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	<title>AskDrCallahan Blog &#187; math</title>
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	<link>http://askdrcallahan.com/blog</link>
	<description>-- Preparing Your Student for College and for Life --</description>
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		<title>What is the DANTES exam?</title>
		<link>http://askdrcallahan.com/blog/2010/08/31/what-is-the-dantes-exam/</link>
		<comments>http://askdrcallahan.com/blog/2010/08/31/what-is-the-dantes-exam/#comments</comments>
		<pubDate>Tue, 31 Aug 2010 06:00:21 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
				<category><![CDATA[College]]></category>
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		<category><![CDATA[math]]></category>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1093</guid>
		<description><![CDATA[defining the DANTES exam. ]]></description>
			<content:encoded><![CDATA[<h3>DANTES Subject Standardized Tests</h3>
<p>DSST Exams are exam series that are college subject specific. They are very similar to the final exams offered by the course subjects should you choose to take the course.</p>
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		<title>Preparing For College: Studying to Get Accepted</title>
		<link>http://askdrcallahan.com/blog/2010/08/24/preparing-for-college-studying-to-get-accepted/</link>
		<comments>http://askdrcallahan.com/blog/2010/08/24/preparing-for-college-studying-to-get-accepted/#comments</comments>
		<pubDate>Tue, 24 Aug 2010 06:00:40 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
				<category><![CDATA[College]]></category>
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		<category><![CDATA[exam]]></category>
		<category><![CDATA[getting]]></category>
		<category><![CDATA[getting into college]]></category>
		<category><![CDATA[homeschool]]></category>
		<category><![CDATA[into]]></category>
		<category><![CDATA[math]]></category>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1137</guid>
		<description><![CDATA[Getting ready for college means studying for the ACT, but it goes way beyond that. Check out these tips for getting ready for your future, not just your university. ]]></description>
			<content:encoded><![CDATA[<p>-       Accredited colleges will have a set ACT and/or SAT score required for entrance as an undergraduate freshman. The requirements are different for graduate and other professional degrees. What this means is, in order to get into their school you have to score high enough on the ACT (American College Test). The highest score is a 36. Many schools change their admission requirements periodically, so you need to check your individual school choice, but many schools require a 25 or higher to get into the school, and a 27 or higher to qualify for academic scholarships.</p>
<blockquote><p><strong> <span style="font-size: large;">If you have decided to go to Paris – now you look at the options for getting there. And – there is more than one. So it is for college – you are NOT to be focused on college YET. That comes later still. Right now we focus on learning from people who have already gone there before – who is living your dream? Who has already gone to Paris – start by asking them before you listen to the travel agencies – learn from the pros.</span></strong></p></blockquote>
<p>-       For more information about the ACT, where to take it, how to take it, how to study, and facts about the exam itself, you can check out their website:</p>
<p><a href="http://www.act.org/news/aapfacts.html">http://www.act.org/news/aapfacts.html</a></p>
<p>-       Most college websites provide information about their college’s entrance requirements. Check under “Admissions” or “Admission Requirements” some college websites hide this information under “Academics” as well, so just poke around the website see what you find.</p>
<p>-       Another way to find out what is required to get into a college is to ask people who attended the college you are interested in. With Facebook and other social media, it isn’t hard to connect with people. <strong> </strong></p>
<p>-       You can also email the professors. Most universities have a faculty page where you can get in touch with them and ask questions. Just locate their email and ask—they don’t mind answering questions. They are teachers, answering questions is what they do for a living .</p>
<p><strong> </strong></p>
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		<title>Creative Teaching: Hands-on Approach</title>
		<link>http://askdrcallahan.com/blog/2010/08/17/creative-teaching-hands-on-approach/</link>
		<comments>http://askdrcallahan.com/blog/2010/08/17/creative-teaching-hands-on-approach/#comments</comments>
		<pubDate>Tue, 17 Aug 2010 06:00:26 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
				<category><![CDATA[Algebra2With Trig]]></category>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1168</guid>
		<description><![CDATA[Find ways to incorporate math into the things your student enjoys already--you know, the things that are outside the classroom and not at a desk or kitchen table.]]></description>
			<content:encoded><![CDATA[<p>Kids will get bored with the same approach to math every class day. Not to mention, if math becomes only a textbook thing, they miss out on the opportunity to learn how to educate themselves not just from a book, but from the world around them. For this reason, today&#8217;s creative teaching idea is hands on activities.</p>
<p><a href="http://askdrcallahan.com/blog/wp-content/uploads/2010/07/Barrel-Racing-Szmurlo.jpg"><img class="aligncenter size-medium wp-image-1167" title="Barrel-Racing-Szmurlo" src="http://askdrcallahan.com/blog/wp-content/uploads/2010/07/Barrel-Racing-Szmurlo-239x300.jpg" alt="" width="239" height="300" /></a></p>
<p>Find ways to incorporate math into the things your student enjoys already&#8211;you know, the things that are outside the classroom and not at a desk or kitchen table. If they like horses and rodeos, do distance/rate/time equations (Algebra 1) at a barrel race. Consider attending a rodeo, and having classwork that day be to write down all of the barrel racing times, then come home and use that information to calculate how fast the horse was running in miles per hour.  When the math is connected to something the students are interested in already, then suddenly the math becomes interesting as well. <a href="http://www.askdrcallahan.com/HWHelp/?page_id=155">Click Here for Some lesson plans and activity ideas to get you started.</a></p>
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		<title>Getting to Know the CLEP test</title>
		<link>http://askdrcallahan.com/blog/2010/08/10/getting-to-know-the-clep-test/</link>
		<comments>http://askdrcallahan.com/blog/2010/08/10/getting-to-know-the-clep-test/#comments</comments>
		<pubDate>Tue, 10 Aug 2010 06:00:14 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1091</guid>
		<description><![CDATA[Now, every college has its own rules and regulations surrounding CLEP exams, how many you can take, etc, so be sure you check into those when considering the CLEP test, but DEFINITELY a good way to cut down on expenses ]]></description>
			<content:encoded><![CDATA[<p><a href="http://askdrcallahan.com/blog/wp-content/uploads/2010/08/images.jpg"><img class="alignleft size-full wp-image-1214" title="images" src="http://askdrcallahan.com/blog/wp-content/uploads/2010/08/images.jpg" alt="" width="259" height="194" /></a>A CLEP test is an examination you can take which, if you pass, will allow you to receive credit for a class—without having to <em>take</em> the class. And the cost of taking the exam is $72 (plus a few bucks assuming you buy a study book) That is substantially less than the $2-300 per class fee, not the mention—once you get a good grade on the CLEP test, you’re finished. You don’t have to go to class, take notes, pass exams, or write papers for that subject. You are walking away with an entire course’s credit hours under your belt and you didn’t even put in half the time, money, and effort that it would have cost to take the course. SMART move.</p>
<p>Most of the freshman level courses are called “Gen Eds” which stands for “General Education”—it is the courses colleges designate as the courses everyone at their university needs to take as a part of their college educational experience. Much of the material covered in these courses is review from high school material. Therefore, a lot of students will find it easy to CLEP out of their freshman 101/102 courses. We had a student once that CLEP-ed out of two years worth of college courses. So he ended up only have to pay tuition for 2 years, and he received a 4-year degree.</p>
<p>Now, every college has its own rules and regulations surrounding CLEP exams, how many you can take, etc, so be sure you check into those when considering the CLEP test, but DEFINITELY a good way to cut down on expenses (and hey, if you don’t HAVE to take the class, why take it?)</p>
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		<title>Getting the most for spending the least – Planning your degree.</title>
		<link>http://askdrcallahan.com/blog/2010/08/03/getting-the-most-for-spending-the-least-%e2%80%93-planning-your-degree/</link>
		<comments>http://askdrcallahan.com/blog/2010/08/03/getting-the-most-for-spending-the-least-%e2%80%93-planning-your-degree/#comments</comments>
