Free Grade 3 Inequality Notation Lesson Plans
Free Grade 3 lesson plans for Inequality Notation: 12 real questions with a full answer key and worked solutions. An inequality gives a range of values. Solve it like an equation, but if you multiply or divide by a negative, flip the sign.
Free
Stretch
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain inequality notation
Explain inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate inequality notation
Calculate inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare inequality notation
Compare inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify inequality notation
Justify inequality notation accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Inequality Notation works
An inequality gives a range of values. Solve it like an equation, but if you multiply or divide by a negative, flip the sign.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Solve 3x + 14 ≥ 35.[1]
- 2.Solve 2x + 7 ≥ 11.[1]
- 3.Solve 4x + 9 ≤ 21.[1]
- 4.Solve 4x + 11 < 31.[1]
- 5.Solve 3x + 14 < 17.[2]
- 6.Solve 5x + 12 < 27.[2]
- 7.Solve 6x + 9 < 27.[2]
- 8.Solve 3x + 13 > 40.[2]
- 9.Solve 5x + 13 ≤ 58 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 2x + 7 > 13 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 3x + 13 ≥ 40 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 5x + 7 < 47 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≥ 7
Subtract 14: 3x ≥ 21. Divide by 3 (positive, so the sign stays): x ≥ 7.
2. x ≥ 2
Subtract 7: 2x ≥ 4. Divide by 2 (positive, so the sign stays): x ≥ 2.
3. x ≤ 3
Subtract 9: 4x ≤ 12. Divide by 4 (positive, so the sign stays): x ≤ 3.
4. x < 5
Subtract 11: 4x < 20. Divide by 4 (positive, so the sign stays): x < 5.
5. x < 1
Subtract 14: 3x < 3. Divide by 3 (positive, so the sign stays): x < 1.
6. x < 3
Subtract 12: 5x < 15. Divide by 5 (positive, so the sign stays): x < 3.
7. x < 3
Subtract 9: 6x < 18. Divide by 6 (positive, so the sign stays): x < 3.
8. x > 9
Subtract 13: 3x > 27. Divide by 3 (positive, so the sign stays): x > 9.
9. x ≤ 9
Subtract 13: 5x ≤ 45. Divide by 5 (positive, so the sign stays): x ≤ 9.
10. x > 3
Subtract 7: 2x > 6. Divide by 2 (positive, so the sign stays): x > 3.
11. x ≥ 9
Subtract 13: 3x ≥ 27. Divide by 3 (positive, so the sign stays): x ≥ 9.
12. x < 8
Subtract 7: 5x < 40. Divide by 5 (positive, so the sign stays): x < 8.
Worked examples
Solve 5x + 4 > 49.
- Subtract 4: 5x > 45.
- Divide by 5 (positive, so the sign stays): x > 9.
- Answer: x > 9
Solve 5x + 14 ≥ 54.
- Subtract 14: 5x ≥ 40.
- Divide by 5 (positive, so the sign stays): x ≥ 8.
- Answer: x ≥ 8
Solve 5x + 14 < 34 and list the positive integers that satisfy it (if finite).
- Subtract 14: 5x < 20.
- Divide by 5 (positive, so the sign stays): x < 4.
- Answer: x < 4
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Forgets to flip the sign when dividing by a negative.
Correction: Test a value to check the direction.
Mixes up < and ≤.
Correction: ≤ includes the boundary; show it with a filled circle.
Teacher tips
- · Show every answer on a number line.
Parent tips
- · Talk about 'at least' and 'no more than' on signs.
Real-life applications
- · Age limits, speed limits, minimum orders.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Inequality Notation lesson plan really free?
- Yes. Every lesson plans on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Equations. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Inequality Notation?
- Move on to Solving Linear Inequalities, Inequalities on a Number Line, Algebraic Expressions, Equations, which build directly on this idea.
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