Ratio Reasoning: Convert Measurements Between Systems

6.AT.3 · Unit 3 · Lesson 7

Name   Period

Objectives / Objetivos

Content Objective: I can use ratio reasoning to convert measurements between the customary and metric systems.

Language Objective: I can explain a conversion between systems using the words conversion factor, approximately, customary, and metric.

Key Idea / Idea clave

Converting Measurements Between Systems. 1. Identify the conversion ratio connecting systems (e.g. 1 in ≈ 2.54 cm, 1 kg ≈ 2.2 lbs). 2. Set up a ratio table or proportion aligning customary and metric units. 3. Multiply or divide by the conversion factor to compute the equivalent measurement

I Notice / Observo

  • I notice one measurement uses a ___ unit and the other uses a ___ unit.
  • I notice the two numbers cannot be compared until they share a ___.

I Wonder / Me pregunto

  • I wonder which amount is actually bigger once I ___ them.

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Convert Measurements Between Systems
Convertir medidas entre sistemas		Rewriting a customary measurement as a metric one, or the reverse, so two amounts can be compared.
Reescribir una medida usual como métrica, o al revés, para poder comparar dos cantidades.
Conversion factor
Factor de conversión		The ratio that links a unit in one system to a unit in the other, such as 1 mile to about 1.609 kilometers.
La razón que relaciona una unidad de un sistema con una del otro, como 1 milla a unos 1.609 kilómetros.
Customary system
Sistema usual		The measurement system used in the United States: inches, feet, miles, ounces, pounds, cups, quarts, gallons.
El sistema de medidas que se usa en Estados Unidos: pulgadas, pies, millas, onzas, libras, tazas, cuartos y galones.
Metric system
Sistema métrico		The measurement system used in most of the world, built on tens: centimeters, meters, kilometers, grams, kilograms, liters.
El sistema de medidas que se usa en casi todo el mundo, basado en decenas: centímetros, metros, kilómetros, gramos, kilogramos y litros.
Approximately
Aproximadamente		Close to, but not exactly equal. Conversions between systems are almost always approximate, so they use the ≈ sign.
Cercano, pero no exactamente igual. Las conversiones entre sistemas casi siempre son aproximadas y usan el signo ≈.
Ratio table
Tabla de razones		A table of equal ratios used to scale a conversion factor up to the amount you actually need.
Una tabla de razones iguales que sirve para escalar un factor de conversión hasta la cantidad que necesitas.

Practice Preview / Vista previa de práctica

  1. 1 kilometer ≈ 0.6 mile. About how many miles is 5 kilometers?
    1. 3 miles
    2. 5.6 miles
    3. 8 miles
    4. 30 miles
  2. 1 pound ≈ 0.45 kilogram. Complete the ratio table, then use it to place a 31-pound dog.
  3. A dog weighs 31 pounds. Flea medicine comes in packages for 4–10 kg, 10–25 kg, and 25–40 kg. Which package is correct?
    1. The 10–25 kg package
    2. The 4–10 kg package
    3. The 25–40 kg package
    4. None — 31 is above every range
  4. Find the error
    1. Step 1: Setup — Which is longer, 5 kilometers or 5 miles? (1 km ≈ 0.6 mi)
    2. Step 2: Step 1 — Both numbers are 5.
    3. Step 3: Step 2 — The units are different, so I compare the numbers: they are equal.
    4. Step 4: Step 3 — 5 kilometers is the same distance as 5 miles.

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: