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07bc801b-3ab1-4603-8c9b-6081492f1097.html
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<!--Do not edit this div tag. It must surround the interaction block-->
<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="c305eb60-f955-4d60-b8ca-09013aef98d6" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--1a-->
<div class="os-raise-ib-pset-problem" data-content-id="d58381a9-a116-4e2c-81b3-94b5b3cd37d1" data-problem-comparator="integer" data-problem-type="input" data-solution="16">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>Here are two patterns of dots.</li>
</ol>
<p>Pattern A</p>
<p><img alt="Four figures, labeled step 0 through 3. Step 0, no dots. Step 1, row of 4 dots. Step 2, 2 rows of 4 dots each. Step 3, 3 rows of 4 dots each." src="https://k12.openstax.org/contents/raise/resources/3c9a638d3d94a27279cdb7074d8c6646bb9233b2"></p>
<p>Pattern B</p>
<p><img alt="Four figures, step 0 through 3. Step 0, 2 dots. Step 1 row of 1 dot above a row of 2 dots. Step 2, 2 rows of 2 dots each, above a row of 2 dots. Step 3, 3 rows of 3 dots each, above row of 2 dots." class="img-fluid atto_image_button_text-bottom" height="120" src="https://k12.openstax.org/contents/raise/resources/09162edcf5ac5e0e874b3d0a4bf64423e00003e7" width="422"></p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li> How many dots will there be in Step 4 of Pattern A?</li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! There will be 4 rows and 4 columns in Step 4.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.2.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 16.
</p>
</div>
</div>
<!--1b-->
<div class="os-raise-ib-pset-problem" data-content-id="bedc6d9a-4d0e-4890-901f-10b2428b8966" data-problem-comparator="integer" data-problem-type="input" data-solution="18">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> How many dots will there be in Step 4 of Pattern B?</li>
</ol>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The relationship is \(n^2+2\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.2.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 18.
</p>
</div>
</div>
<!--1c-->
<div class="os-raise-ib-pset-problem" data-content-id="78ee8dd0-f16f-48fb-9102-636e1d540108" data-problem-type="dropdown" data-retry-limit="1" data-solution="Pattern B" data-solution-options='["Pattern A", "Pattern B"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> Which pattern shows a quadratic relationship between the step number and the number of dots?</li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The relationship is \(n^2+2\).</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.2.3 and 7.2.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is Pattern B. This is because the relationship is \(n^2+2\).
</p>
</div>
</div>
<!--q2-->
<div class="os-raise-ib-pset-problem" data-content-id="5df82e90-55ae-44d5-ad83-882333ba247f" data-problem-type="multiselect" data-solution='["\\(n^2\\)", "\\(n \\cdot n\\)"]' data-solution-options='["\\(n^2\\)", "\\(2n\\)", "\\(n \\cdot n\\)", "\\(n+n\\)", "\\(n+2\\)", "\\(n \\div 2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>Each expression represents the total number of dots in a pattern where \(n\) represents the step number.</li>
</ol>
<p><strong>Select two</strong> expressions that represent a quadratic relationship between the step number and the total number of dots. (If you get stuck, consider sketching the first few steps of each pattern as described by the expression.)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.2.3 and 7.2.4.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are \(n^2\) and \(n \cdot n\).
</p>
</div>
</div>
<!--3a-->
<div class="os-raise-ib-pset-problem" data-content-id="2937ceb9-af8f-40b1-8969-71308b1f2a66" data-problem-comparator="integer" data-problem-type="input" data-solution="32">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>Use the pattern below to answer the questions.</li>
</ol>
<p><img height="155" src="https://k12.openstax.org/contents/raise/resources/951371a3b6b1037f7931fc4c9383339fea0673c6" width="419"></p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li> How many blocks are in Step 4? </li>
</ol>
</ol>
<p> Enter your answer here: </p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The length is always \(n+2\), the width is always \(n+2\), and then \(n\) blocks are subtracted.
</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.3.2 and 7.3.4.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 32.
</p>
</div>
</div>
<!--3b-->
<div class="os-raise-ib-pset-problem" data-content-id="6e40b6dc-235c-482f-a9cc-eeada42e60f2" data-problem-comparator="integer" data-problem-type="input" data-solution="44">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> How many blocks are in Step 5?</li>
</ol>
</ol>
<p> Enter your answer here: </p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The length is always \(n+2\), the width is always \(n+2\), and then \(n\) blocks are subtracted.
</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.3.2 and 7.3.4.
</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 44.
</p>
</div>
</div>
<!--3c-->
<div class="os-raise-ib-pset-problem" data-content-id="fdbe403b-0f9a-4799-ae16-bfce47321e47" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((n+2)^2-n\)" data-solution-options='["\\(n^2-2\\)", "\\(n+6\\)", "\\((n+2)^2-n\\)", "\\((n+2)^2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> How many blocks are in Step \(n\)?</li>
</ol>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The length is always \(n+2\), the width is \(n+2\), and then \(n\) blocks are subtracted.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.3.2–7.3.4. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((n+2)^2-n\).
</p>
</div>
</div>
<!--Do not edit below this line-->
<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>