Lesson Notes By Weeks and Term v3 - Primary 5
Fractions
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Fractions
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Subject: General Mathematics
Class: Primary 5
Term: 1st Term
Week: 2
Theme: Numbers And Numeration
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Watch on YouTubeSee Facebook postchange fraction to decimals and decimals to percentages and vice versa solve quantitative aptitude problems related to percentages state the relationship between fraction and ratio solve quantitative aptitude problem related to ratio
1 = 4$ parts.
Step 2 (Value of one part): ₦$1,200 \div 4 = ₦300$ per part.
Step 3 (Shares): Emeka's share: $3 \times ₦300 = ₦900$.
Ada's share: $1 \times ₦300 = ₦300$.
Check: $₦900 + ₦300 = ₦1,200$.
Type 2: Finding the ratio between two numbers/quantities.
Method: Write the two quantities as a comparison and simplify them to their lowest terms. Ensure units are consistent.
Example: Find the ratio of 15 mangoes to 25 mangoes.
Calculation: $15 : 25$. Divide both sides by the greatest common factor (5): $15 \div 5 : 25 \div 5 = 3 : 5$.
Example: In a class, there are 20 boys and 25 girls. Find the ratio of boys to girls. * Calculation: $20 : 25$.
Divide both sides by 5: $20 \div 5 : 25 \div 5 = 4 : 5$. This section provides the core content knowledge required for the lesson, with clear explanations and step-by-step examples relevant to the Nigerian context. 2.
1. Changing Fractions to Decimals A fraction represents a part of a whole, and it can be converted to a decimal by dividing the numerator by the denominator. The resulting decimal represents the same value in base-10 system.
Method: Divide the numerator by the denominator.
Example 1: Convert $\frac{1}{2}$ to a decimal.
Calculation: $1 \div 2 = 0.5$ Example 2: Convert $\frac{3}{4}$ to a decimal.
Calculation: $3 \div 4 = 0.75$ Example 3: Convert $\frac{2}{5}$ to a decimal. This could represent ₦2 out of ₦
5. Calculation: $2 \div 5 = 0.4$ Example 4: Convert $\frac{7}{10}$ to a decimal.
Calculation: $7 \div 10 = 0.7$ 2.
2. Changing Decimals to Percentages A percentage is a way of expressing a number as a fraction of
1
0
0. The word "percent" means "per hundred" or "out of 100". To convert a decimal to a percentage, multiply by 100 and add the percent symbol (%).
Method: Multiply the decimal by
1
0
0. Example 1: Convert 0.5 to a percentage.
Calculation: $0.5 \times 100 = 50\%$. (E.g., 0.5 of a task is 50% completed).
Example 2: Convert 0.75 to a percentage.
Calculation: $0.75 \times 100 = 75\%$.
Example 3: Convert 0.4 to a percentage.
Calculation: $0.4 \times 100 = 40\%$. (E.g., A student scored 0.4 of the total marks, which is 40%).
Example 4: Convert 0.03 to a percentage.
Calculation: $0.03 \times 100 = 3\%$. 2.
3. Changing Fractions to Percentages There are two main ways to convert a fraction to a percentage: Method 1: Convert to decimal first, then to percentage.
Example: Convert $\frac{1}{4}$ to a percentage.
Step 1 (Fraction to Decimal): $1 \div 4 = 0.25$ Step 2 (Decimal to Percentage): $0.25 \times 100 = 25\%$ Method 2: Multiply the fraction by 100%.
Example: Convert $\frac{3}{5}$ to a percentage. This could represent 3 out of 5 market traders.
Calculation: $\frac{3}{5} \times 100\% = \frac{300}{5}\% = 60\%$ 2.
4. Changing Percentages to Decimals To convert a percentage to a decimal, divide the percentage value by
1
0
0. Remove the percent symbol.
Method: Divide the percentage by
1
0
0. Example 1: Convert 25% to a decimal.
Calculation: $25 \div 100 = 0.25$.
Example 2: Convert 80% to a decimal. (E.g., 80% success rate means 0.8 as a decimal).
Calculation: $80 \div 100 = 0.8$. 2.
5. Changing Percentages to Fractions To convert a percentage to a fraction, write the percentage value as a fraction with a denominator of 100, then simplify the fraction to its lowest terms.
Method: Write the percentage as $\frac{\text{percentage value}}{100}$ and simplify.
Example 1: Convert 75% to a fraction.
Calculation: $75\% = \frac{75}{100}$. Simplify by dividing numerator and denominator by their greatest common factor (25): $\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$.
Example 2: Convert 40% to a fraction. (E.g., 40% of the class preferred local rice).
