GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
MODEL — Multiplication using tokens
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own idea.
What remains if you remove two negative tokens four times from an empty bag?
Write or sketch a prediction before you read on. Use the model below to test it.
Understand
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.
Key Ideas
Removing negative tokens is different from adding negative tokens. Zero pairs make removal from an empty bag possible.
Visualise
Integer token bag
Start with an empty bag. Predict which tokens will remain.
Method
Read both factors separately. For removal, add enough zero pairs first. Remove the requested sign, then count the remaining tokens.
Worked Example
Given
An empty bag; remove two negative tokens four times.
To Find
The value of (−4) × (−2).
Reasoning
Adding zero pairs preserves the starting value of zero.
Solution
- Add 8 zero pairs: 8 positives and 8 negatives.
- Remove 2 negatives in each of 4 groups.
- All 8 positives remain.
Result
(−4) × (−2) = 8.
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
Model (−3) × 2 with tokens.
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 29