EDEXCEL GCSE FOUNDATION MATHS - What is Estimation

Edexcel GCSE Foundation Maths: What is Estimation?

Estimation is a crucial skill in mathematics, allowing you to quickly approximate the answer to a problem without needing to perform exact calculations. This is particularly helpful in real-life situations where you need a quick answer or are working with large or complex numbers.

Why is Estimation Important?

• Quick and Efficient: Estimation helps you find an approximate answer without spending time on lengthy calculations.
• Real-World Applications: You use estimation daily, for instance, when deciding if you have enough money for groceries or how much time it will take to travel to a specific location.
• Checking for Errors: Estimation allows you to verify the reasonableness of your exact calculations by ensuring your answer is close to your estimate.

Techniques for Estimation:

1. Rounding:

• Rounding to the Nearest Whole Number: Round each number to the nearest whole number before performing the calculation.
  • Example:
    • 7.3 + 4.8 ? 7 + 5 = 12
• Rounding to Significant Figures: Round each number to a specific number of significant figures.
  • Example: Rounding 456.82 to 2 significant figures gives 460.

2. Using Compatible Numbers:

• Find numbers that are close to the original numbers but easier to work with.
  • Example:
    • 23 x 9 ? 25 x 10 = 250

3. Using Benchmarks:

• Use common benchmarks (like 10, 100, or 1000) to make estimations.
  • Example:
    • 78 is slightly less than 80, so 78/4 is slightly less than 20.

4. Front-End Estimation:

• Focus on the leftmost digits (the "front end") of the numbers and perform the operation. Then, adjust the result for the remaining digits.
  • Example:
    • 345 + 278 ? 300 + 200 = 500. Since 45 + 78 is about 120, the final estimate would be around 620.

Example:

Problem: A shop sells apples for £1.25 per kg. You need to buy 2.7 kg of apples. Estimate the total cost.

Solution:

• Rounding: Round £1.25 to £1.30 and 2.7 kg to 3 kg.
• Multiplication: 3 x £1.30 = £3.90

Estimated Cost: Approximately £3.90

Note: This is an estimation. The actual cost might be slightly higher or lower than £3.90.

Practice:

• Estimation is a skill that improves with practice.
• Try to estimate answers to everyday situations.
• Look for opportunities to apply estimation techniques when solving math problems.

Summary:

Estimation is a valuable skill that helps you quickly approximate answers, understand the reasonableness of your results, and make informed decisions in real-world situations. By understanding the different techniques and practicing regularly, you can become proficient in estimation and enhance your overall mathematical understanding.