L-Shaped Structure Problems
1. a) Draw the next figure in the sequence. Explain in word how the pattern is increasing.
b) You have 208 identical square pieces. Can you use all the pieces to construct an L-shaped structure
like the ones in figures 2, 3, and 4 shown above? Why or why not?
c) You want to build an L-shaped structure out of toothpicks. Is it possible to use a total of 184
identical toothpicks to create an L-shaped structure like the ones shown above? Why or why not?
d) Each vertex of a square in the L-shaped structure is highlighted with a dot. Is it possible to have
exactly 3,000 dots in an L-shaped like the ones shown above. Explain.
e) Fill in the table and make a graph to show the relationship between the figure numbers and the
number of squares.
Figure #
1
2
3
4
…
100
# of squares
…
How do you determine the number of squares for any figure number?
f) Fill in the table and make a graph to show the relationship between the figure numbers and the
number of toothpicks.
Figure #
1
2
3
4
…
100
# of toothpicks
…
How do you determine the number of toothpicks for any figure number?
g) Fill in the table and make a graph to show the relationship between the figure numbers and the
number of dots.
Figure #
1
2
3
4
…
100
# of dots
…
How do you determine the number of dots for any figure number?
2. Create your own patterns with squares. Answer all questions in #1 using your pattern.