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July 12, 2011 01:26
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| <!DOCTYPE html> | |
| <html data-require="math expressions"> | |
| <head> | |
| <title>Writing Expressions 2</title> | |
| <script src="../khan-exercise.js"></script> | |
| </head> | |
| <body> | |
| <!--1. I am including all the comments here for logic | |
| I also have 6 problem types which is a little excessive (4 is probably enough) | |
| but 6 is the smallest number that gives each | |
| 2. I wrote up all the intermediate hints and put them in the right order for each problem type | |
| but I didn't put it in the code (they are commented out) because I don't know how the hint system will be coded | |
| 3. This means there are a lot of comments in this code, but I think that they are all useful | |
| --> | |
| <!-- COMMENTS FOR LOGIC, actual code below long comment section | |
| Questions can be: | |
| class = "problem" is constant | |
| class = middle" is constant | |
| class = "question" can be: | |
| 1 <p class="question">the sum of <code><var>A</var></code> and the product of <code><var>B</var></code> and <code>x</code></p> | |
| 2 <p class="question">the sum of <code><var>A</var></code> and the quantity of <code><var>B</var></code> times <code>x</code></p> | |
| 3 <p class="question"><code><var>A</var></code> plus the product of <code><var>B</var></code> and <code>x</code></p> | |
| 4 <p class="question"><code><var>A</var></code> plus the quantity of <code><var>B</var></code> times <code>x</code></p> | |
| 5 <p class="question">Take the the product of <code><var>B</var></code> and <code>x</code> and add <code><var>A</var></code>.</p> | |
| 6 <p class="question">Take the quantity of <code><var>B</var></code> times <code>x</code> and add <code><var>A</var></code>.</p> | |
| class = "part-two" can be: | |
| 1 <p class="part-two"><b>the sum of <code><var>D</var></code> and the product of <code><var>C</var></code> and that expression</b> | |
| 2 <p class="part-two"><b>the sum of <code><var>D</var></code> and the quantity of <code><var>C</var></code> times that expression</b> | |
| 3 <p class="part-two"><b><code><var>D</var></code> plus the product of <code><var>C</var></code> and that expression</b> | |
| 4 <p class="part-two"><b><code><var>D</var></code> plus the quantity of <code><var>C</var></code> times that expression</b> | |
| 5 <p class="part-two"><b>Take the product of <code><var>C</var></code> and that expression and then add <code><var>D</var></code>.</b> | |
| 6 <p class="part-two"><b>Take the quantity of <code><var>C</var></code> times that expression and then add <code><var>D</var></code>.</b> | |
| six problem types are 1-4 2-3 3-6 4-5 5-2 6-1, this gives two of each type of phrase every six questions | |
| Hint1: ODD-EVEN for class = "question" (product / quantity) | |
| What is <span class="hint_orange">the product of <code><var>B</var></code> and <code>x</code></span>? | |
| What is <span class="hint_orange">the quantity of <code><var>B</var></code> times <code>x</code></span>? | |
| Hint2: 12 34 56 for class = "question"(the sum of / plus / and add) | |
| What is <span class="hint_blue">the sum of <code><var>A</var></code></span> and <code class="hint_orange"><var>expr(["*", B, "x"])</var></code>? | |
| What is <span class="hint_blue"><code><var>A</var></code> plus</span> <code class="hint_orange"><var>expr(["*", B, "x"])</var></code>? | |
| What does <span class="hint_blue">adding <code><var>A</var></code></span> to <code class="hint_orange"><var>expr(["*", B, "x"])</var></code> do? | |
| Hint3: ODD-EVEN for class = "part-two"(product / quantity) | |
| What is <span class="hint_orange">the product of <code><var>C</var></code> times that expression</span>? | |
| What is <span class="hint_orange">the quantity of <code><var>C</var></code> times that expression</span>? | |
| Hint 4: 12 34 56 for class = "part-two" (the sum of / plus / and add) | |
| What is <span class="hint_blue">the sum of <code><var>A</var></code></span> and <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code>? | |
| What is <span class="hint_blue"><code><var>A</var></code> plus</span> <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code>? | |
