Uvero — STEM Learning

Arrays and Multiplication

An array organises equal groups into rows and columns and shows why factor order may be swapped. An $r$ -by- $c$ array contains $r\times c$ objects. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Multiply rows by counters per row.
$7\times8=56$ .

How many counters are in 7 rows of 8?

Which statement best captures the central mathematical idea in Arrays and Multiplication?

An $r$ -by- $c$ array contains $r\times c$ objects.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Arrays and Multiplication, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for arrays and multiplication.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Arrays and Multiplication?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

An $r$ -by- $c$ array contains $r\times c$ objects.

Represent the given information clearly and identify the operation or relationship required for arrays and multiplication.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.