Ratio Reasoning: Convert Measurements Between Systems
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 / Término | Definition / 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. A rounded conversion factor gives an approximate result, written with ≈; an exact conversion uses =. Cercano, pero no exactamente igual. Un factor de conversión redondeado da un resultado aproximado, escrito con ≈; una conversión exacta usa =. |
| 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
Read each task. Show your work in the spaces provided and explain how you know.
1. 1 kilometer ≈ 0.6 mile. About how many miles is 5 kilometers?
- A 3 miles
- B 5.6 miles
- C 8 miles
- D 30 miles
Answer:
2. 1 pound ≈ 0.45 kilogram. Complete the ratio table, then use it to place a 31-pound dog.
Complete each empty cell. Show your reasoning below.
| Pounds | Kilograms |
|---|---|
| 1 | 0.45 |
| 10 | |
| 30 | |
| 40 |
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?
- A The 4–10 kg package
- B The 10–25 kg package
- C The 25–40 kg package
- D None — 31 is above every range
Answer:
4. Find the error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: