Texas Essential Knowledge and Skills (TEKS):
4.4.D

use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties;

Florida - Benchmarks for Excellent Student Thinking:
MA.4.NSO.2.5

Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value

4th Grade Math - Properties of Multiplication Lesson

a × b = b × a

for example: 4 × 3 = 3 × 4

This property of multiplication is called the commutative property of multiplication.

The models show that 4 rows of 3 and 3 rows of 4 both equal 12.

=

4 × 3

=

3 × 4

(a × b) × c = a × (b × c)

for example: (2 × 3) × 4 = 2 × (3 × 4)

This property of multiplication is called the associative property of multiplication.

The models show that 4 groups of 2 × 3 and 2 groups of 3 × 4 both equal 24.

=

(2 × 3) × 4

=

2 × (3 × 4)

a × (b + c) = a × b + a × c

for example: 2 × (3 + 4) = 2 × 3 + 2 × 4

This property of multiplication is called the distributive property.

The models show that 2 groups of 3 + 4 equal the sum of 2 × 3 and 2 × 4.

=

2 × (3 + 4)

=

2 × 3

+

2 × 4

Similarly, 2 × 7 equals the sum of 2 × 3 and 2 × 4.