Lesson 10.310.3 Small Group · Group 1
Group 1 · Set BSecond form · new problems, same idea
Learning target With my small group, I can use patterns and relationships to make sense of the Tower of Hanoi puzzle and think logically about its solutions — one step at a time, with support.
Remember10.3 Small Group · Group 1
Small cases in a table show a pattern, and the pattern rule predicts cases you never played. Play small cases first. Put the results in a table, and look for a pattern rule.
Words: puzzle (rompecabezas)pattern (patrón)pattern rule (regla del patrón)predict (predecir)organize (organizar)
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1Complete each step, then write the final answer.
A pattern uses the rule “double, then add 1.” It starts 2, 5, 11. What number comes after 11?
Show your workHint Double 11, then add 1.
Final answer: -
2Complete each step, then write the final answer.
An 8-disc tower takes 255 moves. How many moves does a 9-disc tower take?
Show your workHint Use the pattern rule on 255.
Final answer: -
3Complete each step, then write the final answer.
Squares Toothpicks 1 4 2 7 3 10 6 ? Look from each row to the next row. Toothpicks make a row of squares. 1 square uses 4 toothpicks. 2 squares use 7. 3 squares use 10. How many toothpicks do 6 squares use?
Show your workHint Look from each row to the next. What do you add each time?
Final answer: -
4Complete each step, then write the final answer.
The moves 1, 3, 7, 15, 31 are each 1 less than 2, 4, 8, 16, 32. Use this pattern to find the moves for a 10-disc tower.
Show your workHint Keep doubling 2, 4, 8, 16, 32 until you have 10 numbers. Then subtract 1.
Final answer:
Explain your thinkingWhy does one new disc double the old moves, then add 1? Talk about moving the small tower off and back.
Sentence starter First I move the small tower off, which takes ___ moves. · The rule is “double, then add 1” because ___.