Free Grade 3 Working with Cubes Worksheets
Free Grade 3 worksheets for Working with Cubes: 12 real questions with a full answer key and worked solutions. A power tells you how many times to multiply a number by itself. A square root undoes squaring. When multiplying powers of the same base, add the indices.
Free
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with cubes
Identify working with cubes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with cubes
Explain working with cubes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with cubes
Calculate working with cubes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with cubes
Compare working with cubes 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 Cubes works
A power tells you how many times to multiply a number by itself. A square root undoes squaring. When multiplying powers of the same base, add the indices.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Work out 9² and √81.[1]
- 2.Work out 11² and √121.[1]
- 3.Work out 12² and √144.[1]
- 4.Work out 10² and √100.[1]
- 5.Evaluate 3^4.[2]
- 6.Evaluate 2^3.[2]
- 7.Evaluate 2^4.[2]
- 8.Evaluate 3^3.[2]
- 9.Simplify x^2 × x^2 ÷ x^2.[3]
- 10.Simplify x^2 × x^3 ÷ x^4.[3]
- 11.Simplify x^5 × x^4 ÷ x^5.[3]
- 12.Simplify x^6 × x^6 ÷ x^5.[3]
Show answers and working
1. 81 and 9
9² = 9 × 9 = 81 √81 = 9 because 9 × 9 = 81
2. 121 and 11
11² = 11 × 11 = 121 √121 = 11 because 11 × 11 = 121
3. 144 and 12
12² = 12 × 12 = 144 √144 = 12 because 12 × 12 = 144
4. 100 and 10
10² = 10 × 10 = 100 √100 = 10 because 10 × 10 = 100
5. 81
Multiply 3 by itself 4 times. 3 × 3 × 3 × 3 = 81
6. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
7. 16
Multiply 2 by itself 4 times. 2 × 2 × 2 × 2 = 16
8. 27
Multiply 3 by itself 3 times. 3 × 3 × 3 = 27
9. x^2
Multiplying: add the powers → x^4. Dividing: subtract the powers → x^4 ÷ x^2 = x^2.
10. x^1
Multiplying: add the powers → x^5. Dividing: subtract the powers → x^5 ÷ x^4 = x^1.
11. x^4
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^5 = x^4.
12. x^7
Multiplying: add the powers → x^12. Dividing: subtract the powers → x^12 ÷ x^5 = x^7.
Worked examples
Work out 2² and √4.
- 2² = 2 × 2 = 4
- √4 = 2 because 2 × 2 = 4
- Answer: 4 and 2
Evaluate 4^4.
- Multiply 4 by itself 4 times.
- 4 × 4 × 4 × 4 = 256
- Answer: 256
Simplify x^5 × x^4 ÷ x^4.
- Multiplying: add the powers → x^9.
- Dividing: subtract the powers → x^9 ÷ x^4 = x^5.
- Answer: x^5
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Works out 3² as 6.
Correction: 3² means 3 × 3, not 3 × 2.
Multiplies indices when multiplying powers.
Correction: x³ × x⁴ = x⁷ — add, don't multiply.
Teacher tips
- · Write powers out in full before using index laws.
Parent tips
- · Spot square numbers on tiles or a chessboard.
Real-life applications
- · Area in square units, computer storage (powers of 2).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Working with Cubes
One concept, one ecosystem — all of it free.
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Working with Cubes worksheet really free?
- Yes. Every worksheets 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 Cubes, Squares. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Cubes?
- Move on to Cubes in Context, Squares, Square Roots, Index Laws, which build directly on this idea.
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