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Power Up!

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Lesson Plan

Power Up!

Students will be able to understand and apply the concepts of exponents and roots, demonstrating their knowledge through various differentiated activities.

Understanding exponents and roots is crucial for advanced math topics and real-world applications like finance and science. This lesson helps students build a strong foundation.

Audience

8th Grade Students

Time

30 minutes

Approach

Through direct instruction, interactive slides, and differentiated activities.

Materials

Power Up! Slide Deck, Exponent Explorer Worksheet, and Answer Key: Exponent Explorer

Prep

Teacher Preparation

15 minutes

  • Review the Power Up! Slide Deck and familiarize yourself with the content.
    - Print copies of the Exponent Explorer Worksheet (one per student).
    - Review the Answer Key: Exponent Explorer to understand correct responses and thought processes.
    - Ensure projector/smartboard is set up for the slide deck.
    - Group students for differentiated activities if applicable, or explain how individual students can choose their preferred learning style/output method.
    - Gather any optional manipulatives like base-10 blocks or number lines if you plan to offer tactile differentiation.

Step 1

Warm-Up: The Mystery Number

5 minutes

  • Distribute the Warm-Up: The Mystery Number activity.
    - Instruct students to solve the mystery number using their prior knowledge.
    - Discuss answers as a class, connecting to the day's topic.

Step 2

Introduction to Exponents (Process & Interest Differentiation)

7 minutes

  • Present the Power Up! Slide Deck (Slides 1-3).
    - Introduce exponents as a shortcut for repeated multiplication.
    - Provide real-world examples (e.g., doubling a recipe, population growth).
    - Process Differentiation: Offer an option for students to work with a partner to discuss or draw out what an exponent means before direct instruction.
    - Interest Differentiation: Ask students to think of where they might see exponents outside of math class (e.g., video game scores, scientific notation).

Step 3

Understanding Roots (Process & Learning Style Differentiation)

7 minutes

  • Continue with the Power Up! Slide Deck (Slides 4-6).
    - Introduce square roots as the inverse of squaring a number.
    - Discuss perfect squares and their roots.
    - Process Differentiation: Allow students to use calculators for finding square roots if they are struggling with mental math, or provide a multiplication chart as a scaffold.
    - Learning Style Differentiation: For visual learners, draw a number line and show how squaring a number moves you away from zero, and taking a square root brings you back towards it. For kinesthetic learners, use small square tiles to build squares and then find their side lengths.

Step 4

Differentiated Activity: Exponent Explorer

8 minutes

  • Distribute the Exponent Explorer Worksheet.
    - Output Differentiation: Students can choose to solve problems by showing all steps, drawing diagrams, or explaining their reasoning in words.
    - Learning Style Differentiation: Provide a choice of problems: computational, word problems, or conceptual questions that require explanation. Students can work individually or in pairs.
    - Circulate and provide support as needed, prompting students with questions to guide their thinking rather than giving direct answers.

Step 5

Cool-Down: Exit Ticket

3 minutes

  • Distribute the Cool Down: Exponents & Roots Check-In.
    - Students answer a quick question about one new thing they learned or one question they still have.
    - Collect exit tickets to assess understanding and inform future instruction.
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Slide Deck

Power Up!

Understanding Exponents and Roots

Let's unlock some math superpowers!

Welcome students and get them ready for a fun math lesson! Emphasize the exciting title.

What's an Exponent?

Exponents are a shortcut for multiplying the same number many times.

  • Base: The number being multiplied (the big number).
  • Exponent: How many times to multiply the base by itself (the small, raised number).

Introduce the idea of repeated multiplication and how exponents simplify it. Use clear, simple language.

Exponent Examples!

2³ = 2 x 2 x 2 = 8

5² = 5 x 5 = 25

Your Turn!

  • 3⁴ = ?
  • 10² = ?

Give a few examples and ask students to try one or two. Reinforce the vocabulary (base, exponent).

Meet the Roots!

If exponents are about 'powering up' a number, roots are about 'finding the origin'.

  • A square root asks: 'What number, multiplied by itself, gives me this number?'

Transition to roots. Explain that roots are the 'opposite' or inverse of exponents. Start with square roots.

Square Root Symbol & Examples

The square root symbol is called a radical (√).

  • √25 = 5 (because 5 x 5 = 25)
  • √49 = 7 (because 7 x 7 = 49)

Think about it: What is √81?

Show the symbol and give examples of perfect squares. Emphasize that finding the square root 'undoes' the squaring.

Beyond Square Roots: Cube Roots

A cube root asks: 'What number, multiplied by itself three times, gives me this number?'

  • ³√8 = 2 (because 2 x 2 x 2 = 8)
  • ³√27 = 3 (because 3 x 3 x 3 = 27)

Your Turn!

  • ³√64 = ?

Introduce cube roots as an extension, showing the small '3' in the radical sign. Give one or two examples.

Time to Explore!

Now it's your turn to be an Exponent Explorer!

  • Choose how you want to show your work.
  • Choose the types of problems that interest you most.
  • Work individually or with a partner.

Set up the activity. Remind students about the choices they have for showing their work or choosing problem types.

You've Got the Power!

Today, we powered up our math skills by exploring exponents and roots.

These concepts are fundamental building blocks for many exciting areas in math and science!

Get ready for your Cool Down: Exponents & Roots Check-In.

Conclude the lesson and prepare for the cool-down. Reinforce that understanding these concepts builds a strong math foundation.

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Activity

Warm-Up: The Mystery Number!

Instructions: Read the clues below and discover the mystery number! Show your work or explain your reasoning for each clue.

Clue 1: I am a number that, when you multiply me by myself, you get 36.






