tag:blogger.com,1999:blog-25315473777013536782024-03-13T05:38:21.230-07:00Follow my journey....Anonymoushttp://www.blogger.com/profile/04276189350823150354noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-2531547377701353678.post-61672990335687409302013-04-08T07:26:00.002-07:002013-04-08T07:26:26.794-07:00Data Collection and Graph<br />
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">According to Wikipedia, <i>“Data Collection is a process of preparing
and collecting data, for example, as part of a process improvement or similar
project. The purpose of data collecting is to obtain information to keep
record, to make decisions about important issues, or to pass information on to
others. Data are primarily collected to
provide information regarding a specific topic.”<o:p></o:p></i></span></span></div>
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<span lang="EN-US"><i><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></i></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">So, we went on to collect data about
the class age group. Below was the result. <o:p></o:p></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilIhLVSaB7A42zOSRL50Z1zCN_vvRLBvv-n3FAto281pMzbwjqnlXE9VUHigIWLGwYEmUx0dpKIbk5yudcAGo6yzmoieir5YiVcQU_DfY_lXMWGMT0_qnRLyk6Q3tY10unJIkGd15I_C4/s1600/IMG-20130406-WA0002.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilIhLVSaB7A42zOSRL50Z1zCN_vvRLBvv-n3FAto281pMzbwjqnlXE9VUHigIWLGwYEmUx0dpKIbk5yudcAGo6yzmoieir5YiVcQU_DfY_lXMWGMT0_qnRLyk6Q3tY10unJIkGd15I_C4/s1600/IMG-20130406-WA0002.jpg" height="320" width="240" /></a></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">We were asked to tabulate the data in to graph. This
was what our group came out with.<o:p></o:p></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRiGvbXZ-mwepueHZ8728wJFAtbHrPA6pbcR83wRfTqtkZxUMa49DurH7-Z4gSE9DQQZW8hTmmp1fAjY08JTS2-rETIDwgRO3pT-JxYXjWXb6URW-9oay50zwrIpT_2KsXk7MC9Qp3Sic/s1600/IMG-20130406-WA0003.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRiGvbXZ-mwepueHZ8728wJFAtbHrPA6pbcR83wRfTqtkZxUMa49DurH7-Z4gSE9DQQZW8hTmmp1fAjY08JTS2-rETIDwgRO3pT-JxYXjWXb6URW-9oay50zwrIpT_2KsXk7MC9Qp3Sic/s1600/IMG-20130406-WA0003.jpg" height="240" width="320" /></a></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Although
the answer was not wrong, we did it the wrong way as the main idea that we were
given a strip of paper was to see that the graph can be turned into a pie chart
when the edges are connected. It took us a while to visualize the concept but
after looking at what the other group came out with, we managed to understand.<o:p></o:p></span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">From
the graph, we can find the:-<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><u><span lang="EN-US">Mean </span></u></b><span lang="EN-US">– is the average. To find mean, add the numbers and
divide the sum by the number of addends.<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US"><br /></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><u><span lang="EN-US">Median</span></u></b><span lang="EN-US"> – is the middle number in the data set that is
ordered from the least to greatest. When there are two middle numbers, the
median is the mean of the two numbers.<o:p></o:p></span></span></div>
