Write and Solve Equations Using Multiplication or Division Challenge

Grade 6 Math · Unit 8 Challenge Studio (6.AT.8) · Lesson 8-3
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I can solve one-step multiplication and division equations using inverse operations.Puedo resolver ecuaciones de multiplicación y división de un paso usando operaciones inversas.

MissionMisión · Summit TrailSendero a la cumbre · night shiftturno de noche

Every checkpoint gets you higher.Cada punto de control te lleva más alto.

Night falls on the steep part of the trail. The guides have scribbled equations on the trail signs, and every number has to be found with the right inverse operation before the group camps.

Cae la noche en la parte empinada del sendero. Los guías garabatearon ecuaciones en los letreros, y cada número debe hallarse con la operación inversa correcta antes de que el grupo acampe.

Word bankBanco de palabras 4 words4 palabrasinverse operation, coefficient, isolate, …operación inversa, coeficiente, despejar, …
inverse operationoperación inversa
An operation that undoes another one. Multiplication and division are inverses.Una operación que deshace otra. La multiplicación y la división son inversas.
coefficientcoeficiente
The number in front of a letter. In 3x, the coefficient is 3.El número que está delante de una letra. En 3x, el coeficiente es 3.
isolatedespejar
To get the variable by itself on one side of the equation.Dejar la variable sola en un lado de la ecuación.
Division Property of EqualityPropiedad de división de la igualdad
Dividing both sides by the same nonzero number keeps the equation balanced.Dividir los dos lados entre el mismo número distinto de cero mantiene equilibrada la ecuación.

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 Equation Error
  2. A bakery packed muffins into boxes of 8. They made 96 muffins total. Write an equation, solve it, and explain why your answer is reasonable. Then write a different situation that uses division and has the same answer.
  3. Anjali's group carries 9 identical packs of trail mix that weigh 45 pounds in all. She writes 9w = 45, where w is the weight of one pack. What is her step, and what is w?
    • Multiply both sides by 9, so w = 405
    • Subtract 9 from both sides, so w = 36
    • Add 9 to both sides, so w = 54
    • Divide both sides by 9, so w = 5
  4. A guide splits a trail into 6 equal sections. Each section is 2.5 miles long. The equation is t ÷ 6 = 2.5, where t is the length of the whole trail in miles. What is t?
  5. Solve each equation for k. First type the number you use on both sides, then type k.
  6. Two equations are on the trail sign: 4a = 18 and b ÷ 4 = 18. Which pair of solutions is correct?
    • a = 72 and b = 4.5
    • a = 4.5 and b = 72
    • a = 4.5 and b = 4.5
    • a = 72 and b = 72

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 equation to the step that gets the variable alone.
  2. Design a vault puzzle with two keys: write one multiplication equation and one division equation that have the SAME solution. Put each in a short story. Show the inverse operation for each and check both keys by substituting.
  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. Luis solves 7x = 56.
  2. Chen solves 8n = 4.
  3. Mika solves d ÷ 6 = 4.
  4. To solve 2.5y = 10, Salma divides both sides by 2.5 and gets y = 4. Ivan says you cannot divide by a decimal, so he multiplies both sides by 2.5 and gets y = 25. Who is right?
    • Ivan, because decimals only work with multiplication.
    • Salma, because division undoes multiplying by 2.5.
    • Both, because both of them used the number 2.5.
    • Neither, because the answer must be a whole number.
  5. What is the best next move?
    • Divide both sides by 1.25, even though it is a decimal.
    • Multiply both sides by 1.25.
    • Divide 1.25 by 15.
    • Multiply the left side by 4 to clear the decimal.
  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 equation has w = 12 as its solution?
    • 3w = 4
    • w ÷ 3 = 36
    • w ÷ 3 = 4
    • 5w = 17
  2. Solve 0.4n = 6.
  3. Which equation is solved by subtracting 6 from both sides?
    • x ÷ 6 = 30
    • x + 6 = 30
    • 6x = 30
    • x − 6 = 30
  4. The summit is 3 times as high as base camp. The summit is 4,800 feet high. With b for the height of base camp in feet, the equation is 3b = 4800. How high is base camp?
  5. Mika solved k ÷ 9 = 7 and got k = 63. Which check proves her answer?
    • 63 ÷ 9 = 7
    • 63 − 9 = 7
    • 63 × 9 = 7
    • 7 ÷ 9 = 63
  6. Write your own trail problem that fits an equation like ax = b or x ÷ a = b. Solve it by using the inverse operation on both sides, and check your answer in the original equation.