Equivalent Ratios

6.AT.3 · Unit 3 · Lesson 9

Name   Period

Objectives / Objetivos

Content Objective: I can find and check equivalent ratios using multiplication and division.

Language Objective: I can explain my reasoning using the words equivalent ratios, rate, proportion, and simplify.

Key Idea / Idea clave

Proportions & Equivalent Ratios. Formula: a/b = c/d. 1. Two ratios are equivalent if their simplified forms or cross products are equal. 2. Find the scale factor between corresponding terms. 3. Multiply or divide to solve for the missing term in the proportion

I Notice / Observo

  • What quantities are being compared in the recipe?
  • What stays the same when you multiply both ingredients by the same number?

I Wonder / Me pregunto

  • What if we needed to scale DOWN for just 4 people?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Equivalent Ratios
Razones equivalentes		Ratios that compare quantities in the same relationship.
Razones que comparan cantidades en la misma relación.
Ratio
Razón		A way to compare two amounts, like 3 to 2.
Una manera de comparar dos cantidades, como 3 a 2.
Rate
Tasa		A ratio comparing two amounts with different units, like miles per hour.
Una razón que compara dos cantidades con unidades distintas, como millas por hora.
Proportion
Proporción		A math sentence saying two ratios are equal.
Una oración matemática que dice que dos razones son iguales.
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.
Ratio table
Tabla de razones		A table of equal ratios that shows a pattern.
Una tabla de razones iguales que muestra un patrón.

Practice Preview / Vista previa de práctica

  1. Which ratio is equivalent to 2:5?
    1. 4:10
    2. 3:6
    3. 2:10
    4. 5:2
  2. Sort these ratios — which are equivalent to 3:4 and which are not?
  3. Marcus earns $45 for every 3 hours of work. How much does he earn in 8 hours?
    1. $120
    2. $90
    3. $135
    4. $105
  4. Find Marcus's Mistake
    1. Step 1: Set up the ratio — 3 cups : 5 cups = ? : 20 cups
    2. Step 2: Find the multiplier — 20 ÷ 5 = 4
    3. Step 3: Apply to both parts — 3 + 4 = 7
    4. Step 4: Answer — 7 cups : 20 cups

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

Reflection / Reflexión

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