Generating a pattern from a rule
Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur
کارهایی که یادگیرنده بعد از این درس می‌تواند انجام دهد
- Given 'start at 1, add 3', generate terms and notice they alternate odd/even
- Given a shape pattern, predict the next three terms and describe the rule
- Explain why starting at 2 and adding 4 always gives even numbers
۱ · بخوان
A pattern rule tells you two things: where to start, and what to do every time. If the rule is 'start at 1, add 3,' you begin at 1, then add 3 again and again: 1, 4, 7, 10, 13. The step does not have to be adding. 'Start at 3, multiply by 2' gives 3, 6, 12, 24, 48.
Zara makes a shape pattern: circle, square, circle, square, circle. The rule is 'circle, then square, repeat.' The next three shapes are square, circle, square. Some patterns repeat a longer group, like circle, circle, square. Find the group that keeps coming back, then carry it on.
Patterns often hide a surprise the rule never mentions. In 1, 4, 7, 10, 13 the numbers flip odd, even, odd, even. That happens because the step, 3, is odd, and adding an odd number always swaps odd for even. When the step is even the flip never happens: start at 2 and add 4 and every number stays even, because even plus even is even.
A rule sets the start and the step, and once you build the pattern, watch for surprises hiding inside it, like numbers that keep flipping between odd and even.
برای خواندن بیشتر
Factors, multiples, and patterns: FAQ
A pattern rule tells you how to build each new term from the one before. Start at 1 and add 3 gives 1, 4, 7, 10 and so on. Look at the terms: odd, even, odd, even. The rule add 3 flips odd to even and back each time. Writing out the first few terms always reveals what a rule does.
Arithmetic sequences review
Sequences grow by a fixed rule, just like shape patterns grow by a fixed number of sticks. If shapes use 3, 5, 7 sticks, the rule is add 2 and the next shapes use 9, 11, 13. Predicting later terms means applying the rule again and again. For start at 2 with add 4, the 10th term is 2 + 9 x 4 = 38.
Sequences: FAQ
Even rules have even results. Starting at 2 and adding 4 always gives even numbers, because even plus even stays even. This kind of reasoning proves a pattern holds forever, not just for the terms you wrote out. Always ask why a rule behaves as it does, not only what comes next.
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۲ · ببین
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