Free Grade 3 Working with Introducing Inequality Notation Common Errors Lessons
Free Grade 3 lessons for Working with Introducing Inequality Notation Common Errors: 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with introducing inequality notation common errors
Identify working with introducing inequality notation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with introducing inequality notation common errors
Explain working with introducing inequality notation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with introducing inequality notation common errors
Calculate working with introducing inequality notation common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with introducing inequality notation common errors
Compare working with introducing inequality notation common errors 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 Introducing Inequality Notation Common Errors 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 4x + 11 < 23.[1]
- 3.Solve 6x + 13 ≤ 43.[1]
- 4.Solve 3x + 9 > 36.[1]
- 5.Solve 4x + 12 ≤ 44.[2]
- 6.Solve 5x + 7 < 22.[2]
- 7.Solve 5x + 14 ≥ 49.[2]
- 8.Solve 6x + 6 ≥ 24.[2]
- 9.Solve 5x + 9 > 44 and list the positive integers that satisfy it (if finite).[3]
- 10.Solve 4x + 12 ≤ 36 and list the positive integers that satisfy it (if finite).[3]
- 11.Solve 5x + 5 > 25 and list the positive integers that satisfy it (if finite).[3]
- 12.Solve 5x + 6 ≥ 21 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 < 3
Subtract 11: 4x < 12. Divide by 4 (positive, so the sign stays): x < 3.
3. x ≤ 5
Subtract 13: 6x ≤ 30. Divide by 6 (positive, so the sign stays): x ≤ 5.
4. x > 9
Subtract 9: 3x > 27. Divide by 3 (positive, so the sign stays): x > 9.
5. x ≤ 8
Subtract 12: 4x ≤ 32. Divide by 4 (positive, so the sign stays): x ≤ 8.
6. x < 3
Subtract 7: 5x < 15. Divide by 5 (positive, so the sign stays): x < 3.
7. x ≥ 7
Subtract 14: 5x ≥ 35. Divide by 5 (positive, so the sign stays): x ≥ 7.
8. x ≥ 3
Subtract 6: 6x ≥ 18. Divide by 6 (positive, so the sign stays): x ≥ 3.
9. x > 7
Subtract 9: 5x > 35. Divide by 5 (positive, so the sign stays): x > 7.
10. x ≤ 6
Subtract 12: 4x ≤ 24. Divide by 4 (positive, so the sign stays): x ≤ 6.
11. x > 4
Subtract 5: 5x > 20. Divide by 5 (positive, so the sign stays): x > 4.
12. x ≥ 3
Subtract 6: 5x ≥ 15. Divide by 5 (positive, so the sign stays): x ≥ 3.
Worked examples
Solve 3x + 4 ≥ 16.
- Subtract 4: 3x ≥ 12.
- Divide by 3 (positive, so the sign stays): x ≥ 4.
- Answer: x ≥ 4
Solve 6x + 10 > 64.
- Subtract 10: 6x > 54.
- Divide by 6 (positive, so the sign stays): x > 9.
- Answer: x > 9
Solve 6x + 11 > 53 and list the positive integers that satisfy it (if finite).
- Subtract 11: 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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