GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
CONNECT — Properties and expressions
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own idea.
Will 4 × (2 + (−3)) agree with 4 × 2 + 4 × (−3)?
Write or sketch a prediction before you read on. Use the model below to test it.
Understand
Multiplication of integers is commutative and associative, and distributes over addition. These properties help reorganise expressions without changing their value.
Key Ideas
Multiplication properties do not automatically transfer to division. Do not distribute to only one term.
Visualise
A signed distributive array
This array models a positive number of groups. For a negative first factor, add the inverse of each group that many times.
Method
Respect brackets first. Use a named property to rearrange or expand. Evaluate both forms to check the connection.
Worked Example
Given
4 groups, each containing 2 positive and 3 negative tokens.
To Find
The value of 4 × (2 + (−3)), checked by grouping and distribution.
Reasoning
Distribute multiplication over the addition inside each group.
Solution
- Each group totals −1; 4 × (−1) = −4.
- Separately there are 8 positives and 12 negatives.
- 8 + (−12) = −4.
Result
4 × (2 + (−3)) = 4 × 2 + 4 × (−3) = −4.
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
Evaluate 5 × (−3) × 4 using two groupings.
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 39