{"id":4916,"date":"2023-06-23T03:20:32","date_gmt":"2023-06-23T03:20:32","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4916"},"modified":"2025-08-23T00:49:37","modified_gmt":"2025-08-23T00:49:37","slug":"historical-counting-systems-get-stronger","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/historical-counting-systems-get-stronger\/","title":{"raw":"Historical Counting Systems: Get Stronger","rendered":"Historical Counting Systems: Get Stronger"},"content":{"raw":"<p><strong>Counting Board And Quipu<\/strong><\/p>\r\n<p>1)\u00a0\u00a0\u00a0\u00a0\u00a0 In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing.<\/p>\r\n<center>\r\n[caption id=\"attachment_2527\" align=\"alignnone\" width=\"392\"]<img class=\"wp-image-2527\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-300x172.png\" sizes=\"(max-width: 392px) 100vw, 392px\" srcset=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-300x172.png 300w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-65x37.png 65w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-225x129.png 225w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-350x200.png 350w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots.png 599w\" alt=\"Simple depiction of a Peruvian counting board. The key at the bottom shows that black pebbles represent jars, spotted pebbles represent baskets, and striped pebbles represent tools. There are three black pebbles, four spotted pebbles, and four striped pebbles in the outer square regions. There are no black pebbles, one spotted pebble, and one striped pebble in the larger white rectangular compartments. There are three black pebbles, four spotted pebbles, and two striped pebbles in the middle region. There are two black pebbles, four spotted pebbles, and two striped pebbles on the second levels. Finally, there is one black pebble, one spotted pebble, and two striped pebbles on the highest corner levels.\" width=\"392\" height=\"225\" \/> Figure 1. Decipher this quipu board[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>2) \u00a0Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part\u00a0<strong>a<\/strong>\u00a0on the left and moving to the right for parts\u00a0<strong>b<\/strong>\u00a0through\u00a0<strong>d<\/strong>.)<\/p>\r\n<p>(a) [latex]232[\/latex]<\/p>\r\n<p>(b) [latex]5065[\/latex]<\/p>\r\n<p>(c) [latex]23,451[\/latex]<\/p>\r\n<p>(d) [latex]3002[\/latex]<\/p>\r\n<p><strong>Basic Base Conversions<\/strong><\/p>\r\n<p>3) 423 in base 5 to base 10 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 4) 3044 in base 5 to base 10<\/p>\r\n<p>5) 387 in base 10 to base 5 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 6) 2546 in base 10 to base 5<\/p>\r\n<p>7) 110101 in base 2 to base 10 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 8) 11010001 in base 2 to base 10<\/p>\r\n<p>9) 100 in base 10 to base 2 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2002 10) 2933 in base 10 to base 2<\/p>\r\n<p>11) Convert 653 in base 7 to base 10 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 12) Convert 653 in base 10 to base 7<\/p>\r\n<p>13) 3412 in base 5 to base 2 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2002 14) 10011011 in base 2 to base 5<\/p>\r\n<p><strong>Mayan Conversions<\/strong><\/p>\r\n<p><em>Convert the following numbers to Mayan notation. Show your calculations used to get your answers.<\/em><\/p>\r\n<p>&nbsp;<\/p>\r\n<p>15)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]135[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16) [latex]234[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>17)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]360[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 18) [latex]1,215[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>19)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]10,500[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 20) [latex]1,100,000[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p><em>Convert the following Mayan numbers to decimal (base<\/em><em>-[latex]10[\/latex]) numbers. Show all calculations.<\/em><\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>\r\n<p>21)<\/p>\r\n<p><img class=\"alignnone wp-image-2023\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211750\/Untitled210.png\" alt=\"three compartments stacked vertically - from the bottom: two horizontal lines and two dots, two dots, one dot\" width=\"65\" height=\"133\" \/><\/p>\r\n<\/td>\r\n<td>\r\n<p>22)<\/p>\r\n<p><img class=\"alignnone wp-image-2024\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211814\/Untitled38.png\" alt=\"three compartments stacked vertically - from the bottom: one shell, four dots, one dot\" width=\"70\" height=\"135\" \/><\/p>\r\n<\/td>\r\n<td>\r\n<p>23)<\/p>\r\n\r\n\u00a0<img class=\"wp-image-2025 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211839\/Untitled41.png\" alt=\"three compartments - from the bottom: three dots, one shell, three dots\" width=\"74\" height=\"160\" \/><\/td>\r\n<td>\r\n<p>\u00a024)<\/p>\r\n<p><img class=\"wp-image-2026 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211905\/Untitled51.png\" alt=\"4 compartments with mayan symbols - from the bottom: one shell, next, one shell, two horizontal lines stacked, two horizontal lines and two dots stacked.\" width=\"89\" height=\"258\" \/><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p><span style=\"font-size: 10pt;\"><strong>Figure 2.<\/strong>\u00a0<strong>Count these Mayan numbers<\/strong><\/span><\/p>\r\n<p>James Bidwell has suggested that Mayan addition was done by \u201csimply combining bars and dots and carrying to the next higher place.\u201d He goes on to say, \u201cAfter the combining of dots and bars, the second step is to exchange every five dots for one bar in the same position.\u201d After converting the following base [latex]10[\/latex] numbers into vertical Maya notation (in base [latex]20[\/latex], of course), perform the indicated addition:<\/p>\r\n<p>25)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]32[\/latex] + [latex]11[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 26) [latex]82 + 15[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>27)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]35 + 148[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a028) [latex]2412 + 5000[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>29)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]450 + 844[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 30) [latex]10,000 + 20,000[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>31)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]4,500 + 3,500[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a032) [latex]130,000 + 30,000[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>33)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Use the fact that the Mayans had a base-[latex]20[\/latex] number system to complete the following multiplication table. The table entries should be in Mayan notation. Remember: Their zero looked like this\u2026. <em>Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.<\/em><\/p>\r\n<p>(To think about but not write up: Bidwell claims that only these entries are needed for \u201cMayan multiplication.\u201d What does he mean?)<\/p>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>\r\n<p>&nbsp;<\/p>\r\n<p>x<\/p>\r\n<\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\"><img class=\"alignnone wp-image-2027 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\" alt=\"one dot\" width=\"13\" height=\"11\" \/><\/a><\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\"><img class=\"alignnone wp-image-2028 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\" alt=\"two dots\" width=\"17\" height=\"10\" \/><\/a><\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\"><img class=\"alignnone wp-image-2029 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\" alt=\"three dots\" width=\"20\" height=\"10\" \/><\/a><\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\"><img class=\"alignnone wp-image-2030 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\" alt=\"four dots\" width=\"25\" height=\"9\" \/><\/a><\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\"><img class=\"alignnone wp-image-2031 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\" alt=\"one horizontal line\" width=\"25\" height=\"9\" \/><\/a><\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\"><img class=\"alignnone wp-image-2032 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\" alt=\"two horizontal lines stacked\" width=\"27\" height=\"10\" \/><\/a><\/td>\r\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\"><img class=\"alignnone wp-image-2033 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\" alt=\"three horizontal lines stacked\" width=\"26\" height=\"12\" \/><\/a><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\"><img class=\"alignnone wp-image-2027 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\" alt=\"one dot\" width=\"13\" height=\"11\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\"><img class=\"alignnone wp-image-2028 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\" alt=\"two dots\" width=\"17\" height=\"10\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\"><img class=\"alignnone wp-image-2029 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\" alt=\"three dots\" width=\"20\" height=\"10\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\"><img class=\"alignnone wp-image-2030 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\" alt=\"four dots\" width=\"25\" height=\"9\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\"><img class=\"alignnone wp-image-2031 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\" alt=\"one horizontal line\" width=\"25\" height=\"9\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\"><img class=\"alignnone wp-image-2032 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\" alt=\"two horizontal lines stacked\" width=\"27\" height=\"10\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\"><img class=\"alignnone wp-image-2033 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\" alt=\"three horizontal lines stacked\" width=\"26\" height=\"12\" \/><\/a><\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p>&nbsp;<\/p>","rendered":"<p><strong>Counting Board And Quipu<\/strong><\/p>\n<p>1)\u00a0\u00a0\u00a0\u00a0\u00a0 In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing.<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_2527\" aria-describedby=\"caption-attachment-2527\" style=\"width: 392px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2527\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-300x172.png\" sizes=\"(max-width: 392px) 100vw, 392px\" srcset=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-300x172.png 300w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-65x37.png 65w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-225x129.png 225w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots-350x200.png 350w, https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/04\/07212752\/histcountdots.png 599w\" alt=\"Simple depiction of a Peruvian counting board. The key at the bottom shows that black pebbles represent jars, spotted pebbles represent baskets, and striped pebbles represent tools. There are three black pebbles, four spotted pebbles, and four striped pebbles in the outer square regions. There are no black pebbles, one spotted pebble, and one striped pebble in the larger white rectangular compartments. There are three black pebbles, four spotted pebbles, and two striped pebbles in the middle region. There are two black pebbles, four spotted pebbles, and two striped pebbles on the second levels. Finally, there is one black pebble, one spotted pebble, and two striped pebbles on the highest corner levels.\" width=\"392\" height=\"225\" \/><figcaption id=\"caption-attachment-2527\" class=\"wp-caption-text\">Figure 1. Decipher this quipu board<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>2) \u00a0Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part\u00a0<strong>a<\/strong>\u00a0on the left and moving to the right for parts\u00a0<strong>b<\/strong>\u00a0through\u00a0<strong>d<\/strong>.)<\/p>\n<p>(a) [latex]232[\/latex]<\/p>\n<p>(b) [latex]5065[\/latex]<\/p>\n<p>(c) [latex]23,451[\/latex]<\/p>\n<p>(d) [latex]3002[\/latex]<\/p>\n<p><strong>Basic Base Conversions<\/strong><\/p>\n<p>3) 423 in base 5 to base 10 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 4) 3044 in base 5 to base 10<\/p>\n<p>5) 387 in base 10 to base 5 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 6) 2546 in base 10 to base 5<\/p>\n<p>7) 110101 in base 2 to base 10 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 8) 11010001 in base 2 to base 10<\/p>\n<p>9) 100 in base 10 to base 2 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2002 10) 2933 in base 10 to base 2<\/p>\n<p>11) Convert 653 in base 7 to base 10 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003 12) Convert 653 in base 10 to base 7<\/p>\n<p>13) 3412 in base 5 to base 2 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2002 14) 10011011 in base 2 to base 5<\/p>\n<p><strong>Mayan Conversions<\/strong><\/p>\n<p><em>Convert the following numbers to Mayan notation. Show your calculations used to get your answers.<\/em><\/p>\n<p>&nbsp;<\/p>\n<p>15)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]135[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16) [latex]234[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>17)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]360[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 18) [latex]1,215[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>19)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]10,500[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 20) [latex]1,100,000[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p><em>Convert the following Mayan numbers to decimal (base<\/em><em>&#8211;[latex]10[\/latex]) numbers. Show all calculations.<\/em><\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<p>21)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2023\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211750\/Untitled210.png\" alt=\"three compartments stacked vertically - from the bottom: two horizontal lines and two dots, two dots, one dot\" width=\"65\" height=\"133\" \/><\/p>\n<\/td>\n<td>\n<p>22)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2024\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211814\/Untitled38.png\" alt=\"three compartments stacked vertically - from the bottom: one shell, four dots, one dot\" width=\"70\" height=\"135\" \/><\/p>\n<\/td>\n<td>\n<p>23)<\/p>\n<p>\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2025 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211839\/Untitled41.png\" alt=\"three compartments - from the bottom: three dots, one shell, three dots\" width=\"74\" height=\"160\" \/><\/td>\n<td>\n<p>\u00a024)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2026 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21211905\/Untitled51.png\" alt=\"4 compartments with mayan symbols - from the bottom: one shell, next, one shell, two horizontal lines stacked, two horizontal lines and two dots stacked.\" width=\"89\" height=\"258\" \/><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-size: 10pt;\"><strong>Figure 2.<\/strong>\u00a0<strong>Count these Mayan numbers<\/strong><\/span><\/p>\n<p>James Bidwell has suggested that Mayan addition was done by \u201csimply combining bars and dots and carrying to the next higher place.\u201d He goes on to say, \u201cAfter the combining of dots and bars, the second step is to exchange every five dots for one bar in the same position.\u201d After converting the following base [latex]10[\/latex] numbers into vertical Maya notation (in base [latex]20[\/latex], of course), perform the indicated addition:<\/p>\n<p>25)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]32[\/latex] + [latex]11[\/latex]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 26) [latex]82 + 15[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>27)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]35 + 148[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a028) [latex]2412 + 5000[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>29)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]450 + 844[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 30) [latex]10,000 + 20,000[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>31)\u00a0\u00a0\u00a0\u00a0\u00a0 [latex]4,500 + 3,500[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a032) [latex]130,000 + 30,000[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>33)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Use the fact that the Mayans had a base-[latex]20[\/latex] number system to complete the following multiplication table. The table entries should be in Mayan notation. Remember: Their zero looked like this\u2026. <em>Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.<\/em><\/p>\n<p>(To think about but not write up: Bidwell claims that only these entries are needed for \u201cMayan multiplication.\u201d What does he mean?)<\/p>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>\n<p>&nbsp;<\/p>\n<p>x<\/p>\n<\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2027 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\" alt=\"one dot\" width=\"13\" height=\"11\" \/><\/a><\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2028 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\" alt=\"two dots\" width=\"17\" height=\"10\" \/><\/a><\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2029 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\" alt=\"three dots\" width=\"20\" height=\"10\" \/><\/a><\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2030 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\" alt=\"four dots\" width=\"25\" height=\"9\" \/><\/a><\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2031 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\" alt=\"one horizontal line\" width=\"25\" height=\"9\" \/><\/a><\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2032 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\" alt=\"two horizontal lines stacked\" width=\"27\" height=\"10\" \/><\/a><\/td>\n<td>\u00a0<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2033 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\" alt=\"three horizontal lines stacked\" width=\"26\" height=\"12\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2027 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213229\/Untitled61.png\" alt=\"one dot\" width=\"13\" height=\"11\" \/><\/a><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2028 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213251\/Untitled71.png\" alt=\"two dots\" width=\"17\" height=\"10\" \/><\/a><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2029 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213314\/Untitled81.png\" alt=\"three dots\" width=\"20\" height=\"10\" \/><\/a><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2030 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213334\/Untitled91.png\" alt=\"four dots\" width=\"25\" height=\"9\" \/><\/a><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2031 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213353\/Untitled101.png\" alt=\"one horizontal line\" width=\"25\" height=\"9\" \/><\/a><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2032 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213414\/Untitled111.png\" alt=\"two horizontal lines stacked\" width=\"27\" height=\"10\" \/><\/a><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2033 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/21213436\/Untitled121.png\" alt=\"three horizontal lines stacked\" width=\"26\" height=\"12\" 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