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Square Root Sprint

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Lesson Plan

Square Root Sprint

Students will be able to approximate square roots of non-perfect squares to the nearest whole number using the truncation method.

Understanding how to approximate square roots helps us estimate values for numbers that aren't 'neat.' This is useful in real-world situations like estimating distances or areas when exact measurements aren't needed.

Audience

8th Grade Emerging Learners

Time

30 minutes

Approach

Through direct instruction, guided practice, and independent application.

Materials

Whiteboard or Projector, Square Root Sprint Slide Deck, Truncation Practice Worksheet, and Truncation Practice Answer Key

Prep

Teacher Preparation

15 minutes

Step 1

Introduction & Warm-Up (5 minutes)

5 minutes

  • Begin by asking students what a square root is. (e.g., 'What number times itself equals 9?')
    - Introduce the concept of non-perfect squares (e.g., 'What about the square root of 7?').
    - Briefly explain that many square roots are irrational numbers, meaning they go on forever without repeating.

Step 2

Direct Instruction: What is Truncation? (10 minutes)

10 minutes

  • Use the Square Root Sprint Slide Deck to explain how to approximate square roots using truncation.
    - Slide 1: Title Slide
    - Slide 2: What's a Square Root, Anyway? (Review perfect squares)
    - Slide 3: Non-Perfect Problem? (Introduce numbers like √7)
    - Slide 4: Meet Mr. Truncation! (Define truncation in simple terms - 'chop off the decimals!')
    - Slide 5: How To: Step 1 - Find Perfect Squares (Show example with √7 between √4 and √9)
    - Slide 6: How To: Step 2 - Estimate Closer (Explain guessing decimals, e.g., 2.5 * 2.5)
    - Slide 7: How To: Step 3 - Truncate! (Demonstrate chopping off decimals for the whole number approximation)
    - Work through an example together as a class (e.g., √13).

Step 3

Guided Practice (5 minutes)

5 minutes

  • Work through one or two problems from the Truncation Practice Worksheet as a class, encouraging students to explain their steps aloud.
    - Pay close attention to students who might be struggling and offer immediate support and clarification.

Step 4

Independent Practice (8 minutes)

8 minutes

  • Distribute the Truncation Practice Worksheet.
    - Have students complete the remaining problems independently.
    - Circulate around the room, providing individual help as needed.

Step 5

Wrap-Up & Cool-Down (2 minutes)

2 minutes

  • Ask students to share one thing they learned about approximating square roots.
    - Briefly review the main idea of truncation.
    - Collect the worksheets for review.
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Slide Deck

Square Root Sprint: Approximating the Unseen!

How do we find the value of a number that isn't a 'perfect' square?

Welcome students and introduce the day's topic: approximating square roots. Briefly explain that sometimes numbers aren't perfect squares, and we need a way to estimate their square roots.

What's a Square Root, Anyway?

  • A square root is a number that, when multiplied by itself, gives the original number.
  • Example: √9 = 3, because 3 x 3 = 9
  • What are some other perfect squares you know?

Start with a quick review of what a square root is. Ask students for examples of perfect squares. Ensure everyone is on the same page.

Non-Perfect Problem?

  • What about numbers like √7?
  • Is there a whole number that, when multiplied by itself, equals exactly 7?
  • This is where approximating comes in!

Introduce the idea of non-perfect squares. Ask students if they can think of a whole number that, when multiplied by itself, equals 7. This will lead to the need for approximation.

Meet Mr. Truncation!

  • Truncation means to chop off or cut the decimal part of a number.
  • We are looking for the whole number part of the square root.
  • Example: If a calculator says 3.14159, truncating to a whole number gives us 3.

Define truncation simply. Emphasize that we are 'chopping off' or 'cutting' the decimal part to get a whole number estimate.

How To: Step 1 - Find Perfect Squares

  • Find the two perfect squares the number is between.
  • Example: For √7, think of perfect squares:
    • 2 x 2 = 4 (√4)
    • 3 x 3 = 9 (√9)
  • So, √7 is between √4 and √9.

Explain the first step using √7 as an example. Show how to find the two perfect squares it lies between. Encourage students to identify these perfect squares.

