Ratio Reasoning: Convert Measurements within the Same System Challenge

Grade 6 Math · Unit 3 Challenge Studio (6.AT.3c) · Lesson 3-6
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I can use ratio reasoning to convert between units within the same measurement system.Puedo usar el razonamiento con razones para convertir unidades dentro del mismo sistema de medidas.

MissionMisión · Orbit StationEstación orbital · night shiftturno de noche

Mission control needs your math.El control de la misión necesita tus matemáticas.

A docking alarm is blinking and the supply logs use mixed units. Convert each measurement inside its own system to the unit the controls need before the shuttle arrives.

Una alarma de acoplamiento parpadea y los registros de suministros usan unidades mezcladas. Convierte cada medida dentro de su propio sistema a la unidad que piden los controles antes de que llegue el transbordador.

Word bankBanco de palabras 4 words4 palabrasconvert, unit ratio, measurement system, …convertir, razón unitaria, sistema de medidas, …
convertconvertir
To change a measurement to another unit without changing the amount.Cambiar una medida a otra unidad sin cambiar la cantidad.
unit ratiorazón unitaria
A ratio that compares an amount to exactly 1 unit, like 12 inches : 1 foot.Una razón que compara una cantidad con exactamente 1 unidad, como 12 pulgadas : 1 pie.
measurement systemsistema de medidas
A family of units that go together, like customary or metric units.Una familia de unidades que van juntas, como las unidades usuales o las métricas.
perpor
For each one, as in 12 inches per foot.Por cada uno, como en 12 pulgadas por pie.

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. Michael's mother is setting four fence posts. Each post needs 250 ounces of concrete mix, one bag holds 80 ounces, and each bag needs 1 quart of water. How many bags and how many cups of water does she need? Show your conversions.
  3. A coolant tank on the station holds 3.5 liters. The double number line shows liters and milliliters. A pump moves 250 milliliters each cycle. How many cycles does it take to empty the tank?
  4. A solar-array cable is 480 centimeters long. The hatch connector needs 5 meters. Is the cable long enough?
    • Yes, because 480 is more than 5.
    • No, the cable is 20 cm too short.
    • Yes, with 4.3 m of cable to spare.
    • No, the cable is 2 m too short.
  5. The cargo log uses kilograms and grams. Fill in the missing amounts so every row names the same mass in both units.
  6. A water pod holds 3 gallons. The crew fills cups that hold 1 pint. There are 4 quarts in 1 gallon and 2 pints in 1 quart. How many pints are in the pod?

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. Match each measurement with the equal measurement in a different unit.
  2. Make a measurement card for something in your classroom, like a desk or a door. Write its length in feet and in inches. State the unit ratio, show both directions, and add one wrong card that uses the wrong operation. Explain how to catch it.
  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. A technician converted a coolant reading. One step goes wrong. Tap the first step that is wrong.
  2. A cargo officer converted pounds to ounces. One step goes wrong. Tap the first step that is wrong.
  3. A pilot converted gallons to pints. One step goes wrong. Tap the first step that is wrong.
  4. Kai says 3.2 kilometers is 3,200 meters. Lena says 3.2 kilometers is 0.0032 meters. Who is right?
    • Kai: meters are smaller, so multiply by 1,000.
    • Lena: she divided, since kilometers are bigger.
    • Both, because each one uses the factor 1,000.
    • Neither, because 3.2 km is only 32 meters.
  5. What is the best next move?
    • Put them in order by the numbers as written: 0.75, 700, 0.8.
    • Change only Jar P to milliliters and compare it with Jar Q.
    • Change Jar Q to liters by multiplying 700 by 1,000 first.
    • Write all three in the same unit first, then order them.
  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 sample box on the station has a mass of 7.5 kilograms. What is the mass in grams?
  2. An oxygen tank reads 2,400 milliliters. How many liters is that?
  3. A station route is 0.8 kilometers, a second route is 750 meters, and a third is 8,500 centimeters. Which route is the longest?
    • The 750 m route, since 750 is bigger than 0.8
    • The 8,500 cm route, since 8,500 is biggest
    • All three routes are exactly equal in length
    • The 0.8 km route, once all are in meters
  4. A spool holds 45 meters of tether cable. Each tether needs 150 centimeters. How many tethers can be cut from the spool?
  5. Which unit ratio converts feet to yards?
    • 1 foot : 3 yards
    • 3 feet : 1 yard
    • 12 feet : 1 yard
    • 3 yards : 1 foot
  6. Write your own Orbit Station problem that needs a conversion inside one measurement system. State the unit ratio, say whether you multiply or divide and why, and write your answer as a full sentence with its unit.