Sixth Grade · Math · week 24

Inequalities and their graphs

Write and interpret simple inequalities using >, <, >=, and <=, and graph their solutions on a number line.

An inequality compares two amounts that are not necessarily equal, using symbols: > (greater than), < (less than), >= (greater than or equal to), <= (less than or equal to).

Unlike an equation, an inequality usually has MANY solutions, not just one number. "x > 3" means any number greater than 3 makes it true: 3.1, 4, 100, and so on.

To graph an inequality on a number line, use an open circle for > or < (the boundary number is NOT included) and a closed circle for >= or <= (the boundary number IS included), then shade the direction of all the solutions.

📋 For the teacher
Teach it (10–15 min):
  • Practice reading the symbols out loud in full words every time - "greater than or equal to," not just "the wiggly one."
  • Use the open-versus-closed circle rule as a simple test: does the boundary number itself count as a solution?
  • Connect "at least" to >= and "at most" to <= - these phrases show up constantly in word problems.
  • Test a few sample numbers against the inequality, like plugging into an equation, to confirm the shaded direction is correct.
Talk about it:
  • What is the difference between an open circle and a closed circle on an inequality graph?
  • How many solutions does an inequality usually have, compared to an equation?
  • What everyday phrases mean "at least" or "at most"?

Mastery looks like: They write an inequality from a word phrase and correctly graph it with the right circle type and shading direction.

Common stumbles: Using an open circle when the boundary should be included, or the reverse; shading the wrong direction on the number line.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

Number LineCount, add, subtract, and skip-count with animated hops and a friendly voice.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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