5.04:_Growing_Patterns

<p class="lt-math-9852">Here is a pattern made from square tiles.</p>

<section class="box-exercise"><span id="Think_.2F_Pair_.2F_Share"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Think / Pair / Share</span></h2>

<ul>
    <li class="lt-math-9852">Describe how you see this pattern growing.  Be as specific as you can.  Draw pictures and write an explanation to make your answer clear.</li>
    <li class="lt-math-9852">Say as much as you can about this growing pattern.  Can you draw pictures to extend the pattern?</li>
    <li class="lt-math-9852">What mathematical questions can you ask about this pattern?  Can you answer any of them?</li>
</ul>
</section>

<p class="lt-math-9852">Here are some pictures that students drew to describe how the pattern was growing.</p>

<p class="mt-align-center lt-math-9852">Ali's picture</p>

<p class="mt-align-center lt-math-9852">Michael's picture</p>

<p class="mt-align-center lt-math-9852">Kelli's picture</p>

<section class="box-exercise"><span id="Think_.2F_Pair_.2F_Share_2"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Think / Pair / Share</span></h2>

<p class="lt-math-9852">Describe in words how each student saw the pattern growing. Use the students&rsquo; pictures above (or your own method of seeing the growing pattern) to answer the following questions:</p>

<ul>
    <li class="lt-math-9852">How many tiles would you need to build the 5th figure in the pattern?</li>
    <li class="lt-math-9852">How many tiles would you need to build the 10th figure in the pattern?</li>
    <li class="lt-math-9852">How can you compute the number of tiles in any figure in the pattern?</li>
</ul>
</section>

<section class="box-example"><span id="Problem_15"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Problem 15</span></h2>

<p class="lt-math-9852">Hy saw the pattern in a different way from everyone else in class. Here&rsquo;s what he drew:</p>

<p class="mt-align-center lt-math-9852">Hy's picture.</p>

<ol>
    <li class="lt-math-9852">Describe in words how Hy saw the pattern grow.</li>
    <li class="lt-math-9852">How would Hy calculate the number of tiles needed to build the 10th figure in the pattern?</li>
    <li class="lt-math-9852">How would Hy calculate the number of tiles needed to build the 100th figure in the pattern?</li>
    <li class="lt-math-9852">How would Hy calculate the number of tiles needed to build any figure in the pattern?</li>
</ol>
</section>

<p class="lt-math-9852">The next few problems present several growing patterns made with tiles. For each problem you work on, do the following:</p>

<ol>
    <li class="lt-math-9852">Describe in words and pictures how you see the pattern growing.</li>
    <li class="lt-math-9852">Calculate the number of tiles you would need to build the 10th figure in the pattern. Justify your answer based on how the pattern grows.</li>
    <li class="lt-math-9852">Calculate the number of tiles you would need to build the 100th figure in the pattern.</li>
    <li class="lt-math-9852">Describe how you can figure out the number of tiles in any figure in the pattern. Be sure to justify your answer based on how the pattern grows.</li>
    <li class="lt-math-9852">Could you make one of the figures in the pattern using exactly 25 tiles? If yes, which figure?  If no, why not? Justify your answer.</li>
    <li class="lt-math-9852">Could you make one of the figures in the pattern using exactly 100 tiles? If yes, which figure?  If no, why not? Justify your answer.</li>
</ol>

<section class="box-example"><span id="Problem_16"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Problem 16</span></h2>

<section class="box-example"><span id="Problem_17"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Problem 17</span></h2>

<section class="box-example"><span id="Problem_18"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Problem 18</span></h2>

<section class="box-example"><span id="Problem_19"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Problem 19</span></h2>

<section class="box-example"><span id="Problem_20"></span><h2 class="box-legend lt-math-9852"><span class="lt-icon-default">Problem 20</span></h2>

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