Decompose a Number into Parts and Factors
One number can be rebuilt many ways — as sums of two addends or as different factor pairs giving the same product. Learners first see that the same quantity has many additive and multiplicative names, then use factor pieces to test divisibility. Flexible decomposition is the engine behind mental arithmetic and later divisibility work.
grade 2–4 Base-ten numbersOperations Make a Systematic ListOrganize Information in More Ways
Progression (4)
g4 1. Different factor pairs, same product Operations
g3 2. Count groups several equivalent ways Operations
g3 3. One number, many addition expressions Base-ten numbersOperations
g4 4. A number divides by its factor pieces OperationsBase-ten numbers
Bridges to competition (7)
Reasoning problems that extend this idea toward competition:
Distinct masses weighable with given weights Counting
Combine containers to hit a target capacity Number arrangement
Count coin combinations for an amount Counting
Build values from place-valued items Counting
Compute one expression several ways Invariant
Fill circles so paired products match Number arrangement
How often a number appears in the table Counting