The Distributive Property Challenge

Grade 6 Math · Unit 6 Challenge Studio (6.AT.7) · Lesson 6-14
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I can use the distributive property to expand and factor expressions.Puedo usar la propiedad distributiva para desarrollar y factorizar expresiones.

MissionMisión · Home FieldCancha local · night shiftturno de noche

Train like a champion.Entrena como un campeón.

The stadium lights are on and the equipment crew has a stack of order forms with tricky totals. The head coach wants every total checked two different ways before anything ships.

Las luces del estadio están encendidas y el equipo de utilería tiene una pila de pedidos con totales difíciles. El entrenador quiere cada total comprobado de dos maneras diferentes antes de enviar nada.

Word bankBanco de palabras 5 words5 palabrasdistributive property, expand, factor, …propiedad distributiva, desarrollar, factor, …
distributive propertypropiedad distributiva
Multiplying a sum by a number is the same as multiplying each part and adding: a(b + c) = ab + ac.Multiplicar una suma por un número es lo mismo que multiplicar cada parte y sumar: a(b + c) = ab + ac.
expanddesarrollar
To multiply out the parentheses, like 3(x + 4) = 3x + 12.Multiplicar lo que está dentro del paréntesis, como 3(x + 4) = 3x + 12.
factorfactor
A number that divides another evenly. To factor an expression is to pull out a common factor: 3x + 12 = 3(x + 4).Un número que divide exactamente a otro. Factorizar una expresión es sacar un factor común: 3x + 12 = 3(x + 4).
equivalentequivalente
Expressions that always have the same value, whatever the variable is.Expresiones que siempre tienen el mismo valor, sin importar cuál sea la variable.
coefficientcoeficiente
The number in front of a variable, like the 3 in 3x.El número que está delante de una variable, como el 3 en 3x.

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 Distributive Error
  2. Use the distributive property to explain why 6 × 98 can be calculated as 6 × 100 − 6 × 2 = 588. Then create your own example of using the distributive property to make multiplication easier.
  3. Fill in the table
  4. The stadium shop prices a bundle with three different rules. Test each rule at three values of x and fill in the empty cells.
  5. A booster club buys 47 team water bottles at $8 each. Split 47 into 50 − 3 and use the distributive property to find the total cost.
  6. The bleachers have 6 equal sections. Each section has x reserved seats and 8 general seats, as shown in the diagram. Which expression gives the total number of seats?
    • 6x + 48
    • 6x + 8
    • x + 48
    • 6x + 14
  7. The team packs 24 jerseys and 36 pairs of shorts into identical kits, with none left over. Each expression below equals 24 + 36. Which one shows the greatest possible number of kits?
    • 6(4 + 6)
    • 4(6 + 9)
    • 12(2 + 3)
    • 3(8 + 12)

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. Is each expression equivalent to 8(w + 5)? Sort every card into Equivalent or Not equivalent.
  2. Create a bundle problem with a number of bundles outside parentheses and two items inside. Write the expression two ways, a(b + c) and ab + ac, and show that both give the same total for two different values.
  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. Noor expanded 7(w − 3). Find the step where her work first goes wrong.
  2. Tomás wants to factor 24x + 36 completely. Find the step where his reasoning first goes wrong.
  3. Imani expanded 4(3p + 2). Find the step where her work first goes wrong.
  4. At x = 2, Aiden says 5(x + 4) and 5x + 4 both give 14, so they are equivalent. Bea says 5(x + 4) gives 30 and 5x + 4 gives 14, so they are not. Who is right?
    • Aiden. Both expressions give 14.
    • Bea. The two expressions give different values at x = 2.
    • Both. Testing one number can never show anything.
    • Neither. Equivalent expressions must look exactly the same.
  5. What is the best next move?
    • Factor out 3 and write 3(6x + 8).
    • Factor out 18 and write 18(x + 24).
    • Add the terms to get 42x.
    • Factor out 6, the GCF.
  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 expression is equivalent to 4(3x − 5)?
    • 12x − 20
    • 12x − 5
    • 7x − 9
    • 12x + 20
  2. Each of the 15 players on the bench gets a shirt that costs $9 and a hat that costs h dollars, so the total cost is 15(9 + h). If each hat costs $4, what is the total cost in dollars?
  3. Which expression is 28a + 42 written with its greatest common factor pulled out?
    • 7(4a + 6)
    • 2(14a + 21)
    • 14(2a + 3)
    • 14(2a + 42)
  4. Fill in the blank so both sides are equal: 6(m + ___) = 6m + 54. What number goes in the blank?
  5. The table shows the value of two expressions at x = 1, x = 2 and x = 3. The two expressions are equivalent. Which pair of expressions produced the table?
    • 6(x + 3) and 6x + 18
    • 8(x + 2) and 8x + 16
    • 8(x + 2) and 8x + 2
    • 10x + 14 and 8(x + 2)
  6. Create your own problem. Think of two items a team might buy for every player, such as shirts and socks. Write a situation that fits a(b + c) with your own numbers. Find the total two ways, by adding inside first and by distributing first, and explain why both ways match.