Free Grade 3 Working with Inequalities on a Number Line Lesson Plans
Free Grade 3 lesson plans for Working with Inequalities on a Number Line: 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with inequalities on a number line
Explain working with inequalities on a number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with inequalities on a number line
Calculate working with inequalities on a number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with inequalities on a number line
Compare working with inequalities on a number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with inequalities on a number line
Justify working with inequalities on a number line 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 Working with Inequalities on a Number Line 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 + 15 ≥ 18.[1]
- 2.Solve 3x + 3 < 12.[1]
- 3.Solve 4x + 9 < 45.[1]
- 4.Solve 5x + 5 < 15.[1]
- 5.Solve 5x + 8 ≥ 53.[2]
- 6.Solve 5x + 3 < 18.[2]
- 7.Solve 6x + 3 ≤ 27.[2]
- 8.Solve 5x + 13 ≥ 38.[2]
- 9.Solve 3x + 2 ≥ 11 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 4x + 15 > 47 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 3x + 12 > 39 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 4x + 5 > 33 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x ≥ 1
Subtract 15: 3x ≥ 3. Divide by 3 (positive, so the sign stays): x ≥ 1.
2. x < 3
Subtract 3: 3x < 9. Divide by 3 (positive, so the sign stays): x < 3.
3. x < 9
Subtract 9: 4x < 36. Divide by 4 (positive, so the sign stays): x < 9.
4. x < 2
Subtract 5: 5x < 10. Divide by 5 (positive, so the sign stays): x < 2.
5. x ≥ 9
Subtract 8: 5x ≥ 45. Divide by 5 (positive, so the sign stays): x ≥ 9.
6. x < 3
Subtract 3: 5x < 15. Divide by 5 (positive, so the sign stays): x < 3.
7. x ≤ 4
Subtract 3: 6x ≤ 24. Divide by 6 (positive, so the sign stays): x ≤ 4.
8. x ≥ 5
Subtract 13: 5x ≥ 25. Divide by 5 (positive, so the sign stays): x ≥ 5.
9. x ≥ 3
Subtract 2: 3x ≥ 9. Divide by 3 (positive, so the sign stays): x ≥ 3.
10. x > 8
Subtract 15: 4x > 32. Divide by 4 (positive, so the sign stays): x > 8.
11. x > 9
Subtract 12: 3x > 27. Divide by 3 (positive, so the sign stays): x > 9.
12. x > 7
Subtract 5: 4x > 28. Divide by 4 (positive, so the sign stays): x > 7.
Worked examples
Solve 3x + 5 > 29.
- Subtract 5: 3x > 24.
- Divide by 3 (positive, so the sign stays): x > 8.
- Answer: x > 8
Solve 4x + 1 ≤ 33.
- Subtract 1: 4x ≤ 32.
- Divide by 4 (positive, so the sign stays): x ≤ 8.
- Answer: x ≤ 8
Solve 6x + 4 ≥ 46 and list the positive integers that satisfy it (if finite).
- Subtract 4: 6x ≥ 42.
- Divide by 6 (positive, so the sign stays): x ≥ 7.
- Answer: x ≥ 7
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 Working with Inequalities on a Number Line 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 Introducing Inequalities on a Number Line, Solving Linear Inequalities. 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 Working with Inequalities on a Number Line?
- Move on to Inequalities on a Number Line in Context, Inequality Notation, Solving Linear Inequalities, which build directly on this idea.
Related resources
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