Classifying Real Numbers: Mystery Pattern - Free Printable

Let's solve this step-by-step based on the instructions and the image you provided.

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Task Overview

You are given a grid of numbers, and your job is to classify each number as:
- Rational
- Irrational
- Integer
- Whole

Then, color each cell according to the classification using the key:

| Classification | Color |
|----------------|-------|
| Rational | Blue |
| Irrational | Red |
| Integer | Green |
| Whole | Yellow |

> Note: The classifications are hierarchical:
- Whole numbers ⊂ Integers ⊂ Rational numbers
- Irrational numbers are not rational

So:
- A whole number is also an integer and rational.
- An integer is also rational.
- But irrational numbers are not rational.

We will go through each number in the grid and classify it accordingly.

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Definitions Recap

- Whole Numbers: {0, 1, 2, 3, ...} (non-negative integers)
- Integers: {..., -3, -2, -1, 0, 1, 2, 3, ...}
- Rational Numbers: Can be written as a fraction $ \frac{p}{q} $ where $ p, q $ are integers and $ q \ne 0 $. Includes terminating or repeating decimals.
- Irrational Numbers: Cannot be expressed as a fraction. Non-repeating, non-terminating decimals (e.g., $ \pi, \sqrt{2} $).

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Now, let’s classify each number in the grid.

We’ll go row by row.

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Row 1

1. $ \pi $ → Irrational → Red
2. $ -\sqrt{64} = -8 $ → Integer, Rational → Green (since it's an integer, we use green; but if only one color per cell, choose the most specific — but instruction says "color each value", so likely use the most specific category that applies. But since integer implies rational, but the key has separate colors, probably color with integer unless it's not an integer. So use Green for integers, even though they're rational.)
> But note: the key shows Integer as green, Rational as blue. So if a number is an integer, it should be colored green, because it's more specific.
> So: Green
3. $ \frac{18}{3} = 6 $ → Integer, Whole → Yellow (whole numbers get yellow)
4. $ 780 $ → Whole → Yellow
5. $ -\sqrt{16} = -4 $ → Integer → Green
6. $ 13 $ → Whole → Yellow
7. $ -14 $ → Integer → Green
8. $ \frac{70}{7} = 10 $ → Whole → Yellow
9. $ \frac{72}{2} = 36 $ → Whole → Yellow
10. $ \sqrt{36} = 6 $ → Whole → Yellow
11. $ -\sqrt{4} = -2 $ → Integer → Green
12. $ 4\pi $ → Irrational → Red

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Row 2

1. $ 300 $ → Whole → Yellow
2. $ \sqrt{204} $ → Not a perfect square → Irrational → Red
3. $ -34 $ → Integer → Green
4. $ 1.4 $ → Terminating decimal → Rational, not integer → Blue
5. $ \frac{2}{3} $ → Fraction → Rational, not integer → Blue
6. $ -8.2 $ → Decimal → Rational → Blue
7. $ 2\pi $ → Multiple of π → Irrational → Red
8. $ 6.81 $ → Terminating → Rational → Blue
9. $ 12\frac{1}{2} = 12.5 $ → Rational → Blue
10. $ 0.87 $ → Terminating → Rational → Blue
11. $ -\sqrt{121} = -11 $ → Integer → Green
12. $ \sqrt{4} = 2 $ → Whole → Yellow

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Row 3

1. $ 5 $ → Whole → Yellow
2. $ \pi $ → Irrational → Red
3. $ -\frac{50}{10} = -5 $ → Integer → Green
4. $ \sqrt{13} $ → Not perfect square → Irrational → Red
5. $ 8\pi $ → Irrational → Red
6. $ \sqrt{7} $ → Irrational → Red
7. $ \pi^2 $ → $ \pi^2 $ is irrational → Red
8. $ 3.7 $ → Terminating → Rational → Blue
9. $ -9.1 $ → Rational → Blue
10. $ \pi $ → Irrational → Red
11. $ 36 $ → Whole → Yellow
12. $ 250 $ → Whole → Yellow

