<snapdata remixID="9298412"><project name="1920 U8L1p1 Counting Trees" app="Snap! 5.4, http://snap.berkeley.edu" version="1"><notes></notes><thumbnail>data:image/png;base64,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</thumbnail><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="true" codify="false" inheritance="false" sublistIDs="false" scheduled="false" 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struct="atomic" id="2"></list></costumes><sounds><list struct="atomic" id="3"></list></sounds><variables></variables><blocks></blocks><scripts></scripts><sprites><sprite name="Sprite" idx="1" x="0" y="-2.842170943040401e-14" heading="0" scale="1" volume="100" pan="0" rotation="1" draggable="true" costume="0" color="80,80,80,1" pen="tip" id="8"><costumes><list struct="atomic" id="9"></list></costumes><sounds><list struct="atomic" id="10"></list></sounds><blocks></blocks><variables></variables><scripts><comment x="20" y="20" w="636" collapsed="false">Created by Alexander Perez on 02/23/2020&#xD;1920 U8L1p1 Counting Trees (starter file)&#xD;Week 11 Unit 8 Lab 1 Recursive Reporters Counting Trees</comment><comment x="20" y="98" w="610" collapsed="false">1. Open your &quot;U6L1-Tree&quot; project. How many line segments are in a tree of each level? Complete this table. (You can count by eye or have Snap! count for you.)</comment><script x="20" y="164"><block s="clear"></block><block s="setHeading"><l>0</l></block><block s="gotoXY"><l>0</l><l>0</l></block><block s="down"></block><custom-block s="tree 3 size: %n"><l>50</l></custom-block></script><script x="20" y="281"><block s="clear"></block><block s="setHeading"><l>0</l></block><block s="gotoXY"><l>0</l><l>0</l></block><block s="down"></block><custom-block s="tree level: %n size %n"><l>4</l><l>50</l></custom-block></script><comment x="20" y="398" w="610" collapsed="false">2. How does the number of segments in one level compare to the number of segments in the previous level?</comment><comment x="20" y="452" w="616" collapsed="false">Each number is twice the previous one, plus 1.  For example, (2×7)+1 = 15, which is the number below 7 in the table.  Note that we do *not* ask for a closed form formula in terms of the level number!</comment><comment x="20" y="518" w="610" collapsed="false">3. Build a block whose input is a tree number and whose output is the number of segments in that level: segments in tree 7</comment><script x="20" y="572"><custom-block s="iterative segments in tree %s"><l></l><comment w="311" collapsed="true">Alphie and Betty discuss the code they created.</comment></custom-block></script><comment x="20" y="607" w="593" collapsed="false">4. If you haven&apos;t yet, build a recursive reporter that reports the number of segments in a tree of level n.&#xD;Remember that you need to click &quot;Apply&quot; before you can use your block recursively in the Block Editor.</comment><script x="20" y="673"><custom-block s="recursive segments in tree %n"><l>7</l></custom-block></script><script x="20" y="706"><custom-block s="segments in tree %n"><l>7</l></custom-block></script></scripts></sprite></sprites></stage><hidden></hidden><headers></headers><code></code><blocks><block-definition s="label %&apos;text&apos; of size %&apos;size&apos;" type="command" category="pen"><comment x="0" y="0" w="90" collapsed="false">LABEL will stamp text on the stage at the given font size. 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do %&apos;action&apos; and pause all $pause-1-255-220-0" type="command" category="control"><header></header><code></code><translations></translations><inputs><input type="%boolUE"></input><input type="%cs"></input></inputs><script><block s="doDeclareVariables"><list><l>breakpoint</l></list></block><block s="doIf"><block s="evaluate"><block var="test"/><list></list></block><script><block s="doSetVar"><l>breakpoint</l><block var="test"/></block><block s="doShowVar"><l>breakpoint</l></block><block s="doRun"><block var="action"/><list></list></block><block s="doPauseAll"></block><block s="doHideVar"><l></l></block></script></block></script></block-definition><block-definition s="word $arrowRight list %&apos;word&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%txt"></input></inputs><script><block s="doWarp"><script><block s="doReport"><block s="reportTextSplit"><block var="word"/><l><option>letter</option></l></block></block></script></block></script></block-definition><block-definition s="ignore %&apos;x&apos;" type="command" category="control"><header></header><code></code><translations></translations><inputs><input type="%s"></input></inputs></block-definition><block-definition s="tell %&apos;sprite&apos; 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size %&apos;size&apos;" type="command" category="looks"><header></header><code></code><translations></translations><inputs><input type="%n"></input><input type="%n"></input></inputs><script><block s="doIfElse"><block s="reportEquals"><block var="level"/><l>1</l></block><script><block s="forward"><block var="size"/></block><block s="forward"><block s="reportProduct"><block var="size"/><l>-1</l></block></block></script><script><block s="forward"><block var="size"/></block><block s="turnLeft"><l>25</l></block><custom-block s="tree level: %n size %n"><block s="reportDifference"><block var="level"/><l>1</l></block><block s="reportProduct"><block var="size"/><l>0.65</l></block></custom-block><block s="turn"><l>25</l></block><block s="turn"><l>35</l></block><custom-block s="tree level: %n size %n"><block s="reportDifference"><block var="level"/><l>1</l></block><block s="reportProduct"><block var="size"/><l>0.85</l></block></custom-block><block s="turnLeft"><l>35</l></block><block s="forward"><block s="reportProduct"><block var="size"/><l>-1</l></block></block></script></block></script></block-definition><block-definition s="segments in tree %&apos;num&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doDeclareVariables"><list><l>answer</l></list></block><block s="doSetVar"><l>answer</l><l>1</l></block><custom-block s="for %upvar = %n to %n %cs"><l>i</l><block var="num"/><l>10</l><script><block s="doSetVar"><l>answer</l><block s="reportProduct"><block var="answer"/><l>2</l></block></block></script></custom-block><block s="doReport"><block s="reportDifference"><block var="answer"/><l>1</l></block></block></script></block-definition><block-definition s="recursive segments in tree %&apos;level&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%n"></input></inputs><script><block s="doIfElse"><block s="reportEquals"><block var="level"/><l>1</l></block><script><block s="doReport"><l>1</l></block></script><script><block s="doReport"><block s="reportSum"><l>1</l><block s="reportProduct"><l>2</l><custom-block s="recursive segments in tree %n"><block s="reportDifference"><block var="level"/><l>1</l></block></custom-block></block></block></block></script></block></script><scripts><comment x="19" y="250.2" w="330" collapsed="false">Design:&#xD;&#xD;if n is one then&#xD;     report one&#xD;else&#xD;     report (one plus (2 times (recursive (level less one))</comment><comment x="16" y="208.2" w="477" collapsed="true">This is the formula from Unit 8 Lab 1: Recursive Reporters   Working with Recursive Reporters</comment></scripts></block-definition><block-definition s="iterative segments in tree %&apos;n&apos;" type="reporter" category="operators"><header></header><code></code><translations></translations><inputs><input type="%s"></input></inputs><script><block s="doDeclareVariables"><list><l>answer</l></list></block><block s="doSetVar"><l>answer</l><l>1</l></block><custom-block s="for %upvar = %n to %n %cs"><l>i</l><l>1</l><block var="n"/><script><block s="doSetVar"><l>answer</l><block s="reportProduct"><block var="answer"/><l>2</l></block></block></script></custom-block><block s="doReport"><block s="reportDifference"><block var="answer"/><l>1</l></block></block></script><scripts><comment x="11.200000000000045" y="202.56" w="347.6" collapsed="false">8.1.1.3 iterative solution.  This isn&apos;t *wrong*, but students who find this solution should be encouraged to think about it recursively also.</comment></scripts></block-definition></blocks><variables></variables></project><media name="1920 U8L1p1 Counting Trees" app="Snap! 5.4, http://snap.berkeley.edu" version="1"></media></snapdata>