Understand Inequalities and Their Solutions Challenge

Grade 6 Math · Unit 8 Challenge Studio (6.AT.9) · Lesson 8-5
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I can graph the solutions of an inequality on a number line.Puedo graficar las soluciones de una desigualdad en una recta numérica.

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.

Deep water, low light. The reef scientists left graphs and test values on their slate, and you must decide which circles, which shading and which numbers are really solutions.

Aguas profundas, poca luz. Los científicos del arrecife dejaron gráficas y valores de prueba en su pizarra, y debes decidir qué círculos, qué sombreado y qué números son realmente soluciones.

Word bankBanco de palabras 4 words4 palabrassolution set, open circle, closed circle, …conjunto solución, círculo abierto, círculo cerrado, …
solution setconjunto solución
All the numbers that make an inequality true.Todos los números que hacen verdadera una desigualdad.
open circlecírculo abierto
An empty circle on a number line. It shows the boundary number is NOT a solution.Un círculo vacío en una recta numérica. Muestra que el número límite NO es una solución.
closed circlecírculo cerrado
A filled-in circle on a number line. It shows the boundary number IS a solution.Un círculo relleno en una recta numérica. Muestra que el número límite SÍ es una solución.
boundary pointpunto límite
The number on the number line where the solution set starts.El número de la recta numérica donde empieza el conjunto solución.

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 Graphing Error
  2. A theme park has two rides. Ride A requires height h > 48 inches. Ride B requires height h ≥ 48 inches. A child is exactly 48 inches tall. Which ride can they go on? Explain using number line graphs for both inequalities.
  3. The graph shows the water temperatures, in degrees, that a coral species needs. Which inequality does it show, with t for the temperature?
    • t ≥ 24
    • t < 24
    • t ≤ 24
    • t > 24
  4. Camila's reef tank holds at most 6 clownfish. She graphs the number of fish f with f ≤ 6 on a number line. How does her graph look?
    • Closed circle at 6, shaded to the left
    • Open circle at 6, shaded to the left
    • Closed circle at 6, shaded to the right
    • Open circle at 6, shaded to the right
  5. Dive depths d must follow d < 30 meters. For each test depth, type 1 if the inequality is true and 0 if it is false.
  6. Joon tests the values 2, 5, 5.5, 6 and 8 in the inequality n ≥ 5.5. How many of the values are solutions?

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 inequality by the circle you draw at its boundary on a number line.
  2. Make a mystery graph. Describe, or sketch on paper, a number line graph for an inequality of your own. Do NOT write the inequality. Instead, give two clues: one number that IS a solution and one number that is NOT. Then explain how your circle and shading prove your clues.
  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. Joon graphs the inequality x ≥ 6.
  2. Akira graphs the inequality x < 9.
  3. Fiona tests whether n = 7 is a solution of n ≥ 7.
  4. Bruno says that 4.9 is a solution of y < 5. Nia says only whole numbers can be solutions. Who is right?
    • Nia, because a solution has to be a whole number.
    • Bruno; decimals below 5 also work.
    • Neither, because only 4 is a solution.
    • Both, because both of them agree 5 is the boundary.
  5. What is the best next move?
    • Write v > 7, because the shading goes right.
    • Write v ≤ 7, because the circle is at the end.
    • Use the circle and shading together.
    • Write v = 7, because that is where the circle is.
  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 inequality has 8 as a solution?
    • x < 8
    • x > 8
    • x ≥ 8
    • x ≤ 7.9
  2. Which inequality does the graph show?
    • x ≤ 3
    • x < 3
    • x ≥ 3
    • x > 3
  3. What is the least whole number that is a solution of n > 6.5?
  4. Which statement is true about a number line graph of c > 11?
    • The circle at 11 is closed, so 11 is a solution.
    • The circle at 11 is open, so 11 is not a solution.
    • The circle at 11 is open, so 11 is a solution.
    • The shading goes left, because 11 is the greatest value allowed.
  5. A pool allows swimmers who are at least 10 years old. Which description shows the allowed ages a on a number line?
    • Open circle at 10, shaded to the right
    • Closed circle at 10, shaded to the left
    • Closed circle at 10, shaded to the right
    • Open circle at 10, shaded to the left
  6. Choose an inequality about a reef, such as a depth, a temperature or a number of fish. Describe how you would graph it on a number line, then name one number that is a solution and one that is not.