Properties of Operations

Commutative, Associative, and Distributive

Uganda Primary 7 Mathematics
Topic 3 — Term I

The Kampala Storekeeper's Addition Puzzle

A school storekeeper in Kampala adds up:

Which pairs add to a nice number?

Commutative Property for Addition of Numbers

Changing the order does NOT change the sum

Examples:

The order of addends can be rearranged freely.

Commutative Property — Multiplication and Limits

• ✓

Does NOT hold for or :

• ✗
• ✗

Holds for and only.

Associative Property for Addition of Numbers

Changing the grouping does NOT change the sum

Choose the group that makes a nice number:

Associative Property — Multiplication and Limits

• ✓

Fails for :

Chunk 1 Check — True or False?

Chunk 1 Summary of Both Properties

Practical use: rearrange or regroup to make a "nice" number.

Distributive Property — Area Model

Rectangle: width , length

Two ways to calculate the area:

• ✓

Distributive Property — Formal Rule

Expanding direction:

Also works with :

Distributive Property — Factoring Direction

Factoring (reverse) direction:

Common factor is pulled out of both terms.

Distributive Property — Worked Examples

Expand:

Factor:

Check: ✓

Chunk 2 Practice — Expand and Factor

Expand or factor as directed:

1. (expand)
2. (expand)
3. (factor)
4. (factor)

Applying Properties — Three Benchmarks

Three problems to solve efficiently. Name the property used.

Try each before the next slide.

Benchmark 1:

Associative + strategic grouping:

is the "nice pair" — group it first.

Benchmark 2:

Distributive property — near-100 trick:

General rule:

Benchmark 3:

Commutative then associative:

Watch Out! — Misconception 1

Commutativity with subtraction

A learner writes: ✗

What went wrong?

• (a negative — not a whole number)
• ✓ (different value)

Subtraction is NOT commutative.

Watch Out! — Misconception 2

Double-counting in distributive factoring

A learner writes: ✗

Correct:

The factor moves outside, not inside.

Chunk 3 Practice — Name the Property

For each calculation, name the property and find the answer:

Lesson Summary — The Property Card

Payoff: rearrange, regroup, expand, or factor for faster mental arithmetic.