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This question involves creating a new scale drawing based on a different ratio than the original one.

### Problem breakdown:
1. **Original Scale**: The current scale from the playground to the drawing is \( 12 \, \text{in.} \) (real-life inches) to 1 unit length in the drawing.
2. **New Scale Requirement**: You are asked to create a new scale drawing where the new scale is \( 20 \, \text{in.} \) (real-life inches) to 1 unit length in the drawing.
3. **Purpose**: To justify why your new drawing is accurate based on the given change in scale.

### Steps to create a new scale drawing:
1. **Ratio Change**: The new scale increases the ratio from 12 inches to 20 inches per unit length, meaning the drawing will shrink proportionally.
   
   The scaling factor from the original drawing to the new one can be found by comparing the two ratios:
   \[
   \text{Scaling factor} = \frac{12}{20} = \frac{3}{5}.
   \]
   
2. **Implication**: The new drawing will be **smaller** than the original. Specifically, the length of every feature in the new drawing will be \( \frac{3}{5} \) of the length in the original drawing.

### Justification:
- The new scale drawing is accurate because the lengths in the drawing are proportional to the real dimensions, but reduced by the factor \( \frac{3}{5} \). This ensures that the new drawing maintains the correct proportions relative to the real sandbox but reflects the new ratio of 20 inches to 1 unit length.

Would you like more details or have any other questions about this? Here are some related questions:

1. How do you convert between different scale ratios?
2. What happens to areas when changing the scale of a drawing?
3. How would you apply this to irregularly shaped objects, like buildings?
4. What are some practical uses of scale drawings in real life?
5. How would the perimeter of the sandbox change in the new drawing?

**Tip**: When adjusting a scale, make sure to apply the same factor to all dimensions (length, width, height) to maintain accuracy.

The scale drawing at the right shows a sandbox on a playground. The scale from the playground to the drawing is 12 in. to 1 unit length. Draw another scale drawing of the sandbox so that the scale from the playground to the new drawing is 20 in. to 1 unit length. Justify why your drawing is accurate.

Learn how to create a new scale drawing for a sandbox where the scale changes from 12 inches to 1 unit length to 20 inches to 1 unit length. This math problem explores ratios and proportionality, perfect for middle school students in Grades 6-8.

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