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a0106e4 Marcia Lee Add exercise -- comparing fractions 1
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1 <!DOCTYPE html>
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2 <html data-require="math graphie graphie-helpers word-problems">
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3 <head>
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4 <meta charset="UTF-8" />
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5 <title>Comparing fractions 1</title>
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6 <script src="../khan-exercise.js"></script>
7 </head>
8 <body>
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9 <!--
a0106e4 Marcia Lee Add exercise -- comparing fractions 1
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10 Compares fractions that have the same numerator or have the same denominator.
11 TODO: would like to draw overlapping circles or rectangle slices for hints.
12 -->
13 <div class="exercise">
14 <div class="problems">
15 <div id="same-numerator">
16 <div class="vars" data-ensure="DEN_1 !== DEN_2">
17 <var id="NUM_1">randRange( 1, 14 )</var>
18 <var id="DEN_1">randRange( NUM_1 + 1, 15 )</var>
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19
a0106e4 Marcia Lee Add exercise -- comparing fractions 1
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20 <var id="NUM_2">NUM_1</var>
21 <var id="DEN_2">randRange( NUM_2 + 1, 15 )</var>
22
23 <var id="SOLUTION">(function() {
24 if ( DEN_1 < DEN_2 ) {
25 return "&gt;";
26 } else {
27 return "&lt;";
28 }
29 })()</var>
30 <var id="MORE">DEN_1 > DEN_2 ? "more" : "fewer"</var>
31 <var id="SMALLER">DEN_1 > DEN_2 ? "smaller" : "bigger"</var>
32 <var id="LESS">DEN_1 > DEN_2 ? "less" : "more"</var>
33 <var id="BIGGER">SMALLER === "smaller" ? "bigger" : "smaller"</var>
34 </div>
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35
a0106e4 Marcia Lee Add exercise -- comparing fractions 1
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36 <div class="problem">
37 <p>Fill in the blank.</p>
38 <p>
39 <code>\dfrac{<var>NUM_1</var>}{<var>DEN_1</var>}</code>
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40 ____ <code>\dfrac{<var>NUM_2</var>}{<var>DEN_2</var>}</code>
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41 </p>
42 </div>
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43 <p class="solution"><code><var>SOLUTION</var></code></p>
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44 <ul class="choices" data-category="true">
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45 <li><code>&lt;</code></li>
46 <li><code>&gt;</code></li>
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47 </ul>
48 <div class="hints">
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49 <div>
50 <p>This is like comparing two equally sized pizzas where one is cut into <var>DEN_1</var> equal slices and the other is cut into <var>DEN_2</var> equal slices.</p>
4c19def Ben Alpert graphie for comparing_fractions_1
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51 <div style="height: 150px;">
52 <div class="graphie" style="float: left">
53 init({ range: [ [-3, 3], [-3, 3] ], scale: 25 });
54 piechart( [NUM_1, DEN_1 - NUM_1], ["#e00", "#999"], 2 );
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55 </div>
4c19def Ben Alpert graphie for comparing_fractions_1
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56 <div class="graphie" style="float: left">
57 init({ range: [ [-3, 3], [-3, 3] ], scale: 25 });
58 piechart( [NUM_2, DEN_2 - NUM_2], ["#e00", "#999"], 2 );
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59 </div>
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60 </div>
61 </div>
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62 <p>Note that cutting a pizza into more slices will result in smaller slices.</p>
63 <p>The left fraction represents a pizza with <var>MORE</var> slices, and so each slice is <var>SMALLER</var>.</p>
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64 <p><var>NUM_1</var> <var>SMALLER</var> slice<var>plural( NUM_1 )</var> is <var>LESS</var> pizza than <var>NUM_2</var> <var> BIGGER</var> slice<var>plural( NUM_2 )</var>.</p>
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65 <p>So, <code>\dfrac{<var>NUM_1</var>}{<var>DEN_1</var>} <var>SOLUTION</var> \dfrac{<var>NUM_2</var>}{<var>DEN_2</var>}</code>.</p>
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66 </div>
67 </div>
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68
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69 <div id="same-denominator">
70 <div class="vars" data-ensure="NUM_1 !== NUM_2">
71 <var id="NUM_1">randRange( 1, 14 )</var>
72 <var id="DEN_1">randRange( NUM_1 + 1, 15 )</var>
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73
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74 <var id="DEN_2">DEN_1</var>
75 <var id="NUM_2">randRange( 1, DEN_2 - 1 )</var>
76
77 <var id="SOLUTION">(function() {
78 if ( NUM_1 < NUM_2 ) {
79 return "&lt;";
80 } else {
81 return "&gt;";
82 }
83 })()</var>
84 <var id="LESS">NUM_1 < NUM_2 ? "less" : "more"</var>
85 </div>
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86
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87 <div class="problem">
88 <p>Fill in the blank.</p>
89 <p>
90 <code>\dfrac{<var>NUM_1</var>}{<var>DEN_1</var>}</code>
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91 ____ <code>\dfrac{<var>NUM_2</var>}{<var>DEN_2</var>}</code>
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92 </p>
93 </div>
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94 <p class="solution"><code><var>SOLUTION</var></code></p>
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95 <ul class="choices" data-category="true">
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96 <li><code>&lt;</code></li>
97 <li><code>&gt;</code></li>
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98 </ul>
99 <div class="hints">
ababc88 Marcia Lee Add a pie to comparing fractions
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100 <div>
101 <p>This is like considering two equally sized pizzas that have been cut into <var>DEN_1</var> equal slices.</p>
d89d39c Ronald Cheng Fix errors with spelling and grammar. Also changed the test mode condit...
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102 <p>Since both pizzas have the same number of slices, all the slices are the same size.</p>
4c19def Ben Alpert graphie for comparing_fractions_1
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103 <div style="height: 150px;">
104 <div class="graphie" style="float: left">
105 init({ range: [ [-3, 3], [-3, 3] ], scale: 25 });
106 piechart( [NUM_1, DEN_1 - NUM_1], ["#e00", "#999"], 2 );
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107 </div>
4c19def Ben Alpert graphie for comparing_fractions_1
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108 <div class="graphie" style="float: left">
109 init({ range: [ [-3, 3], [-3, 3] ], scale: 25 });
110 piechart( [NUM_2, DEN_2 - NUM_2], ["#e00", "#999"], 2 );
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111 </div>
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112 </div>
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113 </div>
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114 <p><var>plural( NUM_1, "slice" )</var> is <var>LESS</var> pizza than <var>plural( NUM_2, "slice" )</var>.</p>
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115 <p>So, <code>\dfrac{<var>NUM_1</var>}{<var>DEN_1</var>} <var>SOLUTION</var> \dfrac{<var>NUM_2</var>}{<var>DEN_2</var>}</code>.</p>
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116 </div>
117 </div>
118 </div>
119 </div>
120 </body>
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121 </html>
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