Year 10 - Maths
Checking and securing understanding of prime factorisation
Arithmetic procedures: index laws
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.
Lesson Summary
You will learn to write any positive integer uniquely as a product of its prime factors.
Key Notes
- Every positive integer can be broken down into prime factors.
- Every positive integer can be written as a product of its prime factors.
- Prime factor products can be simplified by using index notation.
Vocabulary To Learn
- Product of primes: Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.
- Prime factors: Prime factors are the factors of a number that are, themselves, prime.
- Prime factorisation: Prime factorisation is a method to find the prime factors of a given integer.
Common Mistakes To Avoid
- Use of addition instead of multiplication when the decomposing the number.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Every positive integer can be broken down into prime factors. Every positive integer can be written as a product of its prime factors.
2. Use this key word in a maths sentence and explain it clearly. 'Product of primes'
Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Use of addition instead of multiplication when the decomposing the number. Correction: Reiterate that the product of prime factors is unique. This should also be helped when setting the decomposition out as products rather than just a 'tree'.
More Lessons In This Unit
- Advanced problem solving with the laws of indices Study Guide
- Checking and securing understanding of calculating with fractions and decimals Study Guide
- Checking and securing understanding of calculations involving negative numbers Study Guide
- Checking and securing understanding of converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of roots and integer indices Study Guide
- Converting any recurring decimal to a fraction Study Guide
- Problem solving with the laws of indices Study Guide
- The laws of indices - division Study Guide
- The laws of indices - fractional exponents Study Guide
- The laws of indices - multiplication Study Guide
- The laws of indices - negative and zero exponents Study Guide
- The laws of indices - raising a power to a power Study Guide
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