Determine Equivalent Ratios Using Tables

6.AT.3a · Unit 3 · Lesson 3

Name   Period

Objectives / Objetivos

Content Objective: I can use a ratio table to find equivalent ratios.

Language Objective: I can explain my table using the words ratio table, equivalent ratio, scale factor, and pattern.

Key Idea / Idea clave

Equivalent Ratios & Ratio Tables. 1. Multiply or divide both terms in a ratio by the same non-zero scale factor. 2. In a ratio table, rows and columns maintain the same proportional unit rate. 3. Use additive or multiplicative patterns to find missing values in the table

I Notice / Observo

  • What two quantities are being compared in the recipe?
  • What happens to both quantities when you double the recipe?

I Wonder / Me pregunto

  • What if we only needed to make half the original recipe?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Ratio Tables
Tablas de razones		Tables that organize pairs of equivalent ratios.
Tablas que organizan pares de razones equivalentes.
Ratio table
Tabla de razones		A table of equal ratios that shows a pattern.
Una tabla de razones iguales que muestra un patrón.
Equivalent ratio
Razón 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.
Scale factor
Factor de escala		The number you multiply both parts of a ratio by to get an equal ratio.
El número por el que multiplicas ambas partes de una razón para obtener una razón igual.
Pattern
Patrón		A rule that numbers follow again and again.
Una regla que los números siguen una y otra vez.
Additive pattern
Patrón aditivo		Building new rows of a ratio table by adding each column's own constant amount, so the two columns grow together.
Formar nuevas filas de una tabla de razones sumando a cada columna su propia cantidad constante, para que las dos columnas crezcan juntas.

Practice Preview / Vista previa de práctica

  1. A recipe uses 3 eggs for every 5 cups of flour. How many eggs are needed for 15 cups of flour?
    1. 9
    2. 6
    3. 10
    4. 12
  2. Complete the ratio table for lemon juice to water in Chef Reyes's lemonade recipe (1 cup lemon juice for every 4 cups water).
  3. In a ratio table, the ratio of sugar to butter is 3:2. If you use 12 cups of sugar, how many cups of butter do you need?
    1. 8
    2. 6
    3. 10
    4. 9
  4. Find Devon's Mistake
    1. Step 1: Read the problem — A recipe uses 5 cups of oats for every 2 cups of honey. Complete the table for 3 batches.
    2. Step 2: Find the scale factor — 3 batches → multiply by 3
    3. Step 3: Scale the oats — 5 × 3 = 15 cups of oats
    4. Step 4: Scale the honey — 2 + 3 = 5 cups of honey

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

Reflection / Reflexión

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