| What does <span class="hint_blue">adding <code><var>D</var></code></span> to <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code> do? | |
| --> | |
| <div class="exercise"> | |
| <div class="vars"> | |
| <var id="A">(random() > 0.5 ? -1 : 1) * (rand(9) + 1)</var> | |
| <var id="B">(random() > 0.5 ? -1 : 1) * (rand(9) + 1)</var> | |
| <var id="C">(random() > 0.5 ? -1 : 1) * (rand(9) + 1)</var> | |
| <var id="D">(random() > 0.5 ? -1 : 1) * (rand(9) + 1)</var> | |
| </div> <!-- C ( Bx + A ) + D is the expression we are creating --> | |
| <div class="problems"> | |
| <div id="original"> | |
| <div class="problem"> | |
| <p>First consider the expression for:</p> | |
| </div> | |
| <p class="question">The sum of <code><var>A</var></code> and the product of <code><var>B</var></code> and <code>x</code>.</p> | |
| <p class="middle">Now select the answer that matches the following:</p> | |
| <p class="part-two"><b><code><var>D</var></code> plus the quantity of <code><var>C</var></code> times that expression</b> | |
| <br><br> | |
| <code><var>expr(["+",["*", C,["+",["*", B, "x"], A]], D])</var></code></p> | |
| <p class="solution"><code><var>expr(["+",["*", C,["+",["*", B, "x"], A]], D])</var></code></p> | |
| <!-- Solution: C ( A + Bx ) + D, wrong 1: -C SAME, wrong 2: -C (B + Ax) - D, wrong 3: D ( -A + Bx ) + C, wrong 4: D ( -B + Ax ) + C --> | |
| <ul class="choices" data-show="5" data-none="true"> | |
| <li><code><var>expr(["+",["*", -C,["+",["*", B, "x"], A]], D])</var></code></li> | |
| <li><code><var>expr(["+",["*", -C,["+",["*", A, "x"], B]], D])</var></code></li> | |
| <li><code><var>expr(["+",["*", D,["+",["*", B, "x"], -A]], C])</var></code></li> | |
| <li><code><var>expr(["+",["*", D,["+",["*", A, "x"], -B]], C])</var></code></li> | |
| </ul> | |
| <div class="hints" data-apply="appendContents"> | |
| <!-- | |
| What is <span class="hint_orange">the product of <code><var>B</var></code> and <code>x</code></span>?</p> | |
| What is <span class="hint_blue">the sum of <code><var>A</var></code></span> and <code class="hint_orange"><var>expr(["*", B, "x"])</var></code>?</p> | |
| What is <span class="hint_orange">the quantity of <code><var>C</var></code> times that expression</span>?</p> | |
| What is <span class="hint_blue"><code><var>A</var></code> plus</span> <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code>?</p> | |
| --> | |
| </div> | |
| </div> | |
| <div id="type-2" data-type="original"> | |
| <p class="question">the sum of <code><var>A</var></code> and the quantity of <code><var>B</var></code> times <code>x</code></p> | |
| <p class="part-two"><b><code><var>D</var></code> plus the product of <code><var>C</var></code> and that expression</b> | |
| <div class="hints" data-apply="appendContents"> | |
| <!-- | |
| What is <span class="hint_orange">the quantity of <code><var>B</var></code> times <code>x</code></span>?</p> | |
| What is <span class="hint_blue">the sum of <code><var>A</var></code></span> and <code class="hint_orange"><var>expr(["*", B, "x"])</var></code>?</p> | |
| What is <span class="hint_orange">the product of <code><var>C</var></code> times that expression</span>?</p> | |
| What is <span class="hint_blue"><code><var>A</var></code> plus</span> <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code>?</p> | |
| --> | |
| </div> | |
| </div> | |
| <div id="type-3" data-type="original"> | |
| <p class="question"><code><var>A</var></code> plus the product of <code><var>B</var></code> and <code>x</code></p> | |
| <p class="part-two"><b>Take the quantity of <code><var>C</var></code> times that expression and then add <code><var>D</var></code>.</b> | |
| <div class="hints" data-apply="appendContents"> | |
| <!-- | |
| What is <span class="hint_orange">the product of <code><var>B</var></code> and <code>x</code></span>?</p> | |
| What is <span class="hint_blue"><code><var>A</var></code> plus</span> <code class="hint_orange"><var>expr(["*", B, "x"])</var></code>?</p> | |
| What is <span class="hint_orange">the quantity of <code><var>C</var></code> times that expression</span>?</p> | |
| What does <span class="hint_blue">adding <code><var>D</var></code></span> to <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code> do?</p> | |
| --> | |
| </div> | |
| </div> | |
| <div id="type-4" data-type="original"> | |
| <p class="question"><code><var>A</var></code> plus the quantity of <code><var>B</var></code> times <code>x</code></p> | |
| <p class="part-two"><b>Take the product of <code><var>C</var></code> and that expression and then add <code><var>D</var></code>.</b> | |
| <div class="hints" data-apply="appendContents"> | |
| <!-- | |
| What is <span class="hint_orange">the quantity of <code><var>B</var></code> times <code>x</code></span>?</p> | |
| What is <span class="hint_blue"><code><var>A</var></code> plus</span> <code class="hint_orange"><var>expr(["*", B, "x"])</var></code>?</p> | |
| What is <span class="hint_orange">the product of <code><var>C</var></code> times that expression</span>?</p> | |
| What does <span class="hint_blue">adding <code><var>D</var></code></span> to <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code> do?</p> | |
| --> | |
| </div> | |
| </div> | |
| <div id="type-5" data-type="original"> | |
| <p class="question">Take the the product of <code><var>B</var></code> and <code>x</code> and add <code><var>A</var></code>.</p> | |
| <p class="part-two"><b>The sum of <code><var>D</var></code> and the product of <code><var>C</var></code> and that expression.</b> | |
| <div class="hints" data-apply="appendContents"> | |
| <!-- | |
| What is <span class="hint_orange">the product of <code><var>B</var></code> and <code>x</code></span>?</p> | |
| What does <span class="hint_blue">adding <code><var>A</var></code></span> to <code class="hint_orange"><var>expr(["*", B, "x"])</var></code> do?</p> | |
| What is <span class="hint_orange">the quantity of <code><var>C</var></code> times that expression</span>?</p> | |
| What is <span class="hint_blue">the sum of <code><var>A</var></code></span> and <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code>?</p> | |
| --> | |
| </div> | |
| </div> | |
| <div id="type-6" data-type="original"> | |
| <p class="question">Take the quantity of <code><var>B</var></code> times <code>x</code> and add <code><var>A</var></code>.</p> | |
| <p class="part-two"><b>the sum of <code><var>D</var></code> and the product of <code><var>C</var></code> and that expression</b> | |
| <div class="hints" data-apply="appendContents"> | |
| <!-- | |
| What is <span class="hint_orange">the quantity of <code><var>B</var></code> times <code>x</code></span>?</p> | |
| What does <span class="hint_blue">adding <code><var>A</var></code></span> to <code class="hint_orange"><var>expr(["*", B, "x"])</var></code> do?</p> | |
| What is <span class="hint_orange">the product of <code><var>C</var></code> times that expression</span>?</p> | |
| What is <span class="hint_blue">the sum of <code><var>A</var></code></span> and <code>\color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code>?</p> | |
| --> | |
| </div> | |
| </div> | |
| </div> | |
| <div class="hints"> | |
| <p>Let's break this problem into smaller and easier pieces.</p> | |
| <p id="hint1"></p> <!-- What is <span class="hint_orange">the product of B and x</span>? --> | |
| <p><code><var>B</var> \times x = \color{orange}{<var>expr(["*", B, "x"])</var>}</code></p> | |
| <p id="hint2"></p> <!-- What is <span class="hint_orange">the sum of Bx</span> and <span class="hint_blue">A</span>? --> | |
| <p><code class="hint_orange"><var>B</var>x</code><code class="hint_blue">{} + <var>A</var></code></p> | |
| <p id="hint3"></p> <!-- What is <span class="hint_orange">the quantity of C times that expression</span>? --> | |
| <p><code><var>C</var> \times (<var>B</var>x + <var>A</var>) = \color{orange}{<var>expr(["*", C,["+",["*", B, "x"], A]])</var>}</code></p> | |
| <p id="hint4"></p> <!-- What does <span class="hint_blue">adding D do</span>? --> | |
| <p><code class="hint_orange"><var>expr(["*", C,["+",["*", B, "x"], A]])</var></code><code class="hint_blue">{} + <var>D</var></code></p> | |
| <p>Answer: The entire expression can be written as <code><var>expr(["+",["*", C,["+",["*", B, "x"], A]], D])</var></code></p> | |
| </div> | |
| </div> | |
| </body> | |
| </html> |
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