A pattern goes: star, circle, triangle, star, circle, triangle, star, ___. What comes next?
AStar, because there are more stars in the pattern
BCircle, because it comes after star in the repeating unit
CTriangle, because the pattern needs to end with a triangle
DAny shape, because patterns can change
The repeating unit is 'star, circle, triangle.' After the second star, the unit continues: circle comes next, followed by triangle, then the unit starts over. Extending a pattern means following the rule of the repeating unit — not making a new choice or guessing. The unit always restarts in order.
Question 2 Multiple Choice
A student sees: blue, blue, red, blue, blue, red, blue, blue, ___. She says 'red' comes next. What reasoning did she use?
AShe guessed, since she could not know for sure
BShe found the repeating unit (blue, blue, red) and used it to predict the next element
CShe counted the reds and blues and picked whichever appeared less
DShe assumed patterns always end on their last element
Finding the repeating unit is the core strategy. The unit is 'blue, blue, red' — a three-element chunk. After two blues, the rule says red comes next, starting the unit over again. This is not a guess: the student is applying a rule she has identified. That is what extending a pattern means.
Question 3 True / False
A pattern can primarily be extended if you have seen at least three full repeats of it.
TTrue
FFalse
Answer: False
False. You can extend a pattern once you have identified the repeating unit — which may only require seeing one or two complete copies of it. For a simple AB pattern (red-blue-red), the full unit is visible after the first two elements. The number of repeats needed depends on the length of the unit, not on an arbitrary minimum count.
Question 4 True / False
Extending a pattern is really just predicting — you might be wrong about what comes next.
TTrue
FFalse
Answer: False
False. Extending a pattern is not guessing — it is applying a rule you have identified. Once you find the repeating unit, the next element is determined by the rule, not left to chance. If the pattern is circle-square-circle-square, 'circle' is the correct next element because that is what the rule says. This rule-following is what makes pattern extension a mathematical skill rather than a guessing game.
Question 5 Short Answer
What is the most important step in extending a repeating pattern, and why?
Think about your answer, then reveal below.
Model answer: Finding the repeating unit — the smallest chunk of elements that repeats. Once you know the unit, you can predict any future element by asking where you are in the unit's cycle. Without identifying the unit, you have no rule to apply and can only guess.
The repeating unit is the engine of the pattern. Everything else — predicting the next element, filling in a gap, checking whether a sequence is correct — depends on knowing what the unit is. The key skill in pattern work is not memorizing specific patterns but learning to extract the repeating chunk.