Equivalent Ratios

6.AT.3 · Unit 3 · Lesson 4

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

Multiply or divide both numbers by the same amount to make an equivalent ratio.

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
Ratio
Razón		A way to compare two amounts, like 3 to 2.
Una manera de comparar dos cantidades, como 3 a 2.
Equivalent ratios
Razones equivalentes		Two ratios that mean the same thing.
Dos razones que significan lo mismo.
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 make a ratio smaller while keeping the same comparison.
Hacer una razón más pequeña sin cambiar la comparación.

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: