Uvero — STEM Learning

Linear Number Patterns

A constant first difference gives $T_n=dn+c$ . The coefficient of $n$ is the first difference, and one term determines $c$ . At Grade 10, fluent symbolic work must stay connected to graphs, tables, diagrams and real quantities.

Worked reasoning

The common difference is 5, so $T_n=5n+c$ .
$T_1=4$ gives $5+c=4$ , hence $c=-1$ .

Find the rule for $4,9,14,19,\ldots$ .

Which statement best captures the central mathematical idea in Linear Number Patterns?

The coefficient of $n$ is the first difference, and one term determines $c$ .

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

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 Linear Number Patterns, which move is most reliable?

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for linear number patterns.

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 Linear Number Patterns?

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

The coefficient of $n$ is the first difference, and one term determines $c$ .

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for linear number patterns.

Use substitution, a second representation or a magnitude estimate to verify the result.