Lesson Notes By Weeks and Term v3 - Junior Secondary 1
Fractions
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Fractions
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Subject: General Mathematics
Class: Junior Secondary 1
Term: 2nd Term
Week: 2
Theme: Number And Numeration
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Identify equivalent fractions of any given fraction; Apply equivalent fractions in sharing of commodities, e.g. food, money,etc Solve problems in quantitative aptitude reasoning in equivalent fractions; Find equivalence of any given fraction; Arrange given fractions either in as cending or descending or der; Convert:• fractions to decimals;• decimals to fractions • Convert:• fractions to percentages;• percentages to fractions
This section provides the core content and explanations necessary for the teacher to deliver the lesson effectively. A. Equivalent Fractions Equivalent fractions are fractions that represent the same value or the same part of a whole, even though they look different.
Concept: If a whole is divided into more parts, but a proportionally larger number of those parts are taken, the amount remains the same. For instance, 1/2 of a yam is the same as 2/4 of the same yam.
How to find equivalent fractions: Multiplication: Multiply both the numerator and the denominator by the same non-zero whole number.
Example 1: Find two equivalent fractions for 1/3. (1 × 2) / (3 × 2) = 2/6 (1 × 3) / (3 × 3) = 3/9 So, 1/3, 2/6, and 3/9 are equivalent fractions.
Example 2: Mrs. Ngozi shared 1/4 of her plantain chips with her son. If she had divided the chips into 8 equal parts, how many parts would her son have received?
Solution: We need to find an equivalent fraction for 1/4 with a denominator of
8. To change 4 to 8, we multiply by
2. Therefore, multiply the numerator by 2 as well. (1 × 2) / (4 × 2) = 2/
8. Her son would have received 2 parts.
Division: Divide both the numerator and the denominator by the same non-zero whole number (a common factor). This process is also known as simplifying or reducing a fraction to its lowest terms.
Example 3: Simplify 6/12 to its lowest terms.
Divide both by 2: (6 ÷ 2) / (12 ÷ 2) = 3/6 Divide both by 3: (3 ÷ 3) / (6 ÷ 3) = 1/2 Alternatively, divide both by their greatest common factor (GCF), which is 6: (6 ÷ 6) / (12 ÷ 6) = 1/
2. So, 6/12 is equivalent to 1/
2. B. Ordering Fractions Arranging fractions in ascending (smallest to largest) or descending (largest to smallest) order.
Case 1: Fractions with the Same Denominator Compare the numerators directly. The fraction with the larger numerator is the larger fraction.
Example: Arrange 3/7, 1/7, 5/7 in ascending order.
Comparing numerators: 1 9 >
8. Therefore, the order from largest to smallest is 10/12, 9/12, 8/
1
2. Answer: In descending order, their harvested portions are 5/6 (Bola), 3/4 (Chidi), 2/3 (Audu).
Commentary: This problem demonstrates how to order fractions with different denominators by finding a common denominator, a practical skill for comparing quantities. Question 3 (Fraction to Decimal Conversion): A tailor uses 1/4 of a bolt of fabric for a uniform. Express this amount as a decimal.
Performance Objective Covered: 6 Solution: To convert 1/4 to a decimal, divide the numerator (1) by the denominator (4). 1 ÷ 4 = 0.25 Answer: The tailor uses 0.25 of a bolt of fabric.
Commentary: A straightforward conversion problem reinforcing the division method. Question 4 (Decimal to Fraction Conversion): During the rainy season, the rainfall measured 0.8 meters. Convert this measurement into a fraction in its simplest form.
Performance Objective Covered: 6 Solution: The decimal 0.8 has one digit after the decimal point, so it represents tenths. Write 0.8 as a fraction: 8/
1
0. Simplify the fraction by dividing both the numerator and denominator by their GCF, which is 2. 8 ÷ 2 = 4 10 ÷ 2 = 5 Answer: 0.8 meters is equivalent to 4/5 meters.
