1-on-1 Online Maths Classes for Class 7

Chapter Name	Topics & Subtopics	Learning Objectives
Term 1
Large Numbers Around Us	Introduction to 1 Lakh via Rice Story Writing/Reading Numbers in Indian System (Up to Lakhs) Land of Tens Activity (+10, +100, +1000 Buttons) Expressing Numbers in Multiple Ways (Creative Chitti) Introducing Crore and Arab Indian vs. American Naming Systems Commas, Grouping, Conversions Reading/writing Numbers in Both Systems Comparison Exercises (>, <, =) Exact vs. Approximate Values Rounding Up/down in Real Life Finding Nearest Thousand/lakh/crore Estimating Sums/Differences (Roxie & Estu Problems) Population Table Analysis (Approx. Changes) Quick Multiplication by 10, 100, 1000, Etc. Using Factors (×5, ×25, ×125) Observing Product Patterns (111×111, Etc.) Predicting Digits in Products (2-digit × 2-digit, Etc.) Fascinating Facts (Earth-Sun Distance, Amazon River, Etc.) Challenge Qs (Largest/smallest Numbers, Digit Puzzles)	Build clear conceptual understanding of Large Numbers Around Us and apply the listed Grade 7 concepts.
Arithmetic Expressions	What Are Arithmetic Expressions? Finding the Value of Expressions Writing Expressions for Real-life Situations Comparing Expressions Using >, <, = Need for Brackets in Expressions Converting Subtraction to Addition of Inverse Identifying Terms in Expressions Evaluating Expressions With Multiple Terms Commutative and Associative Properties of Addition Swapping and Grouping Terms Removing Brackets With + and – Signs Simplifying Expressions Step-by-step Distributive Property: A × (B + C) Using Distributive Property for Quick Multiplication Real-World Word Problems With Expressions Creative Expression-Building Challenges	Build clear conceptual understanding of Arithmetic Expressions and apply the listed Grade 7 concepts.
A Peek Beyond the Point	Need for Smaller Units of Measurement Understanding Tenths as Fractions of a Unit Reading and Writing Lengths in Tenths Adding and Subtracting Tenths Extending to Hundredths as Smaller Parts Addition and Subtraction Involving Hundredths Decimal Place Value System (Tenths, Hundredths, Thousandths) Writing and Reading Numbers in Decimal Notation Length Conversions: mm, mm, m Weight Conversions: g, Kg Money Conversions: Rupee and Paise Relating Decimals to Real-world Quantities Representing Decimals on a Number Line Comparing Decimals Using Place Value Identifying Closest Decimals to a Given Number Understanding Zeros in Decimals Adding and Subtracting Decimals Decimal Sequences and Patterns Estimating Sums and Differences of Decimals Decimal Errors in Real Life and Historical Context	Build clear conceptual understanding of A Peek Beyond the Point and apply the listed Grade 7 concepts.
Expressions Using Letter-numbers	Introduction to Variables and Algebraic Expressions Writing Expressions From Word Problems and Real-life Situations Understanding Formulas and Their Uses Revisiting Arithmetic Expressions With Brackets and Terms Substitution: Finding the Value of an Expression Omitting Multiplication Signs Identifying Like and Unlike Terms Simplifying Expressions by Combining Like Terms Using Distributive Property to Simplify Expressions With Brackets Number Machines and Finding Rules Patterns in Sequences, Calendars, and Matchstick Designs Using Algebra to Describe and Verify Patterns	Build clear conceptual understanding of Expressions Using Letter-numbers and apply the listed Grade 7 concepts.
Parallel and Intersecting Lines	Intersecting Lines and Angles Formed Linear Pairs (Sum = 180°) Vertically Opposite Angles (Equal) Perpendicular Lines (Right Angles) Parallel Lines: Definition and Examples Identifying Parallel and Perpendicular Lines in Real Life Angles Formed by a Transversal Corresponding Angles and Their Property Alternate Angles (Equal When Lines Are Parallel) Interior Angles on the Same Side (Sum = 180°) Using Angle Properties to Check if Lines Are Parallel Applying Angle Relationships to Find Unknown Angles Problem-solving With Parallel, Intersecting, and Perpendicular Lines	Build clear conceptual understanding of Parallel and Intersecting Lines and apply the listed Grade 7 concepts.
Number Play	Representing Arrangements Using Numbers Patterns in Sequences From Real-world Contexts (E.g., Height Order) Reasoning About Number Rules Without Exact Values Parity: Odd and Even Numbers Properties of Sums and Differences of Odd/even Numbers Parity of Products (Grids) and Algebraic Expressions Introduction to Magic Squares Row, Column, and Diagonal Sums Constructing a 3×3 Magic Square Using Numbers 1–9 Virahānka-fibonacci Sequence: Introduction and History Pattern: Each Term is the Sum of the Two Previous Terms Occurrences in Poetry, Art, and Nature (E.g., Flower Petals) Introduction to Cryptarithms (Alphametics) Solving Puzzles Where Letters Represent Digits Logical Reasoning and Deduction in Number Puzzles	Build clear conceptual understanding of Number Play and apply the listed Grade 7 concepts.
