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Grade 7
Practical Geometry
Grade 7
1.
Integers
1.1.
Revisiting Basics
1.2.
Operations on Integers
1.2.1.
Addition and Subtraction of Integers
1.2.1.1.
Addition of Integers
1.2.1.2.
Properties of Addition of Integers
1.2.1.3.
Subtraction of Integers
1.2.1.4.
Properties of Subtraction of Integers
1.2.2.
Multiplication and Division of Integers
1.2.2.1.
Multiplication of Integers
1.2.2.2.
Properties of Multiplication of Integers
1.2.2.3.
Division of Integers
1.2.2.4.
Properties of Division of Integers
1.2.3.
Mixed Operations of Integers
1.2.4.
Word Problems on Integers
2.
Prime Numbers
3.
Square Roots and Cube Roots
3.1.
Square Root
3.2.
Cube Root
4.
HCF and LCM
4.1.
HCF (Highest Common Factor)
4.2.
LCM (Lowest Common Multiple)
4.3.
Properties of LCM and HCF
4.4.
Word problems on HCF and LCM
5.
Fractions
5.1.
Revisiting Basics
5.2.
Equivalent Fractions
5.3.
Comparing Fractions
5.3.1.
Comparing Like Fractions
5.3.2.
Comparing Unlike Fractions
5.4.
Operations on Fractions
5.4.1.
Addition of Fractions
5.4.1.1.
Addition of Like Fractions
5.4.1.2.
Addition of Unlike Fractions
5.4.1.3.
Addition of Mixed Fractions
5.4.2.
Subtraction of Fractions
5.4.2.1.
Subtraction of Like Fractions
5.4.2.2.
Subtraction of Unlike Fractions
5.4.2.3.
Subtraction of Mixed Fractions
5.4.3.
Simplify Expressions involving Addition and Subtraction
5.4.4.
Multiplication of Fractions
5.4.4.1.
Simplify Expressions involving Multiplication
5.4.4.2.
Use of 'OF'
5.4.5.
Division of Fractions
5.4.5.1.
Reciprocal of a Fraction
5.4.5.2.
Simplify Expressions involving Division
5.4.6.
Simplification by Using Operations
5.4.7.
Word Problems on Fractions
5.4.7.1.
Word Problems on Addition of Fractions
5.4.7.2.
Word Problems on Subtraction of Fractions
5.4.7.3.
Word Problems on Addition and Subtraction of Fractions
5.4.7.4.
Word Problems on Multiplication of Fractions
5.4.7.5.
Word Problems on Division of Fractions
6.
Rational Numbers
6.1.
Understanding Rational Numbers
6.2.
Equivalent Rational Numbers
6.3.
Comparison of Rational Numbers
6.4.
Representation of Rational Numbers on the Real Line
6.5.
Addition and Subtraction of Rational Numbers
6.5.1.
Addition of Rational Numbers
6.5.2.
Additive Inverse of a Rational Number
6.5.3.
Subtraction of Rational Numbers
6.6.
Multiplication and Division of Rational Numbers
6.6.1.
Multiplication Of Rational Numbers
6.6.2.
Reciprocal of Rational Number
6.6.3.
Division Of Rational Numbers
6.7.
Rational Numbers Lying Between Two Rational Numbers
6.8.
Simplifying Rational Numbers
6.9.
Word Problems on Rational Numbers
7.
Decimals
7.1.
Revisiting Basics
7.2.
Like, Unlike And Equivalent Decimals
7.3.
Ordering And Comparing Decimals
7.4.
Relate Decimals and Fractions
7.4.1.
Convert Decimals to Fractions
7.4.2.
Convert Fractions to Decimals
7.4.3.
Conversion of Metric Units Using Decimals
7.5.
Addition and Subtraction of Decimals
7.5.1.
Addition of Decimals
7.5.2.
Subtraction of Decimals
7.5.3.
Mixed Operations on Decimals: Addition and Subtraction
7.5.4.
Word Problems on Addition and Subtraction of Decimals
7.6.
Multiplication and Division of Decimals
7.6.1.
Multiplication of Decimals
7.6.2.
Division of Decimals
7.6.3.
Word Problems on Multiplication of Decimals
7.6.4.
Word Problems on Division of a Decimal
7.6.5.
Mixed Operations on Decimals
8.
Estimation
9.
Number Pattern
10.
Ratio and Proportion
10.1.
Ratio
10.1.1.
Terms of a Ratio
10.1.2.
Equivalent Ratio
10.1.3.
Ratio in the Simplest Form
10.1.4.
Ratio of Two Quantities by Converting Them in Same Units
10.1.5.
Comparison of Ratios
10.1.6.
Miscellaneous questions on Ratio
10.2.
Proportion
10.2.1.
Terms of a Proportion
10.2.2.
Condition for the given Numbers/Ratios to be in Proportion
10.2.3.
Find the unknown variable when four numbers are in Proportion
10.2.4.
Continued proportion
10.3.
Speed
11.
Unitary Method
11.1.
Problems on Direct Variation
11.2.
Problems on Inverse Variation
12.
Percentage
12.1.
Conversions
12.1.1.
Convert a Fraction into Percentage
12.1.2.
Convert a Percentage into Fraction
12.1.3.
Convert Percentage into a Ratio
12.1.4.
Convert a Ratio into Percentage
12.1.5.
Convert Percentage into Decimal form
12.1.6.
Convert Decimal into Percentage
12.2.
