Fraction comparison worksheet with shaded circle and square models for students to match and compare fractions.

Let's solve this step-by-step based on the worksheet provided.

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Task Overview:

Students are asked to:
1. Shade circle and square models to represent the given fractions.
2. Compare the two fractions in each row using <, >, or =.

We'll go through each problem, determine which fraction is larger (or if they're equal), and explain why.

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Step 1: Understanding the Models

- Circles: Divided into equal parts (e.g., halves, thirds, sixths).
- Squares: Also divided into equal parts (e.g., fourths, eighths).
- Shading one part of a shape represents the numerator (top number) over the total number of parts (denominator).

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Now let’s analyze each problem:

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1.

Fractions: $ \frac{1}{2} \quad \text{vs.} \quad \frac{1}{3} $

- A circle divided into 2 parts → shade 1 → half
- A circle divided into 3 parts → shade 1 → one-third

✔ Comparison: $ \frac{1}{2} > \frac{1}{3} $
→ Half is bigger than one-third.

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2.

Fractions: $ \frac{1}{4} \quad \text{vs.} \quad \frac{1}{3} $

- Square divided into 4 → shade 1 → one-fourth
- Square divided into 3 → shade 1 → one-third

✔ $ \frac{1}{4} < \frac{1}{3} $
→ One-fourth is smaller than one-third.

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3.

Fractions: $ \frac{1}{6} \quad \text{vs.} \quad \frac{1}{8} $

- Rectangle divided into 6 → shade 1 → one-sixth
- Rectangle divided into 8 → shade 1 → one-eighth

✔ $ \frac{1}{6} > \frac{1}{8} $
→ Smaller denominator means larger piece.

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4.

Fractions: $ \frac{1}{8} \quad \text{vs.} \quad \frac{1}{2} $

- Circle divided into 8 → shade 1 → one-eighth
- Circle divided into 2 → shade 1 → one-half

✔ $ \frac{1}{8} < \frac{1}{2} $
→ One-eighth is much smaller than one-half.

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5.

Fractions: $ \frac{1}{2} \quad \text{vs.} \quad \frac{1}{4} $

- Square divided into 2 → shade 1 → half
- Square divided into 4 → shade 1 → one-fourth

✔ $ \frac{1}{2} > \frac{1}{4} $

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6.

Fractions: $ \frac{1}{3} \quad \text{vs.} \quad \frac{1}{6} $

- Circle divided into 3 → shade 1 → one-third
- Circle divided into 6 → shade 1 → one-sixth

✔ $ \frac{1}{3} > \frac{1}{6} $
→ One-third is twice as big as one-sixth.

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7.

Fractions: $ \frac{1}{2} \quad \text{vs.} \quad \frac{1}{8} $

- Square divided into 2 → shade 1 → half
- Rectangle divided into 8 → shade 1 → one-eighth

✔ $ \frac{1}{2} > \frac{1}{8} $

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8.

Fractions: $ \frac{1}{4} \quad \text{vs.} \quad \frac{1}{6} $

- Circle divided into 4 → shade 1 → one-fourth
- Circle divided into 6 → shade 1 → one-sixth

✔ $ \frac{1}{4} > \frac{1}{6} $
→ Fourth is bigger than sixth.

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9.

Fractions: $ \frac{1}{3} \quad \text{vs.} \quad \frac{1}{8} $

- Square divided into 3 → shade 1 → one-third
- Rectangle divided into 8 → shade 1 → one-eighth

✔ $ \frac{1}{3} > \frac{1}{8} $

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10.

Fractions: $ \frac{1}{2} \quad \text{vs.} \quad \frac{1}{6} $

- Circle divided into 2 → shade 1 → half
- Circle divided into 6 → shade 1 → one-sixth

✔ $ \frac{1}{2} > \frac{1}{6} $

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11.

Fractions: $ \frac{1}{4} \quad \text{vs.} \quad \frac{1}{8} $

- Rectangle divided into 4 → shade 1 → one-fourth
- Rectangle divided into 8 → shade 1 → one-eighth

✔ $ \frac{1}{4} > \frac{1}{8} $

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12.

Fractions: $ \frac{1}{4} \quad \text{vs.} \quad \frac{1}{8} $

Same as #11.

✔ $ \frac{1}{4} > \frac{1}{8} $

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✔ Final Answers (Fill in the circles):

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{1}{2} > \frac{1}{3} $ |
| 2 | $ \frac{1}{4} < \frac{1}{3} $ |
| 3 | $ \frac{1}{6} > \frac{1}{8} $ |
| 4 | $ \frac{1}{8} < \frac{1}{2} $ |
| 5 | $ \frac{1}{2} > \frac{1}{4} $ |
| 6 | $ \frac{1}{3} > \frac{1}{6} $ |
| 7 | $ \frac{1}{2} > \frac{1}{8} $ |
| 8 | $ \frac{1}{4} > \frac{1}{6} $ |
| 9 | $ \frac{1}{3} > \frac{1}{8} $ |
| 10 | $ \frac{1}{2} > \frac{1}{6} $ |
| 11 | $ \frac{1}{4} > \frac{1}{8} $ |
| 12 | $ \frac{1}{4} > \frac{1}{8} $ |

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🔍 Key Concept:

When comparing unit fractions (fractions with numerator 1):
> The smaller the denominator, the larger the fraction.

Example:
- $ \frac{1}{2} > \frac{1}{3} > \frac{1}{4} > \frac{1}{6} > \frac{1}{8} $

This is because you're dividing a whole into fewer pieces, so each piece is bigger.

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✔ Summary:

All comparisons are based on understanding that a smaller denominator means a larger piece when the numerator is 1.

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