Lesson Notes By Weeks and Term v3 - Primary 6
Ratio of family size and resources
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Ratio of family size and resources
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Subject: General Mathematics
Class: Primary 6
Term: 2nd Term
Week: 2
Theme: Number And Numeration
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Find ratio of family size and resources Correctly use ratio in relating proportion of resources to family size.
be shared among 5 families, each with 2 parents and 3 children.
Task: Find the ratio of land to the total number of family members.
Step 1: Calculate the total family members. Each family = 2 parents + 3 children = 5 members. Total families = 5 Total family members = 5 families × 5 members/family = 25 members.
Step 2: Identify the quantities. Land = 10 hectares Total Family Members = 25 Step 3: Write the ratio (land to total family members). Ratio = 10 : 25 Step 4: Simplify the ratio. The GCF of 10 and 25 is 5. 10 ÷ 5 = 2 25 ÷ 5 = 5 Simplified Ratio = 2 : 5 Interpretation: This means for every 2 hectares of land, there are 5 family members (or each family member gets 2/5 of a hectare).
A. Definition of Ratio: A ratio is a comparison of two quantities of the same kind. It shows how much of one quantity there is compared to another quantity.
Ratios can be expressed in three ways: Using a colon (e.g., a : b) As a fraction (e.g., a/b) Using the word "to" (e.g., a to b) It is important that the quantities being compared are in the same units. If they are not, they must be converted to the same unit before forming a ratio.
B. Simplification of Ratios: Just like fractions, ratios should always be expressed in their simplest form. To simplify a ratio, both quantities are divided by their greatest common factor (GCF).
Example: The ratio 10 : 15 can be simplified by dividing both numbers by their GCF, which is
5. So, 10 ÷ 5 = 2 and 15 ÷ 5 =
3. The simplified ratio is 2 :
3. C.
Ratio of Family Size and Resources: This concept involves comparing the number of members in a family (family size) to the quantity of a particular resource available to them.
Family Size: Refers to the total number of individuals living in a household (parents, children, other dependents).
Resources: Can be tangible (e.g., income, food items like bags of rice, tubers of yam, plot of land, litres of water) or intangible (e.g., time, attention, educational opportunities).
Understanding the Relationship: When we find the ratio of family size to resources, or vice-versa, we are essentially determining the share or availability of that resource per family member or how many family members share a certain unit of resource. This helps in understanding the proportionality.
Worked Examples (Nigerian Contexts): Example 1: Income and Family Size A family in Kaduna has 2 parents and 4 children, making a total of 6 family members. Their monthly income is ₦60,
0
0
0. Task: Find the ratio of the family's income to its family size.
Step 1: Identify the quantities. Income = ₦60,000 Family Size = 6 members Step 2: Write the ratio in the order requested (income to family size). Ratio = Income : Family Size Ratio = ₦60,000 : 6 Step 3: Simplify the ratio by dividing both sides by the greatest common factor (GCF). The GCF of 60,000 and 6 is 6. ₦60,000 ÷ 6 = ₦10,000 6 ÷ 6 = 1 Simplified Ratio = ₦10,000 : 1 Interpretation: This means for every ₦10,000 of income, there is 1 family member (or, on average, each family member represents ₦10,000 of the total income).
Example 2: Food Resources and Family Size A family of 8 (including parents and children) in a rural village has harvested 24 tubers of yam for a month.
Task: Find the ratio of tubers of yam to the family size.
Step 1: Identify the quantities. Tubers of Yam = 24 Family Size = 8 members Step 2: Write the ratio (tubers of yam to family size). Ratio = Tubers of Yam : Family Size Ratio = 24 : 8 Step 3: Simplify the ratio. The GCF of 24 and 8 is 8. 24 ÷ 8 = 3 8 ÷ 8 = 1 Simplified Ratio = 3 : 1 Interpretation: This means for every 3 tubers of yam, there is 1 family member (or, on average, each family member is allocated 3 tubers of yam).
Example 3: Land Allocation and Family Size A communal land of 10 hectares is to be shared among 5 families, each with 2 parents and 3 children.
Task: Find the ratio of land to the total number of family members.
Step 1: Calculate the total family members. Each family = 2 parents + 3 children = 5 members. Total families = 5 Total family members = 5 families × 5 members/family = 25 members.
Step 2: Identify the quantities. Land = 10 hectares Total Family Members = 25 * Step 3: Write the ratio (land to total family members).
A. Teacher Activities: Introduction (10 minutes): Begin by eliciting students' prior knowledge of ratio. Ask questions like, "What does it mean to compare two things?" or "Can anyone give an example of a ratio they've heard before?" Introduce the day's topic: "Ratio of family size and resources." Explain its importance in everyday life, especially in managing resources within a Nigerian family context.
Present a simple scenario: "Imagine a family with 4 children and 2 parents. If they have 12 slices of bread, how can we share it fairly? How does ratio help us?" Concept Explanation (15 minutes): Clearly define ratio, emphasizing that it's a comparison of two quantities of the same kind or two related quantities. Illustrate with simple non-family examples first (e.g., boys to girls in class, red pens to blue pens). Explain how to simplify ratios using the GCF. Introduce the core concept of family size and resources. Give examples of resources relevant to Nigerian families (e.g., income, food items like garri/rice, land, water, school fees). Walk through Example 1 (Income and Family Size) and Example 2 (Food Resources and Family Size) from the "Key Concepts and Explanations" section, step-by-step, writing clearly on the board. Emphasize the interpretation of the simplified ratio.
