I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.Puedo reconocer cuándo dos cantidades cambian juntas e identificar cuál es la variable independiente y cuál es la variable dependiente.
MissionMisión · Corner KitchenCocina de la esquina · night shiftturno de noche
Cook up the right answer.Cocina la respuesta correcta.
Dinner rush at Corner Kitchen: tickets pile up, the pantry is running low, and the chef needs clear thinking about what depends on what. Sort out each relationship so every order comes out right.
Hora pico de la cena en Corner Kitchen: los pedidos se acumulan, la despensa se está vaciando, y el chef necesita pensar con claridad en qué depende de qué. Aclara cada relación para que cada pedido salga bien.
Word bankBanco de palabras 5 words5 palabrasindependent variable, dependent variable, depends on, …variable independiente, variable dependiente, depende de, …
- independent variablevariable independiente
- The quantity that is chosen or set. It is the input.La cantidad que se elige o se fija. Es la entrada.
- dependent variablevariable dependiente
- The quantity that changes in response to the independent variable. It is the output.La cantidad que cambia en respuesta a la variable independiente. Es la salida.
- depends ondepende de
- One quantity depends on another when changing the first one changes the second. Say it with the responder first: 'The cost depends on the number.'Una cantidad depende de otra cuando cambiar la primera cambia la segunda. Dilo empezando por la que responde: «El costo depende del número».
- quantitycantidad
- Something that can be counted or measured, like 12 muffins or 5 liters.Algo que se puede contar o medir, como 12 muffins o 5 litros.
- table of valuestabla de valores
- A list of matched input and output pairs, one pair in each row.Una lista de pares de entrada y salida que se corresponden, un par en cada fila.
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.
- 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.
- Two quantities are related. Which statement is ALWAYS true?
- The independent variable is always the larger number
- The independent variable is the input used to describe the relationship
- The dependent variable is always measured in dollars
- The independent variable is always listed first in a table
- Give an example where the SAME quantity can be independent in one problem and dependent in another.
- Time is always independent
- Time: chosen when you pick how long to jog, but measured as a result when you run a set distance
- Time is always dependent
- A quantity can never switch roles
- The pizza shop spends $1.15 on cheese per pizza. Which weekly total is correct if it makes 200 pizzas?
- $115
- $201.15
- $230
- $1,150
- Chef Imani needs 96 muffins for a catering order. Each tray makes 12 muffins, and she decides how many trays to bake. Which statement names the variables correctly?
- The number of muffins is independent, because the order says 96.
- Trays are independent; muffin count depends on them.
- Both are independent, because Imani knows both numbers.
- The number 12 is the independent variable.
- Corner Kitchen serves the same number of bowls from every pot of soup. Use the first row to find the rule, then fill in the missing amounts.
- A cook decides how much rice to make, then measures the water it needs. The table shows what he used. Which statement describes the relationship?
- The rice depends on the water: every cup of water needs 2 cups of rice.
- The water depends on the rice: there is always 1 more cup of water than rice.
- Neither depends on the other, because both numbers get bigger.
- The water depends on the rice: every cup of rice needs 2 cups of water.
- Chef Tomás lets a pot of stock simmer. The amount of stock drops by the same amount every 5 minutes, as the table shows. How many liters will be in the pot after 20 minutes?
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.
- Corner Kitchen sells smoothies for $5 each. A customer decides how many to order. Sort each item: is it the independent variable, the dependent variable, or a fixed amount?
- Invent a weather story with two quantities, such as hours and rainfall. Write one question that asks for the independent variable and one that asks for the dependent variable. Solve both with a few input and output pairs.
- 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.
- Mia is describing a catering order. Corner Kitchen charges $6 for each sandwich, and Mia decides how many sandwiches to order.
- Corner Kitchen has 4 ovens. Each oven bakes 9 muffins every hour, and the chef decides how many hours to bake. Hana names the variables.
- A table shows batches of jam and jars filled: 1 batch, 8 jars; 2 batches, 16 jars; 3 batches, 24 jars. The cook decides how many batches to make. Ahmed names the variables.
- Chef Hana decides how many bags of flour to open. Then she counts how many loaves she can make. Leilani says the bags of flour are the independent variable. Dmitri says the loaves are independent, because customers want loaves. Who is right?
- Leilani: Hana chooses the bags, and the number of loaves depends on them.
- Dmitri: the quantity the customers care about is independent.
- Both are right, because the bags and the loaves depend on each other equally.
- Neither: the size of a flour bag is the independent variable.
- What is the best next move?
- Call the temperature independent, because it is what the scientist wants to find out.
- Try the sentence "the ___ depends on the ___" both ways and keep the one that makes sense.
- Say time is not a variable, because the scientist does not change it.
- Say the two quantities do not affect each other.
- 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.
- A baker uses 6 apples for each pie and decides how many pies to bake. Which sentence is correct?
- The number of pies baked depends on the number of apples used.
- The number 6 depends on the number of pies.
- The number of apples used depends on the number of pies baked.
- The apples and the pies do not depend on each other.
- A bakery bakes the same number of cookies on every tray, as the table shows. How many trays does the bakery need to bake 144 cookies?
- A food truck sells tacos for $3 each and is open 8 hours a day. A customer decides how many tacos to buy. Which two quantities are the variables in the relationship between tacos and cost?
- The number of tacos bought and the total cost
- The price of one taco and the number of tacos bought
- The hours the truck is open and the total cost
- The price of one taco and the hours the truck is open
- A kitchen adds the same number of scoops of spice for each bag of rice, as the table shows. How many scoops go with ONE bag?
- Priya tests one oven in two experiments. In Experiment 1 she chooses how many minutes the oven heats and measures its temperature. In Experiment 2 she chooses a temperature and measures how many minutes the oven needs to reach it. Which statement is true?
- Minutes is independent in both experiments, because time always comes first.
- Minutes is independent in Experiment 1 and dependent in Experiment 2.
- Temperature is independent in both experiments, because Priya cares about it.
- Minutes is dependent in Experiment 1 and independent in Experiment 2.
- Think of a relationship from a kitchen, a restaurant or a bakery. Name the two quantities, say which one is independent and which one is dependent, and write the sentence '___ depends on ___'. Then give two examples of an input and its output.