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Florida Grade 6 Math · Algebraic Reasoning

MA.6.AR.1.2: Writing and Graphing Inequalities

What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.

Created by a Florida mom · Published by Tropical Learning LLC

Download Free Worksheet (PDF)See worked examples

What Is Benchmark MA.6.AR.1.2?

Students write a real-world description as an inequality of the form x > a, x < a, x ≥ a, or x ≤ a, and show it on a number line. The variable can be on either side (a < x means the same as x > a).

Words like "at least" mean ≥ and "at most" or "no more than" mean ≤. On a number line, a closed dot includes the number (≥, ≤) and an open dot does not (>, <).

Official benchmarkTranslate a real-world written description into an algebraic inequality in the form of x > a, x < a, x ≥ a or x ≤ a. Represent the inequality on a number line.

On the FAST test: part of the Grade 6 reporting category Algebraic Reasoning, which is about 25–36% of the test.

Worked Examples

Worked Example 1

At Least

You must be at least 48 inches tall to ride a roller coaster. Write and graph an inequality for the height h of riders.
  1. 1"At least 48" means 48 or more: h ≥ 48
  2. 2Draw a closed dot at 48, because 48 is included.
  3. 3Shade to the right, toward greater numbers.
Answer: h ≥ 48

Worked Example 2

Fewer Than

A room holds fewer than 30 students. Write and graph an inequality for the number of students s.
  1. 1"Fewer than 30" does not include 30: s < 30
  2. 2Draw an open dot at 30 and shade to the left.
Answer: s < 30

Common Mistakes to Watch For

Using > for "at least"

Wrong:At least 48 inches: h > 48

"At least" includes the number: h ≥ 48.

Using the wrong dot

Wrong:A closed dot at 30 for s < 30

30 is not included in s < 30, so use an open dot.

Helpful Math Tip

Read the inequality aloud with the variable first: "h is greater than or equal to 48." Then check one number on each side.

Related Grade 6 Skills

MA.6.AR.2.1

Testing Values in Equations and Inequalities

MA.6.AR.1.1

Writing and Reading Algebraic Expressions

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Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.