I can use a table and a graph to determine and analyze the relationship between two variable quantities.Puedo usar una tabla y una gráfica para determinar y analizar la relación entre dos cantidades variables.
MissionMisión · Rooftop GardenJardín en la azotea · night shiftturno de noche
Grow your skills.Haz crecer tus habilidades.
A storm rolls over the Rooftop Garden at night. The barrels are filling at different rates, and the graphs on the shed wall are smudged. Rebuild each one and decide which hose to trust.
Una tormenta pasa de noche sobre el Jardín de la Azotea. Los barriles se llenan a ritmos distintos y las gráficas de la pared del cobertizo están borrosas. Reconstruye cada una y decide en cuál manguera confiar.
Word bankBanco de palabras 5 words5 palabrasgraph, ordered pair, axis, …gráfica, par ordenado, eje, …
- graphgráfica
- A picture on a coordinate plane that shows how two quantities are related. Each point is a pair of values.Un dibujo en un plano de coordenadas que muestra cómo se relacionan dos cantidades. Cada punto es un par de valores.
- ordered pairpar ordenado
- Two numbers (x, y) that name one point. The independent variable comes first.Dos números (x, y) que nombran un punto. La variable independiente va primero.
- axiseje
- One of the two number lines that frame a graph. Each axis is labeled with a quantity.Una de las dos rectas numéricas que enmarcan una gráfica. Cada eje se rotula con una cantidad.
- rate of changetasa de cambio
- How much y changes each time x goes up by 1.Cuánto cambia y cada vez que x sube 1.
- originorigen
- The point (0, 0) where the two axes meet.El punto (0, 0) donde se cruzan los dos ejes.
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.
- Nakai's savings account has a principal of $750 and earns 3.5% simple interest each year. How much interest does Nakai earn in one year?
- $3.50
- $26.25
- $75.00
- $262.50
- After 10 minutes, the Sandia Peak tram has traveled 12,000 feet. The whole ascent is 18,000 feet. How much farther must it travel to reach the top?
- 1,200 feet
- 5,000 feet
- 6,000 feet
- 12,000 feet
- A second tram travels 900 feet per minute. If both trams are graphed on the same axes (minutes vs. feet), how do the graphs compare?
- The 900 ft/min line rises more steeply
- The two lines are identical
- The Sandia Peak line (1,200 ft/min) rises more steeply than the 900 ft/min line
- The 900 ft/min line goes downward
- Nia's rain barrel fills at a steady rate. The graph shows these (hours, liters) points: (1, 8), (2, 16), (3, 24) and (4, 32). Which ordered pair is also on the graph?
- (48, 6)
- (6, 14)
- (6, 48)
- (6, 40)
- Two hoses fill barrels at steady rates. Hose A's points are (1, 4), (2, 8), (3, 12). Hose B's points are (1, 7), (2, 14), (3, 21). After 6 hours, how many more liters has hose B delivered than hose A?
- A sprinkler uses 12 liters of water every hour. Fill in each missing number, with hours as x and liters as y.
- A drip line delivers 7 liters every hour. On a graph of (hours, liters), which ordered pair does NOT fit this relationship?
- (6, 40)
- (3, 21)
- (5, 35)
- (9, 63)
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.
- A graph shows hours on the horizontal axis and liters on the vertical axis. Match each ordered pair to what it means.
- Make a graph riddle. Choose a steady rate and give only words and ONE ordered pair, such as 'a graph through the origin and (4, 20)'. Ask a classmate for the point at a new hour. Write your answer and explain how to find it with the rate of change. Then say what changes if the rate doubles.
- 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.
- Seed packets cost $4 each. Rosa plots the point for 3 packets on a graph with packets on the horizontal axis and cost on the vertical axis.
- A rain gauge collects 5 liters every hour. Kofi wants the point for 3 hours, using the first row: 1 hour, 5 liters.
- A garden graph has hours on the horizontal axis and liters on the vertical axis. Each grid line going up is worth 5 liters. Linh reads a point that is 4 hours across and 3 grid lines up.
- Barrel A gains 4 liters an hour. Barrel B gains 6 liters an hour. Both graphs start at (0, 0) on the same axes. Amir says B's graph is steeper. Ines says A's is steeper because 4 comes first. Who is right?
- Ines: the rate that is written first is steeper.
- Both are the same, because both graphs go up.
- Neither: steepness depends on where the graph starts.
- Amir: B’s rate is greater, so its graph is steeper.
- What is the best next move?
- Add 4 to the last y-value: 270 + 4.
- Multiply 10 by the last y-value: 10 × 270.
- Find how many miles go with 1 hour, then use that change for 10 hours.
- Say the graph cannot tell you, because 10 is not a plotted point.
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.
- On a graph, minutes are on the horizontal axis and liters are on the vertical axis. Which ordered pair shows 12 liters after 3 minutes?
- (12, 3)
- (3, 12)
- (3, 4)
- (3, 15)
- A graph of a steady relationship goes through the origin and the point (4, 28). What is the y-value when x is 9?
- The graph shows the points (1, 6), (2, 12), (3, 18) and (4, 24) for liters of water over hours. What is the rate of change?
- 24 liters per hour
- 4 liters per hour
- 1 liter per hour
- 6 liters per hour
- Hose C's graph goes through the origin and the point (5, 35). Hose D adds 2 more liters every hour than hose C, and also starts at the origin. How many liters has hose D delivered after 5 hours?
- An empty barrel starts to fill at a steady rate. Why does its graph of (hours, liters) include the point (0, 0)?
- Every graph has to start at (0, 0).
- At 0 hours, the empty barrel holds 0 L.
- The origin is where the axes are labeled.
- The first hour always has 0 liters.
- Choose a garden situation with a steady rate, such as liters per hour or dollars per packet. Give three ordered pairs for your graph, say what one point means in words, and explain what the rate of change tells you.