		<pubDate>Tue, 03 Aug 2010 06:00:49 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1089</guid>
		<description><![CDATA[When you are headed to college there are other options besides scholarships to help you cut down the costs of college (of course, combined WITH scholarships and you could potentially create yourself an almost free college experience)

]]></description>
			<content:encoded><![CDATA[<p><strong> </strong></p>
<p>When you are headed to college there are other options besides scholarships to help you cut down the costs of college (of course, combined WITH scholarships and you could potentially create yourself an almost free college experience)</p>
<p>Consider taking the CLEP tests. Most schools will allow you to CLEP out of as many as 45 credit hours of school &#8211; and that is over one whole year.</p>
<p><span style="font-size: 13.3333px;">For military personnel, there is the DANTES program—which helps you take many CLEP, DANTE, and ECS (called “Credit-by-examination” tests) for free. Some options are available to civilians as well, but you will need to check.</span></p>
<p><a href="http://www.military.com/timesaving-programs/dantes-college-credit-by-examination-program">http://www.military.com/timesaving-programs/dantes-college-credit-by-examination-program</a></p>
<p>The website above is a great resource for testing information for military personnel and options open to civilians as well.</p>
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		<title>Preparing for College: Scholarships for Everybody</title>
		<link>http://askdrcallahan.com/blog/2010/08/02/preparing-for-college-scholarships-for-everybody/</link>
		<comments>http://askdrcallahan.com/blog/2010/08/02/preparing-for-college-scholarships-for-everybody/#comments</comments>
		<pubDate>Mon, 02 Aug 2010 06:00:54 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
				<category><![CDATA[College]]></category>
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		<category><![CDATA[scholarship]]></category>

		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1087</guid>
		<description><![CDATA[Not all scholarships are for athletes, academics, and minorities. ]]></description>
			<content:encoded><![CDATA[<p>So many scholarships are missed out on because students do not put forth the time and effort to apply. Sure, some require you to write an essay or to fill out forms, but do you realize how many papers you are signing up to write when you go to college? One essay on the front end to save you thousands of dollars is completely worth it.</p>
<p style="text-align: center;"><strong>You will never know what you might receive unless you apply.</strong></p>
<p>I had a friend in college who won a minority scholarship—full ride to an accredited private university&#8212;and he wasn’t a minority member. He had just applied for the scholarship and no one else had won.</p>
<p>Don’t overburden yourself with the competition factor, either. There are many people who apply for college scholarships, sure—but think about it: how many people do you know who <em>actually</em> received scholarships? Interested to know why?</p>
<p>According to scholarships.com,</p>
<p><em> </em></p>
<p><em><br />
</em></p>
<blockquote><p><em>“…so many of [the students] applying don&#8217;t take the time to properly read or follow the rules and answer the questions thoughtfully, or even correctly. Do everything correctly and you could be one of a small percentage of applicants who even gets considered. Here&#8217;s another way to look at it. What if you spent a total of 50 hours searching and applying for scholarships? And, after all that time and effort, you win two or three scholarships, totaling about $2,000. That&#8217;s $40 per hour, which is at least 4 to 5 times more than you can expect to get paid for doing pretty much any other activity or &#8220;job&#8221;. And that doesn&#8217;t even include the interest you&#8217;d be paying on that money, had you been forced to borrow it from a lender. Apply for as many scholarships as you can and you are bound to win something, provided you make sure to do everything you are asked and follow all of each scholarship provider&#8217;s instructions.”</em></p></blockquote>
<p><em> </em></p>
<p>There are scholarships for everybody, not just high school students. You can get scholarships for entering freshman, sophomores, juniors, seniors, transfer students, undergraduate students, graduate students and even adults who have long since been out of college. Scholarships are EVERYWHERE, for EVERYBODY.</p>
