Write and Represent Inequalities Challenge

Grade 6 Math · Unit 8 Challenge Studio (6.AT.9) · Lesson 8-4
Progress: 0 / 30

I can write inequalities to represent real-world situations.Puedo escribir desigualdades para representar situaciones de la vida real.

MissionMisión · Harbor WorksPuerto de trabajo · night shiftturno de noche

Keep the port running.Mantén el puerto en marcha.

A storm rolls in and the harbor master hands you a stack of damaged signs. Rebuild every rule from clues, and be careful about whether the limit itself is allowed.

Llega una tormenta y el capitán del puerto te entrega una pila de letreros dañados. Reconstruye cada regla con pistas y ten cuidado con si el propio límite está permitido.

Word bankBanco de palabras 4 words4 palabrasinequality, at least / at most, constraint, …desigualdad, al menos / a lo más, restricción, …
inequalitydesigualdad
A math sentence that compares two sides with <, >, ≤ or ≥.Una oración matemática que compara dos lados con <, >, ≤ o ≥.
at least / at mostal menos / a lo más
'At least' means ≥ (this number or more). 'At most' means ≤ (this number or less).«Al menos» significa ≥ (este número o más). «A lo más» significa ≤ (este número o menos).
constraintrestricción
A limit that a solution must follow, like a weight limit.Un límite que una solución debe cumplir, como un límite de peso.
solution setconjunto solución
All the values that make an inequality true.Todos los valores que hacen verdadera una desigualdad.

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 Inequality Error
  2. Write two different real-world situations: one that uses > and one that uses ≥. Explain why the situations need different symbols even though both mean 'bigger.'
  3. The graph shows every weight a harbor crane can lift, in tons. Which inequality describes it, with w for the weight?
    • w > 12
    • w ≥ 12
    • w < 12
    • w ≤ 12
  4. A cargo hold can carry no more than 500 crates, and 230 crates are already loaded. Let c be the number of additional crates. Which inequality shows the limit?
    • c + 230 < 500
    • c + 230 ≤ 500
    • c + 230 ≥ 500
    • c ≤ 500
  5. Each row is a harbor rule. Type the boundary number. Then type 1 if the boundary itself is allowed, or 0 if it is not.
  6. Which situation can be written as x ≥ 30?
    • A ship must carry at least 30 crates.
    • The elevator allows no more than 30 people.
    • Fewer than 30 ships dock today.
    • More than 30 sailors are on shore.

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. Sort each phrase by the symbol it needs.
  2. Invent two arcade signs that sound alike but mean different things, such as 'at most 8 players' and 'fewer than 8 players'. Write each as an inequality. Show one number that works for one sign but not the other, and explain why.
  3. 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.

  1. Imani writes an inequality for 'Harbor passes are for sailors at least 16 years old'.
  2. Pavel writes an inequality for 'The cargo hold holds at most 40 crates'.
  3. Declan writes an inequality for 'The number of boats is more than 7'.
  4. A sign on the dock says 'Maximum load 9 tons'. Marcus writes w ≤ 9. Lupe writes w < 9. Who is right?
    • Lupe, because the load must be below the maximum.
    • Both, because 9 is the boundary in each.
    • Marcus; 9 is allowed, as are lower loads.
    • Neither, because the inequality should be w ≥ 9.
  5. What is the best next move?
    • Write g ≤ 40.
    • Compare 14 + g ≤ 40.
    • Write 14 + g ≥ 40.
    • Write g − 14 ≤ 40.
  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. Which phrase matches y < 15?
    • y is at most 15
    • y is fewer than 15
    • y is at least 15
    • y is no fewer than 15
  2. Which inequality represents 'No fewer than 6 sailors must be on deck'?
    • s ≤ 6
    • s < 6
    • s > 6
    • s ≥ 6
  3. A ferry may carry at most 9 cars. The number of cars c can be 0, 1, 2 and so on, in whole numbers. How many different values of c are allowed?
  4. Which value of p makes p ≥ 50 true?
    • p = 40
    • p = 49.9
    • p = 50
    • p = −60
  5. Which phrase needs a strict symbol, < or >, with no equal line?
    • at most 20 boats
    • fewer than 20 boats
    • no more than 20 boats
    • 20 boats or fewer
  6. Make up a harbor rule that uses a limit, such as a weight, a number of people or a fee. Write it in words and as an inequality, then say whether the boundary number is allowed.