Te reo Māori terms
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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
NA4-9
New NZC (2026)
NZC26-P4-ALG-ER-P-Y9-11NZC26-P3-ALG-ER-K-Y7-08NZC26-P3-ALG-ER-P-Y7-07NZC26-P3-ALG-ER-P-Y7-08
Resources
- Dr Austin Maths - Arithmetic Sequences using the Formula Practice GridQuestions PDF · Answers
- Dr Austin Maths - Arithmetic Sequences and Series Revision Practice GridQuestions PDF · Answers
- Alpha textbook: Sequence patterns, Ex 12.03, pg 194-195
- CorbettMaths on nth termQuestions PDF · Answers
Terminology
- nth term
- term
- term number
- common difference
- first term
- rule
- sequence
- spatial pattern
Task goals
- Find the nth-term rule for a linear number pattern given its first four terms, e.g. $5,\ 8,\ 11,\ 14$.
- Use a given nth-term rule to find a specific term, e.g. term 7 of $4n+2$.
- Use a given nth-term rule to find which term number equals a stated value, e.g. which term of $3n+7$ equals $28$.
- Find the nth-term rule for a growing spatial or tile pattern, then find a specific term.
- Evaluate whether a student's stated nth-term rule for a pattern is correct, explain any error, and give the correct rule.
- Decide whether a given number appears in a linear pattern, using the nth-term rule to justify the answer.
- Derive the nth-term rule from two non-consecutive given terms, e.g. term 4 is $21$ and term 10 is $45$.
- Apply nth-term rules with a negative common difference, e.g. a decreasing pattern such as $31,\ 27,\ 23,\ 19$.
Teaching guidance
- Scope: recognising a linear pattern by a constant first difference, forming and using the nth-term rule (general term = first term + (n-1) x common difference) to find a given term or term number, and extending the pattern -- consolidating the linear-pattern strand of extrapolating linear, quadratic, and exponential patterns; identifying linear, quadratic, and exponential patterns; and determining the nth term of a pattern or spatial pattern into one Year-10-branded page.
- Task decks should cover: extending a linear sequence from its first difference; writing an nth-term rule from a sequence of numbers or a spatial/matchstick pattern; using an nth-term rule to find a given term or to find which term number equals a given value; and, at excellence tier, deciding whether a given value is a term of the sequence.
Where this fits
What leads into this objective, and where it goes next.
Before
Finding x- and y-intercepts
Using tables to explore patterns and graphs
Linear Graphs from Algebraic Rules (Table of Values)
You are here
Linear number patterns and the nth term
Do
Identifying the constant increase or decrease in a linear pattern, using variables and algebraic notation to represent the rule in an equation, and drawing on the rule to make conjectures
Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-11
Also under NA4-9: