Inside a dark cave, Emek and Luna followed groups of glowing rocks. The first group had 2 rocks, the next had 4, then 8, and then 16. Emek first wondered if the same number was being added each time, but Luna noticed a different rule: each group had twice as many rocks as the one before. Ahead, two tunnels were marked by groups of 24 and 32 glowing rocks. They chose the tunnel with 32 rocks and followed the doubling pattern safely out of the cave.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Check how 2 becomes 4, then how 4 becomes 8.
The glowing rock groups were 2, 4, 8, and 16. Which rule describes this pattern?
Add 2 each time.Add 4 each time.Double the number each time.Add 8 each time.Correct! Each group has twice as many rocks as the group before it.
Compare each pair of neighboring groups. The amount added is not always the same.
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Hint
The pattern doubles each time. Think of 32 as two groups of 32.
Emek and Luna chose the tunnel with 32 glowing rocks because it continued the pattern after 16. If the same pattern continues, how many glowing rocks should be in the next group?
Correct! Doubling 32 gives 64.
Use the same doubling rule that changes 16 into 32.
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Hint
Find how much is added from 2 to 4 and then from 4 to 8.
Emek first wondered if the same number was being added each time. Which fact best shows that this cannot be the rule?
From 2 to 4, 2 is added, but from 4 to 8, 4 is added.All the numbers are even.The first group has 2 rocks.There are four groups before the tunnels.Correct! The amount being added changes, so adding the same number each time is not the rule.
Compare how much is added between neighboring groups. If the rule were adding the same number, those amounts would match.
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