Mathematics - Junior Secondary 3 - Variations

Variations

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TERM: 1ST TERM

WEEK 7

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

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

  1. Identify and understand direct and indirect variations.
  2. Solve problems involving direct variation.
  3. Solve problems involving indirect variation.
  4. Express equations for direct and indirect variations.
  5. Apply variations to real-life situations.

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

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

PERIOD 1 & 2: Direct Variation

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1

Introduces the concept of direct variation using simple examples.

Pupils listen and ask questions.

Step 2

Explains the formula for direct variation: y=kxy = kx, where kk is the constant of proportionality.

Pupils observe and take notes.

Step 3

Demonstrates how to solve direct 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:

  • Direct Variation Formula: y=kxy = kx
  • k=yxk = \frac{y}{x}

EVALUATION (5 exercises):

  1. Solve for yy if x=5x = 5 and k=2k = 2.
  2. If y=12y = 12 when x=3x = 3, find kk.
  3. Solve for yy if x=10x = 10 and k=0.5k = 0.5.
  4. If k=4k = 4 and x=7x = 7, what is yy?
  5. Solve for xx when y=24y = 24 and k=3k = 3.

CLASSWORK (5 questions):

  1. If y=8y = 8 when x=4x = 4, find kk.
  2. If k=6k = 6 and x=9x = 9, find yy.
  3. If y=36y = 36 and k=6k = 6, find xx.
  4. If x=15x = 15 and y=45y = 45, find kk.
  5. If k=3k = 3, find yy when x=5x = 5.

ASSIGNMENT (5 tasks):

  1. Solve for yy if x=12x = 12 and k=8k = 8.
  2. Find kk when y=45y = 45 and x=5x = 5.
  3. If y=60y = 60 when x=10x = 10, find kk.
  4. Solve for xx when y=30y = 30 and k=2k = 2.
  5. Create a direct variation word problem and solve it.

 

PERIOD 3 & 4: Indirect Variation

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1

Introduces the concept of inverse (indirect) variation with examples.

Pupils listen and ask questions.

Step 2

Explains the formula for indirect variation: y=kxy = \frac{k}{x}.

Pupils observe and take notes.

Step 3

Demonstrates how to solve indirect 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:

  • Indirect Variation Formula: y=kxy = \frac{k}{x}
  • k=xyk = xy

EVALUATION (5 exercises):

  1. Solve for yy if x=4x = 4 and k=12k = 12.
  2. If y=6y = 6 and x=2x = 2, find kk.
  3. Solve for yy if x=8x = 8 and k=16k = 16.
  4. If k=24k = 24 and x=6x = 6, what is yy?
  5. Solve for xx when y=10y = 10 and k=50k = 50.

CLASSWORK (5 questions):

  1. If y=20y = 20 and x=4x = 4, find kk.
  2. If k=72k = 72 and x=9x = 9, find yy.
  3. If y=30y = 30 and k=60k = 60, find xx.
  4. If x=6x = 6 and y=12y = 12, find kk.
  5. Solve for yy if x=2x = 2 and k=10k = 10.

ASSIGNMENT (5 tasks):

  1. Solve for yy if x=5x = 5 and k=30k = 30.
  2. Find kk when y=16y = 16 and x=8x = 8.
  3. If y=25y = 25 and x=5x = 5, find kk.
  4. Solve for xx when y=40y = 40 and k=200k = 200.
  5. Create an inverse variation word problem and solve it.

 

PERIOD 5: Real-Life Applications of Variations

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1

Introduces real-life examples of variations (e.g., speed, cost, etc.).

Pupils listen and ask questions.

Step 2

Shows how direct and indirect variations can apply to practical situations.

Pupils observe and take notes.

Step 3

Guides pupils through solving real-life variation problems.

Pupils solve real-life problems.

Step 4

Discusses how variations are used in science and economics.

Pupils discuss applications in real life.

EVALUATION (5 questions):

  1. If the cost of an item varies directly with the quantity, find the cost if k=20k = 20 and quantity = 10.
  2. If the speed of a car varies inversely with the time it takes, find the speed if k=60k = 60 and time = 3 hours.
  3. If the area of a rectangle varies directly with its length and indirectly with its width, find the area if k=15k = 15, length = 8, and width = 2.
  4. How does the weight of an object change when the number of objects increases? (Direct or indirect variation?)
  5. Solve for the cost if k=50k = 50 and quantity = 4.

CLASSWORK (5 tasks):

  1. Create a real-life direct variation problem and solve it.
  2. Create a real-life inverse variation problem and solve it.
  3. If the time taken to complete a task is inversely proportional to the number of workers, find the time taken if k=60k = 60 and number of workers = 5.
  4. If the volume of water in a tank varies directly with the height, solve for volume when height = 10 meters and k=5k = 5.
  5. Find the speed of a car if it travels 100 km in 2 hours, assuming direct variation with time.

ASSIGNMENT (5 tasks):

  1. Solve for kk if the cost of 4 items is 80 dollars and the cost varies directly with the number of items.
  2. Solve for the time it takes to fill a tank if the amount of water varies inversely with time.
  3. Create and solve a real-life direct variation word problem.
  4. Create and solve a real-life inverse variation word problem.

Identify an example of joint variation in daily life and explain it.