Free Grade 3 Cubes in Context Lessons
Free Grade 3 lessons for Cubes in Context: 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
Stretch
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain cubes in context
Explain cubes in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate cubes in context
Calculate cubes in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare cubes in context
Compare cubes in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify cubes in context
Justify cubes in context 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 Cubes in Context 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 12² and √144.[1]
- 2.Work out 9² and √81.[1]
- 3.Work out 5² and √25.[1]
- 4.Work out 6² and √36.[1]
- 5.Evaluate 2^3.[2]
- 6.Evaluate 5^3.[2]
- 7.Evaluate 3^4.[2]
- 8.Evaluate 3^3.[2]
- 9.Simplify x^7 × x^4 ÷ x^6.[3]
- 10.Simplify x^7 × x^7 ÷ x^2.[3]
- 11.Simplify x^6 × x^2 ÷ x^5.[3]
- 12.Simplify x^6 × x^3 ÷ x^3.[3]
Show answers and working
1. 144 and 12
12² = 12 × 12 = 144 √144 = 12 because 12 × 12 = 144
2. 81 and 9
9² = 9 × 9 = 81 √81 = 9 because 9 × 9 = 81
3. 25 and 5
5² = 5 × 5 = 25 √25 = 5 because 5 × 5 = 25
4. 36 and 6
6² = 6 × 6 = 36 √36 = 6 because 6 × 6 = 36
5. 8
Multiply 2 by itself 3 times. 2 × 2 × 2 = 8
6. 125
Multiply 5 by itself 3 times. 5 × 5 × 5 = 125
7. 81
Multiply 3 by itself 4 times. 3 × 3 × 3 × 3 = 81
8. 27
Multiply 3 by itself 3 times. 3 × 3 × 3 = 27
9. x^5
Multiplying: add the powers → x^11. Dividing: subtract the powers → x^11 ÷ x^6 = x^5.
10. x^12
Multiplying: add the powers → x^14. Dividing: subtract the powers → x^14 ÷ x^2 = x^12.
11. x^3
Multiplying: add the powers → x^8. Dividing: subtract the powers → x^8 ÷ x^5 = x^3.
12. x^6
Multiplying: add the powers → x^9. Dividing: subtract the powers → x^9 ÷ x^3 = x^6.
Worked examples
Work out 4² and √16.
- 4² = 4 × 4 = 16
- √16 = 4 because 4 × 4 = 16
- Answer: 16 and 4
Evaluate 4^3.
- Multiply 4 by itself 3 times.
- 4 × 4 × 4 = 64
- Answer: 64
Simplify x^6 × x^6 ÷ x^3.
- Multiplying: add the powers → x^12.
- Dividing: subtract the powers → x^12 ÷ x^3 = x^9.
- Answer: x^9
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 Cubes in Context
One concept, one ecosystem — all of it free.
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Learn — Meet the idea.
Practice — Build fluency.
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Assess — Prove mastery.
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Frequently asked
- Is this Grade 3 Cubes in Context lesson really free?
- Yes. Every lessons 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 Working with Cubes, Introducing Cubes, Squares. 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 Cubes in Context?
- Move on to Squares, Square Roots, Index Laws, Standard Index Form, which build directly on this idea.
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