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	Comments on: What Can You Do With This: Annuli	</title>
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		By: Ticket Roll Reworked &#124; Zero-Knowledge Proofs		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-953159</link>

		<dc:creator><![CDATA[Ticket Roll Reworked &#124; Zero-Knowledge Proofs]]></dc:creator>
		<pubDate>Wed, 26 Jun 2013 01:09:14 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-953159</guid>

					<description><![CDATA[[...] first time Dan Meyer came to Edmonton, he had us work on this problem. It was engaging, and a room full of teachers dug right in. The second time he came to Edmonton, he [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] first time Dan Meyer came to Edmonton, he had us work on this problem. It was engaging, and a room full of teachers dug right in. The second time he came to Edmonton, he [&#8230;]</p>
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		<title>
		By: Teaching for Perplexity &#124; The 2013 Sudbury Sessions		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-899107</link>

		<dc:creator><![CDATA[Teaching for Perplexity &#124; The 2013 Sudbury Sessions]]></dc:creator>
		<pubDate>Sun, 19 May 2013 17:52:21 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-899107</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		By: The 2013 Reading Sessions &#124; Perplexity Keynote		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-894124</link>

		<dc:creator><![CDATA[The 2013 Reading Sessions &#124; Perplexity Keynote]]></dc:creator>
		<pubDate>Sat, 18 May 2013 16:38:49 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-894124</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		<title>
		By: The 2013 21CLHK Sessions &#124; Perplexity Keynote		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-686243</link>

		<dc:creator><![CDATA[The 2013 21CLHK Sessions &#124; Perplexity Keynote]]></dc:creator>
		<pubDate>Mon, 21 Jan 2013 03:01:48 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-686243</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		<title>
		By: The 2012 Blue Ribbon Sessions &#124; Perplexity		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-600735</link>

		<dc:creator><![CDATA[The 2012 Blue Ribbon Sessions &#124; Perplexity]]></dc:creator>
		<pubDate>Wed, 05 Dec 2012 20:11:24 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-600735</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		<title>
		By: The 2012 CMC Sessions &#124; Modern Math Teaching		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-593667</link>

		<dc:creator><![CDATA[The 2012 CMC Sessions &#124; Modern Math Teaching]]></dc:creator>
		<pubDate>Fri, 30 Nov 2012 00:55:08 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-593667</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		<title>
		By: The 2012 MISD Sessions &#124; Modern Math Teaching		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-564227</link>

		<dc:creator><![CDATA[The 2012 MISD Sessions &#124; Modern Math Teaching]]></dc:creator>
		<pubDate>Tue, 06 Nov 2012 14:55:38 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-564227</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		<title>
		By: The 2012 NCTM â€” Dallas Sessions &#124; Modern Math Teaching		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-533279</link>

		<dc:creator><![CDATA[The 2012 NCTM â€” Dallas Sessions &#124; Modern Math Teaching]]></dc:creator>
		<pubDate>Mon, 08 Oct 2012 20:57:00 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-533279</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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		<title>
		By: Randy Blackwood		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-492437</link>

		<dc:creator><![CDATA[Randy Blackwood]]></dc:creator>
		<pubDate>Sat, 18 Aug 2012 04:18:24 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-492437</guid>

					<description><![CDATA[Today was our first day of school, so as an intro activity in my PreAP Algebra 2 class,  I took an old roll of tickets that was being thrown away last summer and as the students came in the door, I would greet them, write their seat number on the ticket and hand it to them.  After the some typical 1st day logistics.  I held up the roll of tickets I had and asked them what they would want to know about the roll.  After some thought the typical question was &quot;Hhow many tickets were on the row?&quot;  I wish I could have recorded the discussion in my 2nd hr.  I had a student who proposed measuring the thickness of the ticket, count how many tickets were on the outer layer, measure the width of the roll to determine how many layers there were.  After some discussion another student piped up, but the inner diameter doesn&#039;t have as many tickets.  So we decided to try the first method anyhow, as I said well at least we will know the maximum number of tickets there would be.  I think our calculations were around 1300.  Then another student proposed averaging the number on the inner layer with the outer layer for a better estimate.  I believe the number was around 910.   I used a set of micrometers to measure the thickness of the ticket, and a set of calipers to measure the length of the ticket, as well as diameters, etc.
It was amazing how accurate the correct calculation was.  Prior to class the roll had 1000 tickets.  When I did the measurements I calculated 999.5  After the second hour class I think the number of tickets left was around 940.  I don&#039;t remember the calculated number but is was within 8 of the actual number.  And after my last class of students they calculated 914 tickets, when the actual number should have been about 910.  Pretty awesome stuff.]]></description>
			<content:encoded><![CDATA[<p>Today was our first day of school, so as an intro activity in my PreAP Algebra 2 class,  I took an old roll of tickets that was being thrown away last summer and as the students came in the door, I would greet them, write their seat number on the ticket and hand it to them.  After the some typical 1st day logistics.  I held up the roll of tickets I had and asked them what they would want to know about the roll.  After some thought the typical question was &#8220;Hhow many tickets were on the row?&#8221;  I wish I could have recorded the discussion in my 2nd hr.  I had a student who proposed measuring the thickness of the ticket, count how many tickets were on the outer layer, measure the width of the roll to determine how many layers there were.  After some discussion another student piped up, but the inner diameter doesn&#8217;t have as many tickets.  So we decided to try the first method anyhow, as I said well at least we will know the maximum number of tickets there would be.  I think our calculations were around 1300.  Then another student proposed averaging the number on the inner layer with the outer layer for a better estimate.  I believe the number was around 910.   I used a set of micrometers to measure the thickness of the ticket, and a set of calipers to measure the length of the ticket, as well as diameters, etc.<br />
It was amazing how accurate the correct calculation was.  Prior to class the roll had 1000 tickets.  When I did the measurements I calculated 999.5  After the second hour class I think the number of tickets left was around 940.  I don&#8217;t remember the calculated number but is was within 8 of the actual number.  And after my last class of students they calculated 914 tickets, when the actual number should have been about 910.  Pretty awesome stuff.</p>
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		<title>
		By: The 2012 MCTM Sessions &#124; Keynote		</title>
		<link>/2010/what-can-you-do-with-this-annuli/#comment-427080</link>

		<dc:creator><![CDATA[The 2012 MCTM Sessions &#124; Keynote]]></dc:creator>
		<pubDate>Fri, 04 May 2012 02:25:02 +0000</pubDate>
		<guid isPermaLink="false">/?p=7119#comment-427080</guid>

					<description><![CDATA[[...] LinkThe Ticket Roll [...]]]></description>
			<content:encoded><![CDATA[<p>[&#8230;] LinkThe Ticket Roll [&#8230;]</p>
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