CH03-09 lesson

Graphing Inequalities on a Number Line Learning Activity

A focused Grade 6 learning session for Graphing Inequalities on a Number Line using visual models, worked examples, strategy guidance, and a short mastery check.

Start the lesson Print practice sample
15
minutes
6
lesson parts
11
practice items
Learning goal

Students will build Grade 6 mastery of graphing inequalities on a number line using models, equations, and test-style reasoning.

Student goal: I can solve problems involving graphing inequalities on a number line.

Helpful first: Writing Inequalities
concept

Learn the Idea

Graphing Inequalities on a Number Line means reading, creating, and explaining displays so data can answer real questions.

  • Read the title, labels, and scale before answering.
  • Use the scale value instead of counting marks as ones when the graph is scaled.
  • Compare categories by subtracting or adding values from the display.
  • Explain what the data shows in a complete sentence.
visual model

See the Math

Visual Model 1

Question: Which number line represents the inequality \(x>2\)?

Visual Model 1

  • A. An open circle at \(2\) with an arrow pointing right
  • B. A closed circle at \(2\) with an arrow pointing right
  • C. An open circle at \(2\) with an arrow pointing left
  • D. A closed circle at \(2\) with an arrow pointing left

Why it works: \(x>2\) means \(x\) is strictly greater than \(2\), so use an open circle (not including \(2\)) with the arrow pointing toward larger values.

Answer: An open circle at \(2\) with an arrow pointing right

worked example

Follow a Worked Example

Example 1

Question: Which number line shows the solution to \(x \le -1\)?

Example 1

  • A. Closed circle at \(-1\), arrow pointing right
  • B. Open circle at \(-1\), arrow pointing left
  • C. Closed circle at \(-1\), arrow pointing left
  • D. Closed circle at \(1\), arrow pointing left
  1. \(x \le -1\) means \(x\) equals \(-1\) or is less than \(-1\).
  2. A closed circle (filled) includes \(-1\), and the arrow points left (toward smaller values).

Answer: Closed circle at \(-1\), arrow pointing left

Example 2

Question: What inequality matches this number line?

Example 2

  • A. \(x > 6\)
  • B. \(x < 6\)
  • C. \(x \ge 6\)
  • D. \(x \le 6\)
  1. An open circle at \(6\) means \(6\) is not included.
  2. The arrow points left toward smaller values, so the inequality is \(x < 6\).

Answer: \(x < 6\)

real world

Connect It to a Real Situation

Problem 1

Question: A student needs to score more than \(80\%\) to pass. Which inequality represents passing scores?

  • A. \(s \le 80\)
  • B. \(s < 80\)
  • C. \(s > 80\)
  • D. \(s \ge 80\)

Why it works: "More than \(80\%\)" means strictly greater than \(80\), so the inequality is \(s > 80\) (not \(\ge\)).

Answer: \(s > 80\)

strategy

Avoid Mistakes and Choose a Strategy

  • Ignoring the graph scale.
  • Reading the wrong category or axis label.
  • Answering a comparison question without subtracting.
  • Writing a number without explaining what it represents.
  • Circle the scale before using the graph.
  • Write down the value for each category you compare.
  • Use addition for totals and subtraction for differences.
  • Answer in words so the data result has meaning.
summary

Remember the Key Idea

Graphing Inequalities on a Number Line becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Read the scale before reading the answer.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G6-C03-T09-Q001 About 1 min

Which number line represents the inequality \(x>2\)?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q001
  1. A An open circle at \(2\) with an arrow pointing right
  2. B A closed circle at \(2\) with an arrow pointing right
  3. C An open circle at \(2\) with an arrow pointing left
  4. D A closed circle at \(2\) with an arrow pointing left
Check answer and explanation

Answer A: An open circle at \(2\) with an arrow pointing right

\(x>2\) means \(x\) is strictly greater than \(2\), so use an open circle (not including \(2\)) with the arrow pointing toward larger values.

