On a mountain trail, Emek and Luna found a row of rock piles marking the route home. The first pile had 18 rocks, the second had 15, and the third had 12. The next pile had fallen apart. Luna noticed that each complete pile had 3 fewer rocks than the one before. Emek reasoned that the missing pile should have 9 rocks. They rebuilt it with 9 rocks and checked the pattern: 18, 15, 12, 9. A route marker beneath the pile pointed them safely home.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
The pattern has 3 fewer rocks in each new pile.
Emek says the broken pile should have 9 rocks. Which calculation best checks his answer?
12 + 3 = 1512 - 3 = 912 - 2 = 1012 + 9 = 21Correct! Taking 3 away from 12 gives 9, so the rebuilt pile follows the pattern.
Start with 12 rocks and use the rule of 3 fewer rocks.
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Hint
Continue the rule of 3 fewer rocks from the pile of 9.
Suppose Emek and Luna find one more rock pile after the rebuilt pile of 9 rocks. If the same pattern continues, how many rocks should be in that pile?
Correct! Three fewer than 9 is 6.
Start with 9 and subtract 3 to continue the pattern.
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Hint
Test the friend's rule on the first two numbers, 18 and 15.
Luna checks the pattern 18, 15, 12, 9. A friend says the rule is "subtract 2 each time." Which fact shows that the friend is mistaken?
18 - 2 = 16, not 15.15 + 2 = 17.12 + 2 = 14.9 - 2 = 7.Correct! Subtracting 2 from 18 gives 16, so that rule does not produce the next number, 15.
Test subtracting 2 from the first number and see whether it gives the next number in the pattern.
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