Neft Teacher · Notes Packet

Unit 7 · Standard 6.EE.8

Graph Inequalities

Lesson 7-5

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

Illustration of Number line: A line with numbers in order. You use it to show answers.

A horizontal line with marks at 0, 1, 2, 3, ... showing where values fall

Number line

A line with numbers in order. You use it to show answers.

Illustration of Open circle: An empty circle showing a number is NOT included.

x > 5: open circle at 5 means 5 itself is NOT a solution, but 5.1, 6, 7, ... are

Open circle

An empty circle showing a number is NOT included.

Illustration of Closed circle: A filled-in circle showing a number IS included.

x ≥ 5: closed circle at 5 means 5 IS a solution, and so are 6, 7, 8, ...

Closed circle

A filled-in circle showing a number IS included.

Illustration of Solution set: All the numbers that make the inequality true.

For x > 3, the solution set includes 3.1, 4, 5, 10, 100 — any number greater than 3

Solution set

All the numbers that make the inequality true.

Key Ideas & Notes

Think About It

  • What does 'no earlier than 2:00 PM' mean about the time?
  • Should 2:00 PM itself be included?
  • Which direction on the number line would you shade?

My Notes

Guided Examples

Example 1

Which graph represents x < 5?

Solution: x < 5 means 5 is NOT included (open circle) and values less than 5 are shaded (left).

Answer: A. Open circle at 5, shaded left

Example 2

Which graph represents x ≥ 3?

Solution: x ≥ 3 means 3 IS included (closed circle) and values greater than or equal to 3 are shaded (right).

Answer: A. Closed circle at 3, shaded right

Example 3

Which graph represents x > 8?

Solution: x > 8 means 8 is NOT included (open circle) and values greater than 8 are shaded to the right.

Answer: A. Open circle at 8, shaded right

Write About the Math The Writing Revolution

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

1. Kernel Sentence subject + verb

Model: Number line is a line with numbers in order. You use it to show answers.Recta numérica es una línea con números en orden. La usas para mostrar respuestas.

Write a kernel sentence about number line. Use a subject and a verb.Escribe una oración base sobre recta numérica. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Number line matters in mathRecta numérica importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Number line matters in math because ___.Recta numérica importa en matemáticas porque ___.

butpero

Number line matters in math, but ___.Recta numérica importa en matemáticas, pero ___.

soentonces

Number line matters in math, so ___.Recta numérica importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about number line.Di un hecho verdadero sobre number line.

Number line ___.

QuestionPregunta

Ask a question about number line.Haz una pregunta sobre number line.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about number line.Muestra entusiasmo sobre number line.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with number line.Dile a un compañero qué hacer con number line.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I used a ___ circle because ___.Usé un círculo ___ porque ___.

The arrow points ___ because ___.La flecha apunta ___ porque ___.

This shows a limit like ___.Esto muestra un límite como ___.

Try It

Solve on your own. Check the answer key when you are done.

1. Which graph represents x ≤ 10?

  1. Closed circle at 10, shaded left
  2. Open circle at 10, shaded left
  3. Closed circle at 10, shaded right
  4. Open circle at 10, shaded right
Show your work:

2. A number line shows a closed circle at 8 and is shaded to the left. Which inequality does this represent?

  1. x ≤ 8
  2. x < 8
  3. x ≥ 8
  4. x > 8
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A theme park has two rides. Ride A requires height h > 48 inches. Ride B requires height h ≥ 48 inches. A child is exactly 48 inches tall. Which ride can they go on? Explain using number line graphs for both inequalities.

Sentence starter: For Ride A (h > 48), the graph has a ___ circle at 48. Since 48 > 48 is ___, the child ___ ride A. For Ride B (h ≥ 48), the graph has a ___ circle at 48. Since 48 ≥ 48 is ___, the child ___ ride B.

Show your work:

Reflect — Exit Ticket

How would you graph the inequality x ≥ 9?

  1. Closed circle at 9, shaded right
  2. Open circle at 9, shaded right
  3. Closed circle at 9, shaded left
  4. Open circle at 9, shaded left
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. Closed circle at 10, shaded left — x ≤ 10 means 10 IS included (closed circle) and values less than or equal to 10 are shaded (left).
  2. Try It 2: A. x ≤ 8 — Closed circle means the value is included (≤ or ≥). Shaded left means less than or equal to: x ≤ 8.
  3. Exit Ticket: A. Closed circle at 9, shaded right — x ≥ 9 means 9 is included (closed circle) and values are 9 or greater (shaded right).

Writing (TWR) — what to look for