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<b><u><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Mode</span></span></u></b><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"> – is the number that occurs most often in the data
set. Some data sets do not have a mode
while some have more than one mode.</span><o:p></o:p></span></div>
Anonymoushttp://www.blogger.com/profile/04276189350823150354noreply@blogger.com0tag:blogger.com,1999:blog-2531547377701353678.post-35298775481094369472013-04-08T06:25:00.004-07:002013-04-08T06:25:50.468-07:00Geometry<br />
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">One of the best ways to learn
Geometry – use the geoboard. With children, it is best that the real geoboard
and elastic bands are used rather than having dots given on a piece of paper. <o:p></o:p></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJi4Fgt7tFCi22n95J9HHUa3kheUHqQvx2n0HpZLJLPTO0DbXU9NDNCW1gKRGyrBJ8J09bA-eXjJzCmaPeAlzjY7JXBfM_GMZhD9I5Zd2VmCFvZgYcveIHgMPG3P2QWUOyscTJolziZh8/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJi4Fgt7tFCi22n95J9HHUa3kheUHqQvx2n0HpZLJLPTO0DbXU9NDNCW1gKRGyrBJ8J09bA-eXjJzCmaPeAlzjY7JXBfM_GMZhD9I5Zd2VmCFvZgYcveIHgMPG3P2QWUOyscTJolziZh8/s1600/images.jpg" height="133" width="200" /></a><span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">A geoboard is a mathematical
manipulative used to explore basic concepts in plane geometry such, as
perimeter, area, and the characteristics of triangles and other polygons. It
consist of a physical board with a certain number of nails half driven in ,
around which are wrapped elastic bands. </span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><o:p></o:p></span><br />
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Geoboard were invented and popularized
in the 1950s by an Egyptian mathematician, </span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Caleb Gattegno (1911-1988).<o:p></o:p></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirrV-6LnY1z_utDYthI9RXXEgSqWks8vpnTe4bjgpoeb_wF5yXwnQF7LczVc-RD5dhOEWeRnRGJv2USyf5oOMA9NP4JLbh9BgWK7d6qpRjmMa6MGVDyGOpNSsYbJ_xnmV4d3-Ocd2iig4/s1600/200px-GattegnoBG.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirrV-6LnY1z_utDYthI9RXXEgSqWks8vpnTe4bjgpoeb_wF5yXwnQF7LczVc-RD5dhOEWeRnRGJv2USyf5oOMA9NP4JLbh9BgWK7d6qpRjmMa6MGVDyGOpNSsYbJ_xnmV4d3-Ocd2iig4/s1600/200px-GattegnoBG.jpg" height="200" width="133" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">During our lesson, we were given a paper with
dotted lines and were asked to draw any polygons which only connected to 4
dots. Of coz, the first thing we all drew was a square. When we explored
around, we realized that the possibilities were endless. We could draw on and
on. Then, we were asked to find the area of the shapes. We found out that the
shapes that has no dots in the middle are of 1 unit, the shapes that has 1 dots
in middle are of 2 unit, shapes with 2 dots in the middle are of 3 unit and so
on. We began to see a pattern and it was decided that:-</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Area = <span style="font-size: 15px; line-height: 17px;">x</span></span><span lang="EN-US"> + 1<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Let <span style="font-size: 15px; line-height: 17px;">x</span></span><span lang="EN-US"> = number
of dots inside<o:p></o:p></span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">We came out with an equation!!! Yeah we felt like mathematicians.
Why didn’t the math teachers teach this way back then? It would make learning
math so much easier! And I wouldn’t have flunked on math!<o:p></o:p></span></span></div>
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<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Click on the link below to try on the virtual
geoboard!</span><o:p></o:p></span></div>
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<span lang="EN-US"><a href="http://www.mathplayground.com/geoboard.html"><span style="font-family: Arial, Helvetica, sans-serif;">http://www.mathplayground.com/geoboard.html</span></a></span></div>
Anonymoushttp://www.blogger.com/profile/04276189350823150354noreply@blogger.com0tag:blogger.com,1999:blog-2531547377701353678.post-76600403533766927652013-04-08T01:01:00.003-07:002013-04-08T01:01:40.156-07:00Fractions<span style="font-family: Arial, Helvetica, sans-serif;">Fraction is part of a whole.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">This is a hexagon. The hexagon can be divided into 6 equal parts.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSMyad5HoRFZuAs7YNSaE-LVGOXgnr9z7Vee4Yn-ZKaEFZKvX1LmYwLVJ9v7p5T0izHfSWRWyDvIbbH65CFI4nJH0B3Qt5njcJHjbfXgHot5U6OKLMiK4ChSQNnTs6p3X8N0wuEjzGVwM/s1600/fractions-01-01.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSMyad5HoRFZuAs7YNSaE-LVGOXgnr9z7Vee4Yn-ZKaEFZKvX1LmYwLVJ9v7p5T0izHfSWRWyDvIbbH65CFI4nJH0B3Qt5njcJHjbfXgHot5U6OKLMiK4ChSQNnTs6p3X8N0wuEjzGVwM/s1600/fractions-01-01.gif" height="139" width="320" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Now, each divided piece of the hexagon is 1/6.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4gb6LVthXV7eyRIFSAI04KikTZS1ignRHZ_qxanzWiT2Qjy2nkxkGJi_9TjfeXS5cTG0n9IyZF46ODw3QN7rG1tTC8Lum7OkPwWdRtXWaKvLmFSr-Q_dyf1hAG7hYiEL5-1RgL9fQ4pU/s1600/fractions-01-02.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4gb6LVthXV7eyRIFSAI04KikTZS1ignRHZ_qxanzWiT2Qjy2nkxkGJi_9TjfeXS5cTG0n9IyZF46ODw3QN7rG1tTC8Lum7OkPwWdRtXWaKvLmFSr-Q_dyf1hAG7hYiEL5-1RgL9fQ4pU/s1600/fractions-01-02.gif" height="138" width="320" /></a></div>
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<div style="line-height: 19px; margin-bottom: 18px; margin-top: 15px; text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;">We call the top number the <b>Numerator</b>, it is the number of parts you have.<br />We call the bottom number the <b>Denominator</b>, it is the number of parts the whole is divided into.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPg-nR-jjKUG_SjKCEfyeP1_GvqzYcU2rSqtE2jyrC9ZKp01BWnhmGg8UFhIXprvCfo1wVpUlGFyv_5g3t2Mb2lwmIoZXRayXYLKmcPWSDOBJ2UkbFCH7mzyVP0RnvFOUkpw391PhRmKI/s1600/1_6th.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPg-nR-jjKUG_SjKCEfyeP1_GvqzYcU2rSqtE2jyrC9ZKp01BWnhmGg8UFhIXprvCfo1wVpUlGFyv_5g3t2Mb2lwmIoZXRayXYLKmcPWSDOBJ2UkbFCH7mzyVP0RnvFOUkpw391PhRmKI/s1600/1_6th.gif" height="91" width="320" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Now you can try to count in Fractions.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8DzhCwkE3NAWbC-uRJMavHTFgR__XZlsydfgqgBgn3SGaNvL7VabR6XBw6PsMOpsOwCcRgp7ScJ95-0r_YL1dHwPeWqHgvTfDfFvv7l8K4GGOtX7fdACQcKWMjTKvSfnu09JdxbqJxJQ/s1600/fractions-01-03.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8DzhCwkE3NAWbC-uRJMavHTFgR__XZlsydfgqgBgn3SGaNvL7VabR6XBw6PsMOpsOwCcRgp7ScJ95-0r_YL1dHwPeWqHgvTfDfFvv7l8K4GGOtX7fdACQcKWMjTKvSfnu09JdxbqJxJQ/s1600/fractions-01-03.gif" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">How much of the hexagon is <span style="color: red;">red</span>?</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"> <u>5 red pieces </u></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"> 6 total pieces</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">So 5/6 of the hexagon is <span style="color: red;">red.</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><br /></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">How much of the hexagon is <span style="color: blue;">blue</span>?</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><u>1 blue piece</u></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">6 total pieces</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;">So 1/6 of the hexagon is <span style="color: blue;">blue</span>. </span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">I found this link which is very useful for the teachers to use when introducing Fractions to the children. </span></div>
<div style="text-align: left;">
<a href="http://www.mathsisfun.com/fractions.html">http://www.mathsisfun.com/fractions.html</a></div>
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<br />Anonymoushttp://www.blogger.com/profile/04276189350823150354noreply@blogger.com0tag:blogger.com,1999:blog-2531547377701353678.post-66796287704490896182013-04-07T23:56:00.001-07:002013-04-07T23:56:31.264-07:00Whole numbers<br />
<h2 style="text-align: center;">
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Whole numbers are
simply the numbers, 0,1,2,3,4,5,6…. (and so on). Whole numbers are used for
counting, adding, subtracting, multiplying and dividing. </span><span style="font-family: Arial, sans-serif;"><o:p></o:p></span></span></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirqs5p60ITzAnum5AT7QP1XnPMcFuI9sGtgt0L4HerEt-NqBy-bJXRc3kOr4w5hEjPU-jV1WgJSh9i73zgRbyw6GLigcJnKSL-GrWvSI0h_eU9G0nEpU5Vzqpjr1mU6eR5qN0gMdqc1OY/s1600/number-line-positive.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirqs5p60ITzAnum5AT7QP1XnPMcFuI9sGtgt0L4HerEt-NqBy-bJXRc3kOr4w5hEjPU-jV1WgJSh9i73zgRbyw6GLigcJnKSL-GrWvSI0h_eU9G0nEpU5Vzqpjr1mU6eR5qN0gMdqc1OY/s1600/number-line-positive.gif" height="49" width="320" /></a></div>
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<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">So why do young
children need to understand whole numbers? It can make it easier for children
to understand the properties if integers. Integers and whole numbers are NOT
the same, but all whole numbers are integers. The difference is that integers
include negative numbers, while all whole numbers are non-negative. Zero is
neither positive nor negative.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeas8ER0iPjuEz-yD6n_9wYtxfwBHgIydARFJ48njo8nojKD5fU7bYl-f6Y8HWcPcld1dFGHamnuNId-Hw5FzqkgAFNuRdkqZNq6xsxmBeYcQHTn1FZbCHZ8KxcwVOOTJ7W5z3WFi9DY4/s1600/number-line.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeas8ER0iPjuEz-yD6n_9wYtxfwBHgIydARFJ48njo8nojKD5fU7bYl-f6Y8HWcPcld1dFGHamnuNId-Hw5FzqkgAFNuRdkqZNq6xsxmBeYcQHTn1FZbCHZ8KxcwVOOTJ7W5z3WFi9DY4/s1600/number-line.gif" height="35" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">When the teacher asks
students to round their math answers, the students will need to figure out
simple math in their heads. For example, the price of the pencil box is $1.95 and
a marker cost $0.99 and the child needs to figure out the total amount to make
payments. He will need to round up or down to the nearest whole number to
determine the estimated total. Thus, the price of the pencil box can be rounded
up to $2.00 and the marker to $1.00 to make the total of $3.00.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><u><i>Teachers do take
note:</i></u><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">Please use the
correct terms when teaching.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><b>More than </b>NOT bigger
than<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;"><b>Less than</b> NOT smaller
than (use <b>fewer than</b>)<o:p></o:p></span></div>
Anonymoushttp://www.blogger.com/profile/04276189350823150354noreply@blogger.com0tag:blogger.com,1999:blog-2531547377701353678.post-10153508884102905892013-04-07T23:06:00.001-07:002013-04-07T23:06:25.155-07:00Numbers, Numbers, Numbers!!!!<br />
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<br /></div>
<div class="MsoNormal" style="text-align: start;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">What are numbers?
