GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
MASTER — Applications, pattern machines and reasoning
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own idea.
A correct answer earns 5 marks and an incorrect one loses 2. How do both contributions enter the total?
Write or sketch a prediction before you read on. Use the model below to test it.
Understand
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.
Key Ideas
Distinguish signed displacement from distance travelled. Evidence from a few patterns is not a universal proof.
Visualise
Discover the machine
Source Machine 1: (5, 8, 3) → 10; (−4, −1, −6) → 1; (−3, 10, 2) → 5. Find a rule that fits.
Output: -13
Method
Translate the situation into signed quantities. Write the expression before calculating. Check the result against the original conditions.
Worked Example
Given
Mala answers 30 questions correctly and 20 incorrectly; +5 and −2 marks respectively.
To Find
Mala’s total marks from 30 correct and 20 incorrect answers.
Reasoning
Add the positive and negative contributions.
Solution
- 30 × 5 = 150.
- 20 × (−2) = −40.
- 150 + (−40) = 110.
Result
Mala earns 110 marks.
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
An elevator starts 15 m above ground and descends 3 m per minute for 45 minutes. Find its position.
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 35