I can compare ratios by finding unit rates or using equivalent ratios.Puedo comparar razones hallando tasas unitarias o usando razones equivalentes.
MissionMisión · Rooftop GardenJardín en la azotea · night shiftturno de noche
Grow your skills.Haz crecer tus habilidades.
Frost is coming to the Rooftop Garden, and the gardeners must pick the strongest mix tonight. Compare every pair of ratios fairly, because a wrong pick could cost the whole crop.
Se acerca una helada a Rooftop Garden y los jardineros deben elegir esta noche la mezcla más fuerte. Compara cada par de razones con justicia, porque una mala elección podría costar toda la cosecha.
Word bankBanco de palabras 5 words5 palabrascompare, unit rate, equivalent ratio, …comparar, tasa unitaria, razón equivalente, …
- comparecomparar
- To decide which ratio is greater, less, or equal.Decidir qué razón es mayor, menor o igual.
- unit ratetasa unitaria
- A rate for exactly 1 of something, like the cost for 1 item.Una tasa para exactamente 1 de algo, como el costo de 1 artículo.
- equivalent ratiorazón equivalente
- Two ratios that mean the same thing, like 1:2 and 2:4.Dos razones que significan lo mismo, como 1:2 y 2:4.
- common multiplemúltiplo común
- A number that is a multiple of two or more numbers.Un número que es múltiplo de dos o más números.
- benchmarkpunto de referencia
- A shared amount you scale both choices to so you can compare them.Una cantidad compartida a la que escalas ambas opciones para poder compararlas.
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.
- 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.
- Find Kai's Mistake
- Store A sells 5 notebooks for $12. Store B sells 8 notebooks for $20. Without calculating, a student says Store B must be cheaper because you get more notebooks. Is the student's reasoning valid? Find the unit rates to prove your answer.
- Two garden beds use different soil mixes, shown in the table. Which bed has the richer mix, with more compost for the same amount of soil?
- Bed A: 15 compost per 24 soil beats 14.
- Bed B, because 7 buckets is more than 5.
- Bed B, because it has more soil in the mix.
- The two beds have exactly the same mix.
- Fertilizer Mix X has 9 grams in 6 liters of water. Fertilizer Mix Y has 14 grams in 8 liters of water. How many more grams per liter does the stronger mix have?
- Three watering plans use different amounts for different numbers of plants. Scale each plan to 24 plants and fill in the liters of water.
- Mix P has 3 parts fertilizer for every 5 parts water. Mix Q has 9 parts fertilizer for every 14 parts water. Which statement is correct?
- Mix P is stronger: 42 fertilizer per 70 water beats 45.
- Mix Q is stronger: 45 fertilizer per 70 water beats 42.
- The mixes are equal, because both are about 3 to 5.
- Mix Q is stronger, because 14 water is more than 5 water.
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.
- The gardeners compare two seed plots in each card. Sort each card by the result.
- Write two paint recipes and recommend the one with the stronger color. Compare them using the same amount of white or a unit rate. Explain why comparing only the total cups could mislead.
- 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.
- A gardener compared watering plans. One step goes wrong. Tap the first step that is wrong.
- A gardener compared fertilizer strength as fertilizer to water. One step goes wrong. Tap the first step that is wrong.
- A gardener compared seed density in two plots. One step goes wrong. Tap the first step that is wrong.
- Kai says 3:4 and 5:6 are equal, because in each ratio the second number is 1 more than the first. Lena scales both to 12. Who is right?
- Kai: the difference is the same, so the ratios are the same.
- Both, because 12 is a common multiple of 3 and 4.
- Lena, but she finds that 3:4 is the greater ratio.
- Lena: 3:4 is 9:12 and 5:6 is 10:12, so 5:6 is greater.
- What is the best next move?
- Compare the first terms, 20 and 21, as the seconds match.
- Go back to the original ratios and compare 5 with 7 now.
- Compare 24 and 24, then say the two ratios are equal now.
- 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.
- A garden grew 27 tomatoes on 6 plants. How many tomatoes is that for each plant?
- Which ratio is greater, 5:8 or 3:5?
- 3:5, because 3:5 is greater than 5:8 at 40.
- 5:8, because 25:40 is greater than 24:40.
- 3:5, because 5 is less than 8 in the ratios.
- They are equal, because both differences are small.
- Soil Mix A is 3 compost to 4 soil. Soil Mix B is 5 compost to 7 soil. Scale both to 28 soil. How many more compost does Mix A have than Mix B?
- Three stores sell seed packets. Store X: 6 packets for $4.50. Store Y: 10 packets for $7.20. Store Z: 8 packets for $6.40. Which store has the lowest price per packet?
- Store X, at $0.75 per packet
- Store Z, at $0.80 per packet
- Store Y, at $0.72 per packet
- Store X, lowest total of $4.50
- Mix P uses 3 cups of fertilizer for every 8 cups of water. Mix Q uses 9 cups of fertilizer. How many cups of water make Mix Q exactly as strong as Mix P?
- Write your own garden comparison with two plans that use different amounts. Compare them using unit rates or by scaling to a common amount, say which is greater, and explain why comparing the raw numbers would be unfair.