How can multiplication and division provide new perspectives of number?

Students analyze and apply strategies for multiplication and division within 100.

Multiplication and division are inverse mathematical operations.

Multiplication is repeated addition.

Multiplication can be interpreted in various ways according to context, such as

• equal groups

• an array

• an area

Division can be interpreted in various ways according to context, such as

• equal sharing

• equal grouping

• repeated subtraction

The order in which two quantities are multiplied does not affect the product (commutative property).

The order in which two numbers are divided affects the quotient.

Multiplication or division by 1 results in the same number (identity property).

Numbers can be multiplied or divided in parts (distributive property).

Multiplication strategies include

• repeated addition

• multiplying in parts

• compensation

Division strategies include

• repeated subtraction

• partitioning the dividend

Products can be expressed symbolically using the multiplication sign, 

×

×, factors, and the equal sign.

Quotients can be expressed symbolically using the division sign, 

÷

÷, dividend, divisor, and the equal sign.

A missing quantity in a product or quotient can be represented in different ways, including

• a×b=□

• a×□=c

• □×b=c

• e÷f=□

• e÷□=g

• □÷f=g

A remainder is the quantity left over after division.

A multiplication table shows both multiplication and division facts.

Fact families are groups of related multiplication and division number facts.

Quantities can be composed and decomposed through multiplication and division.

Sharing and grouping situations can be interpreted as multiplication or division.

Multiplication and division strategies can be supported by addition and subtraction.

Multiplication number facts have related division facts.