<snapdata remixID="12994418"><project name="MathLibrary" app="Snap! 9.0, https://snap.berkeley.edu" version="2"><notes></notes><thumbnail>data:image/png;base64,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</thumbnail><scenes select="1"><scene name="MathLibrary"><notes></notes><hidden></hidden><headers></headers><code></code><blocks><block-definition s="is %&apos;big&apos; divisible by %&apos;small&apos; ?" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input><input type="%n"></input></inputs><script><block s="doReport"><block s="reportVariadicEquals"><list><block s="reportModulus"><block var="big"/><block var="small"/></block><l>0</l></list></block></block></script></block-definition><block-definition s="even? %&apos;number&apos;" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doReport"><custom-block s="is %n divisible by %n ?"><block var="number"/><l>2</l></custom-block></block></script></block-definition><block-definition s="integer? %&apos;number&apos;" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doReport"><block s="reportVariadicEquals"><list><block var="number"/><block s="reportRound"><block var="number"/></block></list></block></block></script></block-definition><block-definition s="%&apos;a&apos; ≤ %&apos;b&apos;" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%s"></input><input type="%s"></input></inputs><script><block s="doReport"><block s="reportVariadicOr"><list><block s="reportVariadicLessThan"><list><block var="a"/><block var="b"/></list></block><block s="reportVariadicEquals"><list><block var="a"/><block var="b"/></list></block></list></block></block></script></block-definition><block-definition s="%&apos;a&apos; ≥ %&apos;b&apos;" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%s"></input><input type="%s"></input></inputs><script><block s="doReport"><block s="reportVariadicOr"><list><block s="reportVariadicGreaterThan"><list><block var="a"/><block var="b"/></list></block><block s="reportVariadicEquals"><list><block var="a"/><block var="b"/></list></block></list></block></block></script></block-definition><block-definition s="%&apos;a&apos; ≠ %&apos;b&apos;" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%s"></input><input type="%s"></input></inputs><script><block s="doReport"><block s="reportNot"><block s="reportVariadicEquals"><list><block var="a"/><block var="b"/></list></block></block></block></script></block-definition><block-definition s="is %&apos;mid&apos; between %&apos;low&apos; and %&apos;high&apos; ?" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%s"></input><input type="%s"></input><input type="%s"></input></inputs><script><block s="doReport"><block s="reportVariadicAnd"><list><custom-block s="%s ≥ %s"><block var="mid"/><block var="low"/></custom-block><custom-block s="%s ≤ %s"><block var="mid"/><block var="high"/></custom-block></list></block></block></script><scripts><comment x="14.666666666666666" y="88.8" w="304.6666666666667" collapsed="false">As the lab says, it&apos;s okay to use &quot;&gt;&quot; and &quot;&lt;&quot; instead of &quot;≥&quot; and &quot;≤.&quot;</comment></scripts></block-definition><block-definition s="odd? %&apos;number&apos;" type="predicate" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doReport"><block s="reportNot"><custom-block s="is %n divisible by %n ?"><block var="number"/><l>2</l></custom-block></block></block></script></block-definition><block-definition s="divisors of %&apos;number&apos;" type="reporter" category="lists"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doReport"><block s="reportKeep"><block s="reifyPredicate"><autolambda><custom-block s="is %n divisible by %n ?"><block var="number"/><l></l></custom-block></autolambda><list></list></block><block s="reportNumbers"><l>1</l><block var="number"/></block></block></block></script></block-definition><block-definition s="number of divisors %&apos;number&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doReport"><block s="reportListAttribute"><l><option>length</option></l><custom-block s="divisors of %n"><block var="number"/></custom-block></block></block></script></block-definition><block-definition s="maximum of %&apos;a&apos; and %&apos;b&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input><input type="%n"></input></inputs><script><block s="doReport"><block s="reportIfElse"><block s="reportVariadicGreaterThan"><list><block var="a"/><block var="b"/></list></block><block var="a"/><block var="b"/></block></block></script><scripts><comment x="16" y="87.46666666666665" w="246.66666666666666" collapsed="false">The &quot;reporter IF&quot; used here is the simplest and most elegant solution, and you should show it to students when you debrief this lab, but you&apos;re more likely to get commands, e.g. this:</comment><script x="23" y="172.46666666666667"><block s="doIfElse"><block s="reportVariadicGreaterThan"><list><block var="a"/><block var="b"/></list></block><script><block s="doReport"><block var="a"/></block></script><script><block s="doReport"><block var="b"/></block></script></block></script></scripts></block-definition><block-definition s="minimum of %&apos;a&apos; and %&apos;b&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input><input type="%n"></input></inputs><script><block s="doReport"><block s="reportIfElse"><block s="reportVariadicLessThan"><list><block var="a"/><block var="b"/></list></block><block var="a"/><block var="b"/></block></block></script></block-definition><block-definition s="maximum of list %&apos;data&apos;" type="reporter" category="lists"><header></header><code></code><translations></translations><inputs><input type="%l"></input></inputs><script><block s="doReport"><block s="reportCombine"><block var="data"/><block s="reifyReporter"><autolambda><custom-block s="maximum of %n and %n"><l></l><l></l></custom-block></autolambda><list></list></block></block></block></script></block-definition><block-definition s="minimum of list %&apos;data&apos;" type="reporter" category="lists"><header></header><code></code><translations></translations><inputs><input type="%l"></input></inputs><script><block s="doReport"><block s="reportCombine"><block var="data"/><block s="reifyReporter"><autolambda><custom-block s="minimum of %n and %n"><l></l><l></l></custom-block></autolambda><list></list></block></block></block></script></block-definition><block-definition s="sum of list %&apos;data&apos;" type="reporter" category="lists"><header></header><code></code><translations></translations><inputs><input type="%l"></input></inputs><script><block s="doReport"><block s="reportCombine"><block var="data"/><block s="reifyReporter"><autolambda><block s="reportVariadicSum"><list><l></l><l></l></list></block></autolambda><list></list></block></block></block></script></block-definition><block-definition s="average of list %&apos;data&apos;" type="reporter" category="lists"><header></header><code></code><translations></translations><inputs><input type="%l"></input></inputs><script><block s="doReport"><block s="reportQuotient"><custom-block s="sum of list %l"><block var="data"/></custom-block><block s="reportListAttribute"><l><option>length</option></l><block var="data"/></block></block></block></script><scripts><comment x="14" y="88.8" w="289.3333333333333" collapsed="false">Important note:  It does NOT work to make a block that takes the average of two numbers and then do</comment><script x="19" y="151.13333333333333"><block s="doReport"><block s="reportCombine"><block var="data"/><block s="reifyReporter"><autolambda><custom-block s="average of %n and %n"><l></l><l></l></custom-block></autolambda><list></list></block></block></block></script><script x="15" y="273.8"><block s="reportCombine"><block s="reportNewList"><list><l>5</l><l>100</l><l>200</l></list></block><block s="reifyReporter"><autolambda><custom-block s="average of %n and %n"><l></l><l></l></custom-block></autolambda><list></list></block></block></script><script x="15.333333333333334" y="306.46666666666664"><block s="reportCombine"><block s="reportNewList"><list><l>200</l><l>100</l><l>5</l></list></block><block s="reifyReporter"><autolambda><custom-block s="average of %n and %n"><l></l><l></l></custom-block></autolambda><list></list></block></block></script><comment x="18.333333333333332" y="190.80000399999997" w="303.3333333333333" collapsed="false">This will tempt students because it follows the pattern of the other exercises so far on this page.  But COMBINE can be used only with associative operators, which AVERAGE isn&apos;t.  The last number to be averaged in will have too much influence.  Try these:</comment></scripts></block-definition><block-definition s="average of %&apos;a&apos; and %&apos;b&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input><input type="%n"></input></inputs><script><block s="doReport"><block s="reportQuotient"><block s="reportVariadicSum"><list><block var="a"/><block var="b"/></list></block><l>2</l></block></block></script></block-definition><block-definition s="greatest common divisor of %&apos;a&apos; and %&apos;b&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input><input type="%n"></input></inputs><script><block s="doReport"><block s="reportListItem"><l><option>last</option></l><custom-block s="intersection %l %l"><custom-block s="divisors of %n"><block var="a"/></custom-block><custom-block s="divisors of %n"><block var="b"/></custom-block></custom-block></block></block></script><scripts><comment x="12" y="88.8" w="410" collapsed="false">The expected, and perfectly correct, solution would be</comment><script x="8" y="136.13333333333333"><block s="doReport"><custom-block s="maximum of list %l"><custom-block s="intersection %l %l"><custom-block s="divisors of %n"><block var="a"/></custom-block><custom-block s="divisors of %n"><block var="b"/></custom-block></custom-block></custom-block></block></script><comment x="12" y="173.73333333333338" w="411.3333333333333" collapsed="false">But DIVISORS OF reports a list of the divisors /in order/, and INTERSECTION doesn&apos;t change that, so we already know that the biggest value is at the end of the list.</comment></scripts></block-definition><block-definition s="intersection %&apos;lista&apos; %&apos;listb&apos;" type="reporter" category="lists"><header></header><code></code><translations></translations><inputs><input type="%l"></input><input type="%l"></input></inputs><script><block s="doReport"><block s="reportKeep"><block s="reifyPredicate"><autolambda><block s="reportListContainsItem"><block var="listb"/><l></l></block></autolambda><list></list></block><block var="lista"/></block></block></script><scripts><comment x="10.666666666666666" y="92.8" w="314.6666666666667" collapsed="false">This solution is a little counterintuitive, because it treats the two lists asymmetrically.  We start with LISTA and keep items from it that are also in LISTB.  So, expect students to have trouble thinking of this solution.</comment></scripts></block-definition><block-definition s="make a point" type="command" category="looks"><header></header><code></code><translations></translations><inputs></inputs><script><block s="setSize"><l>5</l></block><block s="down"></block><block s="forward"><l>0</l></block><block s="up"></block></script></block-definition></blocks><stage name="Stage" width="480" height="360" costume="0" color="255,255,255,1" tempo="60" threadsafe="false" penlog="false" volume="100" pan="0" lines="round" ternary="false" hyperops="true" codify="false" inheritance="true" sublistIDs="false" 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</pentrails><costumes><list 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