A Tale of Three Intersecting Lines	What is a Triangle? (Vertices, Sides, Angles) Naming and Notation of Triangles Constructing Equilateral Triangles Using a Compass and Ruler Constructing Triangles Given Three Side Lengths Understanding When Triangles Can/cannot Be Constructed Identifying Isosceles and Scalene Triangles Exploring Impossible Triangles (E.g., 3, 4, 8) Discovering the Triangle Inequality: Each Side < Sum of Other Two Testing and Applying the Inequality Rule Visual Reasoning With Intersecting Circles Constructing Triangles Given Two Sides and the Included Angle Constructing Triangles Given Two Angles and the Included Side Conditions for Triangle Existence (Angle Sum < 180°) Discovering the Angle Sum Property (Sum = 180°) Finding the Third Angle Using Parallel Lines Introducing Exterior Angles and Their Properties Simple Calculations With Exterior Angles What is an Altitude? Constructing Altitudes With Set Squares Classifying Triangles by Sides: Equilateral, Isosceles, Scalene Classifying Triangles by Angles: Acute, Right, Obtuse	Build clear conceptual understanding of A Tale of Three Intersecting Lines and apply the listed Grade 7 concepts.
Working With Fractions	Understanding Multiplication as Repeated Addition With Fractions Multiplying a Whole Number by a Fraction and a Fraction by a Whole Number Real-world Contexts: Distance, Sharing, Cost Converting Products to Mixed Fractions Visualizing Fraction Multiplication Using Unit Squares/area Models Step-by-step Method: Divide Then Multiply Simplifying Before Multiplying (Cancelling Common Factors) Observing When the Product is Greater/less Than the Numbers Multiplied Comparing Products for Fractions <1, >1, and Mixed Cases Understanding That Order Doesn’t Matter: Commutative Property Area of Rectangle With Fractional Sides Rewriting Division as Multiplication (“How Many Times Does It Fit?”) Introducing Reciprocal of a Fraction Comparing Quotient to Dividend Based on Divisor’s Size Multi-step Word Problems (E.g., Sharing, Recipes, Rates) Fraction of a Fraction Problems (E.g., Shaded Areas) Historical Problems From Indian Mathematicians Mixed Practice: Choosing Correct Operations Recap of Multiplication and Division Rules Historical Context: Brahmagupta, Bhaskara Ii, and Indian Contributions Fraction Puzzles and Pattern Exploration (E.g., Product Cascades) Connecting Fractions to Chess Puzzles (Non-attacking Queens)	Build clear conceptual understanding of Working With Fractions and apply the listed Grade 7 concepts.
Term 2
Geometric Twins	Understanding Congruence: Figures That Can Be Superimposed Exactly Identifying Congruent vs. Non-congruent Figures in Real Life and Diagrams Determining What Measurements Are Needed to Recreate a Figure (E.g., Arms and Included Angle) Introduction to Congruence Notation and Corresponding Parts SSS Condition: Triangles With Three Equal Sides Are Congruent Constructing Triangles to Verify SSS SAS Condition: Two Sides and the Included Angle Ensure Congruence Differentiating Between Included and Non-included Angles ASA Condition: Two Angles and the Included Side Ensure Congruence AAS Condition: Two Angles and a Non-included Side Also Ensure Congruence Using Angle Sum Property to Find Missing Angles and Apply AAS Identifying Corresponding Vertices, Sides, and Angles in Congruent Triangles RHS Condition: Right Angle, Hypotenuse, and One Side Ensure Congruence in Right Triangles Applying Congruence to Prove Properties: Angles Opposite Equal Sides Are Equal in Isosceles Triangles Discovering That All Angles in an Equilateral Triangle Are 60° Using Congruence Real-world Examples of Congruent Triangles in Architecture and Designs	Build clear conceptual understanding of Geometric Twins and apply the listed Grade 7 concepts.
Operations With Integers	Representing Integers on a Number Line Ordering and Comparing Integers Understanding Absolute Value Identifying Integers in Real-life Contexts (Temperature, Debt, Elevation) Adding Integers Using Number Line and Rules Subtracting Integers as Adding the Opposite Solving Problems Involving Addition and Subtraction of Integers Real-world Applications (Profit/loss, Temperature Change) Multiplying Integers: Sign Rules and Product of Positives/negatives Dividing Integers: Sign Rules and Quotient of Positives/negatives Relating Multiplication and Division as Inverse Operations Practice With Mixed Operations Commutative, Associative, and Distributive Properties for Integers Additive Identity and Multiplicative Identity Additive Inverse and Multiplicative Inverse Concepts Simplifying Expressions Using Properties Applying Integer Operations to Solve Word Problems Mixed Practice: All Four Operations Error Analysis and Common Misconceptions	Build clear conceptual understanding of Operations With Integers and apply the listed Grade 7 concepts.
