Choosing Quantities to Model
Aligned to N-Q.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
When you model a situation, decide which measurable quantities matter and what units to report them in. A well-chosen quantity makes comparisons fair and meaningful.
Worked examples
Example 1
To compare two pizzas' value, price alone is misleading. Define price per square inch = price / (π × r^2). A $12 pizza of radius 7 in costs 12 / (π × 49) ≈ $0.078 per square inch.
Example 2
To compare job offers, salary alone misleads. Define take-home per hour = (net pay) / (hours actually worked).
Example 3
The quantity you choose is the model. Ranking schools by average score and by score growth produces different winners.
Practice questions
- Suggest a quantity to fairly compare the fuel efficiency of two cars.
- What quantity would fairly compare crowding in two different-sized classrooms?
- Name a quantity to measure how affordable apartments are across cities.
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
Elegir Cantidades para Modelar
Al modelar una situación, decide qué cantidades medibles importan y en qué unidades reportarlas. Una cantidad bien elegida hace que las comparaciones sean justas y con sentido.
Ejemplo 1: Para comparar el valor de dos pizzas, el precio por sí solo engaña. Define precio por pulgada cuadrada = precio / (π × r^2). Una pizza de $12 con radio 7 in cuesta 12 / (π × 49) ≈ $0.078 por pulgada cuadrada.
Ejemplo 2: Para comparar ofertas de trabajo, el salario solo engaña. Define el ingreso neto por hora = (pago neto) / (horas realmente trabajadas).
Ejemplo 3: La cantidad que eliges es el modelo. Clasificar escuelas por promedio y por mejora del promedio produce ganadores distintos.
More Number & Quantity lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required