Percentage of a Quantity
12.3.
Solving Expressions involving Percentages
12.4.
Word Problems on Percentage
13.
Profit and Loss
13.1.
Terms Related to Profit and Loss
13.2.
Problems on Finding the Gain/Loss and Gain%/Loss%
13.3.
Problems on Finding the SP of the Article
13.4.
Problems on Finding the CP of the Article
13.5.
Problems on Finding the Number of Articles
14.
Simple Interest
14.1.
Problems on Calculating the Simple Interest
14.2.
Problems on Calculating the Rate Percent
14.3.
Problems on Calculating Time Period
14.4.
Problems on Calculating the Principal
15.
Exponents
15.1.
Introduction to Exponents
15.2.
Exponent of a Rational Number
15.3.
Express Rational Numbers in Exponential Form
15.4.
Solving Expressions Involving Exponents
15.5.
Laws of Exponents
15.6.
Finding the Unknown from the Given Exponential Equation
15.7.
Standard Form of Large Numbers
15.8.
Standard Form of Small Numbers
15.9.
Expanded Form of Large Numbers
16.
Algebraic Expressions
16.1.
Variables and Constants
16.2.
Types of Algebraic Expressions
16.3.
Finding the Value of an Algebraic Expression
16.4.
Operations on Algebraic Expressions
16.4.1.
Addition of Algebraic Expressions
16.4.2.
Subtraction of Algebraic Expressions
16.4.3.
Addition and Subtraction of Algebraic Expressions
16.4.4.
Multiplication of Algebraic Expressions
16.4.4.1.
Multiplication of Monomials
16.4.4.2.
Multiplication of a Monomial and a Binomial
16.4.4.3.
Multiplication of two Binomials
16.5.
Simplifying Algebraic Expression by Eliminating the Grouping Symbols
17.
Linear Equations in One Variable
17.1.
Solving Linear Equations by the Method of Transposition
17.2.
Word Problems Based on Linear Equations
18.
Mensuration
18.1.
Standard Units of Area
18.2.
Area and Perimeter of a Square
18.3.
Area and Perimeter of a Rectangle
18.4.
Area between Two Rectangles
18.5.
Area and Perimeter of Triangles
18.6.
Area and Perimeter of Parallelogram and Rhombus
18.7.
Circumference and Area of a Circle
18.8.
Area Enclosed Between Two Different Shapes
19.
Volume and Surface Area
19.1.
Three-dimensional Solids
19.2.
Volume and Surface Area of Cubes
19.3.
Volume and Surface Area of Cuboids
19.4.
Volume and Surface Area of Cylinders
20.
Geometry
20.1.
Lines and Angles
20.1.1.
Types of Angles
20.1.1.1.
Complementary and Supplementary Angles
20.1.1.2.
Linear Pair of Angles
20.1.1.3.
Vertically Opposite Angles
20.1.1.4.
Angles Around a Point
20.1.2.
Angles Formed when a Transversal Cuts Two Parallel Lines
20.2.
Triangles
20.2.1.
Classification of Triangles by the Length of the Sides
20.2.2.
Classification of Triangles by the Angles
20.2.3.
Properties of a Triangle
20.2.3.1.
Angle Sum Property of a Triangle
20.2.3.2.
Exterior Angle Property of a Triangle
20.2.3.3.
Triangle Inequality
20.2.3.4.
Pythagoras' Theorem
20.3.
Polygon
20.3.1.
Understanding Polygons
20.3.2.
Diagonals in a Polygon with
n
Sides
20.4.
Quadrilaterals
20.5.
Congruence
20.5.1.
Understanding the Meaning
20.5.2.
Congruence of Triangles
21.
Practical Geometry
21.1.
Construction of a Line Parallel to a Given Line
21.2.
Construction of a Triangle
21.3.
Construction of a Quadrilateral
22.
Reflection and Rotational Symmetry
22.1.
Linear Symmetry
22.1.1.
Linear Symmetry Around Us
22.1.2.
Linear Symmetry in Geometric Figures
22.1.3.
Linear Symmetry in Alphabets
22.2.
Rotational Symmetry
22.2.1.
Rotational Symmetry in Figures
22.2.2.
Rotational Symmetry in Geometric Figures
22.2.3.
Rotational Symmetry in Alphabets
23.
Three-Dimensional Shapes
23.1.
Identifying 3-D Shapes
23.2.
Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Cone, Cylinder, and Sphere)
23.3.
Net of a 3-D Shape
24.
Probability
25.
Data Handling
25.1.
Tabular Representation of Data
25.2.
Mean, Median, and Mode
25.2.1.
Mean
25.2.1.1.
Mean of Ungrouped Data
25.2.1.2.
Mean of Tabulated Data
25.2.2.
Median
25.2.2.1.
Median of Ungrouped Data
25.2.2.2.
Median of Discrete Series
25.2.3.
Mode
25.2.3.1.
Mode of Ungrouped Data
25.2.3.2.
Empirical Formula for Calculating Mode
25.3.
Bar Graphs
25.3.1.
Drawing Bar Graphs
25.3.2.
Interpreting Bar Graphs
25.4.
Pie Charts
25.4.1.
Creating Pie Charts
25.4.2.
Interpreting Pie Charts
25.5.
Line Graphs
25.5.1.
Create Line Graphs
25.5.2.
Interpret Line Graphs
Grade 7 Pakistan School Math
Practical Geometry
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