# IGCSE Foundation: Working with Fractions

## Scheme of work: IGCSE Foundation: Year 10: Term 1: Working with Fractions

#### Prerequisite Knowledge

1. Understanding Fractions
• Concept: Knowing how to identify and represent fractions.
• Example: $\text{A fraction represents a part of a whole, e.g., } \frac{1}{2}, \frac{3}{4}$
2. Basic Arithmetic Operations with Whole Numbers
• Concept: Understanding addition, subtraction, multiplication, and division of whole numbers.
• Example: $2 + 3 = 5, \quad 7 – 4 = 3, \quad 6 \times 2 = 12, \quad \frac{8}{2} = 4$

#### Success Criteria

1. Using Equivalent Fractions
• Performing Calculations: Students should be able to simplify fractions by cancelling common factors.
• Example: $\frac{6}{8} = \frac{3}{4} \text{ by dividing both the numerator and the denominator by 2}$
• Describing Equivalent Fractions: Students should be able to describe how to find and use equivalent fractions.
• Example: $\text{Equivalent fractions represent the same part of a whole, e.g., } \frac{1}{2} = \frac{2}{4} = \frac{4}{8}$
2. Understanding and Using Mixed Numbers and Vulgar Fractions
• Performing Calculations: Students should be able to convert between mixed numbers and improper fractions.
• Example: $2 \frac{1}{2} = \frac{5}{2}$
• Describing Mixed Numbers and Vulgar Fractions: Students should be able to describe the process of converting between mixed numbers and improper fractions.
• Example: $\text{A mixed number has a whole number and a fraction, e.g., } 3 \frac{1}{4}, \text{ while an improper fraction has a numerator larger than the denominator, e.g., } \frac{7}{4}$
3. Identifying Common Denominators
• Performing Calculations: Students should be able to find common denominators for adding and subtracting fractions.
• Example: $\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$
• Describing Common Denominators: Students should be able to explain the need for common denominators in fraction operations.
• Example: $\text{Common denominators are needed to perform addition and subtraction of fractions, e.g., } \frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
4. Ordering and Calculating Fractions
• Performing Calculations: Students should be able to order fractions and calculate a given fraction of a given quantity.
• Example: $\text{Order } \frac{1}{2}, \frac{3}{4}, \frac{1}{3} \text{ as } \frac{1}{3}, \frac{1}{2}, \frac{3}{4}$
• Describing Fraction Calculations: Students should be able to describe the steps to calculate a fraction of a quantity.
• Example: $\frac{1}{4} \text{ of 20 is } 20 \div 4 = 5$

#### Key Concepts

1. Understanding Equivalent Fractions
• Concept: Knowing that equivalent fractions represent the same part of a whole even if they look different.
• Example: $\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$
2. Using Mixed Numbers and Vulgar Fractions
• Concept: Understanding how to convert between mixed numbers and improper fractions.
• Example: $2 \frac{1}{2} = \frac{5}{2}$
3. Identifying Common Denominators
• Concept: Knowing how to find a common denominator to add or subtract fractions.
• Example: $\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
4. Ordering and Calculating Fractions
• Concept: Understanding how to compare and order fractions and calculate a fraction of a quantity.
• Example: $\text{Order } \frac{1}{3}, \frac{1}{2}, \frac{3}{4}$

#### Common Misconceptions

1. Using Equivalent Fractions
• Common Mistake: Students might incorrectly simplify fractions by not dividing both the numerator and the denominator by the same number.
• Example: Simplifying $$\frac{6}{8}$$ as: $\text{Incorrect: } \frac{6}{8} = \frac{3}{8}$ $\text{Correct: } \frac{6}{8} = \frac{3}{4}$
2. Using Mixed Numbers and Vulgar Fractions
• Common Mistake: Students might incorrectly convert between mixed numbers and improper fractions.
• Example: Converting $$2 \frac{1}{2}$$ as: $\text{Incorrect: } 2 \frac{1}{2} = \frac{3}{2}$ $\text{Correct: } 2 \frac{1}{2} = \frac{5}{2}$
3. Identifying Common Denominators
• Common Mistake: Students might incorrectly identify common denominators, leading to incorrect addition or subtraction of fractions.
• Example: Adding $$\frac{1}{3}$$ and $$\frac{1}{4}$$ as: $\text{Incorrect: } \frac{1}{3} + \frac{1}{4} = \frac{2}{7}$ $\text{Correct: } \frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
4. Ordering and Calculating Fractions
• Common Mistake: Students might incorrectly compare or order fractions, leading to incorrect results.
• Example: Ordering $$\frac{1}{2}, \frac{1}{4}, \frac{3}{4}$$ as: $\text{Incorrect: } \frac{1}{2}, \frac{3}{4}, \frac{1}{4}$ $\text{Correct: } \frac{1}{4}, \frac{1}{2}, \frac{3}{4}$
• Common Mistake: Students might incorrectly calculate a fraction of a quantity.
• Example: Calculating $$\frac{1}{4}$$ of 20 as: $\text{Incorrect: } \frac{1}{4} \times 20 = 10$ $\text{Correct: } \frac{1}{4} \times 20 = 5$

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