{"id":643,"date":"2016-04-04T23:32:07","date_gmt":"2016-04-05T03:32:07","guid":{"rendered":"http:\/\/www.coast2coast.me\/carl\/?p=643"},"modified":"2016-04-04T23:32:07","modified_gmt":"2016-04-05T03:32:07","slug":"results-of-my-search-for-good-quadratic-tasks","status":"publish","type":"post","link":"https:\/\/www.coast2coast.me\/carl\/2016\/04\/04\/results-of-my-search-for-good-quadratic-tasks\/","title":{"rendered":"Results Of My Search For Good Quadratic Tasks"},"content":{"rendered":"<p>A few weeks ago I tweeted\u00a0this:<\/p>\n<blockquote class=\"twitter-tweet\" data-width=\"550\">\n<p lang=\"en\" dir=\"ltr\">Does anybody know of a real reason why one would multiply two binomials <a href=\"https:\/\/twitter.com\/hashtag\/MTBoS?src=hash\">#MTBoS<\/a><\/p>\n<p>&mdash; Carl Oliver (@carloliwitter) <a href=\"https:\/\/twitter.com\/carloliwitter\/status\/709466456937865216\">March 14, 2016<\/a><\/p><\/blockquote>\n<p><script async src=\"\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script><\/p>\n<p>This post will list a few of the interesting trends and what I ended up using with my class.<\/p>\n<h4>Perimeter-Area\u00a0Tasks<\/h4>\n<p>The first assignments\u00a0we did in the class revolved around the kids observing and talking about the patterns that they could see in <a href=\"http:\/\/visualpatterns.org\">visual patterns<\/a>, and <a href=\"https:\/\/docs.google.com\/document\/d\/1E7QAnccIrcH0sZpklOhoCxU1WJ4uz8GTpQjhgGQ6c7M\/edit?usp=sharing\">some<\/a>\u00a0<a href=\"https:\/\/docs.google.com\/document\/d\/1BJXx8Qu18SVV5FijPo2P-_P8AbZ0G0Vi3rkpoHc8HGc\/edit?usp=sharing\">instructional<\/a> <a href=\"https:\/\/docs.google.com\/document\/d\/145OqzJSCYgF0OUw9xW_lrWNDqIq3rilgZVt9A7YvdkM\/edit?usp=sharing\">activities<\/a>.\u00a0These usually involve seeing some shape change as it grows from one iteration to the next.<\/p>\n<p>Variables start appearing\u00a0once students see that there are parts of the pattern that add on more shapes\u00a0and use Length x Width,\u00a0or the corresponding area formula, to make some kind of equation.<\/p>\n<p>There\u00a0are also area tasks that involve fixing dimensions, and then finding the area. Here&#8217;s an example from <a href=\"https:\/\/nrich.maths.org\/2663\">NRICH<\/a>. If you give students a certain amount of fence and ask them to find the dimensions of the largest rectangle, or even other shapes, then result will be a quadratic function. The\u00a0resulting\u00a0function compares the variable\u00a0x representing one changing side, to the\u00a0area of the shape.<\/p>\n<h4>Changing-Rate tasks<\/h4>\n<p>Another type of tasks could involve changing rates, by that I mean a rate that is constantly changing. One relationship that was <a href=\"https:\/\/twitter.com\/bowenkerins\/status\/712274837595680769\">suggested via\u00a0twitter<\/a>\u00a0was that &#8216;price x quanity = revenue&#8217;. So like if kids have a price, and then quantity is allowed to vary, then they could make a linear function to find the revenue based on the price. Well sure Carl, but how could that be a quadratic when you just showed it&#8217;s linear?&#8221; Well, what if the price depended on quantity as well? This is actually a real phenomenon, as the price of products\u00a0typically go down as producers try to get you to buy more products. Then students would first have an equation\u00a0that would make sense for price.<\/p>\n<p>I made a task based around this principle that was talking about the &#8216;pay rate x hours = paycheck&#8217; relationships for my old college job. As a dishwasher I\u00a0was paid in both a constant, hourly rate, and a changing &#8220;tip share&#8221; that was handed out in increasing increments as I\u00a0worked more hours. This meant that the worksheet shows a dishwasher with\u00a0a pay rate that changes!\u00a0It&#8217;s a pretty interesting situation to explore.\u00a0Click below to see this task which both looks at the linear function for the pay rate after each hour, and also the quadratic function for total pay after working a number of hours.