GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
Study Materials
Think first. Use AI purposefully. Verify always.
Concise AIMS notes connected to the textbook ideas. Explore each lesson for its model, example and independent practice.
GUESS — Sum and difference of integers
A sum combines the two values. A difference compares the first value with the second; order matters.
Keep a running table of guesses. Check both clues, then swap the pair to see what changes.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 24
Worked example →MOVE — Number line and carrom-coin movements
A signed movement records magnitude and direction: positive is right, negative is left. Final position is the sum of the movements.
Start from zero, mark the first endpoint, then start the second arrow there. Read the final signed position.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 25
Worked example →CANCEL — Tokens, subtraction and additive inverse
A +1 token and a −1 token form a zero pair. Adding a zero pair changes the representation, not the value. Subtracting an integer has the same effect as adding its additive inverse.
Represent the starting value. Add only the zero pairs needed. Remove the requested tokens and count what remains.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 28
Worked example →MODEL — Multiplication using tokens
In this model the first factor tells how many groups to place or remove. A positive first factor places groups; a negative first factor removes groups. The second factor describes each signed group. Start every operation from zero.
Read both factors separately. For removal, add enough zero pairs first. Remove the requested sign, then count the remaining tokens.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 29
Worked example →PATTERN — Discover sign rules and multiplication by ±1
The token model and consistent product patterns explain the sign rules. For two nonzero factors, equal signs give a positive product and different signs give a negative product. A zero factor gives zero.
Continue a product pattern through zero. Check the change at each step. Use multiplication by −1 to connect a number with its additive inverse.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 32
Worked example →REVERSE — Division as reverse multiplication
Division asks for a missing factor. Check a quotient by multiplying it by the divisor. Division by zero is undefined, and dividing two integers need not give an integer.
Rewrite the division as a missing-factor multiplication. Find the factor and check the product. Always check that the divisor is nonzero.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 38
Worked example →CONNECT — Properties and expressions
Multiplication of integers is commutative and associative, and distributes over addition. These properties help reorganise expressions without changing their value.
Respect brackets first. Use a named property to rearrange or expand. Evaluate both forms to check the connection.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 39
Worked example →MASTER — Applications, pattern machines and reasoning
Use signed quantities to model a situation. State what positive and negative mean, form an expression, then interpret the result. Testing several cases can support a conjecture but does not prove every case.
Translate the situation into signed quantities. Write the expression before calculating. Check the result against the original conditions.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 35
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