Topics
Part 1
Fractions in Disguise
Rational Numbers
- Rational Numbers
- Closure Property of Rational Numbers
- Commutative Property of Rational Numbers
- Associative Property of Rational Numbers
- Distributive Property of Multiplication Over Addition for Rational Numbers
- Identity of Addition and Multiplication of Rational Numbers
- Negative Or Additive Inverse of Rational Numbers
- Concept of Reciprocals or Multiplicative Inverses
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
- Multiples and Common Multiples
A Square and A Cube
Linear Equations in One Variable
- Constants and Variables in Mathematics
- Equation in Mathematics
- Expressions with Variables
- Word Problems on Linear Equations
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to Linear Equations
The Baudhayana-Pythagoras Theorem
Power Play
Part 2
Understanding Quadrilaterals
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Basic Concept of Polygons
- Classification of Polygons
- Properties of Quadrilateral
- Sum of Interior Angles of a Polygon
- Sum of Exterior Angles of a Polygon
- Quadrilaterals
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.
A Story of Numbers
Proportional Reasoning-2
Exploring Some Geometric Themes
Practical Geometry
- Geometric Tool
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Some Special Cases
Data Handling
Quadrilaterals
Tales by Dots and Lines
Squares and Square Roots
- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root
Number Play
Algebra Play
Cubes and Cube Roots
We Distribute, Yet Things Multiply
Area
Proportional Reasoning-1
Comparing Quantities
- Ratio
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Basic Concepts of Profit and Loss
- Calculation of Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
Algebraic Expressions and Identities
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Classification of Terms in Algebra
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Expansion of (x + a)(x + b)
Mensuration
Exponents and Powers
Visualizing Solid Shapes
Direct and Inverse Proportions
Factorization
- Factors and Common Factors
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error
Introduction to Graphs
Playing with Numbers
- Definition: Graph
- Graph Paper
- X-axis and Y-axis
- Use of Scale
Definition
A Pictograph is a chart that uses pictures or symbols to represent data. Each picture stands for a specific number of items, making the data easy to understand at a glance.
Maharashtra State Board: Class 6
Graph Paper
Structure of Graph Paper:
1. Grid Formation:
Graph paper consists of a network of bold and faint lines.
The bold lines represent larger units, while the faint lines divide these units into smaller, equal parts.
2. Purpose of the Grid:
This structure helps in choosing a suitable scale.
It also assists in drawing accurate columns or bars based on data values.
3. Axes on Graph Paper:
A horizontal line is drawn near the bottom edge of the paper, known as the X-axis.
On the left side, draw a vertical line perpendicular to the X-axis, which we call the Y-axis.
Example:
The following information is to be represented as a bar graph: The number of different types of vehicles is: 5, 15, 25, and 30. Use the X-axis to represent the types of vehicles. Use the Y-axis to represent the number of vehicles. Take a scale of 5 vehicles = 1 big unit.
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Series: Concept of Bar Graph
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Related QuestionsVIEW ALL [61]
Number of children in six different classes are given below. Represent the data on a bar graph.
| Class | Fifth | Sixth | Seventh | Eighth | Ninth | Tenth |
| Number of children | 135 | 120 | 95 | 100 | 90 | 80 |
- How would you choose a scale?
- Answer the following questions:
- Which class has the maximum number of children? And the minimum?
- Find the ratio of students of class sixth to the students of class eight.
Take the data giving the minimum and the maximum temperature of various cities given in the following table:
| Temperatures of the cities as on 20.6.2006 | ||
| City | Max. | Min. |
| Ahmedabad | 38ºC | 29ºC |
| Amritsar | 37ºC | 26ºC |
| Banglore | 28ºC | 21ºC |
| Chennai | 36ºC | 27ºC |
| Delhi | 38ºC | 28ºC |
| Jaipur | 39ºC | 29ºC |
| Jammu | 41ºC | 26ºC |
| Mumbai | 32ºC | 27ºC |
Plot a double bar graph using the data and answer the following:
- Which city has the largest difference in the minimum and maximum temperature on the given date?
- Which is the hottest city and which is the coldest city?
- Name two cities where maximum temperature of one was less than the minimum temperature of the other.
- Name the city which has the least difference between its minimum and the maximum temperature.
The data given below shows the production of motorbikes in a factory for some months of two consecutive years.
| Months | Feb | May | August | October | December |
| 2008 | 2700 | 3200 | 6000 | 5000 | 4200 |
| 2007 | 2800 | 4500 | 4800 | 4800 | 5200 |
Study the table given above and answer the following questions:
- Draw a double bar graph using appropriate scale to depict the above information and compare them.
- In which year was the total output the maximum?
- Find the mean production for the year 2007.
- For which month was the difference between the production for the two years the maximum?
- In which month for the year 2008, the production was the maximum?
- In which month for the year 2007, the production was the least?
Consider this data collected from a survey of a colony.
| Favourite sport | Cricket | Basket Ball | Swimming | Hockey | Athletics |
| Watching | 1240 | 470 | 510 | 430 | 250 |
| Participating | 620 | 320 | 320 | 250 | 105 |
- Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
- Which sport is most popular?
- Which is more preferred, watching or participating in sports?
