Division Expressions with Fractions and Whole Numbers Challenge

Grade 6 Math · Unit 6 Challenge Studio (6.NOS.1) · Lesson 6-1
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I can explain what dividing with a whole number and a unit fraction means — how many groups fit, or how much is in one group — find the quotient with a model, and check it by multiplying.Puedo explicar qué significa dividir con un número entero y una fracción unitaria (cuántos grupos caben o cuánto hay en un grupo), hallar el cociente con un modelo y comprobarlo multiplicando.

MissionMisión · Sound StudioEstudio de sonido · night shiftturno de noche

Mix the track, then check the math.Mezcla la pista y revisa las matemáticas.

After the last session, the supply closet is a mess: rolls with no labels, tape used up in odd amounts, and a mixing board waiting for repairs. Work out what is left before the next band arrives.

Después de la última sesión, el armario de suministros es un desorden: rollos sin etiqueta, cinta gastada en cantidades extrañas y una mesa de mezclas esperando reparación. Calcula qué queda antes de que llegue la siguiente banda.

Word bankBanco de palabras 5 words5 palabrasquotient, divisor, unit fraction, …cociente, divisor, fracción unitaria, …
quotientcociente
The answer when you divide.La respuesta cuando divides.
divisordivisor
The number you divide by.El número entre el que divides.
unit fractionfracción unitaria
A fraction with 1 on top, like 1/4.Una fracción con 1 arriba, como 1/4.
reciprocalrecíproco
A fraction turned upside down. The reciprocal of 1/4 is 4.Una fracción volteada de arriba abajo. El recíproco de 1/4 es 4.
tape diagramdiagrama de cinta
A bar model cut into equal parts to show sharing or grouping.Un modelo de barra cortado en partes iguales para mostrar reparto o agrupación.

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 Interpretation Error
  2. Dividing 6 by 1/2 gives 12, but dividing 6 by 2 gives 3. How can dividing by a smaller number (1/2) give a bigger answer than dividing by a larger number (2)? Explain using a real-world example.
  3. Spot the Mistake — When the Numerator Is Not 1
  4. The Sound Studio cuts a 6-foot roll of cable into pieces that are each 1/3 foot long. Each patch kit needs 4 pieces. How many complete patch kits can the studio make?
    • 4 kits
    • 18 kits
    • 5 kits
    • 24 kits
  5. The studio records 3/4 of an hour of music and splits it equally into 6 tracks. Two of the tracks are played back to back. How many hours long is that?
  6. The studio is cutting acoustic foam. Fill in each quotient, then check it: multiply the quotient by the divisor to get back the starting number.
  7. A studio engineer used 4 feet of tape. That was 1/5 of the whole roll. How long is the whole roll?
    • 4/5 foot
    • 1/20 foot
    • 9 feet
    • 20 feet

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. Match each studio story to the division expression that solves it.
  2. Write your own food-truck problem that divides a whole number by a unit fraction. Sketch a tape diagram on paper and tell what it shows. Solve with the model and check your quotient by multiplying. Explain what the quotient tells you in your story.
  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. Rosa wants to know how many 1/3-foot pieces fit into a 7-foot cable. Tap the step where her work goes wrong.
  2. Kai finds 5 ÷ 1/6, the number of 1/6-foot pieces in a 5-foot cable. Tap the step where his work first goes wrong.
  3. Mira shares 4/5 of a pan of brownies equally between 2 friends. Tap the step where her work first goes wrong.
  4. Cy says 8 ÷ 4 is greater than 8 ÷ 1/4, because 4 is the bigger divisor. Dee says 8 ÷ 1/4 is greater. Who is right?
    • Dee, because 1/4-size pieces fit many more times into 8
    • Cy, because a bigger divisor gives a bigger quotient
    • Both quotients are equal
    • Neither, because you cannot divide by a fraction
  5. What is the best next move?
    • Multiply 1/3 × 4.
    • Divide 4 by 1/3.
    • Share 1/3 four ways.
  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 situation is modeled by 9 ÷ 1/3?
    • One third of a 9-foot cable
    • A 9-foot cable shared equally by 3 people
    • Number of 1/3-ft pieces in 9 ft
    • A 9-foot cable with 1/3 foot cut off
  2. The studio has 7/8 of a gallon of paint and pours it equally into 2 cans. How many gallons are in each can?
  3. Which of these is greater than 10?
    • 10 ÷ 2
    • 10 ÷ 1/2
    • 1/2 ÷ 10
    • 10 ÷ 5
  4. A mixing board uses 1/3 of a tube of lubricant on 4 equal sliders. What fraction of the whole tube does each slider get?
  5. 12 ÷ 1/4 = 48. Which multiplication checks this answer?
    • 12 × 4 = 48
    • 48 × 4 = 192
    • 48 × 1/4 = 12
    • 12 × 1/4 = 3
  6. Create your own Sound Studio problem that is solved by dividing a whole number by a unit fraction, or a fraction by a whole number. Write the division, solve it, and explain what the answer means.