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<h4>Activity</h4>
<p>In questions 1-3:</p>
<blockquote>
<p>Write as many equations as possible that could represent the relationship between the ages of the
two children in each family described. Be prepared to explain what each part of your equation represents.
</p>
</blockquote>
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="66bf9074-d792-4631-90df-9e43ac474cfb" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>In Family A, the youngest child is 7 years younger than the oldest, who is 18.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here are some samples. <br>
For \(y\), the age of the youngest child:
</p>
<ul>
<li>\( y=18-7\) </li>
<li>\(y+7=18\) </li>
<li>\(18-y=7\) </li>
</ul>
<p>Where 11 is the age of the youngest child:
</p>
<ul>
<li>\(18-7=11\) </li>
<li>\(11+7=18\) </li>
<li>\(18-11=7\) </li>
</ul>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="9e57e254-fbbc-4cfc-b970-39b64caa0421" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>In Family B, the middle child is 5 years older than the youngest child.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here are some samples. <br>
For \(m\), the age of the middle child, and \(y\), the age of the youngest
</p>
<ul>
<li>\(m = y + 5\) </li>
<li>\(y = m - 5\) </li>
</ul>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="9354c775-f16e-4d62-b86b-271d83b06498" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Tyler thinks that the relationship between the ages of the children in Family B can be described with
\(2m-2y=10\), where \(m\) is the age of the middle child and \(y\) is the age of the youngest. Describe how
Tyler came up with this equation.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here ares some samples. <br>
The equation \(m=y+5\), represents the relationship of the ages in Family B, where \(m\) is the age of the middle child
and \(y\) the age of the youngest. Subtracting \(y\) from both sides of the equation and multiplying both sides by
2 results in the equation: \(2m−2y=10\).
</p>
<ul>
<li>When the middle child is 12, the youngest child is 7, and that substituting \(m = 12\) and \(y = 7\) to \(2m - 2y\) gives \(2(12) - 2(7)\) or \(24-14\), which is 10. At all other ages of the two children, the expression \(2m - 2y\) always has a value of 10.</li>
<li>\(2m - 2y = 10\) is twice of \(m - y = 5\). If the difference between m and y is 5, then twice the difference between m and y must be twice of 5, which is 10, so the two equations are still describing the same relationship.</li>
</ul>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="21960cf7-1b6f-4b97-9289-b9aa182c5b55" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q4-->
<div class="os-raise-ib-pset-problem" data-content-id="0fbc11a7-15ba-4119-b47d-156bb3351d1a" data-problem-type="multiselect" data-solution='["\\(3a=9\\)", "\\(\\frac{1}{3} a =1\\)", "\\(a+2=5\\)"]' data-solution-options='["\\(a + 3 =12\\)", "\\(3a=9\\)", "\\(\\frac{1}{3} a =1\\)", "\\(a+2=5\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li><strong>Select three</strong> equations that are equivalent to \(3a + 6 = 15\).
</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answers are \(\frac{1}{3}a=1\), \(a+2=5\), and \(3a=9\). </p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q5-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="522c9289-862e-4fc2-8c0d-fe0d144280a5" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>Explain your reasoning for the equivalent equations in number 4.
</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here are some samples.
</p>
<ul>
<li>The equation \(3a + 6=15\) can be divided by 3 on both sides and becomes \(a +2 = 5\).</li>
<li>When 6 is subtracted from both sides of the equation \(3a +6 = 15\), the equation becomes 3a = 9.</li>
<li>When the equation \(3a + 6 = 15\) has 6 subtracted from both sides and becomes \(3a = 9\), then both sides are
divided by 9, the equivalent equation is \(\frac{1}{3} a = 1\).</li>
</ul>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Start interaction. If multiple interactions appear under "are you ready for more?, they should all have matching "data-wait-for-event", which should also match the "data-fire-event" for the button. Note in this sample, they are all RFM1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="20591220-30a6-450d-968c-78e307aed6fd" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Here is a puzzle:</p>
<ul>
<li>\(m+m=N \)</li>
<li>\(N+N=p \)</li>
<li>\(m+p=Q\)</li>
<li>\(p+Q=? \)</li>
</ul>
<p>Write two expressions that are equivalent to \(p + Q\).</p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer: Your answer may vary, but here is a sample.</p>
<ul>
<li>\(2p+m \)</li>
<li>\(9m \)</li>
</ul>
</div>
</div>
<!--End interaction-->
<br>