tag:blogger.com,1999:blog-31366286317073431952015-09-16T14:18:58.241-04:00Not So Far-Out MathA real-world, real-cool, and really easy (most of the time) way to make math a bit more meaningful for elementary math students of all ages, especially if you happen to be about ten!T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.comBlogger71125tag:blogger.com,1999:blog-3136628631707343195.post-4134200270169659672011-12-04T12:43:00.002-05:002011-12-04T12:49:52.929-05:00Prove or Disprove: 1/2 +1/3 = 2/5<div align="center"><a href="http://3.bp.blogspot.com/-Rd2Gof3w3Fw/Ttuxm-hClKI/AAAAAAAAAU4/hBJpuT03CjI/s1600/fraction.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5682330638032737442" border="0" alt="" src="http://3.bp.blogspot.com/-Rd2Gof3w3Fw/Ttuxm-hClKI/AAAAAAAAAU4/hBJpuT03CjI/s200/fraction.jpg" /></a><br /><br /><br /><div align="center"><strong><span style="color:#666666;">Prove or Disprove: 1/2 + 1/3 = 2/5</span></strong></div><br /><br /><div align="center"><strong><span style="color:#666666;"></span></strong></div><br /><br /><div align="center"><strong><span style="color:#666666;"></span></strong></div>This prompt was handed to my classes last week. They were told that they could use words, numbers, pictures, charts, pieces of paper....in order to prove or disprove the above. They could not just say "yes" or "no". It was quite fun watching the wheels turn! Try it at home.<br /><br /></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com0tag:blogger.com,1999:blog-3136628631707343195.post-72054920039548583802011-10-09T12:55:00.003-04:002011-10-09T13:04:12.877-04:00Word Problem Blues<a href="http://4.bp.blogspot.com/-NcYD4IUgwEo/TpHSQAOciaI/AAAAAAAAAUg/TcWiocRaKr4/s1600/Sample%2Bwork%2B001.JPG"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5661537378961754530" border="0" alt="" src="http://4.bp.blogspot.com/-NcYD4IUgwEo/TpHSQAOciaI/AAAAAAAAAUg/TcWiocRaKr4/s200/Sample%2Bwork%2B001.JPG" /></a><br /><br /><br /><br /><br /><div align="center"><a href="http://4.bp.blogspot.com/-r2lRQgaId_Q/TpHSLkGmDpI/AAAAAAAAAUY/53NbZwhLNhQ/s1600/edited%2BHW%2Bproblem.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 198px; DISPLAY: block; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5661537302693154450" border="0" alt="" src="http://4.bp.blogspot.com/-r2lRQgaId_Q/TpHSLkGmDpI/AAAAAAAAAUY/53NbZwhLNhQ/s200/edited%2BHW%2Bproblem.jpg" /></a> Please click on the images to see a larger version.<br /><br /><br /><br />One of these things is not like the other. Both were answers on a recent HW sheet, and both have similarities. However, only one really answers the question asked. I think that you will be able to tell which is which!<br /><br />When I see a student answer a word problem with only a number, I often remind students that teachers and test graders are among the least intelligent life forms on the planet. Are we talking 21 9/25 tons of elephant poo? 21 9/25 pounds of cheese? Is 21 9/25 even a legitimate answer to the question that was asked? Without a sentence, I simply do not know.<br /><br /><br /><br /><br /><div></div></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com2tag:blogger.com,1999:blog-3136628631707343195.post-56557007757237554162011-09-05T19:49:00.005-04:002011-09-05T20:04:13.897-04:00Split-It!<div align="center"><a href="http://4.bp.blogspot.com/-NrTqkx57RvQ/TmVg2Wxry2I/AAAAAAAAAUQ/3e2kkFfpMZo/s1600/split%2Bwood.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 142px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5649027794549328738" border="0" alt="" src="http://4.bp.blogspot.com/-NrTqkx57RvQ/TmVg2Wxry2I/AAAAAAAAAUQ/3e2kkFfpMZo/s200/split%2Bwood.jpg" /></a><br /><br /><br />09-05-2011<br /><br /><br /><br /><span style="color:#000000;">I had a student ask me recently for some help with an <span id="SPELLING_ERROR_0" class="blsp-spelling-error">EDC</span> component that I call split it! Actually, I had several students ask on behalf of their parents.</span><br /><br />There was a homework problem that asked for students to show strategies to split a number like 7,758.<br /><br />What I look for is a way to make splitting the number easy by using simple mental calculations. Usually, the <span id="SPELLING_ERROR_1" class="blsp-spelling-corrected">first</span> step is to decompose the number into its place values. So, 7,758 becomes<br /><br />7,000 + 700 + 50 + 8 . Then, I ask that a student rewrite any number that they cannot readily split. Usually, these numbers start with odd numbers. We'll look at 7,000.<br /><br />7,000 could be rewritten as 6,000 +1,000 (both of which are easy to split). After that, it's all down hill.<br /><br />The whole number could be rewritten as 6,000 + 1,000 + 600 +100 + 40 + 10 +8, and finding half of these numbers should be <span id="SPELLING_ERROR_2" class="blsp-spelling-error">EZ</span>! 3,000 +500 +300 + 50 +20 +5 +4 = 3,879!</div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com1tag:blogger.com,1999:blog-3136628631707343195.post-85033181290845184372011-06-05T12:17:00.005-04:002011-06-05T12:33:44.854-04:00A Few Thoughts About Operations With Decimals<a href="http://4.bp.blogspot.com/-Df_v0CR_7Q4/TeusNB4iZ0I/AAAAAAAAAUI/NUTut7a0mRk/s1600/meat%2Bdecimals.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 134px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5614770700291303234" border="0" alt="" src="http://4.bp.blogspot.com/-Df_v0CR_7Q4/TeusNB4iZ0I/AAAAAAAAAUI/NUTut7a0mRk/s200/meat%2Bdecimals.jpg" /></a><br /><br /><br /><br /><br /><div><span style="color:#ff0000;">Lately, our class work has centered on getting kids ready for middle school standards. In doing so, we have started working on multiplying numbers that include decimals.</span></div><br />I have posed many questions like: "How much would it cost to purchase 7.3 lbs. of nails @ $11.29?<br /><br /><br />I have encouraged students to do a few things to insure that their answers make sense, which roughly translates into getting the decimal located in the correct position. First, I have asked that students make an estimate that uses only whole numbers. In the case of the nails, we would round 7.3 to 7, and we would round $11.29 down to $11. So our estimate would be $77. We know this estimate is a bit low as we rounded both numbers down, but it is plenty good to let us know where to place the decimal. I have also encouraged students to think about the problem as if it was written as a mixed number times another mixed number. If they do so, it is easy to think about the tenths being multiplied by hundredths, and that has to produce a <span id="SPELLING_ERROR_0" class="blsp-spelling-corrected">denominator</span> of thousandths. That is what your <span id="SPELLING_ERROR_1" class="blsp-spelling-error">math</span> teacher did NOT tell you when he/she said to count up the digits to the right of the decimal in the problem and match that number in the answer.<br /><br /><br />So, our estimate is $77, and the multiplication of 73 X 1129 yields a product of 82417. So it should be pretty obvious that the only place to put the decimal so that you get an <span id="SPELLING_ERROR_2" class="blsp-spelling-corrected">answer</span> close to $77 is after the two...$82.417, and since we have no coin worth a thousandth of a dollar, we round to the nearest hundredth and get $82.42 . <br /><br />Trying to put the math in front of the "<br />tricks",<br /><br />T-CubedT-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com0tag:blogger.com,1999:blog-3136628631707343195.post-521110479551149302011-02-13T14:10:00.005-05:002011-02-13T14:19:58.873-05:00Do You Like Pyramids or Would You Rather Go to Prism?