Compare Ratio Relationships

6.AT.3 · Unit 3 · Lesson 5

Name   Period

Objectives / Objetivos

Content Objective: I can compare ratios by finding unit rates or using equivalent ratios.

Language Objective: I can explain my comparison using the words unit rate, equivalent ratio, compare, and common denominator.

Key Idea / Idea clave

Comparing Ratio Relationships. 1. Convert each ratio to a unit rate (e.g. price per item or miles per gallon). 2. Alternatively, scale both ratios to a common term (like a common denominator). 3. Compare the resulting unit rates to identify the better buy or faster rate

I Notice / Observo

  • What quantities are being compared in each recipe?
  • Can you tell just by looking which recipe has more cocoa per ounce?

I Wonder / Me pregunto

  • What if both chefs used the same amount of milk — then could we compare?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Compare Ratios
Comparar razones		Decide which ratio is greater, less, or equal by using equivalent ratios or unit rates.
Decidir cuál razón es mayor, menor o igual usando razones equivalentes o tasas unitarias.
Unit rate
Tasa unitaria		A rate for just 1 of something, like cost for 1 item.
Una tasa para solo 1 de algo, como el precio de 1 artículo.
Equivalent ratio
Razón equivalente		Two ratios that mean the same thing.
Dos razones que significan lo mismo.
Compare
Comparar		To look at ratios and see which is bigger, smaller, or equal.
Mirar razones para ver cuál es mayor, menor o igual.
Simplify
Simplificar		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.
Common denominator
Denominador común		A bottom number that two fractions can share so you can compare them.
Un número de abajo que dos fracciones pueden compartir para compararlas.

Practice Preview / Vista previa de práctica

  1. Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?
    1. Chef B
    2. Chef A
    3. They use the same amount
    4. Cannot determine
  2. Match each scenario to the correct answer: Which ratio is greater?
  3. Store A sells 3 mangoes for $6. Store B sells 5 mangoes for $9. Which store offers a better price per mango?
    1. Store B
    2. Store A
    3. Same price
    4. Cannot determine
  4. Find Kai's Mistake
    1. Step 1: Read the problem — Compare 3:5 and 4:7. Which ratio is greater?
    2. Step 2: Find common denominator — LCD of 5 and 7 is 35
    3. Step 3: Scale the ratios — 3:5 = 21:35 (3 × 7 = 21). For 4:7, Kai multiplies by 7 again: 4 × 7 = 28, giving 28:35.
    4. Step 4: Conclusion — Since 28 > 21, the ratio 4:7 is greater.

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: