Patterns, Sequences & Algebraic Thinking
MYP Year 2 Mathematics — Patterns, Sequences & Algebraic Thinking
Every question in this topic is really the same question wearing a different costume: find the rule that connects a position number to a value, then use that rule to predict, check, or explain. Steps on a staircase, dots in a square, matchsticks in a row — strip away the picture and you're left with either 'add the same amount' (arithmetic), 'multiply by the same amount' (geometric), or something curvier (quadratic, like square numbers). Spot which one you're dealing with FIRST, and the formula work almost writes itself.
Overview: How This Topic Fits Together
What examiners are actually checking
Behind every 'staircase' or 'dot pattern' question sits one of three engines: constant addition, constant multiplication, or constant second-level change. Your job is diagnosis before calculation — subtract consecutive terms first, always, before reaching for any formula.
- Arithmetic and geometric sequences: recognising the type from a list of numbers, then generating any term with an nth-term formula.
- General rules and nth terms: reversing the formula — given two terms (not necessarily the first two), finding and , or checking whether a target value belongs to the sequence at all.
- Algebraic patterns and expressions: turning a growing picture (matchsticks, tiles, dots) into an algebraic rule in terms of .
- Number patterns and sequences: the 'named' patterns — square numbers, triangular numbers, Fibonacci — and using first/second differences to classify an unfamiliar sequence.
The shape of the chapter
Command terms in this topic — what each one actually demands
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | Give a value or fact with no working required. | AO1 | One mark only — but it must be the exact value/notation asked for (e.g. 'd = 4', not just 'the gap is 4'). |
| Calculate | Produce a numerical answer, showing the method. | AO2 | Method mark for correct substitution into the formula even if arithmetic goes wrong later; skipping straight to a final number risks losing the method mark. |
| Identify | Name or pick out the specific type, term, or feature from given information. | AO1 | Vague answers ('it's a pattern') score 0 — must name the correct type (e.g. 'arithmetic sequence'). |
| Explain | Give reasons using correct mathematical vocabulary, not just a number. | AO2/AO3 | A numerically correct answer with zero written reasoning typically earns 0 on the explain mark. |
| Compare | State at least one similarity AND one difference, both quantified. | AO3 | Listing only differences (or only similarities) drops a mark — markschemes require both sides. |
| Describe | Put the pattern rule into words using correct terminology. | AO1 | 'It goes up' loses the mark; 'increases by a constant common difference of 3' gets it. |
Key point
Overview