<a href="http://3.bp.blogspot.com/-WK8Uadwpuuo/TVgtFY4r6ZI/AAAAAAAAAT8/3MgiUXstxI0/s1600/TRI%2BPYRAMID%2BII.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 129px; DISPLAY: block; HEIGHT: 122px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5573254109473794450" border="0" alt="" src="http://3.bp.blogspot.com/-WK8Uadwpuuo/TVgtFY4r6ZI/AAAAAAAAAT8/3MgiUXstxI0/s200/TRI%2BPYRAMID%2BII.jpg" /></a><br /><a href="http://1.bp.blogspot.com/-ApyxHW0pl-o/TVgtAhDwLoI/AAAAAAAAAT0/bJxyCmG9_u0/s1600/rect%2Bpyramid.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 159px; DISPLAY: block; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5573254025768349314" border="0" alt="" src="http://1.bp.blogspot.com/-ApyxHW0pl-o/TVgtAhDwLoI/AAAAAAAAAT0/bJxyCmG9_u0/s200/rect%2Bpyramid.jpg" /></a><br /><br /><br /><a href="http://1.bp.blogspot.com/-KQHd_Bp_FCY/TVgs7fz5D_I/AAAAAAAAATs/FdqqDmaQ6Jk/s1600/3dg%2Bshapes.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 163px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5573253939534041074" border="0" alt="" src="http://1.bp.blogspot.com/-KQHd_Bp_FCY/TVgs7fz5D_I/AAAAAAAAATs/FdqqDmaQ6Jk/s200/3dg%2Bshapes.jpg" /></a> In our math classes we are currently working on identifying attributes of three dimensional figures (space figures), and most of that work focuses on pyramids and prisms.<br /><br />We do need to become familiar with some basic 3<span id="SPELLING_ERROR_0" class="blsp-spelling-error">DG</span> vocab like: bases, faces, edges, and <span id="SPELLING_ERROR_1" class="blsp-spelling-error">vertices</span>. We also need to be able to find the surface area of said figures. So, I found a couple of links to basic info that might help.<br /><br /><br />http://www.math.com/school/subject3/lessons/S3U4L2GL.html#<br /><br /><br />http://www.mathsisfun.com/geometry/pyramids.htmlT-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com1tag:blogger.com,1999:blog-3136628631707343195.post-53584847384719445552011-01-09T19:54:00.007-05:002011-01-09T20:09:29.196-05:00It's Not Just a Multiple Choice Test!<a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/TSpZHLgHhYI/AAAAAAAAATg/wCeDoK715WM/s1600/9%2B12ths.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5560354669823755650" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/TSpZHLgHhYI/AAAAAAAAATg/wCeDoK715WM/s200/9%2B12ths.jpg" /></a><br /><div><br /><br /></div><div align="center"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5560354552041052786" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/TSpZAUuiGnI/AAAAAAAAATY/3HY8mE7Y4Jg/s200/5%2B12ths.jpg" /><a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/TSpY8uPG2qI/AAAAAAAAATQ/Z0E0Kuu2s5E/s1600/9%2B12ths.jpg"></a><br /><span style="color:#000000;">Years ago, most standardized math tests were using rather low complexity questions. That's not to say that the questions were easy. Some may have been very difficult, but knowing what to do was pretty straight forward.</span></div><div align="center"></div><div align="center"><br /><br />A test might have asked simply asked for the sum of 3/8 + 1/6, and then given four possible answers. </div><div align="center"></div><div align="center"><br /><br />Today, the state of Florida is putting a heavier emphasis on the cognitive complexity level of questions on tests like the <span id="SPELLING_ERROR_0" class="blsp-spelling-error">FCAT</span>.<br /><br /></div><div align="center"></div><br />As an example, a test might ask how much pie was eaten if the shaded portion of the first pie represents the pie before dessert, and the shaded portion of the second pie represents the amount after dessert.<br /><br />This turns a very simple problem into a more cognitively challenging problem.<br /><br />So, what fraction in its lowest terms represents how much pie was eaten?<br /><br />A. 4/12 B. 7/12 C. 1/4 D. 1/3T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com1tag:blogger.com,1999:blog-3136628631707343195.post-64114759805441251732010-12-11T11:06:00.003-05:002010-12-11T11:26:52.003-05:00On a scale of one to dumb....<a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/TQOiQ2Mp_OI/AAAAAAAAATE/tCsDY9jiCyU/s1600/handcuffs.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 161px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5549457576160787682" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/TQOiQ2Mp_OI/AAAAAAAAATE/tCsDY9jiCyU/s200/handcuffs.jpg" /></a><br /><div align="center">Quite recently, I received a comment on my blog from one of the coolest students that I ever taught. Ferney J. sent me a comment about my posting of the "top math jobs", and in her comment she asked if math was needed for a career in criminal justice.<br /><br />At that moment, several things popped into my pea-sized brain. First, I really was happy to "hear" form Ferney. I have been wondering how life in Cally had been for her. So Ferney, if you read this, please send an email address (maybe a school email address).<br /><br />Next, I realized how idiotic the list of top math jobs that I posted was. An actuary was listed as one of the top jobs. Be real. I think that should have been on the list of the "most dreaded" math jobs! </div><div align="center"></div><div align="center">There are millions of careers that require a good math knowledge, and criminal justice is one of them. In fact, the FBI has several special units for folks that have great mathematical abilities. More importantly, everyday quality of life is improved with a good math schema!<br /><br />So on a scale of one to dumb, my choice to post some random Internet math job statistics was DUMB! </div><div align="center"></div><div align="center"><br /><br />Ferney, thanks for continuing to teach this old dog new tricks! </div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com0tag:blogger.com,1999:blog-3136628631707343195.post-2231773162904750162010-12-05T12:59:00.010-05:002010-12-05T13:30:22.158-05:00Fractions, Pizza, Percents, and More<div align="center"><a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/TPvTP6Uj6HI/AAAAAAAAAS8/xCTzaCph6tI/s1600/pizza.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 151px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5547259636343892082" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/TPvTP6Uj6HI/AAAAAAAAAS8/xCTzaCph6tI/s200/pizza.jpg" /></a> <span style="color:#ff0000;">Lately, the class has been involved in answering questions involving the addition and subtraction of fractional amounts.</span></div><p><span style="color:#ff0000;"></span></p><p><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;">Some of the typical equations might look like:<br /><br /></span></p><p align="center"><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;">2 1/4 + (1 1/3 -5/6) or<br /><br /></span></p><p align="center"></p><p align="center"><span style="color:#ff0000;">4 3/10 - (2 3/5 + 7/10) or<br /><br /></span></p><p align="center"></p><p align="center"><span style="color:#ff0000;">(3 3/4 + 2 1/8) - 2 2/7<br /><br /><br /></span></p><p align="center"></p><p align="center"></p><p align="center"><span style="color:#ff0000;">While you might expect for me to be interested in the correct answer as my primary goal, I am actually much more concerned that kids are looking at the amounts and using appropriate strategies based on each unique circumstance.<br /><br /></span></p><p align="center"><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;">We have studied several models that allow students to quickly create common denominators by thinking of such things as equivalent fractions on a clock, equivalent percents, and/or a good old common denominator. The trick is to know when to use each model. </span></p><p align="center"><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;"><br /><br />The first problem is a great opportunity to use a clock model as all of the fractional amounts can be expressed as twelfths. Students should be familiar with clock fractions from the game "Roll around the Clock". 2 3/12 + ( 1 4/12 - 10/12)<br /><br /><br /></span></p><p align="center"><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;">The second problem is perfect for using percents as all of the amounts are very easily converted into percents that are easily added and subtracted. 430% - (260% + 70%)<br /><br /></span></p><p align="center"><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;">The third problem is probably best solved by finding a common denominator as the fraction 2/7 is not easily represented on a clock, because 12 hours and/or 60 minutes cannot evenly be split into seven whole number pieces. Also, without a calculator, finding and using the percent that is equivalent to 2/7 is not practical. (3 6/8 + 2 1/8) - 2 2/7.... 5 7/8 - 2 2/7... 5 49/56 - 2 16/56...= 3 33/56<br /><br /></span></p><p align="center"><span style="color:#ff0000;"></span></p><p align="center"><span style="color:#ff0000;">Of course, this post leaves out many steps, but the most important step is choosing the best strategy with which to work. </span></p><p align="center"></p><p align="center"></p><div align="center"><br /></div><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com2tag:blogger.com,1999:blog-3136628631707343195.post-69159465299285801322010-11-28T20:25:00.004-05:002010-11-28T20:34:59.908-05:00When Does -3 -3 +3 = 12,000,000<div align="center"><a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/TPMBeE0_CiI/AAAAAAAAAS0/U7k-uKI_uhM/s1600/boise%2Bstate.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 116px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5544777182426892834" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/TPMBeE0_CiI/AAAAAAAAAS0/U7k-uKI_uhM/s200/boise%2Bstate.jpg" /></a> </div><div align="center"></div><div align="center">Boise State's kicker missed a field goal in regulation to win their game against Nevada this weekend. The same kicker then went on to miss another in overtime. That's the -3 -3 part.</div><div align="center"></div><div align="center">Nevada's kicker made his attempt in overtime for the win.<br /><br /></div><div align="center"></div><div align="center"></div><div align="center">The loss may mean a loss in $12,000,000 for Boise State as they have no hope in playing in the NCAA Championship game now, and will most like play in the Humanitarian Bowl and receive a much smaller pay check. </div><div align="center"></div><div align="center"></div><div align="center"><br /><br /><br />See, math is COOL and CRUEL! </div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com0tag:blogger.com,1999:blog-3136628631707343195.post-55864359779577180112010-11-21T12:53:00.010-05:002010-11-21T13:15:54.104-05:00Fractions: How Do I Add Thee, Let Me Count the Ways<a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/TOldF2DhcmI/AAAAAAAAASs/oJhNwtA8TRU/s1600/fraction%2Bpizzas.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 117px; DISPLAY: block; HEIGHT: 117px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5542063171447124578" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/TOldF2DhcmI/AAAAAAAAASs/oJhNwtA8TRU/s200/fraction%2Bpizzas.bmp" /></a><br /><div><span style="color:#ff0000;">When it c<span id="SPELLING_ERROR_0" class="blsp-spelling-error">omes</span> to adding fractions, everyone knows that there is only one good way to do it. Right?</span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div></div><div></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;">So, if I were to ask you to add something simple like 1/2 + 1/4, you would say that we have to find the LCD and change 1/2 into 2/4, add, and get a sum of 3/4. Right?<br /><br /> </span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;">Or could I change 1/2 into 50% and 1/4 into 25% and then add and get 75% which is equivalent to 3/4? Possibly?<br /><br /></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;">Or could I say that on a clock, 1/2 is the same as 6/12 and 1/4 is the same as 3/12 and then add and get 9/12 which is the same as 3/4? Any chance? <br /><br /></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;">Admittedly, the problem above is very simple. Also, the problem was designed so that three or more methods could be used easily to solve the problem. Not all problems are so <span id="SPELLING_ERROR_1" class="blsp-spelling-corrected">friendly</span>! In fact, much of what we do in class centers on finding methods that work for the numbers presented. <br /><br /></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div></div><div><span style="color:#ff0000;"></span></div><div></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;"></span></div><div><span style="color:#ff0000;">Please think about how 1/2 + <strong>1/7</strong> would be different. Do you know both percents? Do you know what 1/7 of a clock face looks like? I don't! </span></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com0tag:blogger.com,1999:blog-3136628631707343195.post-34826787545269322432010-11-13T15:01:00.008-05:002010-11-13T15:14:57.103-05:00A Really Cool Fraction Model<a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/TN7u4qBiMjI/AAAAAAAAASk/YvUuAe3Fkfk/s1600/fractions%2BII.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 143px; DISPLAY: block; HEIGHT: 113px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5539127248833098290" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/TN7u4qBiMjI/AAAAAAAAASk/YvUuAe3Fkfk/s200/fractions%2BII.bmp" /></a><br /><div align="center"><a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/TN7u0DZIqtI/AAAAAAAAASc/nh4R1p0JDdM/s1600/fractions.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 97px; DISPLAY: block; HEIGHT: 115px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5539127169743629010" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/TN7u0DZIqtI/AAAAAAAAASc/nh4R1p0JDdM/s200/fractions.bmp" /></a> <a href="http://illuminations.nctm.org/ActivityDetail.aspx?ID=11">http://illuminations.nctm.org/ActivityDetail.aspx?ID=11</a> </div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center">Please click on this link and tell me what you think about this interactive fraction model. You will have to click on the right hand bottom "length" icon and choose "region" to see the circular model, and the circular model is the best. You also want to choose "Wide Range" on the top tabs to see smaller fractional pieces. Try it. It's cool, even if I am a math geek!</div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center">I love to see the regions change size as the denominator is changed. Can you imagine what it would look like if you could show millionths? </div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center">I really think that it takes models like these to really "get" fractions. I know that many students would agree that fractions can be frustrating. Perhaps, visual aids like this can help.</div><div align="center"></div><div align="center"><br /><br /></div><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com1tag:blogger.com,1999:blog-3136628631707343195.post-89895459136782820042010-11-07T11:06:00.006-05:002010-11-07T11:27:32.925-05:00Math Jobs Anyone?