A pattern goes: circle, square, triangle, circle, square, triangle, circle. What comes next?
ACircle — because the last item was a circle
BSquare — because the core unit is circle-square-triangle and square is next in the cycle
CTriangle — because triangles always come after circles
DCircle-square-triangle — because the whole unit repeats at once
The core unit is circle-square-triangle (an ABC pattern). After two full repetitions, 'circle' has started the third repetition — so 'square' comes next. The most common mistake is to repeat the last element (circle again), but that ignores the structure. To extend any pattern correctly, you must find the core unit and determine where you are within it.
Question 2 Multiple Choice
Which of these sequences has the same pattern structure as red-blue-red-blue?
AClap-stomp-clap-stomp — two actions alternating, the same AB structure
BClap-stomp-snap-clap-stomp-snap — three different things in the core unit
CClap-clap-stomp-clap-clap-stomp — clap appears twice in a row
DStomp-stomp-stomp — only one kind of thing repeating
An AB pattern has exactly two distinct elements in the core unit that alternate: A, B, A, B, ... Clap-stomp-clap-stomp has the core unit 'clap-stomp' — two distinct actions taking turns — which is exactly the AB structure of red-blue-red-blue. The materials (colors vs. movements) don't determine the structure; the number and order of distinct elements do. Recognizing the same structure in different materials is the key algebraic insight.
Question 3 True / False
A clap-snap-clap-snap pattern and a red-blue-red-blue pattern have the same mathematical structure.
TTrue
FFalse
Answer: True
Both are AB patterns: a two-element core unit that repeats. The material (sound vs. color) is completely irrelevant to the pattern structure. This is what makes patterns mathematical — you can strip away the specific objects and ask only about the structure: how many distinct elements, in what order. Recognizing the same structure across different materials is the beginning of algebraic thinking.
Question 4 True / False
To find out what comes next in a pattern, you just need to look at the last element and repeat it.
TTrue
FFalse
Answer: False
This is the most common error in pattern extension. For example, in red-blue-red-blue-red, the last element is red — but the next element is blue, because the core unit is red-blue and you are in the middle of a new repetition. You must identify the complete core unit and determine your position within it, then apply what comes next in that unit. Looking only at the last element gives the right answer only by accident.
Question 5 Short Answer
Why do you need to find the core unit of a pattern before you can extend it correctly?
Think about your answer, then reveal below.
Model answer: Because the core unit is what repeats — it defines the full cycle of the pattern. If you only look at the last element, you might guess it repeats, but that is only correct if that element happens to be at the end of the core unit. Only by knowing the full core unit can you determine where you are in the cycle and what correctly comes next.
A pattern is defined by its core unit, not by any individual element. The core unit is the fundamental repeating group. Once identified, you can determine your position within any repetition and predict any future element. Without the core unit, you have no principled basis for prediction — you might get lucky by repeating the last item, but for AB patterns ending mid-cycle, the last-item strategy gives the wrong answer every time.