Mathematics - Junior Secondary 3 - Variations

TERM: 1^ST TERM

WEEK 8

Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Variations
Focus: Joint and Partial Variations

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

1. Identify joint variations in real-life situations.
2. Solve problems involving joint variation.
3. Solve problems involving partial variation.
4. Express equations for joint and partial variations.
5. Apply joint and partial variations to practical situations.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Problem-solving exercises
• Real-life application

INSTRUCTIONAL MATERIALS:
• Whiteboard and marker
• Worksheets
• Flashcards
• Graph paper
• Calculators (optional)

PERIOD 1 & 2: Joint Variation

PRESENTATION:

2 | Explains the formula for joint variation: y=kxzy = kxz. | Pupils observe and take notes. | | Step 3 | Demonstrates how to solve joint variation problems. | Pupils follow along and solve problems. | | Step 4 | Solves a few example problems on the board. | Pupils solve similar problems in class. |

NOTE ON BOARD:

• Joint Variation Formula: y=kxzy = kxz
• k=yxzk = \frac{y}{xz}

EVALUATION (5 exercises):

1. If y=30y = 30, x=3x = 3, and z=5z = 5, find kk.
2. Solve for yy if x=6x = 6, z=4z = 4, and k=2k = 2.
3. If y=50y = 50, x=5x = 5, and z=2z = 2, find kk.
4. Solve for yy if k=3k = 3, x=8x = 8, and z=7z = 7.
5. Find zz if y=72y = 72, x=4x = 4, and k=6k = 6.

CLASSWORK (5 questions):

1. If y=16y = 16, x=4x = 4, and z=2z = 2, find kk.
2. If k=12k = 12, x=3x = 3, and z=5z = 5, find yy.
3. Solve for xx when y=48y = 48, z=6z = 6, and k=8k = 8.
4. If y=120y = 120, k=15k = 15, and z=10z = 10, find xx.
5. Solve for zz if y=80y = 80, x=4x = 4, and k=10k = 10.

ASSIGNMENT (5 tasks):

1. Solve for yy if k=7k = 7, x=3x = 3, and z=4z = 4.
2. If y=36y = 36, k=6k = 6, and z=2z = 2, find xx.
3. Create a joint variation problem and solve it.
4. Solve for zz if y=48y = 48, x=6x = 6, and k=8k = 8.
5. Create and solve a real-life joint variation problem.

PERIOD 3 & 4: Partial Variation

PRESENTATION:

NOTE ON BOARD:

• Partial Variation Formula: y=kx+cy = kx + c
• cc is the constant of variation when x=0x = 0.

EVALUATION (5 exercises):

1. Solve for yy if k=5k = 5, x=3x = 3, and c=2c = 2.
2. If y=20y = 20, x=4x = 4, and k=5k = 5, find cc.
3. Solve for xx if y=45y = 45, k=9k = 9, and c=3c = 3.
4. Find cc if y=15y = 15, x=3x = 3, and k=4k = 4.
5. Solve for yy if k=2k = 2, x=5x = 5, and c=−3c = -3.

CLASSWORK (5 questions):

1. If y=18y = 18, x=2x = 2, and k=6k = 6, find cc.
2. Solve for xx when y=30y = 30, k=5k = 5, and c=10c = 10.
3. Find yy if k=3k = 3, x=7x = 7, and c=8c = 8.
4. Solve for cc when y=42y = 42, k=6k = 6, and x=6x = 6.
5. Find xx when y=50y = 50, k=4k = 4, and c=10c = 10.

ASSIGNMENT (5 tasks):

1. Solve for yy if k=4k = 4, x=6x = 6, and c=5c = 5.
2. If y=35y = 35, x=5x = 5, and k=3k = 3, find cc.
3. Create a partial variation word problem and solve it.
4. Solve for cc if y=40y = 40, x=5x = 5, and k=6k = 6.
5. Solve for xx when y=18y = 18, k=3k = 3, and c=4c = 4.

PERIOD 5: Real-Life Applications of Joint and Partial Variations

PRESENTATION:

EVALUATION (5 exercises):

1. A car’s fuel consumption varies jointly with the distance traveled and the load it carries. If the fuel consumption is 50 liters when the distance is 100 km and the load is 10 tons, find the fuel consumption for a load of 15 tons over 200 km.
2. A company’s profit varies partially with the number of products sold and the price per product. If the profit is 100,000 Naira when 500 products are sold at 200 Naira each, find the profit when 800 products are sold at 250 Naira each, assuming the fixed cost is 50,000 Naira.
3. A worker’s wage varies directly with the number of hours worked and partially with the hourly rate. If a worker earns 2,000 Naira for 8 hours at an hourly rate of 250 Naira, find the wage when the worker works for 10 hours at 300 Naira per hour.
4. A product’s price varies directly with demand and partially with supply. If the price of a product is 150 Naira when demand is 500 units and supply is 400 units, find the price when demand increases to 700 units and supply increases to 600 units.
5. A student’s academic performance varies jointly with study hours and test preparation. If a student’s score is 80 when studying for 10 hours and preparing with 2 hours of tutoring, find the expected score when studying for 15 hours and receiving 3 hours of tutoring.

CLASSWORK (5 questions):

1. Create a joint variation problem involving speed and time and solve it.
2. Create a partial variation problem involving the cost of an item and solve it.
3. Solve for xx in a real-life joint variation problem.
4. Solve for yy in a real-life partial variation problem.

Discuss how variations can apply to daily life and business.