Understand Inequalities and Their Solutions

6.AT.9 · Unit 8 · Lesson 5

Name   Period

Objectives / Objetivos

Content Objective: I can graph the solutions of an inequality on a number line.

Language Objective: I can explain my graph using the words number line, open circle, closed circle, and solution set.

Key Idea / Idea clave

Graphing Inequalities on the Number Line. 1. Draw the boundary circle at the given constant number. 2. Open Circle (○) for < or > (boundary value is not included in solution set). 3. Closed Circle (●) for ≤ or ≥ (boundary value is included). Shade right for >, left for <

I Notice / Observo

  • What does 'no earlier than 2:00 PM' mean about the time?
  • Should 2:00 PM itself be included?

I Wonder / Me pregunto

  • What would the graph look like if the suspect arrived before 2:00 PM?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Graph Inequalities
Representar desigualdades en una recta numérica		Show every solution to an inequality on a number line with a boundary point and an arrow.
Mostrar cada solución de una desigualdad en una recta numérica con un punto límite y una flecha.
Number line
Recta numérica		A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right.
Una recta donde los números se colocan en orden; los números son menores a la izquierda y mayores a la derecha.
Open circle
Círculo abierto		An empty circle showing a number is NOT included.
Un círculo vacío que muestra que un número NO está incluido.
Closed circle
Círculo cerrado		A filled-in circle showing a number IS included.
Un círculo relleno que muestra que un número SÍ está incluido.
Solution set
Conjunto solución		All the numbers that make the inequality true.
Todos los números que hacen verdadera la desigualdad.
Inequality
Desigualdad		A math sentence that compares two sides with <, >, ≤, or ≥.
Una oración matemática que compara dos lados con <, >, ≤ o ≥.

Practice Preview / Vista previa de práctica

  1. Which graph represents x < 5?
    1. Open circle at 5, shaded left
    2. Closed circle at 5, shaded left
    3. Open circle at 5, shaded right
    4. Closed circle at 5, shaded right
  2. Match each inequality to its graph description
    • → ___
    • → ___
    • → ___
  3. Read the graph description and write the inequality it represents. Then graph it.
  4. Find the Graphing Error
    1. Step 1: Inequality — x > 6
    2. Step 2: Circle type — Closed circle at 6
    3. Step 3: Shade direction — Shade right
    4. Step 4: Graph — Closed circle at 6, shaded right

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

Reflection / Reflexión

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