Write Equations to Represent Relationships Between Two Variables Challenge

Grade 6 Math · Unit 9 Challenge Studio (6.AT.11) · Lesson 9-3
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I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.Puedo escribir una ecuación a partir de una tabla o una gráfica para representar la relación entre las variables dependiente e independiente.

MissionMisión · Orbit StationEstación orbital · night shiftturno de noche

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

Alarm on Orbit Station: a data glitch has scrambled the mission log. Rebuild each equation from tables and clues, define every variable, and check each one against more than one row.

Alarma en la Estación Órbita: una falla de datos revolvió el registro de la misión. Reconstruye cada ecuación con tablas y pistas, define cada variable y comprueba cada una con más de una fila.

Word bankBanco de palabras 5 words5 palabrasequation, variable, rate, …ecuación, variable, tasa, …
equationecuación
A math sentence with an equals sign, like d = 9m, that shows how two quantities are related.Una oración matemática con un signo igual, como d = 9m, que muestra cómo se relacionan dos cantidades.
variablevariable
A letter for a quantity that can change.Una letra para una cantidad que puede cambiar.
ratetasa
A fixed amount for every one unit, like 9 kilometers per minute.Una cantidad fija por cada una unidad, como 9 kilómetros por minuto.
define the variablesdefinir las variables
Say exactly what each letter stands for, like 'Let m = minutes'.Decir exactamente qué representa cada letra, como «Sea m = minutos».
constantconstante
A number in an equation that never changes, like the 9 in d = 9m.Un número en una ecuación que nunca cambia, como el 9 en d = 9m.

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. Miguel wants the cost of a full year (12 months) at Recreation World. Using c = 24.95m, what is the total?
    • $36.95
    • $249.50
    • $299.40
    • $300.00
  2. A different gym charges $19.95 per month. How does Miguel's equation change for this gym?
    • The variable changes: c = 24.95x instead of c = 24.95m
    • The rate changes: c = 19.95m instead of c = 24.95m
    • The operation changes: c = 19.95 + m
    • Nothing changes — all gyms have the same equation
  3. What is the benefit of an equation over a table for the membership costs?
    • The equation lists more rows than the table
    • The equation is the only representation that shows the cost increasing
    • The table is always wrong and the equation is always right
    • The equation gives the total cost for ANY number of months, not just the rows listed
  4. A supply drone leaves Orbit Station and flies at a steady speed. The table shows how far it has flown. Which equation matches, with m = minutes and d = kilometers flown?
    • d = m + 8
    • d = 9m
    • m = 9d
    • d = 36m
  5. A water recycler makes 2.5 liters of clean water each day, so w = 2.5d. Here d is the number of days and w is the liters made. A supply pod needs 40 liters to launch. How many days must the recycler run?
  6. A solar panel makes energy by the equation e = 18h, where h is the hours of sunlight and e is the energy units made. Fill in each missing number.
  7. An empty cargo pod always adds the same extra mass to whatever it carries. The table shows the cargo and the total pod mass. Which equation matches?
    • m = 4c
    • m = 5c
    • c = m + 4
    • m = c + 4

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 situation to the equation that models it.
  2. Create two booth price rules, each with a different rate. Define the variables and write both equations. Complete a list of pairs for 1, 2 and 3 items. Then say which booth is the better deal for 10 items, and how the equations tell you without extending your list.
  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 fuel pump on the station uses 6 liters every minute. Zainab writes an equation, with m = minutes and f = liters of fuel used.
  2. The station uses 3 oxygen canisters every day. Luca writes an equation, with d = days and c = canisters used.
  3. A table shows a solar panel: 2 hours, 30 energy units; 4 hours, 60 units. Imani finds the rate, with h = hours and e = energy units.
  4. A table pairs x and y like this: (1, 3), (2, 6), (3, 9), (4, 12). Lena says y = x + 2, because 1 + 2 = 3. Omar says y = 3x. Who is right?
    • Omar: y = 3x works in every row.
    • Lena: y = x + 2 matches the first row.
    • Both: both equations give 3 when x = 1.
    • Neither: the equation should be y = 12x.
  5. What is the best next move?
    • Write c = 4 + n.
    • Write n = 4c.
    • Write c = 12n, using the cost in the first row.
    • Test 4 in another row; write c = 4n.
  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 rover drives 15 meters each minute. Which choice defines the variables correctly?
    • Let m = minutes and d = 15 meters.
    • Let m = a number and d = another number.
    • Let m = minutes and d = total meters driven.
    • Let r = the rover and m = minutes.
  2. A crew meal costs $3.25 per person, so c = 3.25n, where n is the number of people and c is the cost in dollars. What is c when n is 12?
  3. The table shows how y depends on x. Which equation matches?
    • y = x + 5
    • y = 3.5x
    • y = x + 7
    • y = 5x
  4. A drone's battery charges by p = 12h, where h is the hours charging and p is the percent of charge. For how many hours must it charge to reach 96 percent?
  5. Which situation matches the equation y = x + 6?
    • A pod's mass is 6 times its cargo.
    • Mass is 6 tonnes more than cargo.
    • A pod's cargo is 6 tonnes more than its mass.
    • A pod costs $6 for each tonne of cargo.
  6. Write a situation about life on a space station that has a steady rate. Define the variables, write an equation, and use it to find one value. Explain what each part of your equation means using the words variable and rate.