Section 45 Runestone Components

                                                                                                                                                                                                                                                                    <section xml:id="section-runestone-components" label="section-runestone-components" xmlns:pi="http://pretextbook.org/2020/pretext/internal">

                                                                                                                                                                                                                                                                      <title>Runestone Components</title>

                                                                                                                                                                                                                                                                      <idx>Runestone components</idx>

                                                                                                                                                                                                                                                                      <p>
                                                                                                                                                                                                                                                                        One of each interactive Runestone component, each with a moderately complicated set of attributes and features, so this article can serve as a regression test for the whole collection.
                                                                                                                                                                                                                                                                        The final chapter of the sample book is the comprehensive tour, with many variants of each component; here one representative apiece suffices.
                                                                                                                                                                                                                                                                        Fill-in exercises, in both the dynamic and the legacy styles, are exercised thoroughly at <xref ref="section-dynamic-exercises"/> and so are not repeated here.
                                                                                                                                                                                                                                                                        Note that many of these components render, and function, in ordinary offline HTML; a Runestone server adds grading and persistence.
                                                                                                                                                                                                                                                                      </p>

                                                                                                                                                                                                                                                                      <exercise xml:id="regression-truefalse" label="regression-truefalse">

                                                                                                                                                                                                                                                                        <title>True/False, a True Statement</title>

                                                                                                                                                                                                                                                                        <statement correct="yes">

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            The square of a real number is never negative.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <feedback>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Squaring preserves the sign of zero and erases the sign of everything else.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </feedback>

                                                                                                                                                                                                                                                                        <hint>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Consider the three cases: negative, zero, positive.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </hint>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise xml:id="regression-multiplechoice" label="regression-multiplechoice">

                                                                                                                                                                                                                                                                        <title>Multiple Choice, Several Correct, Randomized</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Which of the following are prime numbers?
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <choices randomize="yes" multiple-correct="yes">

                                                                                                                                                                                                                                                                          <choice correct="yes">

                                                                                                                                                                                                                                                                            <statement>

                                                                                                                                                                                                                                                                              <p>

                                                                                                                                                                                                                                                                                <m>2</m>

                                                                                                                                                                                                                                                                              </p>

                                                                                                                                                                                                                                                                            </statement>

                                                                                                                                                                                                                                                                            <feedback>

                                                                                                                                                                                                                                                                              <p>
                                                                                                                                                                                                                                                                                The only even prime.
                                                                                                                                                                                                                                                                              </p>

                                                                                                                                                                                                                                                                            </feedback>

                                                                                                                                                                                                                                                                          </choice>

                                                                                                                                                                                                                                                                          <choice>

                                                                                                                                                                                                                                                                            <statement>

                                                                                                                                                                                                                                                                              <p>

                                                                                                                                                                                                                                                                                <m>1</m>

                                                                                                                                                                                                                                                                              </p>

                                                                                                                                                                                                                                                                            </statement>

                                                                                                                                                                                                                                                                            <feedback>

                                                                                                                                                                                                                                                                              <p>
                                                                                                                                                                                                                                                                                A unit, by convention not a prime.
                                                                                                                                                                                                                                                                              </p>

                                                                                                                                                                                                                                                                            </feedback>

                                                                                                                                                                                                                                                                          </choice>

                                                                                                                                                                                                                                                                          <choice correct="yes">

                                                                                                                                                                                                                                                                            <statement>

                                                                                                                                                                                                                                                                              <p>

                                                                                                                                                                                                                                                                                <m>17</m>

                                                                                                                                                                                                                                                                              </p>

                                                                                                                                                                                                                                                                            </statement>

                                                                                                                                                                                                                                                                            <feedback>

                                                                                                                                                                                                                                                                              <p>
                                                                                                                                                                                                                                                                                Indeed, no divisors but <m>1</m> and itself.
                                                                                                                                                                                                                                                                              </p>

                                                                                                                                                                                                                                                                            </feedback>

                                                                                                                                                                                                                                                                          </choice>

                                                                                                                                                                                                                                                                        </choices>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-parsons" language="python" adaptive="yes" indentation="hide">

