# IGCSE Mathematics Foundation: Fractions, Decimals and Percentages

## Scheme of work: IGCSE Foundation: Year 10: Term 2: Fractions, Decimals and Percentages

#### Prerequisite Knowledge

1. Understanding Place Value
• Concept: Using the place value table to multiply and divide by 10, 100, and 1000.
• Example: $\text{Multiply 35 by 100: } 35 \times 100 = 3500$ $\text{Divide 4200 by 1000: } 4200 \div 1000 = 4.2$
2. Simplifying and Working Out Equivalent Fractions
• Concept: Understanding how to simplify fractions and find equivalent fractions.
• Example: $\text{Simplify } \frac{8}{12} \text{ to } \frac{2}{3} \text{ by dividing the numerator and denominator by their greatest common divisor (4)}.$ $\text{Find an equivalent fraction for } \frac{3}{4} \text{ by multiplying the numerator and denominator by 2: } \frac{6}{8}.$
3. Adding and Subtracting with Decimal Numbers
• Concept: Understanding how to add and subtract decimal numbers.
• Example: $\text{Add } 3.45 + 2.75 = 6.20$ $\text{Subtract } 5.6 – 3.4 = 2.2$

#### Success Criteria

1. Understanding the Meaning of Percentage
• Objective: Understand that ‘percentage’ means ‘number of parts per 100’.
• Example: $\text{Recognize that } 50\% \text{ means } 50 \text{ out of } 100.$
2. Converting Fractions to Decimals and Percentages
• Objective: Use the place value table and equivalent fractions to convert simple fractions to decimals and percentages.
• Example: $\frac{3}{4} = 0.75 = 75\%$
3. Converting Complex Fractions to Decimals and Percentages
• Objective: Convert more complex fractions such as $$\frac{3}{40}$$ to decimals and percentages using division.
• Example: $\frac{3}{40} = 0.075 = 7.5\%$
4. Converting Decimals to Fractions and Percentages
• Objective: Convert decimals to fractions and percentages.
• Example: $0.625 = \frac{625}{1000} = \frac{5}{8} = 62.5\%$
5. Handling Recurring Decimals
• Objective: Convert simple recurring decimals to fractions.
• Example: $0.\overline{6} = \frac{2}{3}$
6. Expressing Percentages as Fractions and Decimals
• Objective: Express percentages as fractions and decimals.
• Example: $80\% = \frac{80}{100} = \frac{4}{5} = 0.8$

#### Key Concepts

1. Understanding the Meaning of Percentage
• Concept: Recognizing that a percentage represents a part out of 100.
• Example: $\text{Understanding that } 25\% \text{ represents } 25 \text{ parts out of } 100.$
2. Converting Fractions to Decimals
• Concept: Using division to convert fractions to decimals.
• Example: $\frac{3}{4} = 3 \div 4 = 0.75$
3. Converting Fractions to Percentages
• Concept: Multiplying the decimal equivalent of a fraction by 100 to find the percentage.
• Example: $0.75 \times 100 = 75\%$
4. Converting Decimals to Fractions
• Concept: Understanding place value to convert decimals to fractions.
• Example: $0.625 = \frac{625}{1000} = \frac{5}{8}$
5. Handling Recurring Decimals
• Concept: Recognizing and converting simple recurring decimals to fractions.
• Example: $0.\overline{6} = \frac{2}{3}$
6. Expressing Percentages as Fractions and Decimals
• Concept: Converting percentages to fractions and decimals.
• Example: $80\% = \frac{80}{100} = \frac{4}{5} = 0.8$

#### Common Misconceptions

1. Understanding the Meaning of Percentage
• Common Mistake: Students might misunderstand the concept of percentage and think it means a part out of any number, not specifically 100.
• Example: $\text{Incorrect: Thinking that } 25\% \text{ of 200 is } 25 \text{.}$ $\text{Correct: } 25\% \text{ of 200 is } 50 \text{ (because } 0.25 \times 200 = 50\text{).}$
2. Converting Fractions to Decimals
• Common Mistake: Students might perform the division incorrectly or forget to use division.
• Example: $\text{Incorrect: } \frac{3}{4} = 4 \div 3 = 1.33$ $\text{Correct: } \frac{3}{4} = 3 \div 4 = 0.75$
3. Converting Fractions to Percentages
• Common Mistake: Students might multiply the fraction directly by 100 without converting to a decimal first.
• Example: $\text{Incorrect: } \frac{3}{4} \times 100 = 75\% \text{ (without first converting } \frac{3}{4} \text{ to } 0.75 \text{).}$ $\text{Correct: } \frac{3}{4} = 0.75 \times 100 = 75\%$
4. Converting Decimals to Fractions
• Common Mistake: Students might incorrectly interpret the place value of decimals when converting to fractions.
• Example: $\text{Incorrect: } 0.625 = \frac{625}{100} = \frac{25}{4}$ $\text{Correct: } 0.625 = \frac{625}{1000} = \frac{5}{8}$
5. Handling Recurring Decimals
• Common Mistake: Students might misunderstand how to represent and convert recurring decimals to fractions.
• Example: $\text{Incorrect: } 0.\overline{6} = \frac{6}{10} = 0.6$ $\text{Correct: } 0.\overline{6} = \frac{2}{3}$
6. Expressing Percentages as Fractions and Decimals
• Common Mistake: Students might incorrectly convert percentages to fractions and decimals by not dividing by 100.
• Example: $\text{Incorrect: } 80\% = \frac{80}{1} = 80$ $\text{Correct: } 80\% = \frac{80}{100} = \frac{4}{5} = 0.8$

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