Uvero — STEM Learning

Pattern Tables and Rules

A pattern table connects term number to term value and helps distinguish recursive and direct rules. Test a proposed rule on several rows, not just one. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Substitute $n=12$ .
$4(12)+1=49$ .

The rule is $T_n=4n+1$ . Find $T_{12}$ .

Which statement best captures the central mathematical idea in Pattern Tables and Rules?

Test a proposed rule on several rows, not just one.

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 Pattern Tables and Rules, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for pattern tables and rules.

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 Pattern Tables and Rules?

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

Test a proposed rule on several rows, not just one.

Represent the given information clearly and identify the operation or relationship required for pattern tables and rules.

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