I can write and evaluate numbers in exponent form using a base and a power.Puedo escribir y evaluar números en forma exponencial usando una base y una potencia.
MissionMisión · Summit TrailSendero a la cumbre · night shiftturno de noche
Every checkpoint gets you higher.Cada punto de control te lleva más alto.
Clouds are rolling in over the ridge. The rangers need quick, careful counts of routes, lamps and steps, and every power has to be evaluated correctly. Look closely at the bases and exponents.
Las nubes avanzan sobre el risco. Los guardabosques necesitan conteos cuidadosos de rutas, lámparas y escalones, y cada potencia debe evaluarse correctamente. Mira bien las bases y los exponentes.
Word bankBanco de palabras 5 words5 palabrasexponent, base, power, …exponente, base, potencia, …
- exponentexponente
- The small raised number that tells how many times the base is used as a factor.El número pequeño elevado que dice cuántas veces se usa la base como factor.
- basebase
- The number that gets multiplied by itself.El número que se multiplica por sí mismo.
- powerpotencia
- A number written with a base and an exponent, like 2³.Un número escrito con una base y un exponente, como 2³.
- evaluateevaluar
- To find the value of an expression.Hallar el valor de una expresión.
- repeated multiplicationmultiplicación repetida
- Multiplying the same factor again and again.Multiplicar el mismo factor una y otra vez.
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.
- Find the Exponent Error
- A new song from the studio is shared online, and the number of shares doubles every hour. Starting with 1 share, write a power expression for the number of shares after 6 hours. Explain why exponential growth is so much faster than adding the same number each hour.
- Fill in the table
- Each fork splits a trail into 2 paths. A hiker passes 5 forks, and each way through is a different route. A ranger puts a $3 marker on every route. How much do the markers cost?
- $30
- $75
- $15
- $96
- On Day 0, one hiker knows about a trail closure. Each day, the number of hikers who know doubles. Fill in how many hikers know on each day.
- Ridge Route has 3⁵ steps. Valley Route has 5³ steps. Which route has more steps, and by how many?
- Valley Route, by 118 steps
- Ridge Route, by 118 steps
- Ridge Route, by 2 steps
- They have the same number of steps
- A trail cairn is built in 4 square layers. The layers have 2², 3², 4² and 5² stones. How many stones are in the whole cairn?
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.
- Work out each power, then sort it by its value.
- Match each power to its value.
- The value of 3 raised to a power is 81. Tap the exponent.
- Invent a story that grows by a power, such as a rumor that spreads or a path that keeps splitting. Write it as a power, expand it, and evaluate it. Then write one mistake a classmate might make.
- 2 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.
- Ilan evaluates 8². Tap the step where his work first goes wrong.
- Lucía evaluates 2⁶. Tap the step where her work first goes wrong.
- Hana evaluates 5⁴. Tap the step where her work first goes wrong.
- Ana says 3⁴ must be double 3², because the exponent doubles from 2 to 4. Ben says that is not true. Who is right?
- Ana, because doubling the exponent doubles the value
- Ben, because 3⁴ = 12
- Ben, because 3⁴ = 81 is nine times 3² = 9
- Neither, because 3⁴ and 3² have the same value
- What is the best next move?
- Work out 3³ the same way: 3 × 3 × 3.
- Add the bases and exponents: 4 + 3 and 2 + 3.
- Add 16 + 3, then use the exponent 3 on the sum.
- Stop here, because 4² + 3³ is already finished.
- 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.
- Which power is the same as 5 × 5 × 5 × 5 × 5 × 5?
- 6⁵
- 5 × 6
- 30¹
- 5⁶
- A chain of trail lamps starts with 1 lit lamp on Day 0. Each day, every lit lamp lights one more, so the number of lit lamps doubles each day. How many lamps are lit on Day 10?
- Which of these is NOT equal to 64?
- 6²
- 8²
- 4³
- 2⁶
- At a trail festival, 1 guide greets 4 hikers, and then each of those hikers greets 4 more hikers, for 3 rounds in all. The number greeted in round 3 is 4³. How many hikers are greeted in round 3?
- Which statement about 2⁵ and 5² is true?
- They are equal, because they use the same digits
- 5² is greater, because 5 is the greater base
- 2⁵ is 10 and 5² is 10, so they are equal
- 2⁵ is greater, because 32 is more than 25
- Create your own Summit Trail problem that uses a power. Tell a story where something multiplies by the same number again and again, write it as a power, and evaluate it. Explain what the base and the exponent mean in your story.