# IGCSE Mathematics Foundation: Degrees of Accuracy

## Scheme of work: IGCSE Foundation: Year 10: Term 5: Degrees of Accuracy

#### Prerequisite Knowledge

1. Rounding to the Nearest Integer
• Concept: Understanding how to round numbers to the nearest whole number based on the value of the decimal part.
• Example: $\text{Round 4.7 to the nearest integer: } 5.$ $\text{Round 4.3 to the nearest integer: } 4.$
2. Rounding to the Nearest Power of Ten
• Concept: Understanding how to round numbers to the nearest ten, hundred, thousand, etc., based on the value of the digits.
• Example: $\text{Round 473 to the nearest ten: } 470.$ $\text{Round 473 to the nearest hundred: } 500.$
3. Rounding to a Given Decimal Place
• Concept: Understanding how to round numbers to a specified number of decimal places.
• Example: $\text{Round 3.14159 to 2 decimal places: } 3.14.$ $\text{Round 3.14159 to 3 decimal places: } 3.142.$

#### Success Criteria

1. Round to a Given Number of Significant Figures or Decimal Places
• Objective: Accurately round numbers to the specified number of significant figures or decimal places.
• Example (Significant Figures): $\text{Round 12345 to 3 significant figures: } 12300.$
• Example (Decimal Places): $\text{Round 3.14159 to 3 decimal places: } 3.142.$
2. Use Estimation to Evaluate Approximations to Numerical Calculations
• Objective: Use estimation techniques to obtain approximate values for numerical calculations, providing a quick check on the reasonableness of answers.
• Example: $\text{Estimate the product of 48.7 and 19.6 by rounding each number to the nearest ten:}$ $50 \times 20 = 1000.$
3. Identify Upper and Lower Bounds Where Values Are Given to a Degree of Accuracy
• Objective: Determine the upper and lower bounds of a value based on its degree of accuracy.
• Example: $\text{For a length measured as 5.6 cm to the nearest tenth, the lower bound is 5.55 cm and the upper bound is 5.65 cm.}$

#### Key Concepts

1. Round to a Given Number of Significant Figures or Decimal Places
• Concept: Rounding to significant figures focuses on the number of meaningful digits, starting from the first non-zero digit, while rounding to decimal places focuses on the digits after the decimal point.
2. Use Estimation to Evaluate Approximations to Numerical Calculations
• Concept: Estimation involves simplifying numbers to easily manageable values to quickly approximate the result of a calculation, providing a useful check on more precise calculations.
3. Identify Upper and Lower Bounds Where Values Are Given to a Degree of Accuracy
• Concept: Upper and lower bounds are the maximum and minimum possible values a measurement can take, based on the given degree of accuracy. This helps in understanding the range within which the true value lies.

#### Common Misconceptions

1. Round to a Given Number of Significant Figures or Decimal Places
• Common Mistake: Confusing significant figures with decimal places, leading to incorrect rounding.
• Example: $\text{Incorrect: Rounding 12345 to 3 decimal places instead of 3 significant figures: } 12345.000.$ $\text{Correct: Rounding 12345 to 3 significant figures: } 12300.$
• Common Mistake: Rounding incorrectly by not following the rounding rules properly.
• Example: $\text{Incorrect: Rounding 3.14159 to 3 decimal places as } 3.141.$ $\text{Correct: Rounding 3.14159 to 3 decimal places as } 3.142.$
2. Use Estimation to Evaluate Approximations to Numerical Calculations
• Common Mistake: Over-simplifying or misapplying the estimation, leading to an estimate that is too inaccurate to be useful.
• Example: $\text{Incorrect: Estimating 48.7 \times 19.6 as } 40 \times 10 = 400.$ $\text{Correct: Estimating 48.7 \times 19.6 by rounding each number to the nearest ten: } 50 \times 20 = 1000.$
3. Identify Upper and Lower Bounds Where Values Are Given to a Degree of Accuracy
• Common Mistake: Incorrectly determining the bounds by not properly understanding the degree of accuracy.
• Example: $\text{Incorrect: For a length measured as 5.6 cm to the nearest tenth, determining the bounds as 5.6 cm and 5.7 cm.}$ $\text{Correct: The lower bound is 5.55 cm and the upper bound is 5.65 cm.}$

### Mr Mathematics Blog

#### Estimating Solutions by Rounding to a Significant Figure

Explore key concepts, FAQs, and applications of estimating solutions for Key Stage 3, GCSE and IGCSE mathematics.

#### Understanding Equivalent Fractions

Explore key concepts, FAQs, and applications of equivalent fractions in Key Stage 3 mathematics.

#### Transforming Graphs Using Function Notation

Guide for teaching how to transform graphs using function notation for A-Level mathematics.