Guided Practice Facilitation (15 minutes): Present a new scenario (e.g., Example 3 on Land Allocation). Guide students through the steps to solve it collectively.
Ask probing questions at each step: "What are the quantities here?", "How do we write this as a ratio?", "What is the next step to simplify it?". Encourage student participation, allowing them to suggest answers and corrections. Ensure clarity on how to interpret the final simplified ratio in terms of resources per family member or vice versa. Activity Setup and Monitoring (10 minutes): Organize students into small groups (e.g., 4-5 students per group). Provide each group with a task card containing a simple, realistic problem involving family size and resources (similar to the guided practice questions). Circulate among the groups, monitoring their progress, offering support, and correcting misconceptions. Observe how students collaborate and apply the concept.
Conclusion and Recap (5 minutes): Bring the class together. Ask selected groups to present their solutions and explanations.
Summarize the key takeaways: definition of ratio, importance of simplification, and how ratios help us understand resource distribution in families. Prepare students for independent practice and evaluation.
B. Student Activities: Active Listening and Participation: Students will listen attentively to the teacher's explanations, ask clarifying questions, and actively participate in class discussions and problem-solving.
Note-Taking: Students will take notes on key definitions, steps for simplification, and worked examples provided by the teacher.
Group Problem-Solving: In small groups, students will work collaboratively to solve assigned problems on ratio of family size and resources, applying the concepts taught. They will discuss strategies and arrive at solutions together.
Presentation: Selected groups will present their solutions and explanations to the class, demonstrating their understanding.
Individual Practice: Students will engage in independent practice exercises to reinforce their learning. The teacher should guide students through these problems, encouraging them to verbalize their steps.
Question 1: A family in Enugu has 7 members (father, mother, and 5 children). Their total monthly family income is ₦140,
0
0
0. Calculate the ratio of their monthly income to the family size.
Solution 1: Step 1: Identify the quantities. Monthly Income = ₦140,000 Family Size = 7 members Step 2: Form the ratio (income to family size). Ratio = ₦140,000 : 7 Step 3: Simplify the ratio. Divide both quantities by their GCF, which is 7. ₦140,000 ÷ 7 = ₦20,000 7 ÷ 7 = 1 Simplified Ratio = ₦20,000 : 1
Commentary: This ratio indicates that for every ₦20,000 of income, there is 1 family member. It helps in understanding the per capita income.
Question 2: In a household in Ibadan, there are 4 adults and 6 children. They have 30 litres of drinking water stored. What is the ratio of litres of water to the total number of people in the household?
Solution 2: Step 1: Calculate the total number of people. Adults = 4 Children = 6 Total People = 4 + 6 = 10 members Step 2: Identify the quantities. Litres of Water = 30 litres Total People = 10 members Step 3: Form the ratio (litres of water to total people). Ratio = 30 : 10 Step 4: Simplify the ratio. Divide both quantities by their GCF, which is 10. 30 ÷ 10 = 3 10 ÷ 10 = 1 Simplified Ratio = 3 : 1
Commentary: This ratio shows that there are 3 litres of water for every 1 person in the household, implying each person can have an average of 3 litres.
Question 3: A community in Abia State distributed 45 bags of rice to 9 families. If each family has an average of 5 members, what is the ratio of bags of rice to the total number of family members receiving the rice?
Solution 3: Step 1: Calculate the total number of family members. Number of families = 9 Average members per family = 5 Total Family Members = 9 families × 5 members/family = 45 members Step 2: Identify the quantities. Bags of Rice = 45 bags Total Family Members = 45 members Step 3: Form the ratio (bags of rice to total family members). Ratio = 45 : 45 Step 4: Simplify the ratio. Divide both quantities by their GCF, which is 45. 45 ÷ 45 = 1 45 ÷ 45 = 1 Simplified Ratio = 1 : 1
Commentary: This ratio indicates that for every 1 bag of rice, there is 1 family member, suggesting that each person received an equivalent share of one bag of rice from the distribution.
Family Budgeting and Resource Allocation: Application: Families regularly use ratios (even unconsciously) when budgeting. For example, a family earning ₦100,000 with 5 members needs to allocate resources like food, school fees, and transport. Understanding the ratio of income to family size (₦20,000:1) helps them determine how much is available per person and prioritize spending. This also extends to sharing food items (e.g., 20 slices of bread for 5 children – a 4:1 ratio of bread to child).
Integration: In Social Studies, discussing family responsibilities and economic well-being; in Home Economics, planning meals and managing household finances.
Community Resource Distribution: Application: During times of need (e.g., flood relief, communal farming projects), aid agencies or community leaders distribute resources like food aid, blankets, or farming tools. Ratios help ensure fair distribution based on household size or number of beneficiaries. For instance, if 50 bags of rice are to be shared among 10 families, the ratio 50:10 simplifies to 5:1, meaning each family gets 5 bags of rice.
Integration: In Civic Education, discussing community service and social justice; in Agricultural Science, planning yield distribution or livestock management per household.
Land and Property Allocation: Application: In many Nigerian communities, land is a crucial resource. When land is inherited or communal land is shared, ratios are often used to determine equitable plots based on the number of heirs or family sizes. For example, if 12 plots are to be shared among 3 sons, the ratio 12:3 simplifies to 4:1, meaning each son gets 4 plots.
Integration: In Social Studies/History, discussing traditional land tenure systems; in Geography, understanding population density and resource availability.