<div align="center"><a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/TNbOztwJNII/AAAAAAAAASU/fr1l8vj-U9w/s1600/money+tree.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 114px; DISPLAY: block; HEIGHT: 123px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5536840179748779138" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/TNbOztwJNII/AAAAAAAAASU/fr1l8vj-U9w/s200/money+tree.bmp" /></a><span style="font-size:130%;color:#ff0000;"> In a financial way, what can a knowledge of math bring your way? Below is a listing of "math" careers. Can you think of others? </span></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"><span style="color:#000099;">The following were recently were listed as the five "best" jobs. </span></div><div align="center"><span style="color:#000099;"></span></div><div align="center"><span style="color:#000099;"></span></div><div align="center"><span style="color:#000099;">They were : </span></div><div align="center"><br /><span style="color:#000099;">software engineer<br />actuary<br />computer systems analyst<br />computer programmer</span></div><div align="center"><span style="color:#000099;">mathematician </span></div><div align="center"></div><div align="center"></div><div align="center"><br />This list was the result of the comparison of two hundred fifty jobs classified according to :<br />income<br />future outlook<br />physical demands<br />job security<br />stress<br />work environment </div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"><br />A List of Professions:</div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center">The following list briefly describes work associated with some mathematics-related professions :<br />actuary-- assemble and analyze statistics to calculate probabilities of death, sickness, injury, disability, unemployment, retirement, and property loss; design insurance and pension plans and ensure that they are maintained on a sound financial basis </div><div align="center"></div><div align="center"><br />mathematics teacher-- introduce students to the power and beauty of mathematics in elementary, junior high, or high school mathematics courses </div><div align="center"></div><div align="center"><br />operations research analyst-- assist organizations (manufacturers, airlines, military) in developing the most efficient, cost-effective solutions to organizational operations and problems; this includes strategy, forecasting, resource allocation, facilities layout, inventory control, personnel schedules, and distribution systems</div><div align="center"></div><div align="center"><br />statistician-- collect, analyze, and present numerical data resulting from surveys and experiments </div><div align="center"></div><div align="center"><br />physician-- diagnose patient illnesses, prescribe medication, teach classes, mentor interns, and do clinical research; students with a good mathematics background will find themselves being admitted to the best medical schools and discover that mathematics has prepared them well for the discipline, analysis, and problem- solving required in the field of medicine</div><div align="center"></div><div align="center"><br />research scientist-- model atmospheric conditions to gain insight into the effect of changing emissions from cars, trucks, power plants, and factories; apply these models in the development of alternative fuels</div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"></div><div align="center"><br />computer scientist-- interface the technology of computers with the underlying mathematical principles of such diverse applications as medical diagnoses, graphics animation, interior design, cryptogrraphy, and parallel computers</div><div align="center"></div><div align="center"><br />inventory strategist-- analyze historical sales data, model forecast uncertainty to design contingency plans, and analyze catalog displays to make them more successful; analyze consumer responses </div><div align="center"></div><div align="center"><br />staff systems air traffic control analyst-- apply probability, statistics, and logistsics to air traffic control operations; use simulated aircraft flight to monitor air traffic control computer systems </div><div align="center"></div><div align="center"><br />cryptologist-- design and analyze schemes used to transmit secret information</div><div align="center"></div><div align="center"><br />attorney-- research, comprehend, and apply local, state, and federal laws; a good background in mathematics will help a student get admitted to law school and assist in the understanding of complicated theoretical legal concepts</div><div align="center"></div><div align="center"><br />economist-- interpret and analyze the interrelationships among factors which drive the economics of a particular organization, industry, or country</div><div align="center"></div><div align="center"><br />mathematics professor-- teach mathematics classes, do theoretical research, and advise undergraduate and graduate students at colleges and universities</div><div align="center"></div><div align="center"><br />environmental mathematician-- work as member of interdisciplinary team of scientists and professionals studying problems at specific Superfund sites; communicate effectively across many academic discilplines and be able to summarize work in writing </div><div align="center"></div><div align="center"><br />robotics engineer-- combine mathematics, engineering, and computer science in the study and design of robots </div><div align="center"></div><div align="center"><br />geophysical mathematician -- develop the mathematical basis for seismic imaging tools used in the exploration and production of oil and gas reservoirs </div><div align="center"></div><div align="center"><br />design -- use computer graphics and mathematical modeling in the design and construction of physical prototypes; integrate geometric design with cost-effective manufacturing of resulting products</div><div align="center"></div><div align="center"><br />ecologist -- study the interrelationships of organisms and their environments and the underlying mathematical dynamics</div><div align="center"></div><div align="center"><br />geodesist -- study applied science involving the precise measurement of the size and shape of the earth and its gravity field </div><div align="center"></div><div align="center"><br />photogrammetrist -- study the applied science of multi-spectral image acquisition from terrestrial, aerial and satellite camera platforms, followed up by the image processing, analysis, storage, display, and distribution in various hard-copy and digital format </div><div align="center"></div><div align="center"></div><div align="center"><br />civil engineer -- plan, design, and manage the construction of land vehicle, aircraft, water, and energy transport systems; analyze and control systems for land vehicular traffic; analyze and control environmental systems for sewage and water treatment; develop sites for industrial, commercial and residential home use; analyze and control systems for storm water drainage and storage; manage construction of foundations, structures and buildings; analyze construction materials ; and surface soils and subterranean material analysis </div><div align="center"></div><div align="center"><br />geomatics engineer -- once known as "surveying engineer", includes geodetic surveying : takes into account the size and shape of the earth, in order to determine the precise horizontal and vertical positions of geodetic reference monuments----ad infinitum...it goes on for 30 lines and make civil engeneering look down right boring!