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2773cd9 @jpulgarin Hints for fractions_cut_and_copy_1
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1 <!DOCTYPE html> <html data-require="math math-format graphie graphie-helpers word-problems slice-clone">
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2 <head>
3 <meta charset="UTF-8" />
4 <title>Fractions cut and copy 1</title>
5 <script src="../khan-exercise.js"></script>
6 </head>
7 <body>
8 <div class="exercise">
9 <div class="vars">
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10 <!-- An integer will be a starting or ending quantity 1/3 of the time -->
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11 <var id="D_PARENT">randRangeWeighted( 3, 12, 1, 1 / 6 )</var>
12 <var id="D_OFFSPRING">D_PARENT === 1 ? randRange( 3, 12 ) : ( rand( 5 ) > 0 ? D_PARENT : 1 )</var>
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13 <div data-ensure="getGCD( N_PARENT * ( D_PARENT === 1 ? D_OFFSPRING : 1 ), N_OFFSPRING * ( D_OFFSPRING === 1 ? D_PARENT : 1 ) ) === 1 && N_PARENT / D_PARENT > N_OFFSPRING / D_OFFSPRING">
14 <var id="N_PARENT">D_PARENT === 1 ? randRange( 1, 4 ) : randRangeExclude( 2, 2 * D_PARENT - 1, [ D_PARENT ] )</var>
15 <var id="N_OFFSPRING">D_OFFSPRING === 1 ? randRange( 1, 4 ) : randRangeExclude( 2, 2 * D_OFFSPRING - 1, [ D_OFFSPRING ] )</var>
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16 </div>
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17 <var id="CODE_PARENT">D_PARENT === 1 ? N_PARENT : mixedOrImproper( N_PARENT, D_PARENT )</var>
18 <var id="CODE_OFFSPRING">D_OFFSPRING === 1 ? N_OFFSPRING : mixedOrImproper( N_OFFSPRING, D_OFFSPRING )</var>
19 <var id="PARENT">N_PARENT / D_PARENT</var>
20 <var id="OFFSPRING">N_OFFSPRING / D_OFFSPRING</var>
21 <var id="ANSWER">OFFSPRING / PARENT</var>
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22 <var id="D">D_PARENT === 1 ? D_OFFSPRING : D_PARENT</var>
23 <var id="N_PARENT_EXPANDED">N_PARENT * ( D_PARENT === 1 ? D : 1 )</var>
24 <var id="N_OFFSPRING_EXPANDED">N_OFFSPRING * ( D_OFFSPRING === 1 ? D : 1 )</var>
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25 </div>
26
27 <div class="problems">
28 <div>
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29 <p class="question">The starting block below is <code><var>CODE_PARENT</var></code> units long. Use the tools to the right to convert the starting block into the goal block that is <code><var>CODE_OFFSPRING</var></code> units long. You can see your progress as the current block.</p>
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30
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31 <p>Starting Block:</p>
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32
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33 <div class="graphie" id="parent_block">
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34 initSliceClone([ "current_block" ]);
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35 init({ range: [ [ 0, 1 ], [ 0, 1 ] ],scale: [ 600, 25 ] });
36 rectchart( [ 1, 0 ], ["#e00", "#999" ] );
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37 </div>
38
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39 <p>Current Block:</p>
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40
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41 <div class="graphie" id="current_block">
42 init({ range: [ [ 0, 1 ], [ 0, 1 ] ],scale: [ 600, 25 ] });
43 rectchart( [ 1, 0 ], ["#e00", "#999" ] );
44 </div>
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45
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46 <p>Goal Block:</p>
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47
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48 <div class="graphie" id="goal_block">
49 init({ range: [ [ 0, 1 ], [ 0, 1 ] ],scale: [ 600 * ANSWER, 25 ] });
50 rectchart( [ 1, 0 ], ["#e00", "#999" ] );
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51 </div>
52
53 <div class="solution" data-type="multiple">
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54 <div style="margin-bottom: 10px;">
154c670 @jpulgarin Align slice and copy buttons + change wording
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55 Cut into
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56 <input type="button" value="-" class="simple-button action-gradient" onclick="KhanUtil.changePieces( false )">
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57 <span id="pieces" style="display: inline-block; width: 54px; text-align: center;">1 piece</span>
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58 <input type="button" value="+" class="simple-button action-gradient" onclick="KhanUtil.changePieces( true )">
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59 </div>
60
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61 <div style="margin-bottom: 10px;">
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62 <span style="display:inline-block; width: 42px;">Copy</span>
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63 <input type="button" value="-" class="simple-button action-gradient" onclick="KhanUtil.changeTimes( false, 'current_block' )" disabled="disabled">
64 <span id="current_block_times" style="display: inline-block; width: 54px; text-align: center;">1 time</span>
65 <input type="button" value="+" class="simple-button action-gradient" onclick="KhanUtil.changeTimes( true, 'current_block' )">
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66 </div>
67
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68 <span class="sol" id="current_block_answer" style="display: none;"><var>roundTo( 3, ANSWER )</var></span>
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69 </div>
2773cd9 @jpulgarin Hints for fractions_cut_and_copy_1
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70
71 <div class="hints">
72 <p data-if="CODE_PARENT !== fraction( N_PARENT, D)">The starting block of length <code><var>CODE_PARENT</var></code> units
73 can be rewritten as <code><var>fraction( N_PARENT_EXPANDED, D )</var></code>.</p>
74 <p data-if="CODE_OFFSPRING !== fraction( N_OFFSPRING, D)">The goal block of length <code><var>CODE_OFFSPRING</var></code> units
75 can be rewritten as <code><var>fraction( N_OFFSPRING_EXPANDED, D )</var></code>.</p>
76 <p>Cutting the starting block by <code>x</code> pieces is the same as dividing it by <code>x</code>.</p>
77 <div>
78 <p>Therefore cutting the starting block into <code><var>N_PARENT_EXPANDED</var></code> pieces is the same as:</p>
79 <p><code>\dfrac{<var>N_PARENT_EXPANDED</var>}{<var>D</var>} ÷ <var>N_PARENT_EXPANDED</var> =
80 \dfrac{<var>N_PARENT_EXPANDED</var>}{<var>D</var>} \cdot \dfrac{1}{<var>N_PARENT_EXPANDED</var>} = \dfrac{1}{<var>D</var>}</code></p>
81 </div>
82 <p>Copying the resulting block <code>y</code> times is the same as multiplying it by <code>y</code>.</p>
83 <div>
84 <p>Therefore copying the resulting block <code><var>N_OFFSPRING_EXPANDED</var></code> times is the same as:</p>
85 <p><code>\dfrac{1}{<var>D</var>} \cdot <var>N_OFFSPRING_EXPANDED</var> = \dfrac{<var>N_OFFSPRING_EXPANDED</var>}{<var>D</var>}</code></p>
86 </div>
87 <div>
88 <p>Notice that we end up with a block the same size as the goal block.</p>
89 <p><strong>Therefore the solution is to cut the starting block into <code><var>N_PARENT_EXPANDED</var></code> pieces and copy the resulting block <code><var>N_OFFSPRING_EXPANDED</var></code> times.</strong></p>
90 </div>
91 </div>
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92 </div>
93 </div>
94 </div>
95 </body>
96 </html>
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