<\/p>\n<iframe src=\"\/\/docs.google.com\/viewer?url=http%3A%2F%2Fwww.coast2coast.me%2Fcarl%2Fwp-content%2Fuploads%2Fsites%2F3%2F2016%2F04%2FWashing-Dishes.docx&hl=en_US&embedded=true\" class=\"gde-frame\" style=\"width:100%; height:500px; border: none;\" scrolling=\"no\"><\/iframe>\n<p class=\"gde-text\"><a href=\"http:\/\/www.coast2coast.me\/carl\/wp-content\/uploads\/sites\/3\/2016\/04\/Washing-Dishes.docx\" class=\"gde-link\">Download (DOCX, 1.29MB)<\/a><\/p>\n<p>I brought this up again in my final project, where kids make a cereal (This one will hopefully gets finished soon, and I will post it then). In my cereal project, I told kids they were going to design a $6.00 box of cereal, it could have a price that had to lower the price by half a penny everytime they wanted to produce more. So they have an equation for the price per box of 6 &#8211; .005Q = P. They and can make a revenue equation by multiplying price by quantity like before (6-.005Q)Q = R.<\/p>\n<h4>Projectile Motion Tasks<\/h4>\n<p>There a bunch of tasks where the kids are given an equation that models certain types of <a href=\"http:\/\/blog.mrmeyer.com\/2010\/wcydwt-will-it-hit-the-hoop\/\">scenarios<\/a>,\u00a0and then they have to apply it to a specific situation. This could be using a graphing calculator to find the coefficients of a function that models a projectiles motion. This could be charting some real or recorded scenario\u00a0where kids have to model the flight of balls, or catapult launched stuff,\u00a0maybe\u00a0even cornhole beanbags. At the end kids find the coefficients for an equation that uses the position vertically and horizontally. It&#8217;s also possible to find <a href=\"http:\/\/zackmillermathblog.com\/2014\/08\/03\/projectile-motion-project-pt-1\/\">tasks<\/a> that\u00a0look at the relationship between time and height.<\/p>\n<h4>My Dream Task<\/h4>\n<p>In my mind I have a dream quadratics task that I wish existed\u00a0but I wasn&#8217;t able to find it or figure it out.\u00a0My dream task would be one where students come up with two linear equations related to the same context and then multiply them to find a new quadratic equation that makes sense in the context. This would mean they could draw all the graphs and see that for any x, they can look up and see the y-value from the two linear equations, and see the resulting\u00a0product lying on the graph of the quadratic function. It seems like it could result in a whole bunch of connection-making and good mathematical discourse.<\/p>\n<p>Have you seen a task like that before? Or any other good tasks? Let me know in the comments!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A few weeks ago I tweeted\u00a0this: Does anybody know of a real reason why one would multiply two binomials #MTBoS &mdash; Carl Oliver (@carloliwitter) March 14, 2016 This post will list a few of the interesting trends and what I ended up using with my class. Perimeter-Area\u00a0Tasks The first assignments\u00a0we did in the class revolved [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false},"categories":[1],"tags":[],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4xz6U-an","_links":{"self":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts\/643"}],"collection":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/comments?post=643"}],"version-history":[{"count":2,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts\/643\/revisions"}],"predecessor-version":[{"id":646,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/posts\/643\/revisions\/646"}],"wp:attachment":[{"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/media?parent=643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/categories?post=643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.coast2coast.me\/carl\/wp-json\/wp\/v2\/tags?post=643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}