# Maths Model

## Trigonometry # Maths Model

Maths model is an intellectual model that uses mathematical expression to explain the function of a system. In schools, students are assigned Maths projects to make them think and learn. They can use their intellectual abilities to create models. These models will help to learn the concepts in a creative way.

Mathematical models are primarily used in the field of Natural Sciences and Engineering disciplines, which covers subjects such as Physics, Biology, and Electrical Engineering. It also has its importance in subjects like social sciences covering subjects like Sociology, Political Science and Economics. Physicists, Computer Scientists, Engineers, and Economists use these models most widely. But here we are going to discuss models based on mathematical concepts for Class 5 to 10.

## Math Models for Class 10

Students of 10th standard can prepare models on multiple topics covered under the syllabus. They can also make use of Maths Formulas to create such models. Besides, the each of these maths model for class 10 help the students to understand the real-life application of important mathematical concepts and formulas. Some of the ideas for making Math models for 10th class are:

• Congruency of Triangles- Draw colourful triangles on a sheet of paper and show the congruent triangles by SSS, SAS, ASA and RHS congruency.
• Circumcentre of different types of triangles- Show the constructions to find the circumcentre of a triangle using colourful papers and threads.
• Types of functions – In a sheet, paste different types of sets using coloured papers and to show the relation between two sets, you can use ice-cream sticks.
• Venn Diagram of sets- Take a chart and draw the Venn diagram of a universal set carrying subsets. Separate them using different colour pencils.
• Circles, tangents, radius, secant, chord, sector. – In a paper chart, draw different types of circles consisting of its radius, tangents, secant, diameter, chord and sector.
• Finding sides and angles of triangles using Trigonometry – Try solving different triangles problems to find the missing sides or angles using trigonometric ratios.

Among these, maths working model for class 10 on trigonometry and maths working model for class 10 geometry related ones are used to solve different problems in other areas also since various concepts are associated with them.

## Maths Model for Class 9

Class 9 students can use the given models for maths concepts. Maths model for class 9 helpful for the students to understand the important of different geometrical concepts in everyday life.

• Angle Sum Property of Quadrilaterals – Draw a quadrilateral in a paper chart and show its angles with different colours. Draw a circle with those different angles to prove the sum of interior angles of a quadrilateral is 360 degrees.
• Area of Rhombus – Draw a rectangle and colour it. Now draw a rhombus inside it with a different colour. Join the diagonals of the rhombus with dotted lines. This model is to prove that the area of a rhombus is equal to half of the product of its diagonals.
• Total Surface area of a Cuboid– Cut and paste different colourful papers to show the surfaces of different sides of the cuboid in a chart. You can also mention the formula for total surface area with a different colour.

## Math Model for Class 8

Class 8 students can also use many creative ideas to create models as per their syllabus such as;

• Pie Chart: In a chart draw a big circle and divide the sections to mention the population of men, women and children in the world. Or you can also create a pie chart for your daily activities like studying, playing, sleeping, etc.
• Algebraic Formulas: You can use blocks of colourful papers and paste in a chart showing the formulas, where each block will show the individual term.
• Polygons: Cut and paste different colourful papers in a white chart to show different types of polygons, in increasing order of sides

## Math Model for Class 7

Here are some suitable models for students of 7th Standard which they can easily create.

• Sum of N Even Numbers: Draw a table in a big sheet of paper, having at least ten rows and columns (you can exceed them). Write and show even numbers in different colours. Now you can show the sum of first n even numbers using the formula n(n+1). You can also use this model to represent the sum of N odd numbers.
• Types of Angles: Students can show different types of angles such as acute angle, right angle, obtuse angle, using colourful pencils or sketch in a big sheet of paper.
• Lines and Transversal: Use thermocol and cut two parallel lines and one transversal in it. Now show all the eight angles formed by a transversal on the intersection with the two lines.

## Math Models for Class 6

Simple models for 6th class students are given here, which they can easily create.

• Prime and Composite Numbers Chart: Draw a table in a paper chart. Write numbers from 1 to 100 in each block. Highlight the prime numbers with a different colour.
• Playing With Fractions: Cut a paper in a circle shape. Now, cut another coloured paper of the same shape and size and divide it into six equal pieces through the centre. These pieces of paper can be used to show the fraction part of the whole circle.
• Clocks: You can create wall clocks using cardboards and needles to show different timings.

## Maths Model for Class 5

Class 5 syllabus covers the basics of Maths concepts. Some of the Maths models for them are:

• Shapes and Angles: Draw different types of shapes such as circle, square, rectangle, etc. in a big paper sheet with colourful sketch pens. Similarly, they can show types of angles.
• Comparing Patterns: Draw different patterns in a chart to compare them. You can also draw shapes of different sizes and show a comparison between them.
• How Many Squares: Draw a big rectangle and draw small squares inside it with different colours to show the number of squares we can draw inside it.
• Numbers: Create an Abacus to count numbers, using thermocol beans and threads encountered with a metallic or wooden frame.

## Working Models in Mathematics

There are various ideas in Maths for which students can make working models. These models can be prepared using handicrafts. Students can also use household things such as colourful papers, ice cream sticks, match sticks, plastic spoons, etc., to create models based on mathematical concepts. Some of the ideas are:

• Arithmetic Operators (+, -, x and ÷)
• Working Models for addition and subtraction
• Show the number of legs for different animals such as birds, cows, octopus, spider, etc.
• Area of circle by cutting the sectors of circle
• Odd and even numbers model with lights
• Pythagoras theorem model
• Venn Diagram model
• Parts of circles model
• Tangent to a circle model
• Conic sections model
• Build a new house and its ambiance using different geometrical shapes
• Show the angle of depression with a 3d model of trigonometry

### Stages of Mathematical Models

The stages or the steps involved in maths models are given below. These steps help in dealing with maths models for classes 10, 9, 8, 7, 6 and 5.

Step 1: Understanding the problem

In this stage, we need to define the real problem and analyse it by making assumptions and overlooking specific factors so that the problem is tractable.

Step 2: Mathematical description and formulation

In this step, we need to describe different aspects of the problem in mathematical terms. This formulation may include defining variables, writing equations or inequalities, gathering data and organising it into tables, making graphs if required, etc.

Step 3: Solving the mathematical problem

In this stage, we need to solve the mathematical problem developed in the previous step using suitable mathematical techniques.

Step 4: Interpreting the solution

In this stage, we need to look at the solution set obtained in the previous step and apply it to the context of the real-life situation given in the beginning.

Step 5: Validating the model

The last step is to validate the model, and this involves checking the results obtained through the above steps to satisfy the given real-life scenario.