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Row 4

1. $ -\sqrt{144} = -12 $ → Integer → Green
2. $ \frac{20}{4} = 5 $ → Whole → Yellow
3. $ 216 $ → Whole → Yellow
4. $ \sqrt{12} $ → $ \sqrt{12} = 2\sqrt{3} $ → Irrational → Red
5. $ -\sqrt{100} = -10 $ → Integer → Green
6. $ -4\sqrt{4} = -4×2 = -8 $ → Integer → Green
7. $ \sqrt{64} = 8 $ → Whole → Yellow
8. $ 8 $ → Whole → Yellow
9. $ \frac{4}{9} $ → Fraction → Rational → Blue
10. $ \sqrt{63} $ → Not perfect square → Irrational → Red
11. $ \frac{75}{5} = 15 $ → Whole → Yellow
12. $ 5.12 $ → Terminating → Rational → Blue

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Row 5

1. $ -1.5 $ → Rational → Blue
2. $ 300 $ → Whole → Yellow
3. $ -48 $ → Integer → Green
4. $ 4\sqrt{1} = 4 $ → Whole → Yellow
5. $ \sqrt{9} = 3 $ → Whole → Yellow
6. $ -\frac{132}{3} = -44 $ → Integer → Green
7. $ 7.43 $ → Terminating → Rational → Blue
8. $ -\sqrt{4} = -2 $ → Integer → Green
9. $ 85 $ → Whole → Yellow
10. $ -0.2 $ → Rational → Blue
11. $ -9.6 $ → Rational → Blue

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Row 6

1. $ 60 $ → Whole → Yellow
2. $ \frac{34}{13} $ → Fraction → Rational → Blue
3. $ \sqrt{61} $ → Not perfect square → Irrational → Red
4. $ 2 $ → Whole → Yellow
5. $ \sqrt{400} = 20 $ → Whole → Yellow
6. $ 826 $ → Whole → Yellow
7. $ \frac{3}{4} $ → Rational → Blue
8. $ -\sqrt{5} $ → Irrational → Red
9. $ \frac{121}{11} = 11 $ → Whole → Yellow
10. $ 7 $ → Whole → Yellow
11. $ \frac{63}{44} $ → Fraction → Rational → Blue
12. $ 4.4 $ → Terminating → Rational → Blue

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Row 7

1. $ 15\pi $ → Irrational → Red
2. $ 5 $ → Whole → Yellow
3. $ \sqrt{22} $ → Not perfect square → Irrational → Red
4. $ \frac{\pi}{3} $ → Multiple of π → Irrational → Red
5. $ 6\pi $ → Irrational → Red
6. $ 0 $ → Whole → Yellow
7. $ 0.75 $ → $ \frac{3}{4} $ → Rational → Blue
8. $ 0^1 = 0 $ → Whole → Yellow
9. $ \sqrt{10} $ → Irrational → Red
10. $ 7\pi $ → Irrational → Red
11. $ 625 $ → Whole → Yellow
12. $ \sqrt{3} $ → Irrational → Red

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Row 8

1. $ -\sqrt{8} = -2\sqrt{2} $ → Irrational → Red
2. $ 10.1 $ → Terminating → Rational → Blue
3. $ -4 $ → Integer → Green
4. $ 3.8 $ → Terminating → Rational → Blue
5. $ \sqrt{21} $ → Irrational → Red
6. $ \sqrt{14.5} $ → Not a perfect square → Irrational → Red
7. $ -\frac{1}{4} $ → Rational → Blue
8. $ 7.83 $ → Terminating → Rational → Blue
9. $ \sqrt{33} $ → Irrational → Red

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Summary of Colors

Now, apply the following coloring rule:
- Whole → Yellow
- Integer (but not whole) → Green
- Rational (but not integer) → Blue
- Irrational → Red

Note: If a number is whole, color yellow (most specific).
If it's integer but not whole (like negative), color green.
If rational but not integer (like fractions, decimals), color blue.
If irrational, color red.

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Final Answer: Color Each Cell

We'll now assign colors to each cell in order.

> Since I can't actually color the image here, I'll list the color for each cell in the same order as the grid.

