At Least, At Most: Writing and Solving Inequalities

About This Resource

A complete Grade 6 math pack on inequalities. Students learn the symbols , ≤ and ≥, translate phrases such as at least and at most, write inequalities for real situations, test whether a value is a solution, show solutions on a number line and solve one-step inequalities. Includes slides with worked examples, a lesson plan, worksheet, quiz, homework, flashcards, a rubric and answer keys.

Overview

An equation has one solution, but an inequality usually has many. Students learn four symbols: < (less than), > (greater than), ≤ (less than or equal to) and ≥ (greater than or equal to), and connect them to everyday phrases: You must be at least 12 means a ≥ 12, and at most 8 people means p ≤ 8. They test values by substituting them, show solutions on a number line with open circles (for < and >) and closed circles (for ≤ and ≥), and solve one-step inequalities by doing the same operation to both sides, just like equations. Real-life contexts include age limits, elevator capacity, speed limits and temperatures.

Resource Details

Subject: Math
Topic: Inequalities
Category: Number Sense
File Type: PDF
File Size: 301.7 KB
Published: 12 Nov 2026
Downloads: 0

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Grade 6 math (ages 11–12) 55 minutes Algebra inequality symbols substitution solving number lines

Learning Objectives

Read and write inequalities using , ≤ and ≥.
Decide whether a value is a solution and show solutions on a number line.
Solve one-step inequalities and write inequalities for real situations.

How to Use This Resource

Start with the slides: a sign says You must be at least 120 cm tall. Ask: "Who can ride? Is 120 cm allowed?"
Teach the symbols and the worked examples, then do worksheet activities 1 and 2 together.
Students complete activities 3 to 6, then use the quiz and send the homework page home.

Classroom Activity Ideas

Human number line: students stand on a floor number line; call out an inequality and students who are solutions step forward.
Sign hunt: students find or invent signs with limits (speed limits, age limits) and write them as inequalities.
Solution or not? Show an inequality and a value; students hold up yes or no cards.

Differentiation

Support: give a symbol and phrase card and use whole numbers on a number line from 0 to 20. Challenge: students write and solve two-step inequalities and explore what happens when both sides are multiplied by a negative number.

Assessment

Use the worksheet and quiz to check reading, testing and solving inequalities. Use the rubric to assess real-life problems and explanations.

Teacher Tips

Students often mix up the symbols. Remind them that the smaller end points to the smaller number. The phrases at least and no less than mean ≥, and at most and no more than mean ≤. This pack uses positive coefficients only, so the inequality sign never needs to be reversed.

What's Included

10-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (7 words with meanings and examples)
Student worksheet (6 activities)
Quiz / assessment (3 parts)
Homework practice page
Printable flashcards: 7 A5 picture cards (separate PDF)
Assessment rubric (4 levels)
Lesson slides (editable PowerPoint)
Editable Word version of all student pages
Complete answer key (also as a separate PDF)