According to Wikipedia, <i>"</i></span><span style="font-family: Arial, sans-serif;"><i>A number is a mathematical object used to count, label and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers."</i></span></div>
<div class="MsoNormal" style="text-align: start;">
<span style="font-family: Arial, sans-serif;"><i><br /></i></span></div>
<div class="MsoNormal" style="text-align: start;">
<span style="font-family: Arial, sans-serif;">Rational Numbers??? Irrational Numbers??? Complex Numbers??? WHAT???</span></div>
<div class="MsoNormal" style="text-align: start;">
<span style="font-family: Arial, sans-serif;"><br /></span></div>
<div class="MsoNormal" style="text-align: start;">
<span style="font-family: Arial, sans-serif;">Ok, let's break down the Math jargon.</span></div>
<div class="MsoNormal" style="text-align: start;">
<span style="font-family: Arial, sans-serif;"><br /></span></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: Arial, sans-serif;"><u><b>Cardinal Numbers</b></u></span></div>
<div style="line-height: 16.5pt; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijBgGNdchQKpJEP-AUz1Q-plfjWZ-hFxb82KzXC6TH4u3XpesI5x9dL5PP3lIF2xwURSMJfYygVx-RfC0RK84Tm1Fmkfxy2fPFA9RYHp70qGbFKq7xfhOEqyDoIp2sTl9YLiQijPcjBkk/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijBgGNdchQKpJEP-AUz1Q-plfjWZ-hFxb82KzXC6TH4u3XpesI5x9dL5PP3lIF2xwURSMJfYygVx-RfC0RK84Tm1Fmkfxy2fPFA9RYHp70qGbFKq7xfhOEqyDoIp2sTl9YLiQijPcjBkk/s1600/images.jpg" height="200" width="140" /></a><span style="font-family: "Arial","sans-serif";">A <b>cardinal number</b> tells <b>"how
many."</b> Cardinal numbers are also known as "counting
numbers," because they <b>show quantity.</b><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Here
are some examples using cardinal numbers:<o:p></o:p></span></div>
<ul type="disc">
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">4 cats<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">10 friends</span></li>
</ul>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: Arial, sans-serif;"><b><u>Ordinal Numbers</u></b></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhu0ogYz50BD_LmR463JUmmSWBtS_KV6i6oFXT2NAf7yaeyi7HkeGfzclUwSRicV6BPf85CV5Y3QYd0yHEAXztxNzYPJ9AYJzO1Rlo3SH67CQzQKRU9-27owgrU_Atsv0v_9jTqSdA8bbk/s1600/images+(1).jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhu0ogYz50BD_LmR463JUmmSWBtS_KV6i6oFXT2NAf7yaeyi7HkeGfzclUwSRicV6BPf85CV5Y3QYd0yHEAXztxNzYPJ9AYJzO1Rlo3SH67CQzQKRU9-27owgrU_Atsv0v_9jTqSdA8bbk/s1600/images+(1).jpg" height="200" width="182" /></a><b><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Ordinal
numbers</span></b><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"> tell the <b>order of
things in a set</b>—first, second, third, etc. Ordinal numbers do not show
quantity. They only <b>show rank or position.</b><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Here
are some examples using ordinal numbers:<o:p></o:p></span></div>
<ul type="disc">
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l2 level1 lfo2; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">2nd fastest<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l2 level1 lfo2; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">5th in line<o:p></o:p></span></li>
</ul>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: Arial, sans-serif;"><b><u>Nominal Numbers</u></b></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYTcBftRUzoV2cBUbrZWDMRifXS4SskdzkHDkZAtGp2-AIIJEy_qh2NtvGhS4hwT2eT5x0mBXzHXaFipXpftOHw8sOPaC-UbJGp05Zv_A_QFyh67MBWfSIh1xz1C93lC8uUdvNUtsN_bQ/s1600/download.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYTcBftRUzoV2cBUbrZWDMRifXS4SskdzkHDkZAtGp2-AIIJEy_qh2NtvGhS4hwT2eT5x0mBXzHXaFipXpftOHw8sOPaC-UbJGp05Zv_A_QFyh67MBWfSIh1xz1C93lC8uUdvNUtsN_bQ/s1600/download.jpg" height="133" width="200" /></a><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">A <b>nominal
number names something</b>—a telephone number, a player on a team. Nominal
