### Mathematics Lab Manual Class 10

Mathematics Lab Manual Class X   lab activities for class 10 with complete observation Tables strictly according to the CBSE syllabus also very useful & helpful for the students and teachers.

### Lesson Plan Math Class 8 | Direct and Inverse Variation CH-4

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS- 8

Lesson Plan for CBSE mathematics class 8 Direct & Inverse Variation, Step by step teaching strategy for mathematics teachers. Perfect lesson plan which makes the teaching learning process perfect

## E-LESSON PLAN MATHEMATICSCLASS-VIIICHAPTER-3 PROFIT, LOSS & DISCOUNT

 RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR NAME OF THE TEACHER DINESH KUMAR CLASS VIII CHAPTER 05 SUBJECT MATHEMATICS TOPIC DIRECT & INVERSE VARIATION DURATION : 8 Class Meetings

## PRE-REQUISITE KNOWLEDGE

• Students should have a good understanding of basic arithmetic operations such as addition, subtraction, multiplication, and division.
• Knowledge of working with fractions and decimals is essential,
• Students should have a solid grasp of proportions and ratios.
• Students should understand the concept of variables and how they represent quantities that can change.
• A basic understanding of algebraic expressions and equations is helpful, as some variation problems might involve setting up and solving equations.

MATERIALS:

Whiteboard and markers (or chalkboard and chalk), Handout with practice problems

LEARNING OBJECTIVES

• Define and differentiate between direct variation and inverse variation.
• Identify real-life scenarios that exhibit direct variation and inverse variation relationships.
• Apply the concept of direct variation to solve problems, including finding constant of variation and using proportional relationships.
• Apply the concept of inverse variation to solve problems, including setting up and solving inverse proportions.
• Analyse word problems and determine whether they involve direct or inverse variation.
• Use mathematical equations and expressions to represent direct and inverse variation relationships.
• Demonstrate confidence in solving a variety of direct and inverse variation problems independently or in groups.

LEARNING OUTCOMES

After studying this lesson students should:

• Recognize and differentiate between direct variation and inverse variation problems in various scenarios.
• Solve problems involving direct variation relationships by setting up and solving proportions, and finding the constant of variation.
• Solve problems involving inverse variation relationships by setting up and solving inverse proportions.
• Apply the concepts of direct and inverse variation to real-world situations, such as speed-time relationships, density and volume, etc.
• Translate real-life problems into mathematical equations and expressions, and vice versa, to represent direct and inverse variation relationships.

RESOURCES

NCERT Text Book,

A Text Book of DAV Board

Resource Material : Worksheets , E-content, Basics and formulas from (cbsemathematics.com)

KEY WORDS:

Direct Variation, Inverse Variation, Ratio, Proportion, Speed,

CONTENT OF THE TOPIC

In this topic we will discuss the detailed explanation of the following concepts:

a) Direct Variation and its implementation in day to day problems.

b) Inverse Variation and its implementation in day to day problems.

LESSON PLAN PROCEDURE

Start the class with a quick review of the concept of proportions and ratios, as these are fundamental to understanding direct and inverse variation.

Ask the students some simple questions related to direct and inverse proportion to gauge their existing knowledge.

Explain to the students the concept of direct and inverse variation.

DIRECT VARIATION:

When two variables change in the same direction, the relationship is called direct variation. As one variable increases, the other increases proportionally, and as one decreases, the other decreases proportionally.

INVERSE VARIATION:

When two variables change in opposite directions, the relationship is called inverse variation. As one variable increases, the other decreases proportionally, and vice versa.

Provide real-life examples for both types of variation, such as distance and time (direct), or speed and time (inverse).

DIRECT VARIATION:

Present a few direct variation problems on the board. For example: "If a car travels at a constant speed of 60 km/h, how far will it travel in 4 hours?"

Guide the students through solving the problem step by step. Show them how to set up a proportion to find the distance.

Allow the students to attempt a few similar problems on their own or in pairs.

Review and discuss the solutions as a class.

Note:

If x and y both increases then there will be a direct variation.

If x and y both increases then there will be a direct variation.

 x a c e g y b d f h

If x and y vary directly then

$\large \bg{black}\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{g}{h}$

INVERSE VARIATION:

Present a few inverse variation problems on the board. For example: "If a certain task can be completed by 6 workers in 8 hours, how many workers are needed to complete the task in 4 hours?"

Guide the students through solving the problem step by step. Show them how to set up an inverse proportion to find the number of workers.

Allow the students to attempt a few similar problems on their own or in pairs.

Review and discuss the solutions as a class.

Note:

If x increases and y decreases then it is an Inverse variation

If x decreases and y increase then it is an Inverse variation

 x a c e g y b d f h

If x and y vary inversely then

$\large \bg{black}a\times b=c\times d=e\times f=g\times h$

COMBINED VARIATION:

If the students grasp the concepts quickly, you can introduce combined variation problems that involve both direct and inverse variations in a single equation.

Summarize the key points of direct and inverse variation.

Encourage students to identify direct and inverse variation relationships in everyday situations.

Provide feedback on their problem-solving skills and address any misconceptions.

MIND MAP

HOMEWORK:

Assign practice problems from the handout for homework. Include a mix of direct and inverse variation problems.

ASSESSMENT:

Observe students' participation and engagement during the class activities.

Review their solutions to the practice problems in the class and homework.

Use their understanding of the concepts to assess their ability to apply direct and inverse variation in different scenarios.

Adjust the complexity of the problems based on the students' skill levels and add more examples if necessary. Encourage students to ask questions during the lesson to clarify any doubts they may have.