Printable Inequality Check Worksheet | Grade 6 Math

This Grade 6 worksheet builds students' ability to test whether a given value satisfies a one-step inequality using substitution. Across 16 problems organized in three progressive parts, students move from testing a single candidate value to evaluating multi-constraint situations, developing the conceptual fluency required by standard 6.EE.B.5.

At a Glance

• Grade: 6 · Subject: Math
• Standard: 6.EE.B.5 — Substitute values into inequalities to determine whether they are solutions
• Skill Focus: Testing candidate values in one-step inequalities by substitution
• Format: 4 pages · 16 problems · Answer key included · PDF
• Best For: Guided practice after direct instruction
• Time: 30–45 minutes

The worksheet spans 4 student-facing pages plus a 2-page answer key. Part A opens with a rule box distinguishing strict inequalities from inclusive ones, then presents 4 problems where students substitute a single candidate value and state whether the resulting statement is true or false. Part B contains 8 problems featuring candidate sets, a structured substitution table, and two multiple-choice items. Part C closes with 4 challenge problems involving boundary-value reasoning, compound constraints, and error analysis.

• Guided practice (Part A, 4 problems): A printed rule box defines strict and inclusive boundary behavior before students test one candidate at a time, keeping cognitive load low while anchoring the substitution procedure.
• Supported practice (Part B, 8 problems): Students test sets of two to four candidate values, complete a pre-formatted substitution table, and choose among answer sets.
• Independent practice (Part C, 4 problems): No scaffolds. Students reason about boundary values, identify a peer's substitution error, and test readings against two simultaneous constraints.

Standards Alignment
Primary standard: 6.EE.B.5 — Which values from a specified set make an inequality true? Supporting work connects to 6.EE.B.8, which asks students to write and graph inequalities representing real-world constraints. Both standard codes can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It
Assign Part A immediately after direct instruction on substitution to check for initial understanding. Use Parts B and C the following day as a formative assessment: watch whether students correctly handle boundary values (e.g., the p = 12 and s = 15.0 items) — consistent errors there signal a need to revisit the strict-vs.-inclusive distinction. For a single-period lesson, the full worksheet fits in 30–45 minutes; Parts A and B alone work as a 20-minute exit check.

Who It's For
Designed for sixth-grade math students encountering one-step inequalities for the first time. Students needing additional support benefit from the rule box and substitution table; students ready for extension are challenged by the dual-constraint greenhouse problem and the error-analysis item in Part C.

This 4-page, 16-problem worksheet targets standard 6.EE.B.5, the skill of using substitution to determine whether a value satisfies an inequality. Research supports structured substitution practice as a foundation for algebraic reasoning: Fisher & Frey (2014) identify gradual-release frameworks — moving students from modeled to guided to independent work — as among the highest-leverage instructional designs for building procedural fluency with conceptual understanding. The three-part progression in this worksheet operationalizes that framework directly, beginning with a rule box and single-value tests, advancing through candidate sets and a pre-formatted table, and culminating in boundary-value reasoning and peer-error analysis. All 16 problems are grounded in real-world contexts that make the abstract substitution process concrete and meaningful for sixth-grade learners. A complete answer key with worked substitution statements is included.