G6-C03-T09-Q002 About 1 min

Which inequality is represented by the number line?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q002
  1. A \(x < 3\)
  2. B \(x \le 3\)
  3. C \(x \ge 3\)
  4. D \(x > 3\)
Check answer and explanation

Answer C: \(x \ge 3\)

A filled (closed) circle at \(3\) with an arrow pointing right indicates the number \(3\) is included and all numbers greater than \(3\) are solutions.

guided

1 question
G6-C03-T09-Q003 About 1 min

Which number line shows the solution to \(x \le -1\)?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q003
  1. A Closed circle at \(-1\), arrow pointing right
  2. B Open circle at \(-1\), arrow pointing left
  3. C Closed circle at \(-1\), arrow pointing left
  4. D Closed circle at \(1\), arrow pointing left
Check answer and explanation

Answer C: Closed circle at \(-1\), arrow pointing left

\(x \le -1\) means \(x\) equals \(-1\) or is less than \(-1\). A closed circle (filled) includes \(-1\), and the arrow points left (toward smaller values).

practice

5 questions
G6-C03-T09-Q004 About 1 min

What inequality matches this number line?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q004
  1. A \(x > 6\)
  2. B \(x < 6\)
  3. C \(x \ge 6\)
  4. D \(x \le 6\)
Check answer and explanation

Answer B: \(x < 6\)

An open circle at \(6\) means \(6\) is not included. The arrow points left toward smaller values, so the inequality is \(x < 6\).

G6-C03-T09-Q005 About 1 min

Graph the inequality \(x \ge -2\) on a number line. Which description matches your graph?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q005
  1. A Closed circle at \(-2\), arrow left
  2. B Open circle at \(-2\), arrow right
  3. C Closed circle at \(-2\), arrow right
  4. D Open circle at \(-2\), arrow left
Check answer and explanation

Answer C: Closed circle at \(-2\), arrow right

\(x \ge -2\) includes \(-2\) (closed circle) and all numbers greater than \(-2\) (arrow points right).

G6-C03-T09-Q006 About 1 min

Which inequality represents "all numbers less than \(5\)"?

  1. A \(x \le 5\)
  2. B \(x < 5\)
  3. C \(x > 5\)
  4. D \(x \ge 5\)
Check answer and explanation

Answer B: \(x < 5\)

"Less than" does not include the boundary value, so we use the strict inequality \(x < 5\) (not \(\le\)).

G6-C03-T09-Q007 About 1 min

Which number line shows \(x < -3\)?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q007
  1. A Open circle at \(-3\), arrow left
  2. B Closed circle at \(-3\), arrow left
  3. C Open circle at \(-3\), arrow right
  4. D Closed circle at \(3\), arrow left
Check answer and explanation

Answer A: Open circle at \(-3\), arrow left

\(x < -3\) means \(-3\) is not included (open circle) and we want all numbers less than \(-3\) (arrow pointing left).

G6-C03-T09-Q008 About 1 min

A temperature must be at most \(32°\text{F}\) to freeze. Which inequality represents this?

  1. A \(T > 32\)
  2. B \(T \ge 32\)
  3. C \(T < 32\)
  4. D \(T \le 32\)
Check answer and explanation

Answer D: \(T \le 32\)

"At most" means "less than or equal to," so the inequality is \(T \le 32\).

exit

3 questions
G6-C03-T09-Q009 About 1 min

Which number line represents \(x \le 0\)?

Graphing Inequalities on a Number Line visual for G6-C03-T09-Q009
  1. A Open circle at \(0\), arrow left
  2. B Closed circle at \(0\), arrow right
  3. C Open circle at \(0\), arrow right
  4. D Closed circle at \(0\), arrow left
Check answer and explanation

Answer D: Closed circle at \(0\), arrow left

\(x \le 0\) includes \(0\) (closed circle) and all numbers less than \(0\) (arrow points left).

G6-C03-T09-Q010 About 1 min

Which inequality means "all numbers greater than or equal to \(-5\)"?

  1. A \(x > -5\)
  2. B \(x < -5\)
  3. C \(x \le -5\)
  4. D \(x \ge -5\)
Check answer and explanation

Answer D: \(x \ge -5\)

"Greater than or equal to" uses the \(\ge\) symbol, so the inequality is \(x \ge -5\).

G6-C03-T09-Q011 About 1 min

A student needs to score more than \(80\%\) to pass. Which inequality represents passing scores?

  1. A \(s \le 80\)
  2. B \(s < 80\)
  3. C \(s > 80\)
  4. D \(s \ge 80\)
Check answer and explanation

Answer C: \(s > 80\)

"More than \(80\%\)" means strictly greater than \(80\), so the inequality is \(s > 80\) (not \(\ge\)).

Keep the learning path connected
Previous skillWriting Inequalities Recommended nextTwo Quantities That Change Together Same strandExponents and Order of Operations Same strandTranslating Words into Expressions
Page UP