GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
GUESS — Sum and difference of integers
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own idea.
Sum 25, difference 11: which ordered pair fits both clues?
Write or sketch a prediction before you read on. Use the model below to test it.
Understand
A sum combines the two values. A difference compares the first value with the second; order matters.
Key Ideas
Swapping numbers preserves their sum but reverses their difference.
Visualise
Sum & difference lab
Find a pair with sum 25 and first − second = 11. Change one value, then check both clues.
Compare each result with its clue.
Method
Keep a running table of guesses. Check both clues, then swap the pair to see what changes.
Worked Example
Given
Two numbers have sum 25 and first minus second equal to 11.
To Find
The first and second integers whose sum is 25 and ordered difference is 11.
Reasoning
Test both the sum and the ordered difference.
Solution
- 18 + 7 = 25.
- 18 − 7 = 11.
- Reversing the pair gives 7 − 18 = −11.
Result
First 18, second 7.
AIMS Method
- A — Attempt independently
Predict before calculating. - I — Investigate the idea
Identify signs, order and operation. - M — Make connections
Connect movements, tokens and expressions. - S — Scrutinise your reasoning
Check the sign, value and original conditions.
Think first. Use AI purposefully. Verify always.
Focused Practice
Find the pair with sum 4 and difference 12.
Check & Feedback
Explain the key idea to someone who made the mistake described above. Use a model or a checked example.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 24