Year 10 - Maths
Checking and securing understanding of calculations involving negative numbers
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 evaluate calculations involving positive and negative integers.
Key Notes
- Addition of negative integers can be made easier by considering zero pairs.
- Subtractions can all be re-written as additions of the additive inverse.
- The rules for multiplying with negative numbers can be extended to division.
Vocabulary To Learn
- Additive inverse: The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.
- Absolute value: The absolute value of a number is its distance from zero. E.g. 5 and (−5) are both 5 away from zero and so both have an absolute value of 5
Common Mistakes To Avoid
- That addition will always make the result bigger.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Addition of negative integers can be made easier by considering zero pairs. Subtractions can all be re-written as additions of the additive inverse.
2. Use this key word in a maths sentence and explain it clearly. 'Additive inverse'
The additive inverse of a number is a number that, when added to the original number, gives the sum of 0. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: That addition will always make the result bigger. Correction: If pupils are struggling with the concept that adding can make an integer smaller encourage them to use counters and form zero pairs.
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 converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of prime factorisation 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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