# Multiplicative Reasoning

Multiplication is an operation that opens the door to a wide range of mathematical ideas, like place value, division, fractions, decimals, ratios…..

Arrays or Area Models offer a highly visual, highly efficient and perceptually attractive model to support not just remembering the facts BUT MORE important developing mastery of the number properties that frame algebra.

The Commutative Property, the Associative Property, the Distributive Property

Inverse Operations  Identity of One and Zero.

the facts by folding, Cuisenaire Rods and grid paper

The area model can extend to decimals. In order to keep the imagery a focus, students need to develop fluency with moving between decimals and fractions as they describe the relationships. So 0.4 is expressed both orally and in writing as four tenths. From work with developing imagery for decimals students are aware that tenths times tenths create hundredths. This understanding then allows them to mentally compute. So 3 * 0.4 is another way to express 3 times four tenths… I see 3 sets of 4 tenths or a rectangle that is 3 one way but only 4 tenths the other. The result is 12 tenths, expressed as 0.12.