Determine Equivalent Ratios Using Graphs

6.AT.3a · Unit 3 · Lesson 4

Name   Period

Objectives / Objetivos

Content Objective: I can graph the values from a ratio table as points on the coordinate plane.

Language Objective: I can explain my graph using the words coordinate plane, ordered pair, origin, and proportional.

Key Idea / Idea clave

Graphing Equivalent Ratios. 1. Form ordered pairs (x, y) from columns or rows in a ratio table. 2. Plot the points on the coordinate plane. 3. Proportional Relationship: Points form a straight line passing through the origin (0, 0)

I Notice / Observo

  • What two quantities could we put on the x-axis and y-axis?
  • What pattern do you see in the ratio table values?

I Wonder / Me pregunto

  • What if the points did NOT form a straight line — what would that mean?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Graph Ratio Tables
Representar tablas de razones en una gráfica		Plot the paired values from a ratio table as ordered pairs.
Ubicar los valores emparejados de una tabla de razones como pares ordenados.
Coordinate plane
Plano cartesiano		A grid with a line going across and a line going up to plot points.
Una cuadrícula con una línea horizontal y una vertical para marcar puntos.
Ordered pair
Par ordenado		Two numbers (x, y) that tell where a point is on a grid.
Dos números (x, y) que dicen dónde está un punto en una cuadrícula.
Linear pattern
Patrón lineal		Points that make a straight line on a grid.
Puntos que forman una línea recta en una cuadrícula.
Proportional
Proporcional		Two amounts that grow together at the same rate.
Dos cantidades que crecen juntas al mismo ritmo.
Origin
Origen		The point (0, 0) where the two grid lines cross.
El punto (0, 0) donde se cruzan las dos líneas de la cuadrícula.

Practice Preview / Vista previa de práctica

  1. A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?
    1. (8, 24)
    2. (7, 20)
    3. (8, 22)
    4. (10, 24)
  2. Chef Reyes uses 3 cups of flour for every 1 cup of sugar. Plot the ordered pairs from the ratio table: (1,3), (2,6), (3,9), (4,12).
  3. Points from a ratio table are plotted at (1, 4), (2, 8), and (3, 12). What is the ratio of y to x for each point?
    1. 4:1
    2. 1:4
    3. 2:8
    4. 3:4
  4. Find Jada's Mistake
    1. Step 1: Read the ratio table — Cookies: 2, 4, 6 | Cups of milk: 1, 2, 3
    2. Step 2: Write ordered pairs — (1, 2), (2, 4), (3, 6)
    3. Step 3: Plot the points — Plotted (1,2), (2,4), (3,6) on the grid
    4. Step 4: Conclusion — The x-axis is cookies and y-axis is cups of milk

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

Reflection / Reflexión

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