<p>Not all scholarships are for athletes, academics, and minorities. There are many scholarships for students with a GPA minimum of 2.5 (a totally achievable GPA, I might add).</p>
<p>If you don’t want to do the all of the searching to find the scholarships right for you, you might consider using a service like <a href="http://www.scholarships.com/">scholarships.com </a>to pair you up with scholarship options right for you. (Scholarships.com is totally free, whereas many others charge a fee for the same service)</p>
<p>Some scholarships only offer $1000 to the winner, and many students balk at the idea of putting forth a lot of effort just to get a $1000 scholarship because they consider $1000 to be a drop in a huge bucket when it comes to college expenses.</p>
<p>But I wouldn’t be too hasty. If you get several $1000 scholarships, you can put a nice dent in your college education, PLUS consider all of the textbooks and supplies you will have to buy&#8211;$1000 interest free would be fantastic, and it beats the socks off a bank loan—a debt most students carry on after college.</p>
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		<title>Supplementing your math courses</title>
		<link>http://askdrcallahan.com/blog/2010/07/30/supplementing-your-math-courses/</link>
		<comments>http://askdrcallahan.com/blog/2010/07/30/supplementing-your-math-courses/#comments</comments>
		<pubDate>Fri, 30 Jul 2010 06:00:04 +0000</pubDate>
		<dc:creator>Cassidy Cash</dc:creator>
				<category><![CDATA[Algebra2With Trig]]></category>
		<category><![CDATA[Calculus]]></category>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1073</guid>
		<description><![CDATA[Ideas on making math fun and exciting and going WAY beyond the textbook. ]]></description>
			<content:encoded><![CDATA[<p>Sometimes when you teach math, you might want to supplement the material. If you get a good math course, you do not necessarily need to add materials for a better education, but you might want to add things in to make it more fun.</p>
<p>For instance, if your kids are prone to asking the &#8220;why do I have to learn this?&#8221; question, you might choose to add in some activities with math instead of making every day a textbook day.</p>
<p>Some ideas for supplementing material might be to study area by measuring the area of each room in your house, then adding it together to get the area of your whole house. Students often have fun (and a lot of laughs) trying to measure around furniture, etc. If you&#8217;re brave, you can measure the attic too!</p>
<p>Some other ideas I&#8217;ve found is when students like to say &#8220;I will never use this after school&#8221;, instead of trying to argue with them, I offer a challenge:</p>
<p>&#8220;Ok,&#8221; I say, &#8220;If you are so sure you&#8217;re right about that, I challenge you to go through an entire day&#8211;from the moment you get up, until the moment you go to bed again&#8211;you cannot use any math. No numbers, no figures, no adding, subtracting, algebra, or geometry, or anything. No math at all.&#8221;</p>
<p>&#8220;no homework?!&#8221; they immediately ask. Which, I concede, &#8220;No, not even homework.&#8221;</p>
<p>So we try it. Then they are surprised to learn that they immediately can&#8217;t tell time, can&#8217;t cook anything, can&#8217;t drive, can&#8217;t read road signs, can&#8217;t buy anything at the store, can&#8217;t count their allowance, can&#8217;t pack a suitcase (because you have to know how many of each clothing item you might need&#8211;that&#8217;s math). They can&#8217;t even use the remote, because that&#8217;s channels&#8211;that&#8217;s math.</p>
<p>Math is everywhere in life, it is the fabric things are made of. Without math, the world could not function. But rather than try to talk your kids into this belief, it is easier to show them.</p>
<p>This kind of supplementation is called &#8220;real world activities&#8221; it gets your kids out of the desk and into the world around them. Math can be fun, and real for students, if you look for creative ways to do it.</p>
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		<title>MIT uses same textbooks as AskDrCallahan</title>
		<link>http://askdrcallahan.com/blog/2010/07/27/mit-uses-same-textbooks-as-askdrcallahan/</link>
		<comments>http://askdrcallahan.com/blog/2010/07/27/mit-uses-same-textbooks-as-askdrcallahan/#comments</comments>
		<pubDate>Tue, 27 Jul 2010 15:46:08 +0000</pubDate>
		<dc:creator>Dr. Callahan</dc:creator>
				<category><![CDATA[Calculus]]></category>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1064</guid>
		<description><![CDATA[MIT uses same textbook as AskDrCallahan. They even break their course work up the way we do. We also tell you about their awesome openware program so you can take MIT courses at home. Check it out!]]></description>
