Follow a Collatz-style rule with negative numbers until it loops, and find three consecutive integers with a given product.
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Even: halve it. Odd: times −3, then add 1.
Start with any integer.
Repeat with the new number.
The book's chain from −7, with one printing slip fixed.
Problem. Follow the rule starting from . (Textbook p. 42)
Run the rule from new starting numbers and describe what happens.
Math Talk, Textbook p. 43. Try the rule with different starting numbers, such as and . Describe the patterns you see.
Show each step until it repeats.
Show each step until it repeats.
Compare the endings.
Numbers that follow one after another, like −3, −2, −1.
Consecutive integers come one after another, each 1 more than the last: or .
Figure it Out Q9(a) solved with sign-first thinking.
Problem. Find 3 consecutive numbers with a product of . (Textbook p. 43, Q9a)
Find three consecutive integers whose product is 120.
Figure it Out, Textbook p. 43, Q9(b): find 3 consecutive numbers with a product of 120.
The product is positive and fairly big. Try numbers around 5.
4 × 5 = , and 20 × 6 = .
So the numbers are 4, 5 and .
Would −6, −5, −4 work? Their product is , so no.