Free Grade 3 Equations Quizzes
Free Grade 3 quizzes for Equations: 12 real questions with a full answer key and worked solutions. An equation is a balance. Do the same thing to both sides until the letter is on its own, then check by substituting back.
Free
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify equations
Identify equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain equations
Explain equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate equations
Calculate equations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare equations
Compare equations 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 Equations works
An equation is a balance. Do the same thing to both sides until the letter is on its own, then check by substituting back.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Solve x + 10 = 22.[1]
- 2.Solve x + 8 = 17.[1]
- 3.Solve x + 14 = 14.[1]
- 4.Solve x + 1 = 1.[1]
- 5.Solve 2x + 14 = 16.[2]
- 6.Solve 2x + 1 = 15.[2]
- 7.Solve 7x + 20 = 34.[2]
- 8.Solve 2x + 3 = 5.[2]
- 9.Solve 8x + 5 = 3x + 45.[3]
- 10.Solve 2x + 8 = 1x + 11.[3]
- 11.Solve 6x + 12 = 1x + 17.[3]
- 12.Solve 6x + 13 = 5x + 5.[3]
Show answers and working
1. x = 12
Subtract 10 from both sides: x = 12. Check: 1 × 12 + 10 = 22.
2. x = 9
Subtract 8 from both sides: x = 9. Check: 1 × 9 + 8 = 17.
3. x = 0
Subtract 14 from both sides: x = 0. Check: 1 × 0 + 14 = 14.
4. x = 0
Subtract 1 from both sides: x = 0. Check: 1 × 0 + 1 = 1.
5. x = 1
Subtract 14 from both sides: 2x = 2. Divide by 2: x = 1. Check: 2 × 1 + 14 = 16.
6. x = 7
Subtract 1 from both sides: 2x = 14. Divide by 2: x = 7. Check: 2 × 7 + 1 = 15.
7. x = 2
Subtract 20 from both sides: 7x = 14. Divide by 7: x = 2. Check: 7 × 2 + 20 = 34.
8. x = 1
Subtract 3 from both sides: 2x = 2. Divide by 2: x = 1. Check: 2 × 1 + 3 = 5.
9. x = 8
Subtract 3x from both sides: 5x + 5 = 45. Subtract 5: 5x = 40. Divide by 5: x = 8.
10. x = 3
Subtract 1x from both sides: 1x + 8 = 11. Subtract 8: 1x = 3. Divide by 1: x = 3.
11. x = 1
Subtract 1x from both sides: 5x + 12 = 17. Subtract 12: 5x = 5. Divide by 5: x = 1.
12. x = -8
Subtract 5x from both sides: 1x + 13 = 5. Subtract 13: 1x = -8. Divide by 1: x = -8.
Worked examples
Solve x + 15 = 24.
- Subtract 15 from both sides: x = 9.
- Check: 1 × 9 + 15 = 24.
- Answer: x = 9
Solve 4x + 16 = 36.
- Subtract 16 from both sides: 4x = 20.
- Divide by 4: x = 5.
- Check: 4 × 5 + 16 = 36.
- Answer: x = 5
Solve 8x + 13 = 6x + -3.
- Subtract 6x from both sides: 2x + 13 = -3.
- Subtract 13: 2x = -16.
- Divide by 2: x = -8.
- Answer: x = -8
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Does an operation to only one side.
Correction: Keep the balance — both sides, every time.
Uses the wrong inverse (subtracts to undo multiplying).
Correction: Undo × with ÷ and + with −.
Teacher tips
- · Always ask pupils to substitute their answer back in.
Parent tips
- · 'I think of a number' puzzles at dinner.
Real-life applications
- · Working out an unknown price or time from a total.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Equations
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Equations quiz really free?
- Yes. Every quizzes 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 Algebraic Expressions, Number Sense. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Equations?
- Move on to Inequalities, Sequences, Quadratics, Simultaneous Equations, which build directly on this idea.
Related resources
Stuck on Equations? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor