Comments for X·Y Points http://xycharts.com/wp Multiplication and Graphing: Mastering the Basics Wed, 08 Sep 2010 02:18:19 +0000 http://wordpress.org/?v=2.6.1 Comment on The Visual Integration of Multiplication and Graphing by Ryan http://xycharts.com/wp/?p=7#comment-15 Ryan Tue, 02 Sep 2008 16:38:43 +0000 http://xycharts.com/wp/?p=7#comment-15 The X.Y chart is a wonderful tool for automating this "first principle" in Mathematics. It is not to be underestimated how important single digit multiplication is for the prospects of a young child's math education. The X.Y chart is a wonderful tool for automating this “first principle” in Mathematics. It is not to be underestimated how important single digit multiplication is for the prospects of a young child’s math education.

]]> Comment on The Two Dimensional Times Table by admin http://xycharts.com/wp/?p=11#comment-14 admin Thu, 28 Aug 2008 17:36:30 +0000 http://xycharts.com/wp/?p=11#comment-14 Thanks for commenting. I've added the html to generate the modified tables that you suggest. <center> <table border="2"> <caption align=center><h3> Addition Table With Zero </h3> </caption> <caption align=center><h4> 9+9=18 BUT 100 squares </h4> </caption> <tr bgColor="#ffff00" align="center"> <td width=15>+</td> <td width=15>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> </tr> <tr bgColor=Fuschia align="center"> <td width=15 bgcolor="#ffff00">0</td> <td width=15>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">1</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">2</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">3</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00" width=15>4</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">5</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">6</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> <td>15</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">7</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> <td>15</td> <td>16</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">8</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> <td>15</td> <td>16</td> <td>17</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">9</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> <td>15</td> <td>16</td> <td>17</td> <td>18</td> </tr> </table> <br><br> <center><h3> Multiplication Table With Zero</h3> <table border="2"> <caption align=center><h4> 7x8=56 but 72 squares in rectangle </h4> </caption> <tr bgColor="#ffff00" align="center"> <td width=15>·</td> <td width=15>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td >9</td> </tr> <tr bgColor=Fuschia align="center"> <td width=15 bgColor="#ffff00">0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td bgcolor=white>0</td> <td bgcolor=white>0</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">1</td> <td>0</td> <td width=15>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td bgcolor=white>8</td> <td bgcolor=white>9</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">2</td> <td>0</td> <td>2</td> <td>4</td> <td>6</td> <td>8</td> <td>10</td> <td>12</td> <td>14</td> <td bgcolor=white>16</td> <td bgcolor=white>18</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">3</td> <td>0</td> <td>3</td> <td>6</td> <td>9</td> <td>12</td> <td>15</td> <td>18</td> <td>21</td> <td bgcolor=white>24</td> <td bgcolor=white>27</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00" width=15>4</td> <td>0</td> <td>4</td> <td>8</td> <td>12</td> <td>16</td> <td>20</td> <td>24</td> <td>28</td> <td bgcolor=white>32</td> <td bgcolor=white>36</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">5</td> <td>0</td> <td>5</td> <td>10</td> <td>15</td> <td>20</td> <td>25</td> <td>30</td> <td>35</td> <td bgcolor=white>40</td> <td bgcolor=white>45</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">6</td> <td>0</td> <td>6</td> <td>12</td> <td>18</td> <td>24</td> <td>30</td> <td>36</td> <td>42</td> <td bgcolor=white>48</td> <td bgcolor=white>54</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">7</td> <td>0</td> <td>7</td> <td>14</td> <td>21</td> <td>28</td> <td>35</td> <td>42</td> <td>49</td> <td bgcolor=white>56</td> <td bgcolor=white>63</td> </tr> <tr align=center bgcolor=Fuschia> <td bgColor="#ffff00">8</td> <td>0</td> <td>8</td> <td>16</td> <td>24</td> <td>32</td> <td>40</td> <td>48</td> <td>56</td> <td bgcolor=white>64</td> <td bgcolor=white>72</td> </tr> <tr align=center> <td bgColor="#ffff00">9</td> <td>0</td> <td>9</td> <td>18</td> <td>27</td> <td>36</td> <td>45</td> <td>54</td> <td>63</td> <td>73</td> <td>81</td> </tr> </table> </center> <br> Do you see the problem that the zeros cause in the multiplication table? If zero is a factor then the product is zero and would not have an area. Thanks for commenting. I’ve added the html to generate the modified tables that you suggest.

Addition Table With Zero

9+9=18 BUT 100 squares

+ 0 1 2 3 4 5 6 7 8 9
0 0 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9 10
2 2 3 4 5 6 7 8 9 10 11
3 3 4 5 6 7 8 9 10 11 12
4 4 5 6 7 8 9 10 11 12 13
5 5 6 7 8 9 10 11 12 13 14
6 6 7 8 9 10 11 12 13 14 15
7 7 8 9 10 11 12 13 14 15 16
8 8 9 10 11 12 13 14 15 16 17
9 9 10 11 12 13 14 15 16 17 18


Multiplication Table With Zero

7×8=56 but 72 squares in rectangle

· 0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 54
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 73 81



Do you see the problem that the zeros cause in the multiplication table? If zero is a factor then the product is zero and would not have an area.

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