Commentary: This shows the process of taking a decimal, placing it over the appropriate power of 10, and then reducing it to the simplest form. Question 5 (Fraction to Percentage & Quantitative Aptitude): In a small village primary school, 3 out of every 5 pupils passed their end-of-term mathematics examination. What percentage of pupils passed?
Performance Objective Covered: 3, 7 Solution: The fraction of pupils who passed is 3/
5. To convert this fraction to a percentage, multiply it by 100%. * (3/5) × 100% = (3 × 100) / 5 % = 300 / taking a decimal, placing it over the appropriate power of 10, and then reducing it to the simplest form. Question 5 (Fraction to Percentage & Quantitative Aptitude): In a small village primary school, 3 out of every 5 pupils passed their end-of-term mathematics examination. What percentage of pupils passed?
Performance Objective Covered: 3, 7 Solution: The fraction of pupils who passed is 3/
5. To convert this fraction to a percentage, multiply it by 100%. (3/5) × 100% = (3 × 100) / 5 % = 300 / 5 % = 60%.
Answer: 60% of the pupils passed the examination. *
Commentary: This combines fraction to percentage conversion with a quantitative reasoning scenario, requiring learners to first identify the fraction representing the pass rate.
Differentiation Strategies: Flexible Grouping: Group learners with mixed abilities for collaborative problem-solving, allowing stronger learners to support weaker ones.
Varied Tasks: Assign tasks of varying complexity. For instance, some groups might focus on equivalent fractions by multiplication, while others tackle simplifying complex fractions or ordering multiple fractions with different denominators.
Remediation (for struggling learners): Visual Aids: Use concrete manipulatives such as fraction strips, fraction circles, or play dough to physically demonstrate equivalent fractions and the concept of parts of a whole. Repeated hands-on activities can solidify understanding.
Step-by-Step Breakdown: Break down complex problems into smaller, manageable steps. For example, when ordering fractions with different denominators, guide them explicitly through finding the LCM first, then converting each fraction, and finally comparing numerators.
Targeted Practice: Provide additional practice sheets focusing on one specific skill at a time (e.g., only finding equivalent fractions, then only converting fractions to decimals).
Peer Tutoring: Pair a struggling learner with a more proficient one for one-on-one support during practice sessions.
Extension (for high-achieving learners): Complex Problem Solving: Present multi-step word problems that require the integration of several fractional concepts (e.g., "If 2/5 of students prefer jollof rice, and 1/3 of the remaining students prefer fried rice, what percentage of students prefer fried rice?").
Fractional Operations: Introduce advanced concepts like adding, subtracting, multiplying, or dividing fractions as an early exposure, connecting to finding common denominators or simplifying products.
Real-World Data Analysis: Task them with finding real-world data (e.g., population demographics, economic statistics from Nigeria) expressed as fractions or percentages, and then asking them to convert or compare these values and draw conclusions. For example, comparing the fraction of children attending primary school in different states. Number And Numeration
Sharing Food and Resources (Community/Culture): When a family prepares a meal like jollof rice or pounded yam, understanding fractions is crucial for sharing it equally among family members or guests. For instance, knowing that 1/2 of a meal is the same as 2/4 helps ensure fair distribution, especially during festive gatherings or when serving specific portions. This relates directly to the Nigerian cultural practice of communal eating and sharing. Market Transactions and Budgeting (Economy): Nigerians frequently deal with fractions when buying and selling. A market woman might sell "half a basket of tomatoes" or give a "quarter portion of gari." Budgeting also relies on fractions; for example, a household might decide to spend 1/3 of its income on food and 1/4 on rent. Converting these to percentages (e.g., 33.3% on food, 25% on rent) helps in financial planning and comparison. Land Allocation and Property (Geography/Economy): In many rural Nigerian communities, land is often divided and inherited in fractional portions. Knowing how to calculate equivalent fractions and order them helps in understanding who owns how much land. For instance, if one sibling inherits 1/4 of the family land and another inherits 2/8, understanding equivalence clarifies that they received equal portions. This also extends to urban property where a plot might be leased or sold as a fraction of a larger block.