Finding Common Ground	Understanding Common Factors Through a Real-world Tiling Problem Finding Common Factors by Listing All Factors Defining the Highest Common Factor (Hcf) Introducing Prime Numbers and the Prime Factorization Method Finding All Factors of a Number Using Its Prime Factorization Using Prime Factorizations to Determine the Hcf of Two Numbers Understanding the Concept of Common Prime Factor Subparts Identifying the Minimum Occurrence of Each Prime for the HCF Exploring Common Multiples Through Real-world Contexts Defining the Lowest Common Multiple (LCM) Finding the LCM by Listing Multiples Introducing the Method for Finding Lcm Using Prime Factorization Making General Statements About Hcf and Lcm for Special Number Pairs Observing the Effect of Doubling Numbers on Their Hcf Learning the Efficient Division Method to Find Hcf and Lcm Together Discovering the Relationship: HCF × LCM = Product of the Two Numbers Applying HCF and LCM to Solve Varied Word Problems Solving Advanced Problems Involving Remainders and Divisibility	Build clear conceptual understanding of Finding Common Ground and apply the listed Grade 7 concepts.
Another Peek Beyond the Point	Recap of Decimals and Place Value Converting Fractions to Decimals Dividing by 10, 100, 1000 Using Decimal Shift Multiplying Decimals Using Fractions Observing Decimal Places in Multiplication Framing a Rule for Decimal Multiplication Understanding When a Product is Greater or Less Than the Numbers Dividing Decimals by Whole Numbers Using Fractions Long Division Method (Place Value Procedure) Regrouping Ones Into Tenths, Hundredths, Etc. Placing the Decimal Point in the Quotient Division With Decimal Divisors Converting Divisor to Whole Number by Shifting Decimal Exploring Non-terminating Decimals (E.g., 10 ÷ 3) Cyclic Numbers and Repeating Decimals Leap Year Problem: Decimals in Calendar Calculations Real-life Applications: Shopping, Measurement, Speed Problem-solving Using Decimal Operations	Build clear conceptual understanding of Another Peek Beyond the Point and apply the listed Grade 7 concepts.
Connecting the Dots	Distinguishing Statistical Questions From Statements Introduction to Representative Values and the Arithmetic Mean Calculating the Mean as “fair‑share” Real‑world Examples of Averages Understanding the Median of a Dataset Identifying Outliers and Their Effect on Mean vs. Median Comparing Mean and Median in Different Scenarios Dot Plots as a Visual Tool for Data Distribution Creating and Interpreting Dot Plots Analysing Variability, Spread, and Clusters in Data Using Dot Plots to Compare Groups (E.g., Boys vs. Girls Heights) Relating Mean and Median to Dot Plot Patterns Introduction to Bar Graphs and Clustered (Double‑bar) Graphs Steps for Reading and Interpreting Graphs Comparing Data Across Categories and Time Using Graphs Real‑world Examples: Rocket Launches, Daylight Hours, Cricket Graphs Deeper Data Comparison Across Multiple Datasets (E.g., Heights Over Decades) Drawing Inferences From Tables and Graphs Planning and Presenting Small Data‑collection Projects	Build clear conceptual understanding of Connecting the Dots and apply the listed Grade 7 concepts.
Constructions and Tilings	Constructing Symmetrical “eyes” Using Arcs Definition and Construction of the Perpendicular Bisector Constructing a 90° Angle at a Point on a Line Historical Note: Construction Methods in Šulba‑sūtras Bisecting a Given Angle Using Ruler and Compass Constructing 45°, 60°, and 120° Angles Copying a Given Angle to a New Location Constructing Parallel Lines by Copying Corresponding Angles Constructing Arch Designs (Trefoil and Pointed Arches) Constructing a Regular Hexagon Using Equilateral Triangles Drawing 6‑pointed Stars and Related Designs Creative Construction of Complex Geometric Patterns Introduction to Tiling With Tangram Pieces Tiling Rectangular Grids With 2×1 Tiles Using Colour Arguments to Decide Tilability Tiling the Plane With Regular Polygons and Artistic Tessellations	Build clear conceptual understanding of Constructions and Tilings and apply the listed Grade 7 concepts.
Finding the Unknown	Introduction to Equations Through Weighing Scale Problems Matchstick Patterns and Framing Equations Definition of Equation, Lhs, Rhs, and Solving Solving Equations Using Inverse Operations Adding/subtracting the Same Number to Both Sides Multiplying/dividing Both Sides by the Same Number Systematic Solution of Linear Equations Solving Equations With Variables on Both Sides Simplifying Equations Involving Brackets Verifying Solutions by Substitution Forming Equations From Word Problems (Party Planning, Savings, Etc.) Problems With Two Unknowns Reduced to One Unknown Generating Equations With Given Solutions History of Algebra: Brahmagupta, Al‑khwarizmi, and Bijaganita Identifying and Correcting Common Errors in Solving Equations	Build clear conceptual understanding of Finding the Unknown and apply the listed Grade 7 concepts.