Use Ratio Reasoning

6.AT.3 · Unit 3 · Lesson 6

Name   Period

Objectives / Objetivos

Content Objective: I can use ratio reasoning to solve problems with proportions and scaling.

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

Key Idea / Idea clave

Find the scale factor, then multiply both parts; cross-multiply to check a proportion.

I Notice / Observo

  • How many times bigger is 120 compared to 8?
  • What operation would help you scale both ingredients?

I Wonder / Me pregunto

  • What if we had a different number of guests — like 60 or 200?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Proportion
Proporción		A math sentence saying two ratios are equal.
Una oración matemática que dice que dos razones son iguales.
Cross-multiply
Multiplicación cruzada		Multiplying across two ratios to check if they are equal.
Multiplicar en cruz dos razones para ver si son iguales.
Scale
Escalar		To multiply or divide both parts of a ratio by the same number.
Multiplicar o dividir ambas partes de una razón por el mismo número.
Equivalent
Equivalente		Having the same value.
Tener el mismo valor.
Unit rate
Tasa unitaria		A rate for just 1 of something. You find it by dividing.
Una tasa para solo 1 de algo. La encuentras al dividir.

Practice Preview / Vista previa de práctica

  1. A recipe uses 4 cups of broth for every 10 servings. How many cups of broth are needed for 30 servings?
    1. 12
    2. 8
    3. 14
    4. 40
  2. Chef Reyes's appetizer uses 5 cups of tomatoes for every 3 cups of mozzarella. Scale the recipe for different group sizes.
  3. A chef uses the proportion 3/7 = x/28 to scale a recipe. What is x?
    1. 12
    2. 14
    3. 9
    4. 21
  4. Find Priya's Mistake
    1. Step 1: Set up the proportion — 5/8 = x/32
    2. Step 2: Find the scale factor — 32 ÷ 8 = 4
    3. Step 3: Solve for x — 5 + 4 = 9
    4. Step 4: Answer — x = 9

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

Reflection / Reflexión

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