A pattern goes: triangle, circle, circle, triangle, circle, circle, triangle, circle, circle. What are the next three shapes?
ATriangle, triangle, triangle
BCircle, circle, circle
CTriangle, circle, circle
DCircle, triangle, circle
The repeating unit is triangle-circle-circle (an ABC pattern). After the third complete cycle ends with circle-circle, the pattern starts over: triangle, circle, circle. Identifying the core unit (three elements long) is the key — then extending is just repeating that unit.
Question 2 Multiple Choice
The number pattern 5, 10, 15, 20, 25 continues with the rule 'add 5.' What is the 8th number in this pattern?
A35
B40
C45
D50
The pattern is 5, 10, 15, 20, 25, 30, 35, 40. The 8th number is 40. You can find it by continuing the 'add 5' rule: 25 + 5 = 30 (6th), 30 + 5 = 35 (7th), 35 + 5 = 40 (8th). Knowing the rule lets you extend to any position without listing every term.
Question 3 True / False
Extending a pattern backward (figuring out what came before the first shown element) requires the same rule as extending it forward.
TTrue
FFalse
Answer: True
The rule works in both directions. If a pattern adds 3 each step (4, 7, 10, 13...), then going backward means subtracting 3: the term before 4 would be 1. If a pattern repeats circle-square, then going backward from circle-square-circle... the previous element would be square. The rule defines the pattern in both directions.
Question 4 Short Answer
If you can correctly predict the next element in a pattern, does that prove you understand the rule? Explain why or why not.
Think about your answer, then reveal below.
Model answer: Not necessarily. Getting the next element right might be a lucky guess or based on a shallow observation. Understanding the rule means you can extend the pattern many steps forward, extend it backward, explain why each element is what it is, and recognize the same rule in a different context. For example, knowing the next color in red-blue-red-blue is red shows some recognition, but stating 'the pair red-blue repeats' and being able to say what the 20th element would be shows genuine understanding.
This is why teachers ask students to explain their reasoning, not just give the next answer. The explanation reveals whether the student has grasped the underlying rule or is just pattern-matching the surface. True understanding is testable by asking for distant terms (what is the 50th element?) or by presenting the same pattern in different materials.