                                                                                                                                                                                                                                                                        <title>Parsons, Vertical, Partial Ordering</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Arrange the blocks to define a function and then call it.
                                                                                                                                                                                                                                                                            There is more than one correct order, a paired distractor, and an unneeded block.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <blocks> <block order="3" name="define">

                                                                                                                                                                                                                                                                        <cline>def double(x):</cline>

                                                                                                                                                                                                                                                                        <cline>    return 2 * x</cline>

                                                                                                                                                                                                                                                                        </block> <block order="1" name="input" depends="define">

                                                                                                                                                                                                                                                                        <choice correct="yes">

                                                                                                                                                                                                                                                                          <cline>n = int(input())</cline>

                                                                                                                                                                                                                                                                        </choice>

                                                                                                                                                                                                                                                                        <choice>

                                                                                                                                                                                                                                                                          <cline>n = input()</cline>

                                                                                                                                                                                                                                                                        </choice>

                                                                                                                                                                                                                                                                        </block> <block order="2" depends="input">

                                                                                                                                                                                                                                                                        <cline>print(double(n))</cline>

                                                                                                                                                                                                                                                                        </block> <block order="4" correct="no">

                                                                                                                                                                                                                                                                        <cline>import antigravity</cline>

                                                                                                                                                                                                                                                                        </block> </blocks>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-parsons-horizontal" language="natural">

                                                                                                                                                                                                                                                                        <title>Parsons, Horizontal, Reused Blocks</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Assemble a familiar proverb.
                                                                                                                                                                                                                                                                            Two of the blocks are each used twice.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <blocks layout="horizontal" randomize="yes" reuse="yes"> <block xml:id="regression-block-early">early</block> <block xml:id="regression-block-to">to</block> <block ref="regression-block-early" order="1"/> <block ref="regression-block-to" order="2"/> <block order="3">bed</block> <block order="4">and</block> <block ref="regression-block-early" order="5"/> <block ref="regression-block-to" order="6"/> <block order="7">rise</block> </blocks>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-cardsort">

                                                                                                                                                                                                                                                                        <title>Cardsort, with Distractors</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Sort each function by its growth rate.
                                                                                                                                                                                                                                                                            One category has no members, and one function fits no category.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <cardsort> <match> <response>Polynomial</response> <premise order="2"><m>n^2</m></premise> <premise order="4"><m>100 n^3</m></premise> </match> <match> <response>Exponential</response> <premise order="1"><m>2^n</m></premise> </match> <match> <response>Constant</response> </match> <match> <premise order="3"><m>n \log n</m></premise> </match> </cardsort>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-matching">

                                                                                                                                                                                                                                                                        <title>Matching, Premises with References</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Match each derivative rule to its name.
                                                                                                                                                                                                                                                                            One rule matches two names.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <matching> <premise ref="regression-response-product"><m>(fg)' = f'g + fg'</m></premise> <premise ref="regression-response-chain regression-response-composite"><m>(f \circ g)' = (f' \circ g) \cdot g'</m></premise> <response xml:id="regression-response-product" order="2">Product Rule</response> <response xml:id="regression-response-chain" order="1">Chain Rule</response> <response xml:id="regression-response-composite" order="3">Composite Rule</response> </matching>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-clickablearea">

                                                                                                                                                                                                                                                                        <title>Clickable Areas, Code</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Click every line that mutates the list <c>data</c>.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <areas language="python">

                                                                                                                                                                                                                                                                        <cline>data = [3, 1, 2]</cline>

                                                                                                                                                                                                                                                                        <cline><area>data.sort()</area></cline>

                                                                                                                                                                                                                                                                        <cline><area correct="no">total = sum(data)</area></cline>

                                                                                                                                                                                                                                                                        <cline><area>data.append(total)</area></cline>

                                                                                                                                                                                                                                                                        </areas>

                                                                                                                                                                                                                                                                        <feedback>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Reading a list is not mutating it.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </feedback>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-select">

                                                                                                                                                                                                                                                                        <title>Select, an A/B Experiment</title>

                                                                                                                                                                                                                                                                        <select grade="ab-experiment" experiment-name="sample-article-regression" questions="regression-truefalse regression-multiplechoice"/>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-shortanswer" attachment="yes">