numbers do not show quantity or rank. They are used only to <b>identify
something.</b><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Here
are some examples using nominal numbers:<o:p></o:p></span></div>
<ul type="disc">
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l1 level1 lfo3; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Bus 147<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l1 level1 lfo3; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Phone number 91234567 <o:p></o:p></span></li>
</ul>
<div style="text-align: justify;">
<span style="font-family: Arial, sans-serif;"><span style="line-height: 22px;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: Arial, sans-serif;"><b><u>Rational Numbers</u></b></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">A
rational number is a number that can be written as a <b>ratio</b>. That means it can
be written as a <b>fraction,</b> in which both the <b>numerator</b> (the number on top) and
the <b>denominator</b> (the number on the bottom) are<b> whole numbers</b>.<o:p></o:p></span></div>
<ul type="disc">
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l3 level1 lfo4; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">The number 8 is a rational
number because it can be written as the fraction 8/1.<o:p></o:p></span></li>
<li class="MsoNormal" style="line-height: 16.5pt; mso-list: l3 level1 lfo4; mso-margin-bottom-alt: auto; tab-stops: list .5in; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Likewise, 3/4 is a rational
number because it can be written as a fraction. <div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPmIGPQCo0JzKo7K4ZcAvIOitDDqawfZw-hZS-uKOo_QCsv77mrGSIwDQUW7JqQoGymNNuYNA1LZUXa7iZtTLtiayYW_eK5rzKF3N8oZ3rt7Z3Xxca9hDBozIhH3GKL2nrbzTSne-mdj0/s1600/images+(2).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPmIGPQCo0JzKo7K4ZcAvIOitDDqawfZw-hZS-uKOo_QCsv77mrGSIwDQUW7JqQoGymNNuYNA1LZUXa7iZtTLtiayYW_eK5rzKF3N8oZ3rt7Z3Xxca9hDBozIhH3GKL2nrbzTSne-mdj0/s1600/images+(2).jpg" /></a></div>
<o:p></o:p></span></li>
</ul>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<br /></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-family: Arial, sans-serif;"><b><u>Irrational Numbers</u></b></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggzbW0_YXU1uezbDQ4ux_GjbdajEmp7xJHYUxCpaIvCgZWUkLUGwwVfqGnR2veqj6PSLwm1QSWgczGxEfHJrzpSCFs1PMI4Qyi_c2rRdkazWRUaP6RZxiXoyGk5ujw-3gpYGHe6PKYLBk/s1600/download+(1).jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggzbW0_YXU1uezbDQ4ux_GjbdajEmp7xJHYUxCpaIvCgZWUkLUGwwVfqGnR2veqj6PSLwm1QSWgczGxEfHJrzpSCFs1PMI4Qyi_c2rRdkazWRUaP6RZxiXoyGk5ujw-3gpYGHe6PKYLBk/s1600/download+(1).jpg" height="143" width="200" /></a><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">All
numbers that are not rational are considered irrational. An irrational number
can be written as a <b>decimal</b>, but not as a fraction.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">An
irrational number has endless non-repeating digits to the right of the decimal
point. Here are some irrational numbers:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; margin-bottom: 5.0pt; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">π = 3.141592…</span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">Although
irrational numbers are not often used in daily life, they do exist on the
number line. In fact, between 0 and 1 on the number line, there are an infinite
number of irrational numbers!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 16.5pt; mso-margin-bottom-alt: auto; text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><br /></span></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<br /></div>
<div class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph;">
<span style="font-family: "Arial","sans-serif"; font-size: 12.0pt;">And you think it ends
here? Think again, there are also Prime Numbers, Cute Numbers, Perfect Numbers
(yep that’s right CUTE and PERFECT), Complex numbers, Odd and Even Numbers, and
