Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 3rd Term
Week: 9
Age: 16 years
Duration: 45 minutes
Subject: Further Mathematics
Curriculum Theme: Applied Mathematics
Previous Lesson: Dynamics: Projectiles, Trajectory and Inclined Projection.
Topic: INVENTORY MODEL
Subject Matter: Meaning of inventory model (method for managing stock levels and costs), concept of inventory, definitions of important terms in inventory, holding cost, ordering cost, computation of optimal quantity (EOQ model)

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define inventory and inventory model.
Explain the terms holding cost and ordering cost.
State the formula for Economic Order Quantity (EOQ).

Affective Domain:

Appreciate the importance of managing inventory in real-world scenarios.
Develop interest in optimizing business costs through inventory models.

Psychomotor Domain:

Compute the Economic Order Quantity (EOQ) using the given formula.
Solve simple problems involving inventory costs.

Participate actively in class discussions on inventory management.

Reference Materials

The following resources were used in planning this lesson:

Senior Secondary Schools Education Curriculum
State Unified Scheme of Work
New Further Mathematics for Senior Secondary Schools by P.N. Okeke.
https://www.investopedia.com/terms/i/inventorymodel.asp
https://www.quickbooks.com/accounting/inventory-management/

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts depicting items on inventory (e.g., a warehouse, shop shelves).
Whiteboard and markers.

Rationale for the Lesson

This lesson helps pupils understand how businesses manage their stock to avoid shortages or excess, which can save money. It enables pupils to apply mathematical concepts to real-world business problems, preparing them for future studies or careers in commerce and management.

Prerequisite/Previous Knowledge

Pupils have basic knowledge of business operations, costs, and simple algebraic computations.

Lesson Content/Board Summary

INVENTORY MODEL

Meaning of Inventory Model

An inventory model is a mathematical method used to manage stock levels and associated costs. Its primary goal is to determine the optimal quantity of goods to order or produce to meet demand while minimizing the total inventory costs.

Concept of Inventory

Inventory refers to the stock of goods, materials, or products that a business holds for future use or sale. This can include raw materials, work-in-progress, or finished goods.

Important Terms in Inventory

The following are important terms related to inventory management:

Holding Cost (or Carrying Cost) – This is the cost associated with storing inventory over a period. Examples include warehouse rent, insurance, depreciation, obsolescence, spoilage, and security costs. It is usually expressed per unit per year.
Ordering Cost (or Setup Cost) – This is the cost incurred each time an order is placed. Examples include administrative costs for processing an order, transportation costs, inspection costs, and clerical work related to purchasing. It is usually expressed per order.
Economic Order Quantity (EOQ) – This is the optimal order quantity that a business should purchase to minimize the total inventory costs (which include holding costs and ordering costs). It is the point where ordering costs and holding costs are approximately equal.

Economic Order Quantity (EOQ) Model

The EOQ model is a widely used inventory control technique that helps determine the ideal order quantity. The formula is:

EOQ = √(2DS / H)

Where:

D = Annual Demand (total number of units required per year)
S = Ordering Cost per order
H = Holding Cost per unit per year

Worked Examples

Example 1:
A company has an annual demand of 10,000 units. The cost to place an order is N500, and the holding cost per unit per year is N20. Calculate the Economic Order Quantity (EOQ).

Solution:
Step 1: Identify the given values.
D = 10,000 units
S = N500 per order
H = N20 per unit per year

Step 2: Apply the EOQ formula.
EOQ = √(2DS / H)
EOQ = √(2 × 10,000 × 500 / 20)

Step 3: Perform the calculation.
EOQ = √(10,000,000 / 20)
EOQ = √500,000
EOQ ≈ 707.11 units

Step 4: Round to a practical whole number (since units cannot be fractional).
EOQ ≈ 707 units

Example 2:
A retail store sells 12,000 units of a product annually. The ordering cost is N100 per order, and the holding cost is N5 per unit per year. Determine the optimal order quantity for the store.

