay Worksheets – Cuemath – Printable pages for population, radioactive decay, and interest situations.

D. Linear vs Exponential & Modeling from Data

8. 🎮 Desmos Card Sort: Exponentials vs Others

   • Card Sort: Exponentials – Desmos – Sort graphs/equations/tables into matching exponential sets; helps you recognize exponential patterns.

9. 🌐 Comparing Growth Types & Modeling

   • Exponentials – Comparing Growth & Determining Functions – MathBitsNotebook – Scroll down for “Comparing Growth of Functions” and “Determining Exponential Functions” plus practice links.

10. 🌐 Understanding Linear and Exponential Models – Practice

    • Understanding Linear and Exponential Models – Exercise (PBS/CA) – Online problems deciding which type of model fits a scenario.

Use these especially for problems like the tree-growth, tuition, population, and regression-style questions from the Unit 5 test.

🧾 Vocabulary and Key Ideas

Same format as before (the version you liked).

• Exponent – The small number that tells how many times to multiply the base by itself (in 343^434, the 4).

• Base – The number being repeatedly multiplied in an exponential expression (in 343^434, the 3).

• Power – A whole expression with a base and an exponent, like 535^353.

• Exponential Expression – An expression where a variable may appear in the exponent, like 2x2^x2x or 53x5^{3x}53x.

• Exponential Function – A function of the form f(x)=abxf(x)=ab^xf(x)=abx, where a≠0a\neq0a=0 and b>0, b≠1b>0,\ b\neq1b>0, b=1.

• Initial Value – The starting amount in an exponential function; the value of f(0)f(0)f(0), usually the coefficient aaa.

• Growth Factor – For exponential growth, the number you multiply by each step, b>1b>1b>1 in f(x)=abxf(x)=ab^xf(x)=abx.

• Decay Factor – For exponential decay, the factor 0<b<10<b<10<b<1 that you multiply by each step.

• Percent Rate of Change – The percentage by which a quantity increases or decreases each step, related to b=1±rb=1\pm rb=1±r.

• Exponential Growth – When a quantity increases by the same factor (or percent) over equal time intervals.

• Exponential Decay – When a quantity decreases by the same factor (or percent) over equal time intervals.

• Linear Function – Grows by adding the same amount each step (constant difference), usually f(x)=mx+bf(x)=mx+bf(x)=mx+b.

• Common Ratio – The number you multiply by to get from one term to the next in an exponential pattern or geometric sequence.

• Asymptote – A line that a graph gets closer and closer to but never touches; for basic exponentials, usually y=0y=0y=0.

• Domain – All possible input (x) values for a function.

• Range – All possible output (y) values for a function.

💬 Tips for Success

• Rewrite in “real math words.”
  When you see 2(1.06)^t, say “start at 2, grow by 6% each time unit.” That makes story problems easier.

• Check if change is additive or multiplicative.

  • Add/subtract the same amount → likely linear.

  • Multiply by the same factor → exponential.

• Watch your exponent rules.

• Use tables for graphs.
  For tricky exponentials, plug in a few x-values (like -2, -1, 0, 1, 2) and plot to see the shape.

• Label parts of the function.
  On tests, write small notes: a= initial value, b= growth/decay factor, r= percent. It helps with interpretation questions.

🌍 Real-Life Connections

Use these if students want context or an extension.

• 🎥 Zombies & Exponential Growth
  Exponential Growth with Zombies – MashUp Math – Shows how a zombie outbreak can be modeled by exponential growth.
  
  

• 🌐 Aphids, Scooters, and Growth/Decay
  Percent of Increase/Decrease – MathBitsNotebook – Uses bugs and scooter value to show exponential growth/decay in everyday situations.
  
  

These match the types of population, money, and decay problems students see in Unit 5.

Unit 6