<br /></div><p align="left"><span style="font-size:180%;color:#ff0000;">I know my favorite,and I get to do it each day! </span></p><p align="left"><span style="font-size:180%;color:#ff0000;"></span></p><p align="left"><span style="font-size:180%;color:#ff0000;">I also know my least favorite, a cryptologist. I hate Soduko! </span></p><p align="left"><span style="font-size:180%;color:#ff0000;"></span></p><p align="left"></p><p align="left"><span style="font-size:180%;color:#ff0000;"></span></p><p align="center"><span style="font-size:180%;color:#ff0000;">What about you?</span></p><p><br /></p>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com4tag:blogger.com,1999:blog-3136628631707343195.post-41302502315073964752010-10-31T12:53:00.003-04:002010-10-31T13:05:09.103-04:00...Favorite Math Book? Well, uh...let me see...<a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/TM2hWCcefGI/AAAAAAAAASM/EwZCtcC5I8A/s1600/fly+on+the+ceiling.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 86px; DISPLAY: block; HEIGHT: 129px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5534256917093710946" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/TM2hWCcefGI/AAAAAAAAASM/EwZCtcC5I8A/s200/fly+on+the+ceiling.bmp" /></a><br /><div><br /><br /><div align="center"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 116px; DISPLAY: block; HEIGHT: 116px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5534255219829062322" border="0" alt="" src="http://3.bp.blogspot.com/_Sa0xkkIcGww/TM2fzPpDOrI/AAAAAAAAASE/UBF_Co6u8R8/s200/sbg.bmp" /> <img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 130px; DISPLAY: block; HEIGHT: 130px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5534255062707485330" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/TM2fqGUWOpI/AAAAAAAAAR8/035CxlwEGLE/s200/one+grain+of+rice.bmp" /><br />Well, I am about to ask a rather stupid, or at least risky, question. What is your favorite math book? I fully expect to get a few responses from math teachers, but I hold out little hope that the general populace will have much of an opinion. </div><br /><div align="center"></div><br /><div align="center"></div><br /><div align="center">As for me, two of the pictures above show my favorite math books, and the other is my least favorite. Can you guess which is which?<br /><br /><div></div></div></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com5tag:blogger.com,1999:blog-3136628631707343195.post-21182141472361518312010-10-24T13:19:00.004-04:002010-10-24T13:33:01.484-04:00What Kind of a Math-Person are You?<a href="http://3.bp.blogspot.com/_Sa0xkkIcGww/TMRtgTSDcyI/AAAAAAAAAR0/CBzlRD2UQGE/s1600/math+brain.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 115px; DISPLAY: block; HEIGHT: 133px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5531666644017050402" border="0" alt="" src="http://3.bp.blogspot.com/_Sa0xkkIcGww/TMRtgTSDcyI/AAAAAAAAAR0/CBzlRD2UQGE/s200/math+brain.bmp" /></a><br /><div><a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/TMRrSugQZUI/AAAAAAAAARs/A4iozQKxt1o/s1600/math+geek.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 98px; DISPLAY: block; HEIGHT: 116px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5531664211782952258" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/TMRrSugQZUI/AAAAAAAAARs/A4iozQKxt1o/s200/math+geek.bmp" /></a><br /><br /><div align="center"><span style="color:#ff0000;">What kind of a math person are you? That's a pretty tough question to answer without some help. So, I will supply some help.</span></div><br /><div align="center"><span style="color:#ff0000;"></span></div><br /><div align="center"><span style="color:#ff0000;">Pick just one of the following problems, and think about how you would go about the math. Would you need tools (paper & pencil, a calculator, just your brain)? If you worked mentally, would you see pictures in your head? If so what would they be? Would you see numbers being carried, borrowed, or traded? Do you see numbers stacked vertically? </span></div><br /><div align="center"><span style="color:#ff0000;"></span></div><br /><div align="center"><span style="color:#ff0000;">Well, here goes...</span></div><br /><div align="center"><span style="color:#ff0000;"></span></div><br /><div align="center"><span style="color:#ff0000;">27 + 53</span></div><br /><div align="center"><span style="color:#ff0000;"></span></div><br /><div align="center"><span style="color:#ff0000;">53 - 27</span></div><br /><div align="center"><span style="color:#ff0000;"></span></div><br /><div align="center"><span style="color:#ff0000;">2,456 divided by 12</span></div><br /><div align="center"><span style="color:#ff0000;"></span></div><br /><div align="center"><span style="color:#ff0000;">27 X 53</span></div></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com3tag:blogger.com,1999:blog-3136628631707343195.post-86383590369855081142010-10-16T20:34:00.005-04:002010-10-16T21:01:12.220-04:00What do you think our kids should be learning in math?<a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/TLpFiR5ibYI/AAAAAAAAARk/qtwId6Kxaak/s1600/wally+world.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 104px; DISPLAY: block; HEIGHT: 133px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5528807947773308290" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/TLpFiR5ibYI/AAAAAAAAARk/qtwId6Kxaak/s200/wally+world.bmp" /></a><br /><div><a href="http://3.bp.blogspot.com/_Sa0xkkIcGww/TLpFafupl0I/AAAAAAAAARc/Wciz0kDpA9w/s1600/atm+receipt.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 100px; DISPLAY: block; HEIGHT: 132px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5528807814046783298" border="0" alt="" src="http://3.bp.blogspot.com/_Sa0xkkIcGww/TLpFafupl0I/AAAAAAAAARc/Wciz0kDpA9w/s200/atm+receipt.bmp" /></a><br />If I were in charge of the math world, I would have classrooms full of calculators, check books, receipts, and bank statements. It seems pretty clear that most "math energy" in our world is spent balancing our assets against our material wishes. It is also clear that many students graduate from high school without these basic skills. </div><div> </div><div> </div><div> </div><div></div><div>I also think that textbook publishers have a pretty warped view of what real world math is all about. If Bobby, Suzy and Sam have to share any more pizzas, I think that I may become ill (it sounds real world, but it really isn't), ditto for 2n X 48z cubed = the square root of pi.</div><div> </div><div> </div><div> </div><div></div><div>Having said this, I do deeply value building a deep understanding of basic number sense and mental math abilities. If this ability is developed early, higher math certainly becomes more <span id="SPELLING_ERROR_0" class="blsp-spelling-corrected">manageable</span>, and more mundane daily math tasks become less of a mystery. </div><div> </div><div> </div><div> </div><div></div><div>What do you think?<br /></div><div></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com3tag:blogger.com,1999:blog-3136628631707343195.post-29980119042721375012010-10-10T13:19:00.004-04:002010-10-10T13:28:11.582-04:00I Don't Want to be a Hater, but..........<div align="center"><a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/TLH2IWNZ-QI/AAAAAAAAARU/c2HJjWXRo9I/s1600/haterade.