How To: Step 2 - Estimate Closer (Mental Math)

  • Since √7 is between √4 (which is 2) and √9 (which is 3), we know √7 is '2 point something'.
  • Let's try to get a bit closer mentally:
    • 2.5 x 2.5 = 6.25
    • 2.7 x 2.7 = 7.29
  • So √7 is somewhere between 2.5 and 2.7. It's still '2 point something'!

Guide students through the estimation process. This involves a bit of trial and error with decimals. For this lesson, we are focusing on the whole number truncation, but this step helps them understand why it's between those numbers.

How To: Step 3 - Truncate!

  • No matter how many decimals we find, the number still starts with '2'.
  • When we truncate the square root of 7 to a whole number, we just take the '2'.
  • So, the truncated approximation of √7 is 2!

Conclude the example by showing how to truncate. Reiterate that we are only interested in the whole number part for this method.

Let's Try Another: √13

  • Step 1: Find the perfect squares it's between.
  • Step 2: Estimate closer (it will be '3 point something').
  • Step 3: Truncate to the whole number!

Work through another example with the class, like √13. Ask students to participate in finding the perfect squares and then the whole number approximation through truncation.

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Worksheet

Truncation Practice: Approximating Square Roots

Name: ________________________

Date: ________________________

Directions: For each number, find the whole number approximation of its square root using the truncation method. Show your work by identifying the two perfect squares the number falls between.

Example:

Approximate √7

  1. Find the two perfect squares it's between:
    √4 (which is 2) < √7 < √9 (which is 3)

  2. What's the whole number part?
    Since √7 is between 2 and 3, its whole number part is 2.

  3. Truncated approximation: 2

Practice Problems:

  1. Approximate √10






  2. Approximate √18






  3. Approximate √27






  4. Approximate √40






  5. Approximate √55






  6. Approximate √70






  7. Approximate √85






  8. Approximate √99






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Answer Key

Truncation Practice: Approximating Square Roots - Answer Key

Directions: For each number, find the whole number approximation of its square root using the truncation method. Show your work by identifying the two perfect squares the number falls between.

Practice Problems:

  1. Approximate √10

    • Find the two perfect squares it's between:
      √9 (which is 3) < √10 < √16 (which is 4)
    • What's the whole number part?
      Since √10 is between 3 and 4, its whole number part is 3.
    • Truncated approximation: 3

  2. Approximate √18

    • Find the two perfect squares it's between:
      √16 (which is 4) < √18 < √25 (which is 5)
    • What's the whole number part?
      Since √18 is between 4 and 5, its whole number part is 4.
    • Truncated approximation: 4

  3. Approximate √27

    • Find the two perfect squares it's between:
      √25 (which is 5) < √27 < √36 (which is 6)
    • What's the whole number part?
      Since √27 is between 5 and 6, its whole number part is 5.
    • Truncated approximation: 5

  4. Approximate √40

    • Find the two perfect squares it's between:
      √36 (which is 6) < √40 < √49 (which is 7)
    • What's the whole number part?
      Since √40 is between 6 and 7, its whole number part is 6.
    • Truncated approximation: 6

  5. Approximate √55

    • Find the two perfect squares it's between:
      √49 (which is 7) < √55 < √64 (which is 8)
    • What's the whole number part?
      Since √55 is between 7 and 8, its whole number part is 7.
    • Truncated approximation: 7

  6. Approximate √70

    • Find the two perfect squares it's between:
      √64 (which is 8) < √70 < √81 (which is 9)
    • What's the whole number part?
      Since √70 is between 8 and 9, its whole number part is 8.
    • Truncated approximation: 8

  7. Approximate √85

    • Find the two perfect squares it's between:
      √81 (which is 9) < √85 < √100 (which is 10)
    • What's the whole number part?
      Since √85 is between 9 and 10, its whole number part is 9.
    • Truncated approximation: 9

  8. Approximate √99

    • Find the two perfect squares it's between:
      √81 (which is 9) < √99 < √100 (which is 10)
    • What's the whole number part?
      Since √99 is between 9 and 10, its whole number part is 9.
    • Truncated approximation: 9
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Square Root Sprint • Lenny Learning