Use a simplified distance scale

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Diagram length equals represented million kilometers divided by million kilometers per centimeter. Formula: a/b. Variable key: a = represented distance (million km), b = scale (million km/cm)
• Distinct worked inputs and result: A distinct model uses 10 million km/cm for 70 million km: 70/10=7 cm.
• Assessment case 1: Supplied case 1: represented distance (million km)=100; scale (million km/cm)=20, using the explicitly named quantities. Diagram length equals represented million kilometers divided by million kilometers per centimeter. What result follows?
• Assessment case 2: Supplied case 2: represented distance (million km)=180; scale (million km/cm)=30, using the explicitly named quantities. Diagram length equals represented million kilometers divided by million kilometers per centimeter. What result follows?
• Assessment case 3: Supplied case 3: represented distance (million km)=240; scale (million km/cm)=40, using the explicitly named quantities. Diagram length equals represented million kilometers divided by million kilometers per centimeter. What result follows?
• Assessment case 4: Supplied case 4: represented distance (million km)=150; scale (million km/cm)=25, using the explicitly named quantities. Diagram length equals represented million kilometers divided by million kilometers per centimeter. What result follows?
• Assessment case 5: Supplied case 5: represented distance (million km)=360; scale (million km/cm)=60, using the explicitly named quantities. Diagram length equals represented million kilometers divided by million kilometers per centimeter. What result follows?
• Assessment case 6: Supplied case 6: represented distance (million km)=400; scale (million km/cm)=50, using the explicitly named quantities. Diagram length equals represented million kilometers divided by million kilometers per centimeter. What result follows?

Learn the idea

A scale converts a represented distance to a diagram length. These supplied distances are fictional model values; actual solar-system diagrams often distort distances and sizes differently.

Diagram length equals represented million kilometers divided by million kilometers per centimeter. The formula in the supplied model is a/b. Variable key: a = represented distance (million km), b = scale (million km/cm). Divide real-model distance by scale distance per centimeter. This scale covers distance, not necessarily object size.

A distinct model uses 10 million km/cm for 70 million km: 70/10=7 cm. Use the same scale for every compared distance. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with represented distance (million km)=101; scale (million km/cm)=20. Expected result: 5.05 cm. Explain what changes and keep this assumption: Use the same scale for every compared distance.

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