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 118px; DISPLAY: block; HEIGHT: 94px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5526468841021503746" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/TLH2IWNZ-QI/AAAAAAAAARU/c2HJjWXRo9I/s200/haterade.bmp" /></a> <span style="color:#ff0000;">What is the thing that you most hated about math or a math class? </span></div><p><span style="color:#ff0000;"></span> </p><p><span style="color:#ff0000;">For me, the thing that I could never understand was teachers assigning 53 similar problems for homework! I can remember sitting at home from the age of about 11 to the age of 17 thinking that the teachers must be quite thick if they did not realize that if I could do two problems, I could do 53 problems. We also never <span id="SPELLING_ERROR_0" class="blsp-spelling-corrected">went</span> over more than two problems in the classroom. So, I am still confused and angry. I mean, I could have played a million more minutes of soccer under the street light! </span></p><p><span style="color:#ff0000;"></span> </p><p><span style="color:#ff0000;">Peace,</span></p><p><span style="color:#ff0000;"></span> </p><p><span style="color:#ff0000;">T-Cubed</span></p><div align="center"><br /></div><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com4tag:blogger.com,1999:blog-3136628631707343195.post-21831064739460365862010-10-03T14:03:00.006-04:002010-10-03T14:32:55.648-04:00What Fun is Football Without Math?<a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/TKjF_cORRFI/AAAAAAAAARM/Kco6QXtwfGs/s1600/bama+football.bmp"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 95px; DISPLAY: block; HEIGHT: 127px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5523882636668388434" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/TKjF_cORRFI/AAAAAAAAARM/Kco6QXtwfGs/s200/bama+football.bmp" /></a><br /><div align="center">How does math improve your life? </div><div align="center"> </div><div align="center"> </div><div></div><div>Maybe it doesn't, but as I sat and watched the <span id="SPELLING_ERROR_0" class="blsp-spelling-corrected">lizards</span> get pummeled by the Tide, I really enjoyed understanding all of the math involved in football. It must really stink not to understand things like, "11 carries for 42 yards" or "allowed two <span id="SPELLING_ERROR_1" class="blsp-spelling-error">TDs</span> in nine red-zone trips". </div><div> </div><div>Today, as I watch the <span id="SPELLING_ERROR_2" class="blsp-spelling-error">NASCAR</span> race, thousandths of a second or thousandths of an inch could make all the difference in the world, or Jimmie Johnson could just win like always...</div><div></div><div>So, I challenge you to answer the question. How does math impact your life daily? </div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com3tag:blogger.com,1999:blog-3136628631707343195.post-39044474831828877082010-08-18T08:47:00.003-04:002010-08-18T09:11:28.073-04:00For 2010-2011; What math should your kiddo know?<a href="http://3.bp.blogspot.com/_Sa0xkkIcGww/TGvbwawgqNI/AAAAAAAAAQ8/Mztljisynic/s1600/toy+pic+3.jpg"><img id="BLOGGER_PHOTO_ID_5506736594253555922" style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 200px; CURSOR: hand; HEIGHT: 150px; TEXT-ALIGN: center" alt="" src="http://3.bp.blogspot.com/_Sa0xkkIcGww/TGvbwawgqNI/AAAAAAAAAQ8/Mztljisynic/s200/toy+pic+3.jpg" border="0" /></a><br /><div>Perhaps the most important, and also the least understood, information that a parent can have relates to the exact information that a student should be learning in their classroom. This is extremely <span class="blsp-spelling-corrected" id="SPELLING_ERROR_0">important</span> this year as Florida has adopted new standards in many subjects. For me the New Generation Math Standards should drive my instruction each day. For students and parents, these standards should provide a guide as well.<br /><br />Really, every parent should expect a teacher to cover all of the concepts listed in these standards, and they should ask questions if they think something is being overlooked. The really cool thing is that these standards are not top-secret. In fact by logging on to <a href="http://www.floridastandards.org/Standards/FLStandardSearch.aspx">http://www.floridastandards.org/Standards/FLStandardSearch.aspx</a> anyone on the planet can find out what should be going on in the classroom. Having said that, this does not mean that all children will master all of these standards. Some kids will fly. Some kids will struggle, and most will do both, but at least the standards make the big picture a bit more transparent (not a pun, but it is great for parents). So, please look at these standards often.</div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com4tag:blogger.com,1999:blog-3136628631707343195.post-87729777765625408042010-04-25T13:41:00.003-04:002010-04-25T13:49:25.368-04:00What is a "Normal" Cat?<a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/S9R_Eshs0CI/AAAAAAAAAQ0/uvbaAln71rY/s1600/cat+weight.JPG"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 86px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5464131966555967522" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/S9R_Eshs0CI/AAAAAAAAAQ0/uvbaAln71rY/s200/cat+weight.JPG" /></a><br /><div><a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/S9R-_M1_byI/AAAAAAAAAQs/oBQVQkmZqWU/s1600/cat+fur+color.JPG"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 145px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5464131872151793442" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/S9R-_M1_byI/AAAAAAAAAQs/oBQVQkmZqWU/s200/cat+fur+color.JPG" /></a><br /><br /><div align="center"><a href="http://3.bp.blogspot.com/_Sa0xkkIcGww/S9R-5M5gheI/AAAAAAAAAQk/6rrJI_dEqzU/s1600/jasper+belly.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 188px; DISPLAY: block; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5464131769087329762" border="0" alt="" src="http://3.bp.blogspot.com/_Sa0xkkIcGww/S9R-5M5gheI/AAAAAAAAAQk/6rrJI_dEqzU/s200/jasper+belly.jpg" /></a> Please click on the thumbnail images to make them larger.</div><div align="center"> </div><div align="center"><span style="color:#ff0000;">So, just what is a normal cat? How could a student explain what normal is? Is it easier if you have numbers? Why or why not? What do you do with nonnumerical or categorical data? Can a cat have a mean (average) fur color? If not, how would you describe "normal" fur color. What kinds of charts or graphs would help? Is a sampling of 14 cats enough to represent all of the cats in the world? If not, how many should be sampled?</span></div><div align="center"><span style="color:#ff0000;"></span> </div><div align="center"><span style="color:#ff0000;">Is my cat's belly the most disgusting thing that you have ever seen?<br /></span><span style="color:#ff0000;">Inquiring minds want to know!<br /></span><br /></div><div align="center"></div></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com4tag:blogger.com,1999:blog-3136628631707343195.post-21909459556195352532010-03-20T22:27:00.003-04:002010-03-20T22:34:08.060-04:00Dude, this is like totally circular!<a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/S6WFlYlvo3I/AAAAAAAAAQc/7VwAug66lgs/s1600-h/Da%27s+10th+BD+007.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 133px; DISPLAY: block; HEIGHT: 200px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5450909801304269682" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/S6WFlYlvo3I/AAAAAAAAAQc/7VwAug66lgs/s200/Da%27s+10th+BD+007.jpg" /></a><br /><div align="center"></div><br /><div align="center"></div><br /><div align="center"></div><br /><div align="center"></div><br /><div align="center"><a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/S6WEPVDDlJI/AAAAAAAAAQU/PBHYcL4IXmk/s1600-h/circles+002.