{"id":72386,"date":"2020-05-21T13:39:01","date_gmt":"2020-05-21T17:39:01","guid":{"rendered":"http:\/\/schools.wrdsb.ca\/athome\/?page_id=72386"},"modified":"2020-05-25T13:22:14","modified_gmt":"2020-05-25T17:22:14","slug":"yohaku-multiplication-puzzles-revisited","status":"publish","type":"page","link":"https:\/\/schools.wrdsb.ca\/athome\/learn\/elementary-home\/elementary-2\/math\/math-grades-4-6\/puzzles-and-riddles\/yohaku-multiplication-puzzles-revisited\/","title":{"rendered":"Yohaku Multiplication Puzzles (Revisited)"},"content":{"rendered":"<h5>Puzzles and Riddles<\/h5>\n<h2>Learning Goals:<\/h2>\n<ul>\n<li>Multiply and divide whole numbers using a variety of tools and strategies<\/li>\n<li>Determine the missing numbers in equations<\/li>\n<li>Develop and apply reasoning skills to make and test math predictions<\/li>\n<\/ul>\n<h2>The Challenge:<\/h2>\n<p>The goal of these three-by-three yohaku puzzles is to find which boxes to place the numbers 1-9, so that each row and column multiplies to the corresponding products at the right and bottom. You can repeat digits, if you want!<\/p>\n<p>Here is an example that has been solved. You can see in the centre column that 4 x 2 = 8, and then 8 x 9 = 72.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-72387\" src=\"http:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1.png\" alt=\"An example solution of a three-by-three yohaku puzzle where numbers need to multiply down to the products 40, 72, and 30 (at the bottom), as well as across to the products 48, 50, and 36 (down the right side.) From left to right, the solved digits are 2, 4, 6 (top row), 5, 2, 5 (middle row), and 4, 9, 1 (bottom row).\" width=\"450\" height=\"440\" srcset=\"https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1.png 1206w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-300x294.png 300w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-768x751.png 768w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-1024x1002.png 1024w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-50x50.png 50w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-165x161.png 165w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-1140x1115.png 1140w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-945x925.png 945w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_1-750x734.png 750w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-72389\" src=\"http:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2.png\" alt=\"A beginner difficulty three-by-three yohaku puzzle where numbers need to multiply down to the products 4, 18, and 70 (at the bottom), as well as across to the products 24, 42, and 5 (down the right side.) The centre left, bottom left, and bottom middle digits have all been filled in as 1's.\" width=\"450\" height=\"444\" srcset=\"https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2.png 1200w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-300x296.png 300w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-768x758.png 768w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-1024x1010.png 1024w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-50x50.png 50w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-100x100.png 100w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-165x163.png 165w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-1140x1125.png 1140w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-945x932.png 945w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_2-750x740.png 750w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-72391\" src=\"http:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3.png\" alt=\"A medium difficulty three-by-three yohaku puzzle where numbers need to multiply down to the products 24, 72, and 210 (at the bottom), as well as across to the products 24, 120, and 126 (down the right side.) The top right digit has been filled in as a 4, and the bottom middle digit has been filled in as a 9.\" width=\"450\" height=\"440\" srcset=\"https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3.png 1210w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-300x293.png 300w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-768x750.png 768w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-1024x1000.png 1024w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-50x50.png 50w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-165x161.png 165w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-1140x1114.png 1140w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-945x923.png 945w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_3-750x733.png 750w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-72392\" src=\"http:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4.png\" alt=\"A medium difficulty three-by-three yohaku puzzle where numbers need to multiply down to the products 40, 48, and a missing number (at the bottom), as well as across to the products 28, 144, and 90 (down the right side.)\" width=\"450\" height=\"446\" srcset=\"https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4.png 1192w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-150x150.png 150w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-300x297.png 300w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-768x762.png 768w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-1024x1015.png 1024w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-50x50.png 50w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-100x100.png 100w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-165x164.png 165w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-1140x1130.png 1140w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-945x937.png 945w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_4-750x744.png 750w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-72393\" src=\"http:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5.png\" alt=\"A three-by-three yohaku puzzle where numbers need to multiply down to the products 60, 21, and 288 (at the bottom), as well as across to the products 24, 40, and 378 (down the right side.)\" width=\"450\" height=\"447\" srcset=\"https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5.png 1198w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-150x150.png 150w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-300x298.png 300w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-768x763.png 768w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-1024x1017.png 1024w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-50x50.png 50w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-100x100.png 100w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-165x164.png 165w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-1140x1132.png 1140w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-945x939.png 945w, https:\/\/schools.wrdsb.ca\/athome\/files\/2020\/05\/Yohaku_2_5-750x745.png 750w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/p>\n<h3>Questions and Prompts to Support your Child:<\/h3>\n<ul>\n<li>What have you tried so far? What could we try together?<\/li>\n<li>If that combination of numbers didn\u2019t work out, what could you try instead?<\/li>\n<li>If you feel stuck, it might help to start by thinking about the products around the outside, listing potential sets of three numbers that could multiply to get these answers. Then start looking for matching numbers from these lists &#8211; those could be the numbers that work in the intersecting blanks!<\/li>\n<\/ul>\n<h3>Extensions &amp; Adaptations:<\/h3>\n<ul>\n<li>If calculations are feeling too tricky, grab a calculator!<\/li>\n<li>This might be our first time experiencing multiplication focused around more than 2 factors. Try thinking about pairing up factors in different ways before multiplying with the third. How could we represent multiplication with three factors, since 2-dimensional arrays will no longer quite make sense?<\/li>\n<li>Do any of these puzzles have more than one possible solution? How can you prove it?<\/li>\n<li>Try creating your own yohaku puzzle by starting with nine different digits in the boxes, multiplying to get the products to the right and below, then erasing the original numbers<\/li>\n<li>Check out <a href=\"https:\/\/www.yohaku.ca\/\" target=\"_blank\" rel=\"noopener\">yohaku.ca<\/a> for many more puzzles &#8211; including some more challenging options!<\/li>\n<\/ul>\n<p>Adapted from <a href=\"http:\/\/yohaku.ca\" target=\"_blank\" rel=\"noopener\">Yohaku.ca<\/a> and <a href=\"https:\/\/nrich.maths.org\/\" target=\"_blank\" rel=\"noopener\">NRICH Math<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The goal of these three-by-three yohaku puzzles is to find which boxes to place the numbers 1-9, so that each row and column multiplies to the corresponding products at the right and bottom. <\/p>\n","protected":false},"author":15985,"featured_media":0,"parent":72901,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-72386","page","type-page","status-publish","hentry","category-elementary"],"_links":{"self":[{"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/pages\/72386","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/users\/15985"}],"replies":[{"embeddable":true,"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/comments?post=72386"}],"version-history":[{"count":0,"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/pages\/72386\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/pages\/72901"}],"wp:attachment":[{"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/media?parent=72386"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/categories?post=72386"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schools.wrdsb.ca\/athome\/wp-json\/wp\/v2\/tags?post=72386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}