Free Grade 3 Introducing Inequality Notation Techniques Lessons
Free Grade 3 lessons for Introducing Inequality Notation Techniques: 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.
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Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing inequality notation techniques
Explain introducing inequality notation techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing inequality notation techniques
Calculate introducing inequality notation techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing inequality notation techniques
Compare introducing inequality notation techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing inequality notation techniques
Justify introducing inequality notation techniques 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 Introducing Inequality Notation Techniques 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 5x + 6 > 11.[1]
- 2.Solve 4x + 9 > 21.[1]
- 3.Solve 4x + 15 < 47.[1]
- 4.Solve 3x + 4 > 19.[1]
- 5.Solve 6x + 2 < 8.[2]
- 6.Solve 5x + 10 < 15.[2]
- 7.Solve 5x + 4 < 24.[2]
- 8.Solve 4x + 3 < 7.[2]
- 9.Solve 2x + 11 ≥ 29 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 2x + 1 > 3 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 5x + 7 ≥ 12 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 3x + 12 ≤ 24 and list the positive integers that satisfy it (if finite).[3]
Show answers and working
1. x > 1
Subtract 6: 5x > 5. Divide by 5 (positive, so the sign stays): x > 1.
2. x > 3
Subtract 9: 4x > 12. Divide by 4 (positive, so the sign stays): x > 3.
3. x < 8
Subtract 15: 4x < 32. Divide by 4 (positive, so the sign stays): x < 8.
4. x > 5
Subtract 4: 3x > 15. Divide by 3 (positive, so the sign stays): x > 5.
5. x < 1
Subtract 2: 6x < 6. Divide by 6 (positive, so the sign stays): x < 1.
6. x < 1
Subtract 10: 5x < 5. Divide by 5 (positive, so the sign stays): x < 1.
7. x < 4
Subtract 4: 5x < 20. Divide by 5 (positive, so the sign stays): x < 4.
8. x < 1
Subtract 3: 4x < 4. Divide by 4 (positive, so the sign stays): x < 1.
9. x ≥ 9
Subtract 11: 2x ≥ 18. Divide by 2 (positive, so the sign stays): x ≥ 9.
10. x > 1
Subtract 1: 2x > 2. Divide by 2 (positive, so the sign stays): x > 1.
11. x ≥ 1
Subtract 7: 5x ≥ 5. Divide by 5 (positive, so the sign stays): x ≥ 1.
12. x ≤ 4
Subtract 12: 3x ≤ 12. Divide by 3 (positive, so the sign stays): x ≤ 4.
Worked examples
Solve 3x + 15 ≤ 27.
- Subtract 15: 3x ≤ 12.
- Divide by 3 (positive, so the sign stays): x ≤ 4.
- Answer: x ≤ 4
Solve 6x + 4 ≥ 46.
- Subtract 4: 6x ≥ 42.
- Divide by 6 (positive, so the sign stays): x ≥ 7.
- Answer: x ≥ 7
Solve 4x + 3 ≥ 19 and list the positive integers that satisfy it (if finite).
- Subtract 3: 4x ≥ 16.
- Divide by 4 (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
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- What should a learner already know before this?
- Start with Introducing Inequality Notation Essentials, Equations. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Introducing Inequality Notation Techniques?
- Move on to Introducing Inequality Notation Word Problems, Introducing Inequality Notation Common Errors, Working with Inequality Notation, Inequality Notation in Context, which build directly on this idea.
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