Clue 2: I am a number that, when you multiply me by myself three times, you get 8.






Clue 3: I am the result of taking the number 4 and using 2 as my exponent.






Mystery Number Challenge: What is the sum of the answers from Clue 1, Clue 2, and Clue 3?






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Worksheet

Exponent Explorer Worksheet

Instructions: Choose at least one problem from each section to complete. Show your work clearly using numbers, words, or diagrams. Feel free to use the method that helps you understand best!

Section 1: Powering Up! (Exponents)

Computational Practice:

  1. Calculate: 7²


  2. Calculate: 2⁵


  3. Calculate: 10³


Word Problems:

  1. A rare bacterium doubles its population every hour. If you start with 1 bacterium, how many will there be after 4 hours? Express your answer using an exponent and then calculate the total.





  2. Sarah saves $3 every day. On day 1, she has $3. On day 2, she multiplies her savings by 3. On day 3, she multiplies her new total by 3 again. If she continues this pattern, how much money will she have after 4 days? Write an exponent expression and solve.





Conceptual Challenge:

  1. Explain in your own words what 6³ means. How is it different from 6 x 3?










Section 2: Getting to the Root! (Roots)

Computational Practice:

  1. Find the square root of 64 (√64).


  2. Find the square root of 121 (√121).


  3. Find the cube root of 27 (³√27).


Word Problems:

  1. A square garden has an area of 100 square feet. What is the length of one side of the garden? (Hint: Think about square roots!)





  2. You have a cubic box with a volume of 8 cubic inches. What is the length of one side of the box? (Hint: Think about cube roots!)





Conceptual Challenge:

  1. Imagine you are explaining square roots to a younger student. What drawing or analogy would you use to help them understand what a square root is? Draw or describe your idea.










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Answer Key

Answer Key: Exponent Explorer

Section 1: Powering Up! (Exponents)

Computational Practice:

  1. 7²
    • Thought Process: The base is 7, and the exponent is 2. This means 7 multiplied by itself 2 times.
    • Answer: 7 x 7 = 49
  2. 2⁵
    • Thought Process: The base is 2, and the exponent is 5. This means 2 multiplied by itself 5 times.
    • Answer: 2 x 2 x 2 x 2 x 2 = 32
  3. 10³
    • Thought Process: The base is 10, and the exponent is 3. This means 10 multiplied by itself 3 times.
    • Answer: 10 x 10 x 10 = 1000

Word Problems:

  1. A rare bacterium doubles its population every hour. If you start with 1 bacterium, how many will there be after 4 hours? Express your answer using an exponent and then calculate the total.
    • Thought Process: Doubling means multiplying by 2. After 1 hour: 1x2. After 2 hours: (1x2)x2 = 1x2². After 3 hours: 1x2³. After 4 hours: 1x2⁴.
    • Answer: 2⁴ = 16 bacteria
  2. Sarah saves $3 every day. On day 1, she has $3. On day 2, she multiplies her savings by 3. On day 3, she multiplies her new total by 3 again. If she continues this pattern, how much money will she have after 4 days? Write an exponent expression and solve.
    • Thought Process: This is repeated multiplication by 3. Day 1: 3¹. Day 2: 3². Day 3: 3³. Day 4: 3⁴.
    • Answer: 3⁴ = 81 dollars

Conceptual Challenge:

  1. Explain in your own words what 6³ means. How is it different from 6 x 3?
    • Thought Process: Focus on the definition of exponent vs. simple multiplication.
    • Answer: 6³ means you multiply 6 by itself three times (6 x 6 x 6), which equals 216. It is different from 6 x 3 because 6 x 3 means you add 6 three times, which equals 18. Exponents are for repeated multiplication, while simple multiplication (like 6 x 3) is a shortcut for repeated addition.

Section 2: Getting to the Root! (Roots)

Computational Practice:

  1. Find the square root of 64 (√64).
    • Thought Process: What number, when multiplied by itself, gives 64?
    • Answer: 8 (because 8 x 8 = 64)
  2. Find the square root of 121 (√121).
    • Thought Process: What number, when multiplied by itself, gives 121?
    • Answer: 11 (because 11 x 11 = 121)
  3. Find the cube root of 27 (³√27).
    • Thought Process: What number, when multiplied by itself three times, gives 27?
    • Answer: 3 (because 3 x 3 x 3 = 27)

Word Problems:

  1. A square garden has an area of 100 square feet. What is the length of one side of the garden?
    • Thought Process: Area of a square is side * side. So we need the square root of the area.
    • Answer: √100 = 10 feet
  2. You have a cubic box with a volume of 8 cubic inches. What is the length of one side of the box?
    • Thought Process: Volume of a cube is side * side * side. So we need the cube root of the volume.
    • Answer: ³√8 = 2 inches

Conceptual Challenge:

  1. Imagine you are explaining square roots to a younger student. What drawing or analogy would you use to help them understand what a square root is? Draw or describe your idea.
    • Thought Process: Focus on making the abstract concept concrete and relatable.
    • Answer: (Possible answers include, but are not limited to): You could draw a square made of 9 smaller blocks. The square root of 9 is 3 because it takes 3 blocks to make one side of the square. Or, think of a family: the 'square' is like the child, and the 'square root' is like one of its parents – the one that, when joined with itself, creates the child.
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Cool Down

Cool Down: Exponents & Roots Check-In

Instructions: Take a moment to reflect on today's lesson. Please answer one of the following questions.

  1. What is one new thing you learned about exponents or roots today?






  2. What is one question you still have about exponents or roots?






  3. How do you think understanding exponents or roots might be useful in the real world?






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