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5450908322884719762" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/S6WEPVDDlJI/AAAAAAAAAQU/PBHYcL4IXmk/s200/circles+002.jpg" /></a> Please click on the thumbnail image to make it larger. </div><br /><div align="center"></div><br /><div align="center"><span style="color:#ff0000;">Use your visual glossary and please identify the following:</span></div><br /><div align="center"><span style="color:#ff0000;">All of the radiuses (AKA Radii)</span></div><br /><div align="center"><span style="color:#ff0000;">All of the diameters</span></div><br /><div align="center"><span style="color:#ff0000;">All of the the chords</span></div><br /><div align="center"><span style="color:#ff0000;">The centerpoint</span></div><br /><p><span style="color:#ff0000;"></span></p><br /><p align="center"><span style="color:#ff0000;">Calculate the circumference (the photo shows the length of the radius). </span></p><br /><div align="center"><br /></div><br /><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com3tag:blogger.com,1999:blog-3136628631707343195.post-46996470439380480342010-02-21T13:17:00.003-05:002010-02-21T13:24:20.597-05:00Coordinate Grids Using Negative Numbers<div align="center"><a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/S4F41YtlFgI/AAAAAAAAAQM/zS8v88vKJvg/s1600-h/EOS+cams+035.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5440762683402294786" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/S4F41YtlFgI/AAAAAAAAAQM/zS8v88vKJvg/s200/EOS+cams+035.jpg" /></a> Please click on the thumbnail image to see a larger version :-} </div><div align="center"> </div><div align="center"><span style="color:#ff0000;">In 5<span id="SPELLING_ERROR_0" class="blsp-spelling-error">th</span> grade coordinate grids go to four quadrants! Please see if you can locate points C and D so that you could create a square by connecting all of the coordinates. </span></div><p align="center"><span style="color:#ff0000;">Some hints:</span></p><p align="center"><span style="color:#ff0000;">Always start at the origin</span></p><p align="center"><span style="color:#ff0000;">Think (left or right, then up or down...plot a point)</span></p><p align="center"><span style="color:#ff0000;">Negative numbers on the X axis ask you to move left</span></p><p align="center"><span style="color:#ff0000;">Negative numbers on the Y axis ask you to move down</span></p><p align="center"><span style="color:#ff0000;">I reached point B by moving right 30 from the origin and then moving down to the -10 on the Y axis. I plotted a point at the intersection of the two line segment found at (30, -10).</span></p><p align="center"><span style="color:#ff0000;"></span> </p><p align="center"><span style="color:#ff0000;">Best of luck! </span></p><p><span style="color:#ff0000;"></span> </p><div align="center"><br /></div><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com8tag:blogger.com,1999:blog-3136628631707343195.post-55366005176485583362010-02-07T15:47:00.003-05:002010-02-08T07:48:36.773-05:00Guess My Rule....If you know Geometry!<a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/S28nE771qKI/AAAAAAAAAQE/n9Gorr_AakA/s1600-h/gmr.jpg"><img id="BLOGGER_PHOTO_ID_5435606241021110434" style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 200px; CURSOR: hand; HEIGHT: 150px; TEXT-ALIGN: center" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/S28nE771qKI/AAAAAAAAAQE/n9Gorr_AakA/s200/gmr.jpg" border="0" /></a><br /><div align="center"><span style="color:#3366ff;">A long time ago, little Tommy was sitting in his classroom, and the teacher asked, "Tommy, can you use the word "geometry" in a sentence?". Tommy said, "Sure! One night an acorn fell asleep, and the next day it wake up and said,'Gee I'm a tree!' ".</span></div><div align="center"><span style="color:#3366ff;"></span></div><div align="center"><span style="color:#3366ff;">All kidding aside, one of the simplest, and yet deepest, ways to explore your knowledge of geometry is to play a game called Guess My Rule. It's simple. You put three or four polygons that follow a certain rule inside a circle and a couple that do not follow the rule outside of the circle. Then, you have someone "Guess My Rule". </span></div><div align="center"><span style="color:#3366ff;"></span></div><div align="center"><span style="color:#3366ff;">So, what do think my rule is? Please don't be cute and say "polygons with less than five sides". While, the shapes inside the circle do have less than five sides (the ones on the outside do as well), my rule is a bit more complex :-} </span></div><div align="center"></div><div align="center"><span style="color:#3366ff;">Oh, a hint you wish? Well, I always investigate polygons by looking at their sides and angles! </span></div><div align="center"></div><div align="center"><span style="color:#3366ff;">Have fun! </span></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com14tag:blogger.com,1999:blog-3136628631707343195.post-13423658660755009172010-01-10T12:43:00.005-05:002010-01-10T13:19:36.731-05:00How Do You Read That Decimal?<a href="http://3.bp.blogspot.com/_Sa0xkkIcGww/S0oSB6jzsJI/AAAAAAAAAP8/nSpxsbtn0pA/s1600-h/decimals+001.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5425168525229797522" border="0" alt="" src="http://3.bp.blogspot.com/_Sa0xkkIcGww/S0oSB6jzsJI/AAAAAAAAAP8/nSpxsbtn0pA/s200/decimals+001.jpg" /></a> The picture above tells a thousand stories! Well, actually it might t<span id="SPELLING_ERROR_0" class="blsp-spelling-corrected">ell</span> a tenth of a story or a hundredth of a story or a thousandth of a story depending on where the decimal point is and what digits follow the <span id="SPELLING_ERROR_1" class="blsp-spelling-corrected">decimal</span> point!<br /><br />I cringe every time that I hear TV reporters read decimals, especially weather forecasters, because they always say things like the barometric pressure is "29 POINT 92 inches", and these guys are scientists? Yikes! I hate to think that scientists are not <span id="SPELLING_ERROR_2" class="blsp-spelling-corrected">concerned</span> with things like place value. 29.92 should be read as twenty-nine AND ninety-two hundredths. Maybe students do <span id="SPELLING_ERROR_3" class="blsp-spelling-corrected">understand</span> that 29 point 92 is almost 30, but maybe they don't. Anyway, reading decimal values using correct place value is a good place to start.<br /><br />SO,<br /><br />.7 is seven tenths<br />.70 is seventy hundreds<br />.700 is seven hundred thousandths<br /><br />Simple, say the number like a whole number, and then say the SMALLEST place value. (and thousandths are <span id="SPELLING_ERROR_4" class="blsp-spelling-error">waaaayyyyy</span> smaller than tenths-don't believe me? ---try cutting your pizza into 1,000 equal pieces versus ten equal pieces:-} )<br /><br />However, we are not limited to looking at decimal numbers and only reading them as decimals. Huh? Well, .7, .70, .700 are all also 70%, and they can all be written as fractions as well.<br /><br />So, which way should we read a decimal? In short, in whatever way makes the most sense for the problem. The work above shows three ways to read each decimal, percent or fraction. If I was trying to enter 1/8 on a cheap calculator, I probably would have to use .125. If I wanted to describe the same quantity to a person, I would probably say 12 1/2%, as I have learned that most folks have a pretty good "percent schema". If I was trying to add 1/8 to a simple fraction like 1/4, I'd leave both as fractions (1/8 + 2/8 = 3/8 <span id="SPELLING_ERROR_5" class="blsp-spelling-error">woohooo</span>).