Solution:
Step 1: Identify the given values.
D = 12,000 units
S = N100 per order
H = N5 per unit per year

Step 2: Apply the EOQ formula.
EOQ = √(2DS / H)
EOQ = √(2 × 12,000 × 100 / 5)

Step 3: Perform the calculation.
EOQ = √(2,400,000 / 5)
EOQ = √480,000
EOQ ≈ 692.82 units

Step 4: Round to a practical whole number.
EOQ ≈ 693 units

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher asks pupils about their experiences with shops, supermarkets, or warehouses, focusing on how these places manage their goods or stock.
Pupils’ Activity: Pupils share their observations and ideas about managing stock.
Learning Point: Pupils relate the concept of stock management to real-life situations.

Step 2: Meaning of Inventory Model and Concept of Inventory

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains the meaning of an inventory model and the general concept of inventory using the pupils’ shared experiences.
Pupils’ Activity: Pupils listen attentively, define inventory in their own words, and copy notes.
Learning Point: Pupils understand what inventory and inventory models are.

Step 3: Important Terms in Inventory

Time: 8 minutes
Teaching Skill: Definition/Elaboration
Teacher’s Activity: The teacher defines and explains important terms like holding cost and ordering cost, providing practical examples for each.
Pupils’ Activity: Pupils listen, ask questions for clarity, and write down the definitions.
Learning Point: Pupils grasp the definitions and significance of holding and ordering costs.

Step 4: Introduction to Economic Order Quantity (EOQ)

Time: 5 minutes
Teaching Skill: Introduction/Motivation
Teacher’s Activity: The teacher introduces the Economic Order Quantity (EOQ) as a tool used by businesses to minimize total inventory costs, linking it to the previously discussed costs.
Pupils’ Activity: Pupils listen and understand the purpose of EOQ.
Learning Point: Pupils recognize EOQ as an important cost-optimization tool.

Step 5: EOQ Formula and Variables

Time: 5 minutes
Teaching Skill: Formula Presentation
Teacher’s Activity: The teacher presents the EOQ formula on the board and explains each variable (D, S, H) and its meaning.
Pupils’ Activity: Pupils copy the formula and the explanation of its variables into their notebooks.
Learning Point: Pupils know the EOQ formula and the meaning of its components.

Step 6: Worked Examples

Time: 10 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher solves the two worked examples from the lesson content on the board, explaining each step clearly.
Pupils’ Activity: Pupils follow the steps, ask questions, and copy the solutions.
Learning Point: Pupils learn how to apply the EOQ formula to solve practical problems.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define inventory model.
Distinguish between holding cost and ordering cost.
State the formula for Economic Order Quantity (EOQ) and explain each variable.
A company has an annual demand of 8,000 units. The ordering cost is N200 per order, and the holding cost is N10 per unit per year. Calculate the EOQ.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson and assigns homework: find out other inventory models apart from EOQ.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their understanding and prepare for future learning.

Lesson Keywords

Inventory – Stock of goods or materials held by a business.
Inventory Model – A method for managing stock levels and costs.
Holding Cost – Cost of storing inventory.
Ordering Cost – Cost of placing an order.
EOQ – Economic Order Quantity, the optimal order size that minimizes total inventory costs.
Demand – The total number of units required over a period.

Differentiation

For pupils who grasp the concept quickly, the teacher can provide additional complex problems or discuss the limitations of the EOQ model. For pupils who are struggling, the teacher will provide simplified examples, one-on-one guidance, or pair them with more advanced pupils for peer tutoring.

Note for teachers using this lesson plan

Ensure that pupils clearly understand the difference between holding cost and ordering cost, as this is fundamental to the EOQ model. Emphasize the practical application of the EOQ formula in real-world business scenarios to make the lesson more relevant and engaging. Encourage pupils to ask questions and work through the examples step-by-step.