Write and Evaluate Algebraic Expressions Challenge

Grade 6 Math · Unit 6 Challenge Studio (6.AT.6a) · Lesson 6-5
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I can write an algebraic expression for a real situation and evaluate it for a given value of the variable.Puedo escribir una expresión algebraica para una situación real y evaluarla para un valor dado de la variable.

MissionMisión · Reef RescueRescate del arrecife · night shiftturno de noche

Protect the coral, one calculation at a time.Protege el coral, un cálculo a la vez.

Night falls over the reef, and the crew's dive plans are written as expressions. One wrong number could leave coral unprotected, so decode each plan, compare them, and check every value.

Cae la noche sobre el arrecife y los planes de buceo del equipo están escritos como expresiones. Un número equivocado podría dejar el coral sin protección, así que descifra cada plan, compáralos y revisa cada valor.

Word bankBanco de palabras 5 words5 palabrasvariable, coefficient, constant, …variable, coeficiente, constante, …
variablevariable
A letter that stands for a number that can change.Una letra que representa un número que puede cambiar.
coefficientcoeficiente
The number that multiplies a variable, like the 6 in 6t.El número que multiplica a una variable, como el 6 en 6t.
constantconstante
A number on its own that never changes, like the 15 in 6t + 15.Un número solo que nunca cambia, como el 15 en 6t + 15.
substitutesustituir
To replace a variable with a number.Reemplazar una variable por un número.
evaluateevaluar
To find the value of an expression after you substitute, using the order of operations.Hallar el valor de una expresión después de sustituir, usando el orden de las operaciones.

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. Find the Translation Error
  2. Field day needs one $4.25 item per student plus a one-time $23.50 shipping fee. Write the expression, then find the cost for 30 students AND for 60 students. Does doubling the students double the cost? Explain.
  3. Write a real-world situation that could be modeled by the expression 4n + 10. Explain what the variable n represents, what the coefficient 4 means, and what the constant 10 represents.
  4. The Reef Rescue boat charges a $40 launch fee plus $15 for each diver. The team is choosing between a trip with 4 divers and a trip with 6 divers. How many more dollars does the 6-diver trip cost than the 4-diver trip?
  5. The table shows two ways to rent snorkel gear. Mei will rent gear for 5 hours. Which plan costs less, and by how much?
    • Plan B is $3 cheaper
    • Plan A is $15 cheaper
    • Plan A is $3 cheaper
    • Plan B is $45 cheaper
  6. A dive tank starts at 200 psi and loses 3 psi every minute underwater, so after m minutes it holds 200 − 3m psi. Complete each row.
  7. A coral nursery has 5 tanks. Each tank holds c coral fragments plus 2 spare fragments. Which expression gives the total number of fragments in the nursery, and how many fragments is that when c = 9?
    • 5c + 2; 47 fragments
    • 5(c + 2); 55 fragments
    • c + 2 + 5; 16 fragments
    • 5 + 2c; 23 fragments

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. Each card describes one number in an expression. Does the number multiply the variable (a coefficient), or is it added just once (a constant)?
  2. Match each phrase to the expression that says the same thing.
  3. A survey counts 4 sea stars in each of n tide pools, and then 3 swim away. Evaluate 4n − 3 for n = 7, then tap the tick mark with that value.
  4. Invent a situation with a price for each item and a one-time fee. Define your variable, write the algebraic expression, and evaluate it for two different values of the variable.
  5. 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.

  1. A tide-pool tour costs $6 for each visitor plus a one-time $20 set-up fee. Kai wrote an expression for v visitors. Tap the step where his thinking goes wrong.
  2. The expression 6k + 14 gives the cost, in dollars, of renting k kayak seats. Isla evaluated it for k = 3. Tap the step where her work goes wrong.
  3. The crew counted c crabs in a tide pool. Tomás wrote an expression for '12 fewer than the number of crabs.' Tap the step where his work goes wrong.
  4. Marisol says 5n and n + 5 mean the same thing, because both have a 5 and an n. Dev says they are different, because 5n means 5 × n. Who is right?
    • Dev is right: 5n means 5 times n, and n + 5 means 5 more than n.
    • Marisol is right, because both use a 5 and an n.
    • Both are right, because the order of the symbols does not matter.
    • Neither is right, because the value depends on what n is.
  5. What is the best next move?
    • Let c be Lena's cards, then write 2c + 5.
    • Let c be Lena's cards, then write 5 − 2c.
    • Let c be Lena's cards, then write 2c − 5.
    • Let s be Sam's cards, then write 2s − 5.
  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. In the expression 6t + 15, which statement is true?
    • The coefficient is 6 and the constant is 15.
    • The coefficient is 15 and the constant is 6.
    • The variable is 6t, because it has a letter.
    • 6t and 15 are like terms, because both are in the expression.
  2. A reef photographer charges $3.50 for each photo plus a one-time $12 trip fee. How much does she charge for 20 photos?
  3. Which expression means 'three more than five times the number of turtles, t'?
    • 3t + 5
    • 8t
    • 5t + 3
    • 5(t + 3)
  4. Which story matches the expression 20 − 4d?
    • A bucket holds 20 liters of seawater. Each test adds 4 liters, and d is the number of tests.
    • A bucket holds 4 liters of seawater. Each test uses 20 liters, and d is the number of tests.
    • A team shares 20 liters of seawater equally among d tests.
    • A bucket holds 20 liters of seawater. Each test uses 4 liters, and d is the number of tests.
  5. Evaluate 2(g + 3) + 5 when g = 4.
  6. Create your own Reef Rescue problem. Describe a situation with one amount that repeats and one amount that is paid or added only once. Write the expression with a variable, tell what the coefficient and the constant mean, and evaluate it for a number you choose.