<br /><br />So, for a fifth grader what is important to know?<br /><br />.5 or .50 or .500...is the decimal way to say 1/2<br />So, .675 = 67 1/2 hundredths or 67 1/2 % or 67.5 %<br />.33333333 is the decimal way to say 1/3<br />.66666666 is the decimal way to say 2/3<br />1 whole = 100% 2 wholes = 200% .....<br />So, 3 1/2 = 350% or 3.5<br /><br />Be flexible, and remember that the word POINT is dead and buried!<br /><br /><br /><br /><div></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com3tag:blogger.com,1999:blog-3136628631707343195.post-91481746450207637822009-11-22T09:47:00.004-05:002009-11-22T10:15:01.295-05:00Fractions on a Clock Face.<a href="http://4.bp.blogspot.com/_Sa0xkkIcGww/SwlPRiaCoPI/AAAAAAAAAP0/GOAIFknf0Mk/s1600/clock+fractions+003.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5406939990347391218" border="0" alt="" src="http://4.bp.blogspot.com/_Sa0xkkIcGww/SwlPRiaCoPI/AAAAAAAAAP0/GOAIFknf0Mk/s200/clock+fractions+003.jpg" /></a><br /><div><a href="http://1.bp.blogspot.com/_Sa0xkkIcGww/SwlPMqE34NI/AAAAAAAAAPs/aZEFxxQHviw/s1600/clock+fractions+001.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5406939906506744018" border="0" alt="" src="http://1.bp.blogspot.com/_Sa0xkkIcGww/SwlPMqE34NI/AAAAAAAAAPs/aZEFxxQHviw/s200/clock+fractions+001.jpg" /></a><br /><br /><div align="center"><a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/SwlPHu2EKlI/AAAAAAAAAPk/gbXQ5ZUANTo/s1600/clock+fractions+002.jpg"><img style="TEXT-ALIGN: center; MARGIN: 0px auto 10px; WIDTH: 200px; DISPLAY: block; HEIGHT: 150px; CURSOR: hand" id="BLOGGER_PHOTO_ID_5406939821887466066" border="0" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/SwlPHu2EKlI/AAAAAAAAAPk/gbXQ5ZUANTo/s200/clock+fractions+002.jpg" /></a> Please click on the thumbnails to enlarge the photographs. </div><div align="center"> </div><div align="center"><span style="color:#ff0000;">One great way to get students to see that they can list several names for one fraction is by exploring what we could name each section of a clock face that has had the hands placed on different numbers. We always leave one hand at 12, and our clocks have equal length arms so we never know know whether we are looking at an hour hand or a minute hand. </span></div><span style="color:#ff0000;"></span></div><div> </div><div><span style="color:#ff0000;">Starting with the bottom clock, we see that one hand is on the 12 and one hand is on the 2. Most students first see this as 2 out of 12 hours, and they write the fraction 2/12. Many also see that this could be 10 out of 60 minutes, or 10/60. From that point, many notice that neither of these fractions is stated in its lowest terms. Most then "chop-chop" 2/12 (divide by 2/2) to get the fraction 1/6. Many then can say that 16 2/3% of the clock face has been "covered up" or "rotated through". </span></div><div> </div><div><span style="color:#ff0000;">The next picture up shows one hand on the 12 and one on the 8. This shows 8/12 or 40/60. Again, neither fraction is in lowest terms. Many students will just see this as 2/3, as 4/12 looks like 1/3, but to prove it, one could divide 40/60 by 10/10 to get 4/6. Then one could divide 4/6 by 2/2 to get 2/3. We have mathematical PROOF! Most students now see that 8/12 is the same as 2/3, and that is the same as 66 2/3%. SWEET! </span></div><div> </div><div><span style="color:#ff0000;">The goal in all of this is to be able to add fractions with unlike denominators. The third picture up illustrates the addition of 1/4 + 2/3. 1/4 is seen to be equivalent to 3/12 and 2/3 was proven to be equivalent to 8/12. So, we get 3/12 + 8/12 = 11/12. </span></div><div><span style="color:#ff0000;"></span> </div><div><span style="color:#ff0000;">We might also get 25% + 66 2/3% = 91 2/3% but 91 2/3 / 100 is not in its lowest terms, and most middle school teachers would simply freak-out if the answer is presented in a percent. So, even though the % is correct, I would emphasize finding the answer as a fraction in its lowest terms. </span></div><div> </div><div><span style="color:#ff0000;">One last note, please remember that any fraction can be stated as another equivalent fraction simply by multiplying or dividing the fraction by the number 1, and any fraction where the numerator and denominator are the same (N/N) equals 1. </span></div><div> </div><div><span style="color:#ff0000;">So, 32/48 divided by 16/16 , still has the value of 32/48, but it is more universally recognized as 2/3. 400/500 = 4/5 not because "you can drop the zeros", but because 400/500 divided by 100/100 = 4/5! </span></div><div><span style="color:#ff0000;"></span> </div><div><span style="color:#ff0000;">Similarly, 3/4 = 9/12, because 3/4 X 3/3 = 9/12. 5/6 = 10/12, because 5/6 X 2/2 =10/12!</span></div><div><span style="color:#ff0000;"></span> </div><div><span style="color:#ff0000;">I hope you are not confused, but if you are, please send me your comments :0} </span></div><div align="center"><br /><br /><br /></div><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com4tag:blogger.com,1999:blog-3136628631707343195.post-79162015914801131452009-11-09T17:01:00.003-05:002009-11-09T17:16:29.448-05:00Fractions Are Instructions to Divide! Sir!<div align="center"><a href="http://2.bp.blogspot.com/_Sa0xkkIcGww/SviRgtTh7NI/AAAAAAAAAPc/KP_nqiEFcxo/s1600-h/SS110909.jpg"><img id="BLOGGER_PHOTO_ID_5402227744134261970" style="DISPLAY: block; MARGIN: 0px auto 10px; WIDTH: 200px; CURSOR: hand; HEIGHT: 150px; TEXT-ALIGN: center" alt="" src="http://2.bp.blogspot.com/_Sa0xkkIcGww/SviRgtTh7NI/AAAAAAAAAPc/KP_nqiEFcxo/s200/SS110909.jpg" border="0" /></a> Please click on the thumbnail to make the photo larger. </div><div align="center"> </div><div align="center">Just how do you go about solving a question like: What is 3/12 of 36 penguins? There seems to be an almost endless <span class="blsp-spelling-corrected" id="SPELLING_ERROR_0">list</span> of strategies that don't work well. However, there is one strategy that works VERY well. </div><div align="center"> </div><div align="center">In my class, I have the kids repeat, military style, "Fractions are instructions to divide by the denominator and then multiply by the numerator! Sir!" </div><div align="center"> </div><div align="center">Almost all kids can remember this"direct order". Many do not, however, know what needs dividing up, or into how many groups. In the problem above, the 36 penguins need to be divided into 12 even groups, and that puts 3 <span class="blsp-spelling-corrected" id="SPELLING_ERROR_1">penguins</span> in each group. 3 would be a fine answer to the question, "What is 1/12 of 36 penguins?", but is not a good answer for 3/12. This is where the "and multiply by the numerator" comes into play. We need to take into account 3 of the 12 equal groups of penguins, or 3 X 3 = 9 penguins. </div><div align="center"> </div><div align="center">The work also shows an array of 36 "penguins", and it would be quite correct to say that 3/12 could be understood as 3 out of every 12. This is a great model for small numbers, but I would not want to split up 3600 penguins into an array! </div><div align="center"> </div><div align="center">So, "Fractions are an instruction to divide by the denominator and then multiply the answer by the numerator! Sir!" <br /></div><div align="center"></div>T-Cubedhttp://www.blogger.com/profile/14484303546451641752noreply@blogger.com4