			<content:encoded><![CDATA[<p>One of our customers contacted us today because he took our Calculus 1 course. He wanted to take Calculus 2, but since AskDrCallahan didn&#8217;t offer a DVD course for Calculus 2, he decided to take it at MIT.</p>
<p style="text-align: center;"><img class="aligncenter" src="http://www.mranderson-frhsd.com/mranderson/calculus.jpg" alt="" width="367" height="244" /></p>
<p>We loved the fact that MIT was second to us in his list of options. Ha!</p>
<p>Anyway, he was emailing us because MIT&#8217;s Openware courses (<a href="http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/index.htm">which you can view here</a>) were saying that they used the same textbook as we were using, so they contacted us about whether or not that is the book we would use.</p>
<p>If you&#8217;re interested as well, YES we would. The book we chose for Calculus 1 actually contains enough material to teach Calculus 1-3. Different schools break it up a little differently, so it depends on what school you&#8217;re dealing with as to what they consider the &#8220;division points&#8221; for each course, but we think it is pretty neat that MIT chose the same thing we did. <img src='http://askdrcallahan.com/blog/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
<p>Their openware courses are actually a great option for parents if you&#8217;re interested in teaching Calculus 2 or 3 in high school. (and yes, some people do!)They don&#8217;t do video, but still it is MIT at home. We thought it was a cool option.</p>
<p>MIT seems to follow a course plan of</p>
<p>18.01</p>
<p>18.02</p>
<p>18.03</p>
<p><a href="http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/index.htm">You can look at it here</a>. Just extra material to support your effort!</p>
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		<title>Psychologists attribute high scores on standardized tests to &#8220;home schooling&#8221;</title>
		<link>http://askdrcallahan.com/blog/2010/07/19/psychologists-attribute-high-scores-on-standardized-tests-to-home-schooling/</link>
		<comments>http://askdrcallahan.com/blog/2010/07/19/psychologists-attribute-high-scores-on-standardized-tests-to-home-schooling/#comments</comments>
		<pubDate>Mon, 19 Jul 2010 06:00:46 +0000</pubDate>
		<dc:creator>Dr. Callahan</dc:creator>
				<category><![CDATA[Cooperative and Tutoring]]></category>
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		<category><![CDATA[standards. standardized tests]]></category>
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		<guid isPermaLink="false">http://askdrcallahan.com/blog/?p=1058</guid>
		<description><![CDATA[Psychologists attribute high scores on standardized tests to "home schooling"]]></description>
			<content:encoded><![CDATA[<p>I just thought you guys might like this article. <a href="http://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools">Click Here to Read. </a></p>
<p><img class="alignleft" src="http://www.psychologytoday.com/files/u123/mathphobia.jpg" alt="" width="246" height="268" /></p>
<p>The article was published in Psychology Today and it takes a look at not only how the adult mindset towards education has evolved over the years, but also makes some suggestions about what we should really be valuing in our kids&#8217; education. Personally, I was surprised to learn that math teaching across the board (whether in affluent sections of town or the poorest ghettos) was equally pathetic. The article attributes the higher scores of affluent kids on standardized test to the &#8220;home schooling&#8221; parents provided for them. Interesting read, but do you agree with their findings? What are your thoughts about &#8220;modern&#8221; education?</p>
<p>Kind of sad, really, that parents think extra education is needed, when really if we would just put home school standards in the classroom to start with, students could be well educated AND have fun evenings instead of extra work.</p>
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		<title>Homeschool Elementary Math that Prepares Kids For Highschool Algebra and Beyond</title>
		<link>http://askdrcallahan.com/blog/2010/07/16/homeschool-elementary-math-that-prepares-kids-for-highschool-algebra-and-beyond/</link>
		<comments>http://askdrcallahan.com/blog/2010/07/16/homeschool-elementary-math-that-prepares-kids-for-highschool-algebra-and-beyond/#comments</comments>
		<pubDate>Fri, 16 Jul 2010 19:48:39 +0000</pubDate>
		<dc:creator>Dr. Callahan</dc:creator>
				<category><![CDATA[Ideas and Opinions]]></category>
		<category><![CDATA[Kids math]]></category>
