I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.Puedo escribir expresiones numéricas a partir de una situación real y evaluarlas usando el orden de las operaciones, incluidas las potencias.
MissionMisión · Harbor WorksPuerto de trabajo · night shiftturno de noche
Keep the port running.Mantén el puerto en marcha.
After a storm, the harbor office finds several shipping sheets with mistakes in them. Find the wrong step, fix the order of operations, and rewrite each bill correctly.
Después de una tormenta, la oficina del puerto encuentra varias hojas de envío con errores. Encuentra el paso equivocado, corrige el orden de las operaciones y reescribe cada factura correctamente.
Word bankBanco de palabras 5 words5 palabrasnumerical expression, evaluate, order of operations, …expresión numérica, evaluar, orden de las operaciones, …
- numerical expressionexpresión numérica
- A math phrase made of numbers and operations, with no equal sign and no variable.Una frase matemática hecha de números y operaciones, sin signo de igual y sin variable.
- evaluateevaluar
- To find the single value of an expression by doing its operations in order.Hallar el único valor de una expresión haciendo sus operaciones en orden.
- order of operationsorden de las operaciones
- The agreed order, remembered as PEMDAS: Parentheses, Exponents, Multiply and Divide, then Add and Subtract. Multiply and divide share a rank, so go left to right. Add and subtract do too.El orden acordado, que se recuerda como PEMDAS: Paréntesis, Exponentes, Multiplicación y División, y luego Adición y Sustracción. Multiplicar y dividir tienen el mismo rango, así que se hacen de izquierda a derecha. Sumar y restar también.
- 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.
- grouping symbolssímbolos de agrupación
- Parentheses or brackets. The work inside them is done first.Paréntesis o corchetes. El trabajo dentro de ellos se hace primero.
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 error
- Seven friends split the bill for a pizza party. They order 4 pizzas at 3² dollars each, plus a one-time $6 delivery fee. Write ONE numerical expression for what each friend owes, evaluate it, and explain why the grouping symbols matter.
- Fill in the table
- A Harbor Works ship carries 4 stacks with 3² containers in each stack, plus 6 loose containers on the deck. Which expression gives the total number of containers?
- (4 × 3)² + 6
- 4 × 3² + 6
- 4 × 3 × 2 + 6
- 4 + 3² + 6
- The harbor charges a dock fee of 5² dollars, plus a crane fee of $12 for each of 4 containers, minus a discount of 2³ dollars. Write one expression and evaluate it. What is the total fee in dollars?
- Evaluate two expressions in order, one step at a time. Fill in the result of each step.
- Five dockworkers share the cost of 3 pallets that cost 2³ dollars each, plus a $16 rope fee. Which expression gives what each dockworker pays?
- 3 × 2³ + 16 ÷ 5
- (3 × 2³ + 16) × 5
- (3 × 2 × 3 + 16) ÷ 5
- (3 × 2³ + 16) ÷ 5
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.
- Evaluate each expression in the correct order. Is its value equal to 20?
- Match each expression to its value.
- Evaluate 5 + 3² × 2 − 4. Tap its value.
- Write two numerical expressions with the same numbers, 2, 3 and 4, and a power, but with different grouping symbols. Evaluate each step by step and explain why their values differ.
- 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.
- Tavi evaluates 6 + 2 × 3². Tap the step where his work first goes wrong.
- Sade evaluates 3 × 4². Tap the step where her work first goes wrong.
- Pia writes an expression for 6 crates that each hold 2³ items, plus 5 extra items, and evaluates it. Tap the step where her work first goes wrong.
- Ana says (8 − 2)² and 8 − 2² have the same value, because they use the same numbers and symbols. Ben says they are different. Who is right?
- Ana, because the same numbers always give the same value
- Ben, because 8 − 2² equals 36 and (8 − 2)² equals 4
- Ben, because parentheses change what comes first
- Neither, because both equal 4 when you work them out
- What is the best next move?
- Subtract 64 − 81 first, then multiply by 2.
- Multiply 2 × 64 first, then subtract 81.
- Stop here, because both powers are worked out.
- Multiply 2 × 64 × 81.
- 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.
- Evaluate 5 × 2³ − 4².
- A crane lifts 3 loads of 2⁴ kilograms each and then a 5 kilogram hook. Which expression gives the total weight lifted?
- 3 × 2⁴ + 5
- 3 × 2 × 4 + 5
- (3 × 2)⁴ + 5
- 3 × 2⁴ × 5
- Evaluate (18 − 6) ÷ 2² + 3².
- Which expression has the greatest value?
- 2 + 3 × 4²
- (2 + 3) × 4²
- (2 + 3 × 4)²
- 2 + (3 × 4)²
- A ship has 5 deck rows with 2² containers in each, and 3 hold rows with 3² containers in each. Write one expression and evaluate it. How many containers are on the ship?
- Create your own Harbor Works problem with a power. Tell a story, write ONE numerical expression that includes a power, evaluate it step by step, and explain why the order of operations matters.