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Add exercise: One Step Equations 0.5 #7532

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6 changes: 3 additions & 3 deletions exercises/alternate_exterior_angles_2.html
Expand Up @@ -25,7 +25,7 @@
<div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question">Solve for <code>x</code>:</p>
<p class="solution" data-forms="integer"><var>SOLUTION</var></p>
<p class="solution" data-type="rational"><var>SOLUTION</var></p>
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If you leave off the type completely (<p class="solution">), it will accept decimals like 37.0 as well.

<div class="graphie" id="parallel-lines">

var eq1 = A + "x + " + B + "^\\circ";
Expand All @@ -44,9 +44,9 @@
</div>

<div class="hints">
<p>We learned in Alternate exterior angles 1 that alternate interior angles are equal. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals?playlist=Geometry" data-youtube-id="gRKZaojKeP0">Watch this video</a> to understand why.</p>
<p>Alternate exterior angles are equal to one another. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals?playlist=Geometry" data-youtube-id="gRKZaojKeP0">Watch this video</a> to understand why.</p>
<div>
<p>Set the <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> equal to the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code>.</p>
<p>The <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> and the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code> are alternate interior angles. Therefore, we can set them equal to one another.</p>
<p><code>\color{<var>BLUE</var>}{<var>A</var>x + <var>B</var>} = \color{<var>ORANGE</var>}{<var>C</var>x + <var>D</var>}</code></p>
</div>

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6 changes: 3 additions & 3 deletions exercises/alternate_interior_angles_2.html
Expand Up @@ -25,7 +25,7 @@
<div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question">Solve for <code>x</code>:</p>
<p class="solution" data-forms="integer"><var>SOLUTION</var></p>
<p class="solution" data-type="rational"><var>SOLUTION</var></p>
<div class="graphie" id="parallel-lines">

var eq1 = A + "x + " + B + "^\\circ";
Expand All @@ -44,9 +44,9 @@
</div>

<div class="hints">
<p>We learned in Alternate interior angles 1 that alternate interior angles are equal. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals?playlist=Geometry" data-youtube-id="gRKZaojKeP0">Watch this video</a> to understand why.</p>
<p>Alternate interior angles are equal to one another. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals?playlist=Geometry" data-youtube-id="gRKZaojKeP0">Watch this video</a> to understand why.</p>
<div>
<p>Set the <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> equal to the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code>.</p>
<p>The <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> and the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code> are alternate interior angles. Therefore, we can set them equal to one another.</p>
<p><code>\color{<var>BLUE</var>}{<var>A</var>x + <var>B</var>} = \color{<var>ORANGE</var>}{<var>C</var>x + <var>D</var>}</code></p>
</div>

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6 changes: 3 additions & 3 deletions exercises/corresponding_angles_2.html
Expand Up @@ -25,7 +25,7 @@
<div>
<p>The two horizontal lines are parallel, and there is a third line that intersects them as shown below.</p>
<p class="question">Solve for <code>x</code>:</p>
<p class="solution" data-forms="integer"><var>SOLUTION</var></p>
<p class="solution" data-type="rational"><var>SOLUTION</var></p>
<div class="graphie" id="parallel-lines">

var eq1 = A + "x + " + B + "^\\circ";
Expand All @@ -44,9 +44,9 @@
</div>

<div class="hints">
<p>We learned in Corresponding Angles 1 that vertical angles are equal. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals" data-youtube-id="H-E5rlpCVu4">Watch this video</a> to understand why.</p>
<p>Corresponding angles are equal to one another. <a class="related-video" href="/video/angles-formed-by-parallel-lines-and-transversals" data-youtube-id="H-E5rlpCVu4">Watch this video</a> to understand why.</p>
<div>
<p>Set the angle measures equal to one another.</p>
<p>The <code>\color{<var>BLUE</var>}{\text{blue angle}}</code> and the <code>\color{<var>ORANGE</var>}{\text{orange angle}}</code> are corresponding angles. Therefore, we can set them equal to one another.</p>
<p><code>\color{<var>BLUE</var>}{<var>A</var>x + <var>B</var>} = \color{<var>ORANGE</var>}{<var>C</var>x + <var>D</var>}</code></p>
</div>

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111 changes: 111 additions & 0 deletions exercises/one_step_equations_0.5.html
@@ -0,0 +1,111 @@
<!DOCTYPE html>
<html data-require="math math-format expressions">
<head>
<meta charset="UTF-8" />
<title>One-step equations 0.5</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="LETTERS">"abkmnpvxy"</var>
<var id="X">LETTERS.charAt( randRange( 0, LETTERS.length - 1 ) )</var>
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Maybe we need a randFromString helper.

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Or just randFromArray( "abkmnpvxy".split( "" ) ).

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Or randVar()

</div>
<div class="problems">
<div id="add-subtract" data-weight="4">
<div class="vars" data-ensure="Y !== Z">
<var id="INDEX">randRange( 0, 1 )</var>
<var id="Y">randRangeNonZero( -20, 19 )</var>
<var id="Z" data-ensure="Z > Y">randRange( 1, 20 )</var>
<var id="Y_SIGN">Y > 0 ? "-" : "+"</var>
<var id="LEFT">[expr( ["+", X, Y] ), Z][INDEX]</var>
<var id="RIGHT">[Z, expr( ["+", X, Y] )][INDEX]</var>
</div>
<p class="question">Solve for <var>X</var>.</p>
<p><code>\large{<var>LEFT</var> = <var>RIGHT</var>}</code></p>
<div class="solution" data-forms="integer"><var>Z - Y</var></div>
<div class="hints">
<div>
<p><var>Y > 0 ? "Subtract" : "Add"</var> <var>abs(Y)</var> <var>Y > 0 ? "from" : "to"</var> both sides.</p>
<p data-if="INDEX === 0"><code>\large{<var>X</var>\color{blue}{<var>Y_SIGN</var><var>abs( Y )</var>} = <var>RIGHT</var>\color{blue}{<var>Y_SIGN</var><var>abs( Y )</var>}}</code></p>
<p data-else><code>\large{<var>LEFT</var>\color{blue}{<var>Y_SIGN</var><var>abs( Y )</var>} = <var>X</var>\color{blue}{<var>Y_SIGN</var><var>abs( Y )</var>}}</code></p>
</div>
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I wonder if it makes sense to split this into two hints. It could be that people know how to add/subtract to/from both sides but don't know that they should?

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Like it - added.

<div>
<p>Simplify.</p>
<div data-if="INDEX === 0">
<p><code>\large{<var>X</var> = <var>Z - Y</var>}</code></p>
</div>
<div data-else>
<p><code>\large{<var>Z - Y</var> = <var>X</var>}</code></p>
</div>
</div>
</div>
</div>
<div id="multiply" data-weight="2">
<div class="vars">
<var id="INDEX">randRange( 0, 1 )</var>
<var id="Y">randRange( 2, 10 )</var>
<var id="Z">randRange( 1, 9) * Y</var>
<var id="LEFT">[expr( ["*", Y, X] ), Z][INDEX]</var>
<var id="RIGHT">[Z, expr( ["*", Y, X] )][INDEX]</var>
</div>
<p class="question">Solve for <var>X</var>.</p>
<p><code>\large{<var>LEFT</var> = <var>RIGHT</var>}</code></p>
<div class="solution" data-type="rational"><var>Z / Y</var></div>
<div class="hints">
<div data-if="INDEX === 0">
<p>Divide both sides by <var>Y</var>.</p>
<p><code>\large{\dfrac{<var>X</var>}{\color{blue}{<var>Y</var>}} = \dfrac{<var>Z</var>}{\color{blue}{<var>Y</var>}}}</code></p>
</div>
<div data-else>
<p>Divide both sides by <var>Y</var>.</p>
<p><code>\large{\dfrac{<var>Z</var>}{\color{blue}{<var>Y</var>}} = \dfrac{<var>X</var>}{\color{blue}{<var>Y</var>}}}</code></p>
</div>
<div>
<p>Simplify.</p>
<div data-if="INDEX === 0">
<p><code>\large{<var>X</var> = <var>Z / Y</var>}</code></p>
</div>
<div data-else>
<p><code>\large{<var>Z / Y</var> = <var>X</var>}</code></p>
</div>
</div>
</div>
</div>
<div id="divide" data-weight="1">
<div class="vars">
<var id="INDEX">randRange( 0, 1 )</var>
<var id="Y">randRange( 2, 10 )</var>
<var id="Z">randRange( 2, 10)</var>
</div>
<p class="problem"><b>Solve for <var>X</var>.</b></p>
<p class="question"><code>\large{\dfrac{<var>X</var>}{<var>Y</var>} = <var>Z</var>}</code></p>
<div class="solution" data-type="rational"><var>Z * Y</var></div>
<div class="hints">
<div>
<p>Multiply both sides by <var>Y</var>.</p>
<p><code>\large{\dfrac{<var>X</var>}{<var>Y</var>} \cdot {\color{blue}{<var>Y</var>}} = <var>Z</var> \cdot {\color{blue}{<var>Y</var>}}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>\large{<var>X</var> = <var>Z * Y</var>}</code></p>
</div>
</div>
</div>
<div id="divide-right" data-type="divide" data-weight="1">
<p class="question"><code>\large{<var>Z</var> = \dfrac{<var>X</var>}{<var>Y</var>}}</code></p>
<div class="hints">
<div>
<p>Multiply both sides by <var>Y</var>.</p>
<p><code>\large{<var>Z</var> \cdot {\color{blue}{<var>Y</var>}} = \dfrac{<var>X</var>}{<var>Y</var>} \cdot {\color{blue}{<var>Y</var>}}}</code></p>
</div>
<div>
<p>Simplify.</p>
<p><code>\large{<var>Z * Y</var> = <var>X</var>}</code></p>
</div>
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Maybe an extra X = ZY hint at the end?

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Like it - added.

</div>
</div>
</div>
</div>
</body>
</html>