Calculation: $40\% = \frac{40}{100}$.
Simplify by dividing by 20: $\frac{40 \div 20}{100 \div 20} = \frac{2}{5}$. 2.
6. Changing Decimals to Fractions To convert a decimal to a fraction, determine the place value of the last digit in the decimal. Write the decimal as a fraction with the digits after the decimal point as the numerator and the corresponding place value (e.g., 10 for tenths, 100 for hundredths) as the denominator. Then simplify the fraction.
Method: Write the decimal as a fraction over a power of 10 and simplify.
Example 1: Convert 0.6 to a fraction.
Explanation: The last digit '6' is in the tenths place.
Calculation: $0.6 = \frac{6}{10}$.
Simplify by dividing by 2: $\frac{6 \div 2}{10 \div 2} = \frac{3}{5}$.
Example 2: Convert 0.25 to a fraction. (E.g., N0.25 is $\frac{1}{4}$ of a Naira).
Explanation: The last digit '5' is in the hundredths place.
Calculation: $0.25 = \frac{25}{100}$.
Simplify by dividing by 25: $\frac{25 \div 25}{100 \div 25} = \frac{1}{4}$. 2.
7. Relationship between Fraction and Ratio * Fraction: A of 10 and simplify.
Example 1: Convert 0.6 to a fraction.
Explanation: The last digit '6' is in the tenths place.
Calculation: $0.6 = \frac{6}{10}$.
Simplify by dividing by 2: $\frac{6 \div 2}{10 \div 2} = \frac{3}{5}$.
Example 2: Convert 0.25 to a fraction. (E.g., N0.25 is $\frac{1}{4}$ of a Naira).
Explanation: The last digit '5' is in the hundredths place.
Calculation: $0.25 = \frac{25}{100}$.
Simplify by dividing by 25: $\frac{25 \div 25}{100 \div 25} = \frac{1}{4}$. 2.
7. Relationship between Fraction and Ratio Fraction: A fraction (e.g., $\frac{1}{2}$, $\frac{3}{4}$) represents a part of a whole. The denominator shows the total number of equal parts, and the numerator shows how many of those parts are being considered.
Ratio: A ratio compares two or more quantities. It shows how much of one quantity there is compared to another.
Ratios can be written in three ways: Using a colon: `a : b` As a fraction: $\frac{a}{b}$ Using the word "to": `a to b` Connection: A fraction expresses a part-to-whole relationship (e.g., if $\frac{2}{5}$ of a class are boys, then 2 parts are boys and 5 parts are the whole class). A ratio can express a part-to-part relationship (e.g., the ratio of boys to girls is 2:3) or a part-to-whole relationship (e.g., the ratio of boys to the total class is 2:5, which is a fraction).
Key Idea: When a ratio describes parts of a whole, it can be directly related to fractions. For example, if the ratio of yam to maize in a farm plot is 2:3, the total parts are $2+3=5$. The fraction of yam is $\frac{2}{5}$, and the fraction of maize is $\frac{3}{5}$. 2.
8. Solving Quantitative Aptitude Problems Related to Percentages These problems often involve finding a percentage of a given quantity or finding the whole quantity when a percentage is given.
Type 1: Finding a percentage of a number.
Method: Convert the percentage to a decimal or fraction and multiply by the number.
Example 1: A market trader offers a 10% discount on an item that costs ₦2,
5
0
0. How much is the discount?
Calculation: $10\% = 0.10$. Discount = $0.10 \times ₦2,500 = ₦250$.
Example 2: In a village of 500 people, 60% are farmers. How many farmers are there?
Calculation: $60\% = \frac{60}{100} = \frac{3}{5}$. Number of farmers = $\frac{3}{5} \times 500 = 3 \times 100 = 300$ farmers.
Type 2: Finding a number given its percentage.
Method: If a percentage of a number is given, divide the given value by the percentage (converted to decimal or fraction) to find the whole.
Example: If 20% of the students in a school are 80 students, what is the total number of students in the school?
Calculation: $20\% = 0.20$. Let the total number of students be 'x'. Then $0.20 \times x = 80$. So, $x = \frac{80}{0.20} = \frac{80}{\frac{1}{5}} = 80 \times 5 = 400$ students. 2.
9. Solving Quantitative Aptitude Problems Related to Ratio Ratio problems involve comparing quantities, sharing quantities, or finding unknown quantities based on a given ratio.
Type 1: Sharing in a given ratio.
Method: Add the parts of the ratio to find the total number of parts. Divide the total quantity by the total number of parts to find the value of one part. Multiply the value of one part by each number in the ratio to find the share of each.
