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Staircase Towers

Write down what the pattern is, using complete sentences. How many cubes will there be in the 10 th tower? How many cubes will there be in the n th tower? Explain how you know your formula works (in complete sentences).

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Staircase Towers

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  1. Write down what the pattern is, using complete sentences. • How many cubes will there be in the 10th tower? • How many cubes will there be in the nth tower? • Explain how you know your formula works (in complete sentences). • On a clean sheet of printer paper show the relation between the tower number and the number of cubes, in each of the 5 representations: • Pictorially • Verbally • Table • Formula • Graphically Staircase Towers Tower 1 Tower 2 Tower 3 Tower 4

  2. Growing Dots At the beginning At two minutes At one minute

  3. Growing Dots At the beginning At two minutes At one minute New each time

  4. Growing Dots At the beginning At two minutes At one minute New each time Constant center dot

  5. Growing Dots At the beginning At two minutes At one minute New each time Constant center dot The dot started with one single dot. Every time the dot got surrounded by 4 and each time they stacked to make an x.

  6. Growing Dots At the beginning At two minutes At one minute New each time Constant center dot The pattern started with one single dot. Every time the dot got surrounded by 4 and each time they stacked to make an x.

  7. Growing Dots At the beginning At two minutes At one minute New each time Constant center dot The pattern started with one single dot. Every time the dot got surrounded by 4 more dots and each time they stacked to make an x.

  8. Growing Dots At the beginning At two minutes At one minute Growing Dots-total dots at a given minute +1 New each time Total Dots Constant center dot The pattern started with one single dot. Every time the dot got surrounded by 4 more dots and each time they stacked to make an x. +4 The center dot that is always there How many dots that get added each time Minutes +4 +1 +4 +1 y=total dots t=minutes +4 +1

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