#### Row 1
1. $ \pi $ → Red
2. $ -\sqrt{64} = -8 $ → Green
3. $ \frac{18}{3} = 6 $ → Yellow
4. $ 780 $ → Yellow
5. $ -\sqrt{16} = -4 $ → Green
6. $ 13 $ → Yellow
7. $ -14 $ → Green
8. $ \frac{70}{7} = 10 $ → Yellow
9. $ \frac{72}{2} = 36 $ → Yellow
10. $ \sqrt{36} = 6 $ → Yellow
11. $ -\sqrt{4} = -2 $ → Green
12. $ 4\pi $ → Red

#### Row 2
1. $ 300 $ → Yellow
2. $ \sqrt{204} $ → Red
3. $ -34 $ → Green
4. $ 1.4 $ → Blue
5. $ \frac{2}{3} $ → Blue
6. $ -8.2 $ → Blue
7. $ 2\pi $ → Red
8. $ 6.81 $ → Blue
9. $ 12.5 $ → Blue
10. $ 0.87 $ → Blue
11. $ -\sqrt{121} = -11 $ → Green
12. $ \sqrt{4} = 2 $ → Yellow

#### Row 3
1. $ 5 $ → Yellow
2. $ \pi $ → Red
3. $ -5 $ → Green
4. $ \sqrt{13} $ → Red
5. $ 8\pi $ → Red
6. $ \sqrt{7} $ → Red
7. $ \pi^2 $ → Red
8. $ 3.7 $ → Blue
9. $ -9.1 $ → Blue
10. $ \pi $ → Red
11. $ 36 $ → Yellow
12. $ 250 $ → Yellow

#### Row 4
1. $ -12 $ → Green
2. $ 5 $ → Yellow
3. $ 216 $ → Yellow
4. $ \sqrt{12} $ → Red
5. $ -10 $ → Green
6. $ -8 $ → Green
7. $ 8 $ → Yellow
8. $ 8 $ → Yellow
9. $ \frac{4}{9} $ → Blue
10. $ \sqrt{63} $ → Red
11. $ 15 $ → Yellow
12. $ 5.12 $ → Blue

#### Row 5
1. $ -1.5 $ → Blue
2. $ 300 $ → Yellow
3. $ -48 $ → Green
4. $ 4 $ → Yellow
5. $ 3 $ → Yellow
6. $ -44 $ → Green
7. $ 7.43 $ → Blue
8. $ -2 $ → Green
9. $ 85 $ → Yellow
10. $ -0.2 $ → Blue
11. $ -9.6 $ → Blue

#### Row 6
1. $ 60 $ → Yellow
2. $ \frac{34}{13} $ → Blue
3. $ \sqrt{61} $ → Red
4. $ 2 $ → Yellow
5. $ 20 $ → Yellow
6. $ 826 $ → Yellow
7. $ \frac{3}{4} $ → Blue
8. $ -\sqrt{5} $ → Red
9. $ 11 $ → Yellow
10. $ 7 $ → Yellow
11. $ \frac{63}{44} $ → Blue
12. $ 4.4 $ → Blue

#### Row 7
1. $ 15\pi $ → Red
2. $ 5 $ → Yellow
3. $ \sqrt{22} $ → Red
4. $ \frac{\pi}{3} $ → Red
5. $ 6\pi $ → Red
6. $ 0 $ → Yellow
7. $ 0.75 $ → Blue
8. $ 0 $ → Yellow
9. $ \sqrt{10} $ → Red
10. $ 7\pi $ → Red
11. $ 625 $ → Yellow
12. $ \sqrt{3} $ → Red

#### Row 8
1. $ -\sqrt{8} $ → Red
2. $ 10.1 $ → Blue
3. $ -4 $ → Green
4. $ 3.8 $ → Blue
5. $ \sqrt{21} $ → Red
6. $ \sqrt{14.5} $ → Red
7. $ -\frac{1}{4} $ → Blue
8. $ 7.83 $ → Blue
9. $ \sqrt{33} $ → Red

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✔ Final Instructions for You

Now that you have the classification, follow these steps:

1. Color the Key:
- Rational → Blue
- Integer → Green
- Whole → Yellow
- Irrational → Red

2. Color Each Cell in the grid according to the above list.

For example:
- $ \pi $ → Red
- $ 6 $ → Yellow
- $ -8 $ → Green
- $ 1.4 $ → Blue

And so on.

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✔ Answer Summary:
Use the color scheme:
- Red for irrational numbers (like $ \pi, \sqrt{2}, \sqrt{3}, \dots $)
- Green for integers (positive/negative whole numbers)
- Yellow for whole numbers (0, 1, 2, 3, ...)
- Blue for rational numbers that are not integers (fractions, decimals)

This completes the task.

Let me know if you'd like a printable version or a visual guide!