Maths (estimating )

• What is the difference between estimating and guessing?

  Estimating is a method of rough calculation that provides an answer close to the true value.
• When is estimating typically used?

  Estimating is used when a rough answer is sufficient or to check the accuracy of a fully worked answer.
• How do you estimate a calculation involving multiple numbers?

  • Round each number to one or two significant figures.
  • Perform the calculation with the rounded numbers.
• What is the difference between estimating and guessing?

  Estimating is a method of rough calculation that provides an answer close to the true value, while guessing is random.
• How would you round the numbers 19.1 and 7.4 for estimation?

  Round 19.1 up to 20 and 7.4 down to 7.
• When is estimating typically used?

  Estimating is used when a rough answer is sufficient or to check the accuracy of a fully worked answer.
• What is the estimated product of 20 and 7?

  140
• How do you begin the process of estimating a calculation?

  You round each of the numbers involved to something more reasonable and easier to work with.
• How would you estimate the denominator using 186.3 and 43.3?

  Round 186.3 up to 190 and 43.3 down to 40, then calculate 190 - 40.
• To how many significant figures should numbers typically be rounded when estimating?

  Numbers are generally rounded to one or two significant figures.
• What is the estimated result of the fraction $\frac{140}{150}$ after simplification?


  Approximately 1
• If you round 19.1 and 7.4 for estimation, what do they become?

  19.1 rounds to 20 and 7.4 rounds to 7.
• Why is estimation useful in real-life scenarios?

  Estimation helps provide a quick idea of costs or measurements without needing exact calculations.
• What is the estimated numerator when rounding 19.1 and 7.4?

  The estimated numerator is $20 \times 7 =$$140$.
• How would you estimate the area of a garden measuring 13.2 meters by 7.7 meters?

  Round 7.7 meters to 8 meters and 13.2 meters to 13 meters, then multiply to get an area of 104 square meters.
• What is the estimated cost per square meter of turf if you round 14.30 pounds to a simpler figure?

  Approximately 14 pounds
• How do you estimate the denominator when rounding 186.3 and 43.3?

  You round 186.3 to 190 and 43.3 to 40, giving $190 - 40 =$$150$.
• How do you estimate the total cost of turf for the garden?

  Multiply the estimated cost per square meter (17 pounds) by the estimated area (100 square meters).
• What is the estimated total cost of the turf for the garden?

  1700 pounds
• What fraction do you get after simplifying $\frac{140}{150}$?


  The simplified fraction is $\frac{14}{15}$.
• How does rounding affect the accuracy of an estimate?

  Rounding can lead to errors, but if done evenly, it can cancel out some inaccuracies.
• What can you conclude about the estimated answer of $\frac{14}{15}$?


  The estimated answer is approximately one.
• What would happen if all values were rounded up in the estimation process?

  The estimate would likely be higher and less accurate than if values were rounded evenly.
• What are the key points about estimating in calculations?

  • Estimating is not guessing; it provides a close approximation.
  • Round numbers to one or two significant figures.
  • Useful for quick calculations and checking accuracy.
  • Helps in real-life scenarios like budgeting and planning.
• How would you estimate the area of a garden measuring 13.2 meters by 7.7 meters?

  You round 7.7 meters to 8 meters and 13.2 meters to 13 meters, giving an area of $8 \times 13 =$$104 \text{ square meters}$.
• How do you estimate the cost per square meter of turf?

  You assume each square meter costs 14 pounds instead of 14 pounds 30 and round the tax to 20, giving a cost of approximately 17 pounds per square meter.
• What is the estimated total cost for the turf if the area is rounded down to 100 square meters?

  The estimated total cost is $17 \times 100 =$$1700 \text{ pounds}$.
• How close was the estimate compared to the actual cost of the turf?

  The estimate was close, with the actual cost being 1715 pounds.
• Why was the estimate close to the actual cost?

  The estimate was close because rounding was done evenly, which canceled out many errors.
• What would have happened if all values were rounded up?

  If all values were rounded up, the estimate could have been significantly higher, around 2016 pounds.
• What is the purpose of estimating in calculations?

  • Provides a rough answer when exact values are not necessary
  • Helps check the accuracy of fully worked answers
  • Useful in real-life scenarios for budgeting and planning
• What are the steps to estimate the cost of laying astro turf in a garden?

  1. Estimate the area of the garden by rounding dimensions.
  2. Estimate the cost per square meter by rounding prices and tax.
  3. Multiply the estimated area by the estimated cost per square meter.