                                                                                                                                                                                                                                                                        <title>Short Answer, with Attachment</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Describe, in a sentence or two, the difference between a sequence and a series.
                                                                                                                                                                                                                                                                            Attach a photograph of your handwritten scratch work.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <response/>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-activecode">

                                                                                                                                                                                                                                                                        <title>ActiveCode, Decorated</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Run the program, then modify the highlighted line so it counts down instead.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <program label="regression-activecode-program" interactive="activecode" language="python" line-numbers="yes" highlight-lines="2" download="yes">

                                                                                                                                                                                                                                                                          <code>
                    for i in range(5):
                        print(i)
                                                                                                                                                                                                                                                                          </code>

                                                                                                                                                                                                                                                                        </program>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <exercise label="regression-codelens">

                                                                                                                                                                                                                                                                        <title>CodeLens, with a Checkpoint</title>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
                                                                                                                                                                                                                                                                            Step the visualization and answer the question it poses.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        <program label="regression-codelens-program" interactive="codelens" language="python" starting-step="2">

                                                                                                                                                                                                                                                                          <code>
                    a = 5
                    b = a + 2
                    c = a * b
                                                                                                                                                                                                                                                                          </code> <checkpoint line="3" answer="35"> <prompt>What value is assigned to <c>c</c>?</prompt>

                                                                                                                                                                                                                                                                          <feedback>
Multiply the current values of <c>a</c> and <c>b</c>.
                                                                                                                                                                                                                                                                          </feedback>

                                                                                                                                                                                                                                                                          </checkpoint>

                                                                                                                                                                                                                                                                        </program>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                      <query label="regression-query" visibility="all">

                                                                                                                                                                                                                                                                      <statement>

                                                                                                                                                                                                                                                                        <p>
Which topic in this article did you find most challenging?
                                                                                                                                                                                                                                                                        </p>

                                                                                                                                                                                                                                                                      </statement>

                                                                                                                                                                                                                                                                      <choices>

                                                                                                                                                                                                                                                                        <choice>

                                                                                                                                                                                                                                                                          <p>
The Fundamental Theorem
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </choice>

                                                                                                                                                                                                                                                                        <choice>

                                                                                                                                                                                                                                                                          <p>
Displayed mathematics
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </choice>

                                                                                                                                                                                                                                                                        <choice>

                                                                                                                                                                                                                                                                          <p>
Table calisthenics
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </choice>

                                                                                                                                                                                                                                                                      </choices>

                                                                                                                                                                                                                                                                      </query> <datafile label="regression-datafile" xml:id="regression-datafile" filename="regression.csv" editable="no" hide="yes" rows="4" cols="30">

                                                                                                                                                                                                                                                                      <pre>
                x,y
                1,1
                2,4
                3,9
                                                                                                                                                                                                                                                                      </pre> </datafile>

                                                                                                                                                                                                                                                                      <exercise xml:id="regression-dual" label="regression-dual">

                                                                                                                                                                                                                                                                        <title>A Dual Exercise (Experimental)</title>

                                                                                                                                                                                                                                                                        <dynamic>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
Work the embedded exercise.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                          <interactive label="regression-dual-interactive" iframe="https://opendsax.cs.vt.edu/OpenDSA/Exercises/List/AlistInsertPRO.html" width="100%"/>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        </dynamic> <static>

                                                                                                                                                                                                                                                                        <statement>

                                                                                                                                                                                                                                                                          <p>
An exercise about array-based list insertion goes here, in an output with no interaction.
                                                                                                                                                                                                                                                                          </p>

                                                                                                                                                                                                                                                                        </statement>

                                                                                                                                                                                                                                                                        </static>

                                                                                                                                                                                                                                                                      </exercise>

                                                                                                                                                                                                                                                                    </section>

<datafile label="regression-datafile" xml:id="regression-datafile" filename="regression.csv" editable="no" hide="yes" rows="4" cols="30" xmlns:pi="http://pretextbook.org/2020/pretext/internal">

                                                                                                                                                                                                                                                                      <pre>
                x,y
                1,1
                2,4
                3,9
                                                                                                                                                                                                                                                                      </pre> </datafile>