Defining Quantities for Modeling
Aligned to N-Q.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
When you model a real situation, you first choose which quantities to measure and how to combine them. A good quantity is measurable, relevant, and makes the comparison you care about fair. Rates and ratios (per person, per square foot) let you compare unequal things.
Worked example
Two towns want to compare crowding. Town A has 9,000 people; Town B has 40,000. Raw counts mislead, so define density = people / area. Town A covers 3 sq mi: 9000/3 = 3000 per sq mi. Town B covers 20 sq mi: 40000/20 = 2000 per sq mi. Town A is more crowded.
Practice questions
- To rank two pizzas by value, what single quantity (a ratio) should you compute?
- A team scored 240 points in 12 games. Define and compute a quantity that lets you compare it to a team with 300 points in 20 games.
- Explain why 'total library books' is a poor quantity for comparing how well two schools serve their students, and give a better one.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Definir cantidades para modelar
Al modelar una situación real, primero eliges qué cantidades medir y cómo combinarlas. Una buena cantidad es medible, relevante y hace justa la comparación que te importa. Las tasas y razones (por persona, por pie cuadrado) permiten comparar cosas desiguales.
Ejemplo: Dos pueblos quieren comparar su congestión. El pueblo A tiene 9,000 personas; el B, 40,000. Los conteos crudos engañan, así que define densidad = personas / área. A cubre 3 mi²: 9000/3 = 3000 por mi². B cubre 20 mi²: 40000/20 = 2000 por mi². El pueblo A está más congestionado.
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