Example: Share ₦1,200 between Emeka and Ada in the ratio 3:
1. Step 1 (Total parts): $3 + 1 = 4$ parts.
Step 2 (Value of one part): ₦$1,200 \div 4 = ₦300$ per part.
Step 3 (Shares): Emeka's share: $3 \times ₦300 = ₦900$.
Ada's share: $1 \times ₦300 = ₦300$.
Check: $₦900 + ₦300 = ₦1,200$.
Type 2: Finding the ratio between two numbers/quantities.
Method: Write the two quantities as a comparison and simplify them to their lowest terms. Ensure units are consistent.
Example: Find the ratio of 15 mangoes to 25 mangoes.
Calculation: $15 : 25$. Divide both 3.
1. Introduction (10 minutes)
Teacher Activity: Begin by reviewing fractions.
Ask questions like: "What is a fraction?", "Give examples of fractions you use every day." (e.g., half a cup of garri, a quarter of an orange). Introduce the idea that fractions can be expressed in different forms.
Student Activity: Students share examples and answer review questions. They listen actively for the introduction of new concepts. 3.
2. Presentation / Content Development (30 minutes)
Teacher Activity 1: Fraction, Decimal, Percentage Conversions (15 minutes) Demonstrate step-by-step conversion processes on the board (e.g., $\frac{1}{4} \rightarrow 0.25 \rightarrow 25\%$). Use examples from daily life (e.g., "If I eat $\frac{1}{2}$ of my bread, what percentage of bread have I eaten?"). Guide students through examples of converting percentages back to decimals and fractions (e.g., "A market offers 20% discount. What fraction is this?"). Emphasize the importance of simplification for fractions.
Student Activity 1: Students observe and copy examples. They may volunteer to try simple conversions on mini-whiteboards or notebooks.
Teacher Activity 2: Relationship between Fraction and Ratio (10 minutes) Explain what a ratio is using concrete examples (e.g., using students in the class: "Ratio of boys to girls," "Ratio of students wearing uniforms to those not"). Illustrate how a part-to-whole ratio can be written as a fraction (e.g., "If there are 3 boys and 2 girls, the ratio of boys to girls is 3:
2. The fraction of boys in the group is $\frac{3}{5}$"). Use visual aids like divided circles or rectangular strips to represent fractions and then show how they relate to ratios.
Student Activity 2: Students participate in forming ratios based on classroom demographics or objects provided. They discuss the difference and similarities between fractions and ratios.
Teacher Activity 3: Quantitative Aptitude Problems (15 minutes) Work through examples of percentage problems (e.g., calculating 25% of ₦800). Work through examples of ratio problems (e.g., sharing ₦1,500 between two children in the ratio 2:3). Break down each problem into smaller, manageable steps. Encourage students to identify keywords in word problems that indicate percentages or ratios.
Student Activity 3: Students actively follow the steps, asking questions for clarification. They attempt similar problems alongside the teacher or in small groups. 3.
3. Application / Guided Practice (20 minutes)
Teacher Activity: Provide a few practice problems for students to solve in pairs or small groups. Circulate around the classroom to provide support, correct misconceptions, and check progress.
Student Activity: Students work collaboratively to solve problems. They present their solutions and explain their reasoning to the class. 3.
4. Conclusion (5 minutes)
Teacher Activity: Summarize the key concepts learned: conversions between fractions, decimals, and percentages; understanding the fraction-ratio relationship; and solving problems involving percentages and ratios. Assign homework.
Student Activity: Students ask any final questions and note down homework.
Budgeting and Finance (Economy/Community): Application: Understanding discounts in markets (e.g., "20% off all goods this festive season"), calculating interest on savings (e.g., "Our bank offers 5% interest per annum"), or managing household budgets (e.g., "30% of our income goes to food").
Local Context: Students can calculate the actual price of a textbook after a 10% discount from a bookseller or determine how much their parents spend on fuel if it's a certain percentage of their transport allowance. Sharing Resources and Equity (Community/Culture): Application: Dividing communal land, inherited property, or farming yield among family members or community groups according to agreed-upon ratios.
Local Context: If a family inherits 5 hectares of land, and it is to be shared among 3 siblings in the ratio 2:2:1, students can calculate the exact portion each sibling receives. Or sharing profit from a joint venture in a cooperative. Understanding Statistics and Data (Community/Environment): Application: Interpreting percentages in news reports (e.g., "70% of voters participated in the last election," "Only 40% of waste is properly disposed of in our city"), or comparing population demographics (e.g., ratio of adults to children in a community).
Local Context: Discussing newspaper headlines that mention percentages of school enrollment, immunization rates, or crop yield increases. Analyzing the ratio of different types of trees in a local forest.