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0e95f18 @marcia Add new line for integration regex to grab header stuffs
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1 <!DOCTYPE html>
2 <html data-require="math math-format graphie graphie-helpers word-problems slice-clone">
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3 <head>
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4 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
5 <title>Fractions cut and copy 1</title>
6 <script src="../khan-exercise.js"></script>
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7 </head>
8 <body>
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9 <div class="exercise">
10 <div class="vars">
11 <!-- An integer will be a starting or ending quantity 1/3 of the time -->
12 <var id="D_PARENT">randRangeWeighted( 3, 12, 1, 1 / 6 )</var>
13 <var id="D_OFFSPRING">D_PARENT === 1 ? randRange( 3, 12 ) : ( rand( 5 ) > 0 ? D_PARENT : 1 )</var>
14 <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">
15 <var id="N_PARENT">D_PARENT === 1 ? randRange( 1, 4 ) : randRangeExclude( 2, 2 * D_PARENT - 1, [ D_PARENT ] )</var>
16 <var id="N_OFFSPRING">D_OFFSPRING === 1 ? randRange( 1, 4 ) : randRangeExclude( 2, 2 * D_OFFSPRING - 1, [ D_OFFSPRING ] )</var>
17 </div>
18 <var id="CODE_PARENT">D_PARENT === 1 ? N_PARENT : mixedOrImproper( N_PARENT, D_PARENT )</var>
19 <var id="CODE_OFFSPRING">D_OFFSPRING === 1 ? N_OFFSPRING : mixedOrImproper( N_OFFSPRING, D_OFFSPRING )</var>
20 <var id="PARENT">N_PARENT / D_PARENT</var>
21 <var id="OFFSPRING">N_OFFSPRING / D_OFFSPRING</var>
22 <var id="ANSWER">OFFSPRING / PARENT</var>
23 <var id="D">D_PARENT === 1 ? D_OFFSPRING : D_PARENT</var>
24 <var id="N_PARENT_EXPANDED">N_PARENT * ( D_PARENT === 1 ? D : 1 )</var>
25 <var id="N_OFFSPRING_EXPANDED">N_OFFSPRING * ( D_OFFSPRING === 1 ? D : 1 )</var>
26 </div>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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27
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28 <div class="problems">
29 <div>
30 <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>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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31
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32 <p>Starting Block:</p>
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33
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34 <div class="graphie" id="parent_block">
35 initSliceClone([ "current_block" ]);
36 init({ range: [ [ 0, 1 ], [ 0, 1 ] ],scale: [ 600, 25 ] });
37 rectchart( [ 1, 0 ], [ "#e00", "#999" ] );
38 </div>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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39
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40 <p>Current Block:</p>
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41
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42 <div class="graphie" id="current_block">
43 init({ range: [ [ 0, 1 ], [ 0, 1 ] ],scale: [ 600, 25 ] });
44 rectchart( [ 1, 0 ], [ "#e00", "#999" ] );
45 </div>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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46
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47 <p>Goal Block:</p>
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48
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49 <div class="graphie" id="goal_block">
50 init({ range: [ [ 0, 1 ], [ 0, 1 ] ],scale: [ 600 * ANSWER, 25 ] });
51 rectchart( [ 1, 0 ], [ BLUE, "#999" ] );
52 </div>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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53
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54 <div class="solution" data-type="multiple">
55 <div style="margin-bottom: 10px;">
56 Cut into
57 <input type="button" value="-" class="simple-button action-gradient" onclick="KhanUtil.changePieces( false )">
58 <span id="pieces" style="display: inline-block; width: 54px; text-align: center;">1 piece</span>
59 <input type="button" value="+" class="simple-button action-gradient" onclick="KhanUtil.changePieces( true )">
60 </div>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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61
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62 <div style="margin-bottom: 10px;">
63 <span style="display:inline-block; width: 42px;">Copy</span>
64 <input type="button" value="-" class="simple-button action-gradient" onclick="KhanUtil.changeTimes( false, 'current_block' )" disabled="disabled">
65 <span id="current_block_times" style="display: inline-block; width: 54px; text-align: center;">1 time</span>
66 <input type="button" value="+" class="simple-button action-gradient" onclick="KhanUtil.changeTimes( true, 'current_block' )">
67 </div>
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68
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69 <span class="sol" id="current_block_answer" style="display: none;"><var>roundTo( 3, ANSWER )</var></span>
70 </div>
2773cd9 @jpulgarin Hints for fractions_cut_and_copy_1
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71
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72 <div class="hints">
73 <p data-if="CODE_PARENT !== fraction( N_PARENT, D)">The starting block of length <code><var>CODE_PARENT</var></code> units
74 can be rewritten as <code><var>fraction( N_PARENT_EXPANDED, D )</var></code>.</p>
75 <p data-if="CODE_OFFSPRING !== fraction( N_OFFSPRING, D)">The goal block of length <code><var>CODE_OFFSPRING</var></code> units
76 can be rewritten as <code><var>fraction( N_OFFSPRING_EXPANDED, D )</var></code>.</p>
77 <p>Cutting the starting block into <code>x</code> pieces is the same as dividing it by <code>x</code>.</p>
78 <div>
79 <p>Therefore cutting the starting block into <code><var>N_PARENT_EXPANDED</var></code> pieces is the same as:</p>
80 <p><code>\dfrac{<var>N_PARENT_EXPANDED</var>}{<var>D</var>} ÷ <var>N_PARENT_EXPANDED</var> =
81 \dfrac{<var>N_PARENT_EXPANDED</var>}{<var>D</var>} \cdot \dfrac{1}{<var>N_PARENT_EXPANDED</var>} = \dfrac{1}{<var>D</var>}</code></p>
82 </div>
83 <p>Copying the resulting block <code>y</code> times is the same as multiplying it by <code>y</code>.</p>
84 <div>
85 <p>Therefore copying the resulting block <code><var>N_OFFSPRING_EXPANDED</var></code> times is the same as:</p>
86 <p><code>\dfrac{1}{<var>D</var>} \cdot <var>N_OFFSPRING_EXPANDED</var> = \dfrac{<var>N_OFFSPRING_EXPANDED</var>}{<var>D</var>}</code></p>
87 </div>
88 <div>
89 <p>Notice that we end up with a block the same size as the goal block.</p>
90 <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>
91 </div>
92 </div>
93 </div>
94 </div>
95 </div>
ebb3ac5 @jpulgarin Add fractions_cut_and_copy_1.html
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96 </body>
97 </html>
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