Equivalent Ratios Challenge

Grade 6 Math · Unit 3 Challenge Studio (6.AT.3) · Lesson 3-9
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I can find and check equivalent ratios using multiplication and division.Puedo hallar y comprobar razones equivalentes usando la multiplicación y la división.

MissionMisión · Sound StudioEstudio de sonido · night shiftturno de noche

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

Late-night session: the band wants the same sound in a stadium, a school gym and a tiny café. Scale every mix and prove the ratios stay equivalent before the doors open.

Sesión de madrugada: la banda quiere el mismo sonido en un estadio, un gimnasio escolar y una cafetería pequeña. Escala cada mezcla y demuestra que las razones siguen siendo equivalentes antes de abrir las puertas.

Word bankBanco de palabras 4 words4 palabrasequivalent ratios, simplify, proportion, …razones equivalentes, simplificar, proporción, …
equivalent ratiosrazones equivalentes
Ratios that compare quantities in the same relationship, made by multiplying or dividing both parts by the same number.Razones que comparan cantidades en la misma relación, formadas al multiplicar o dividir las dos partes por el mismo número.
simplifysimplificar
To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio.Escribir una razón con números más pequeños que compara igual. 6:8 y 3:4 son la misma razón.
proportionproporción
A math sentence saying two ratios are equal, like 2/3 = 10/15.Una oración matemática que dice que dos razones son iguales, como 2/3 = 10/15.
ratio tabletabla de razones
A table of equal ratios that shows a pattern.Una tabla de razones iguales que muestra un patrón.

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 Marcus's Mistake
  2. A store sells 3 pens for $2. Another store sells 9 pens for $6. Are these equivalent ratios? If so, prove it using at least two different methods (simplifying, scaling, or cross-multiplying).
  3. Fill in the table
  4. At the studio's radio show, Maya plays 4 rock songs for every 6 pop songs. Today's long show has 15 pop songs. How many rock songs keep the same ratio?
  5. Ines's mix uses 6 parts guitar to 9 parts vocals. Which new mix sounds exactly the same?
    • 12 parts guitar to 15 parts vocals
    • 9 parts guitar to 6 parts vocals
    • 10 parts guitar to 15 parts vocals
    • 12 parts guitar to 9 parts vocals
  6. Farid's drum pattern plays 12 kick hits for every 20 claps. Complete each row so it stays equivalent to 12 : 20.
  7. Quinn's recording choir has 40 singers. There are 3 sopranos for every 2 altos, and everyone is either a soprano or an alto. How many singers are sopranos?

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. The studio saves every mix as a preset. Simplify each ratio, then sort the mix into the preset it matches.
  2. Design a model boat with three parts: a mast, a boom and a rail. Give each length in feet and in inches. Show that each pair is an equivalent ratio to 1 : 12. Then scale all three by the same factor and show the new pairs.
  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. Mina's recording booth has 3 microphones for every 7 headphone sets. She plans a bigger booth with 12 microphones. How many headphone sets keep the same ratio? Tap the first step where her work goes wrong.
  2. Bao simplifies the ratio of 18 trumpets to 24 trombones in the marching band. Tap the first step where his work goes wrong.
  3. A concert sold 5 student tickets for every 8 adult tickets. A second concert sold 9 student tickets for every 12 adult tickets. Rin says the two ratios are equivalent. Tap the first step where her work goes wrong.
  4. An album has 2 hip-hop tracks for every 3 jazz tracks (2:3). Tess says 3:2 is an equivalent ratio because it uses the same two numbers. Omar says the order matters. Who is right?
    • Tess, because the numbers are the same, just in a new order.
    • Omar. 3:2 means 3 hip-hop per 2 jazz, a different album.
    • Both, because a ratio can be written in any order you like.
    • Tess, because 3:2 simplifies to 2:3 when you reduce it.
  5. What is the best next move?
    • Say yes, because 20 and 30 are both bigger than 12 and 18.
    • Subtract: 18 − 12 = 6 and 30 − 20 = 10, so they are not equivalent.
    • Divide 20 and 30 both by 10, then compare it with 2 : 3.
    • Divide only the 20 by 10 to get 2 : 30, then compare it.
  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. Zola's merch table sold 28 shirts and 42 posters. Which ratio of shirts to posters is equivalent to 28:42 and in simplest form?
    • 2:3
    • 3:2
    • 14:21
    • 27:41
  2. Dolores prints 35 pages of sheet music for 20 musicians. At the same rate, how many pages does she print for 12 musicians?
  3. Marcus tests whether two knob settings, 6/8 and 9/12, are equivalent with cross products. Which sentence is correct?
    • They are not equivalent, because 6 × 9 = 54 and 8 × 12 = 96.
    • They are not equivalent, because 6 + 12 = 18 and 8 + 9 = 17.
    • They are not equivalent, because 9 is greater than 6.
    • They are equivalent, because 6 × 12 and 8 × 9 both equal 72.
  4. A producer records 150 minutes for every 20 minutes of finished music. How many minutes of recording does Hiro need for 8 minutes of finished music?
  5. Paloma's concert uses 4 spotlights for every 7 floodlights. The stage has 24 spotlights. How many lights are there in all?
  6. Create your own equivalent-ratio problem about a mix, a playlist or a stage. Write a starting ratio and an equivalent ratio, and explain how you know they are equivalent.