Ratio Reasoning: Convert Measurements Between Systems Challenge

Grade 6 Math · Unit 3 Challenge Studio (6.AT.3c) · Lesson 3-7
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I can use ratio reasoning to convert measurements between the customary and metric systems.Puedo usar el razonamiento con razones para convertir medidas entre el sistema usual y el sistema métrico.

MissionMisión · Robot LabLaboratorio de robots · night shiftturno de noche

Test, measure, improve.Prueba, mide, mejora.

Night shift at Robot Lab: one wall of the test track is marked in miles, the other in kilometers, and the scoreboard flashes both. Compare the robots fairly before the morning demo.

Turno de noche en el Laboratorio de Robots: una pared de la pista de pruebas está marcada en millas, la otra en kilómetros, y el marcador muestra las dos. Compara los robots de forma justa antes de la demostración de la mañana.

Word bankBanco de palabras 5 words5 palabrasconversion factor, customary system, metric system, …factor de conversión, sistema usual, sistema métrico, …
conversion factorfactor de conversión
The ratio that links a unit in one system to a unit in the other, such as 1 kg to about 2.2 lb.La razón que une una unidad de un sistema con una unidad del otro, como 1 kg con unas 2.2 lb.
customary systemsistema usual
The measurement system used in the United States: inches, miles, pounds and quarts.El sistema de medidas que se usa en Estados Unidos: pulgadas, millas, libras y cuartos de galón.
metric systemsistema métrico
The measurement system used in most of the world, built on tens: centimeters, kilometers, kilograms and liters.El sistema de medidas que se usa en casi todo el mundo, basado en decenas: centímetros, kilómetros, kilogramos y litros.
approximately (≈)aproximadamente (≈)
Close to, but not exactly equal. A result from a rounded factor is written with ≈.Cercano, pero no exactamente igual. Un resultado con un factor redondeado se escribe con ≈.
reasonablenesssentido lógico
Checking that the size of an answer makes sense for the situation.Revisar que el tamaño de una respuesta tenga sentido en la situación.

Stage 1 of 5Etapa 1 de 5

Start StrongEmpieza fuerte

Each rung is harder than the last, and the numbers change every time.

Cada peldaño es más difícil que el anterior y los números cambian cada vez.

  1. 6 fresh problems with new numbers each time (interactive only).

Stage 2 of 5Etapa 2 de 5

Stretch Your ThinkingAmplía tu pensamiento

Plan, solve, then check that your answer makes sense.

Planea, resuelve y revisa que tu respuesta tenga sentido.

  1. Find the error
  2. The Golden Gate Bridge can hold about 35,924,000 pounds. An average midsize car weighs about 1,524 kilograms. Using 1 kilogram ≈ 2.2 pounds, about how many midsize cars could be on the bridge at one time? Explain each step, and say why your answer is an estimate.
  3. Fill in the table
  4. Priya ships a robot kit by air. It has a 3.5 kg sensor pack, a 6 kg motor set, and a 9.5 kg frame. The airline limit is 40 lb. Use 1 kg ≈ 2.2 lb. How does the kit compare with the limit?
    • Under the limit: 19 is less than 40
    • Over the limit by about 1.8 pounds
    • Under the limit by about 31 pounds
    • Under the limit by about 69 kilograms
  5. Sofía's delivery cart drives a 90-kilometer test route in 2 hours at a steady speed. The track limit is 25 mi/h. Use 1 km ≈ 0.6 mi. By about how many mi/h is the cart faster than the limit?
  6. Imani fills 16 robots with 1.25 L of coolant each. The lab buys coolant in 1-quart bottles, and 1 L ≈ 1.06 qt. How many bottles must Imani buy so every robot gets its full amount?
    • 19 bottles
    • 20 bottles
    • 21 bottles
    • 22 bottles
  7. Robot Lab inventory sheet. Change each part's mass to the OTHER system with 1 kg ≈ 2.2 lb. Type the number only.