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		<description><![CDATA[Grade school math prep for higher math is actually quite simple. Children need to see math more than do math.  The basics needed are; Addition Subtraction Multiplication Division Fractions Geometric shapes Time Space Granted that can include a lot of stuff such as mastery of addition includes knowing the placeholders of base 10 number system. [...]]]></description>
			<content:encoded><![CDATA[<p>Grade school math prep for higher math is actually quite simple. Children<br />
need to see math more than do math.  The basics needed are;</p>
<p>Addition<br />
Subtraction<br />
Multiplication<br />
Division<br />
Fractions<br />
Geometric shapes<br />
Time<br />
Space</p>
<p>Granted that can include a lot of stuff such as mastery of addition includes<br />
knowing the placeholders of base 10 number system. The one’s place, the<br />
ten’s place, etc. Fractions are going to take you into the 1/100 place and<br />
such. But still its addition, start simple and grow.</p>
<p>Basically, all of those concepts can be taught at home without purchasing much at all. Paper, pencil and a clock can get you a long way. But doing math as you go throughout the day gets you a lot further. We wrote a lot on chalk boards and made lots of games out of numbers and shapes and time. We are always noticing shapes and calling them by their correct names. We add as we go along -&#8221;We counted 10 steps. There are 5 floors. How many steps are<br />
there to the top?&#8221;</p>
<p>One thing we do that I haven’t seen in any curriculum for grade school is to use the alphabet for blank spaces to make formulas.  Use the word &#8216;formula&#8217;<br />
and use X, Y or something else. This is critical to make the move to Algebra easy. Such as</p>
<p>1+ X = 2</p>
<p>Write this on your chalkboard (we wrote it on the driveway), and say something like “what do you need to add to 1 to get 2?”</p>
<p>Out on the driveway it’s a game and a mystery, then when they get to the course called Algebra, they have already done it. We were always told that<br />
children had to reach a certain age to understand this abstract notation. I have found this is not the case. My son could do this as soon as he could<br />
and 1 and 1. I just wrote it with a blank first  1 + ____ = 2 and later with the X and told him the X was the blank. He got that. I left all sorts of<br />
mysteries on the driveway or large cardboard boxes and the chalkboard. He had a blast figuring them out.</p>
<p>See this picture:</p>
<p style="text-align: center;"><img class="aligncenter" src="http://askdrcallahan.com/blog/wp-content/uploads/2010/05/daniel-and-the-cups.jpg" alt="" width="453" height="604" /> This is our son learning sums and geometry. Some of the math is more than he currently comprehends and he has no idea that he’s learning, but when he gets there it won’t scare him or look odd.</p>
<p>We did math this way only through the 2rd grade. Our cover school requires taking the SAT beginning in the 4th grade (each cover is different), so we<br />
decided 3rd grade was a good time to begin expressing math on paper. So after looking around a lot, we finally picked http://www.mathmammoth.com<br />
worksheets. It does a great job of moving into new techniques and concepts as well as continuing to enforce prior skills. It approaches problems in a<br />
common sense way so that the math can easily be applied to the real world. For example, it teaches to add in a way that can be done in your head not<br />
just on paper. Such as adding 16 and 20 you don’t just pull down the 6 on the right side and add the 1 and 2 to get 36.  You add the tens and get 30<br />
and the ones and get 6 for 36. That can be done in your head and is useful for adding in life when paper and pencil and desk are not always readily<br />
available. We do these sheets and still do the activities as well as pointing out math everywhere we see it.</p>
<p>Think of math like you think of language. First you learn to speak it before you read and write it. Kids should be able to speak math and understand it</p>
<p>before they are reading and writing it.  Its not just an activity, it is a language that explains a lot of things in this world that words just can’t do.</p>
<p>Don’t get bogged down on when to move children to Algebra. If they understand the basic math concepts outlined above, then they can go on to<br />
express math in algebraic terms. Its just a more sophisticated way of expressing math. The higher you go in math the more detailed you can express how something in this world works.</p>
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