Topics
Number System (Including Estimation and Approximation)
Theme 1 : Numbers
Number System(Consolidating the Sense of Numberness)
Number System
Ratio and Proportion
Numbers in Indian and International Systems (With Comparison)
Theme 2 : Ratio, Proportion and Arithmetic Problems
Estimation
Numbers in India and International System (With Comparison)
Natural Numbers and Whole Numbers (Including Number Line and Patterns)
Theme 3 : Algebra
Algebra
Theme 4 : Geometry
Geometry
Place Value
Negative Numbers and Integers
Natural Numbers and Whole Numbers (Including Patterns)
Mensuration
Theme 5 : Mensuration
Sets
Fractions
Data Handling
Negative Numbers and Integers
Theme 6 : Statistics
Decimal Fractions
Number Line
Playing with Numbers (Including H.C.F. and L.C.M.)
HCF and LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Ratio and Proportion (Including Unitary Method)
Percent (Percentage)
Sets
Ratio
Idea of Speed, Distance and Time
Fundamental Concepts (With operations on Algebraic Expressions)
Proportion (Including Word Problems)
Framing Algebraic Expressions (Including Substitution and Linear Equations)
Unitary Method
Fundamental Concepts (Including Angles and their Properties)
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Triangles (Including Types and Properties of Triangles)
Decimal Fractions
Percent (Percentage)
Quadrilaterals
Idea of Speed, Distance and Time
Circles
Symmetry
Fundamental Concepts
Constructions
Fundamental Operations (Related to Algebraic Expressions)
Recognition of Solids
Substitution (Including Use of Brackets as Grouping Symbols)
Perimeter and Area of Plane Figures
Framing Algebraic Expressions (Including Evaluation)
Data Handling (Including Mean and Median)
Simple (Linear) Equations (Including Word Problems)
Fundamental Concepts
Angles (With Their Types)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
The Circle
Symmetry (Including Constructions on Symmetry)
Recognition of Solids
Perimeter and Area of Plane Figures
Data Handling (Including Pictograph and Bar Graph)
Mean and Median
Estimated time: 7 minutes
- Introduction
- The Substitution Process
- Example 1
- Example 2
- Key Points Summary
CISCE: Class 6
Introduction
Algebraic expressions combine numbers, variables (letters), and operation signs to form mathematical statements. An expression’s value changes when you replace its variables with different numbers—this process is called substitution.
CISCE: Class 6
The Substitution Process
- Step 1: Identify the variable in the expression
- Step 2: Replace the variable with the given number
- Step 3: Follow the order of operations (BODMAS)
- Step 4: Calculate the final answer
CISCE: Class 6
Example 1
- Write the expression:
-
Substitute x = 2, the value of the expression 3x + 2 = 3 × 2 + 2 = 6 + 2 = 8
-
Substitute x = 0, the value of the expression 3x + 2 = 3 × 0 + 2 = 0 + 2 = 2
- Substitute x = −2, the value of the expression 3x + 2 = 3 × (−2) + 2 = −6 + 2 = −4, and so on.
CISCE: Class 6
Example 2
If x = 5, y = 6 and z = 10, find the value of
(i) `(3x^2)/(x)` = `(3×5^2)/(5)` = `"3 × 5 × 5" / 5` = 3 × 5 = 15
Alternative method:
`(3x^2)/(x)` = `"3 × x × x" / x` = 3 × x = 3 × 5 = 15
CISCE: Class 6
Key Points Summary
-
Substitution transforms expressions into numbers.
-
Always replace every occurrence of a variable.
-
Follow order of operations (BODMAS).
-
Use parentheses for negative values.