the list goes on. So think twice if you think that teaching young children is
an easy job!<o:p></o:p></span></div>
Anonymoushttp://www.blogger.com/profile/04276189350823150354noreply@blogger.com0tag:blogger.com,1999:blog-2531547377701353678.post-64264895587519774282013-03-30T04:05:00.000-07:002013-03-30T04:15:08.328-07:00Mathematics and Young Children<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj02BxPmTP4MFS6m4tW-v6ESt0pZXfLF58WztkKdDSKaoDM7CdWoMaDpN1dPthNBxc1FtDmNBo50AfbEmrRJDo7n5LR0jiQaWSmzA4su3RBjNkicy73LZT0w3Uaca1lMhJgSR11qqoV8SQ/s1600/boy-and-abacus.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj02BxPmTP4MFS6m4tW-v6ESt0pZXfLF58WztkKdDSKaoDM7CdWoMaDpN1dPthNBxc1FtDmNBo50AfbEmrRJDo7n5LR0jiQaWSmzA4su3RBjNkicy73LZT0w3Uaca1lMhJgSR11qqoV8SQ/s200/boy-and-abacus.jpg" width="133" /></a></div>
<br />
<div class="MsoNormal" style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;">How do we teach Mathematics to
young children? I strongly agree that the teachers need to thoroughly
understand the concept and content that they are teaching. Equipped with the
essential mathematical knowledge, teachers will then be able to be an effective
math teacher who will provide high quality mathematics education for the
children. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEI0OqCvKv43G8UeLjXKZ9mgBVIToSwGbnkDYviNdklyQW7o7_DMpGC-axFfQ5osAUsNa_nC1uYo4xComtJdFBNMQDo9-KHaDbu7bC0Jc59aNA-u1zT2tUw0jptQ6ZWjqRaLg3CASbFLU/s1600/mm8_kids1.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="146" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEI0OqCvKv43G8UeLjXKZ9mgBVIToSwGbnkDYviNdklyQW7o7_DMpGC-axFfQ5osAUsNa_nC1uYo4xComtJdFBNMQDo9-KHaDbu7bC0Jc59aNA-u1zT2tUw0jptQ6ZWjqRaLg3CASbFLU/s200/mm8_kids1.gif" width="200" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqzaFn5NbtWWGyudXpXhDBgoeEM9L3puaSqUrjbo4MrhV8Qh2tkmmU4fPf5rt4pUw_SUGCdct-HVtg85bk9KjnYbC7M9VU-a2S3u1H83rE4vXjf-f27da7SW0te9uw3s2_MQzLaFEY-HA/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="149" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqzaFn5NbtWWGyudXpXhDBgoeEM9L3puaSqUrjbo4MrhV8Qh2tkmmU4fPf5rt4pUw_SUGCdct-HVtg85bk9KjnYbC7M9VU-a2S3u1H83rE4vXjf-f27da7SW0te9uw3s2_MQzLaFEY-HA/s200/images.jpg" width="200" /></a><span style="font-family: Arial, Helvetica, sans-serif;">In school, we teach math in a fun way by using
games and real life experiences. For example, when teaching ordinal numbers, we
get the children involved in a race using toy cars. The children will stand side
by side behind the line and push their cars across. The children will get to identify
and label which car came first, second, third, etc. We like to emphasize to the
children that math is used in everyday life and is all around us. We bring the
children out to walk in the neighborhood and identify all the numbers and shapes.
When teaching about money, we set up a supermarket corner for the children to get
involved in counting money. Apart from that, the children also went to the
local supermarket to have the real experience in purchasing with real money. </span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">According to Jean Piaget,
constructivism is the key to learning math. He believed that learners are not
blank slates but rather creators of their own learning. It is said that children
build or construct their own knowledge by integrating new concepts into existing
mental structures. Children create or recreate mathematical concepts in their
own minds. Lev Vygotsky on the other hand,
believed that information which is internalized depends on whether it was within
a learner’s zone of proximal development (ZPD). It refers to the difference
between what a learner can do without help (on his own) and what he can do with
help. Teachers need not strictly choose between the two theories, but in fact
we need to create opportunities for the children to construct ideas or to
provide tools to promote mediation in the classroom.</span></div>
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