Stage 3 of 5Etapa 3 de 5

InvestigateInvestiga

Use the model to test an idea. Then check it.

Usa el modelo para probar una idea. Luego compruébala.

  1. Robot Lab checks every conversion before it goes on a label. Use 1 mi ≈ 1.6 km, 1 kg ≈ 2.2 lb, 1 L ≈ 1.06 qt and 1 in = 2.54 cm. Sort each claim.
  2. Write a packing label for an expedition tool that shows its length in inches and in centimeters. State the conversion factor, show both directions, and mark any rounded answer with approximately.
  3. 4 fresh problems with new numbers each time (interactive only).

Stage 4 of 5Etapa 4 de 5

Find and FixEncuentra y corrige

Somebody made a mistake. Find the step and fix it.

Alguien cometió un error. Encuentra el paso y corrígelo.

  1. Aisha changes a 33-pound battery to kilograms. She uses 1 kg ≈ 2.2 lb. Tap the first step where her work goes wrong.
  2. Mateo needs a cable at least 30 cm long. The only cable in the bin is labeled 12 in. Use 1 in = 2.54 cm. Tap the first step that goes wrong.
  3. Ravi changes 8 liters of paint to quarts with the label 1 L ≈ 1.06 qt. Tap the first step that goes wrong.
  4. A test rig weighs 150 lb. Kofi changes it to kilograms. He multiplies by 0.45 (1 lb ≈ 0.45 kg) and gets 67.5 kg. Lena divides by 2.2 (1 kg ≈ 2.2 lb) and gets about 68.2 kg. Who is right?
    • Only Kofi. Multiplying is the only correct way to convert it.
    • Only Lena. Dividing is the only correct way to convert it.
    • Both. Each uses a rounded factor, so answers differ a little.
    • Neither. The answers differ, so one of them must be a mistake.
  5. What is the best next move?
    • Use the fact to write both lengths in one unit, then compare.
    • Compare 30 and 70. Since 70 is greater, the board is longer.
    • Say they are equal, because both are measures of length.
    • Say they cannot be compared: one is customary, one is metric.
  6. 1 fresh problem with new numbers each time (interactive only).

Stage 5 of 5Etapa 5 de 5

Prove Your UnderstandingDemuestra tu comprensión

Say how sure you are, solve, then create a problem of your own.

Di qué tan seguro estás, resuelve y luego crea un problema tuyo.

  1. A courier robot must drive 12 km to a partner lab in Canada. Use 1 km ≈ 0.6 mi. About how far is that in miles?
    • 7.2 mi
    • 12.6 mi
    • 20 mi
    • 72 mi
  2. Robot Lab's chart says 1 in = 2.54 cm is exact. The factors 1 mi ≈ 1.6 km, 1 kg ≈ 2.2 lb and 1 L ≈ 1.06 qt are rounded. Which sentence may use an equals sign?
    • 5 miles = 8 km
    • 5 kg = 11 pounds
    • 5 in = 12.7 cm
    • 5 liters = 5.3 qt
  3. Camila can run either test course at the lab. One course is 5 mi long and the other is 8 km long. Use 1 mi ≈ 1.6 km. Which course is longer?
    • The 8 km course, because 8 is more than 5.
    • They are about the same length once converted.
    • The 5 mi course, since a mile is longer than a km.
    • They cannot be compared, since the units differ.
  4. A water tank at the lab holds 53 qt. Each robot test uses 2 L. Use 1 L ≈ 1.06 qt. How many full tests can the tank supply?
  5. A robot arm can lift at most 10 kg. In a lab test, a scale reads 24.2 lb for the load on the arm. Use 1 kg ≈ 2.2 lb. By how many kilograms is the load over the arm's limit?
  6. Create your own Robot Lab conversion problem. Pick a measurement in one system and a conversion factor, then change it to the other system. Show your work, write = or ≈ correctly, and explain why your answer is reasonable.