1 minute read
Topic A Multiplication as Multiplicative Comparison
In topic A, students use models and multiplicative comparison language to represent multiplicative relationships.
In prior grades, students compare quantities through additive comparison where one quantity is more than or less than another quantity and use addition or subtraction to find the unknown quantity or difference. Multiplicative comparison presents a new way to relate quantities. Students recognize that a figure in a number or shape pattern does not increase by the same amount each time. Rather, the increase is a result of multiplying by the same factor each time. Students use visual models, including tape diagrams, as tools to demonstrate the multiplicative relationship between quantities. Once they understand the multiplicative relationship, students find an unknown quantity by using multiplication or division.
Multiplicative comparison gives students another way to interpret multiplication. For example, they see 15 = 3 × 5 as 15 is 3 times as many as 5. This interpretation of multiplication is foundational throughout grade 4 as students describe place value relationships, identify multiples of whole numbers and fractions, and convert measurement units. It also prepares students for multiplication as scaling in grade 5.
Students apply multiplicative comparison to the contexts of measurements and units of money. They interpret and represent a variety of measurement comparisons and use language specific to the contexts such as times as long as, times as heavy as, and times as far as. Students also compare units of money—pennies, dimes, and dollars—by using times as much as relationships. Students recognize similarities between place value units and the relationship of increasing units of money (i.e., each increasing unit from pennies to dimes to dollars is 10 times as much as the previous unit).
In topic B, students use multiplicative comparisons to relate place value units up to 1,000,000.
