{"id":159,"date":"2017-01-31T12:49:06","date_gmt":"2017-01-31T18:49:06","guid":{"rendered":"https:\/\/chalkdoc.com\/?p=159"},"modified":"2019-08-18T14:55:51","modified_gmt":"2019-08-18T20:55:51","slug":"quadratics-day-1","status":"publish","type":"post","link":"https:\/\/chalkdoc.com\/quadratics-day-1\/","title":{"rendered":"The Sample Hack: Quadratics"},"content":{"rendered":"\n

Given the chance, students can teach themselves many of the trickiest concepts in math. \u00a0Now… to\u00a0want\u00a0<\/em>to teach themselves. \u00a0The typical student wouldn’t be thrilled about the prospect\u00a0of teaching themselves by reading a textbook, streaming a video, or listening to a pre-recorded lecture. \u00a0So long as\u00a0there are new recipes to test or hikes to try, I\u00a0wouldn’t be either.<\/p>\n\n\n\n

Why the Sample Hack?<\/strong><\/h2>\n\n\n\n

Most\u00a0people like puzzles–certainly far more than a lecture–so long as they feel challenging and solvable. \u00a0So, when introducing new concepts, I like to begin with a Sample Hack. \u00a0The Sample Hack is simple: Students see a series of examples of the new idea, then try to reverse engineer it. \u00a0Sometimes I give them all the information they need, sometimes I give them part of it, and sometimes I slowly reveal new critical pieces. \u00a0This can work for just about any topic and is\u00a0very\u00a0<\/em>easy to design.<\/p>\n\n\n\n

Here’s an example for quadratics. \u00a0Students split into teams and receive\u00a0ten quadratic functions and their corresponding graphs. \u00a0By finding patterns among the functions, their goals for the day are to define and understand quadratics. \u00a0The activity breaks down into two stages, unless you’re feeling ambitious and add the optional third.<\/p>\n\n\n\n

Implementation<\/strong><\/h2>\n\n\n\n

Stage 1<\/strong><\/h3>\n\n\n\n

Given the features of quadratics and the patterns they see among these examples, each team creates\u00a0as many questions as possible about quadratics. \u00a0(For example: \u00a0Why do some go up and some go down? \u00a0Why are they curved? \u00a0How can you tell where they start? \u00a0Could you make one that’s a line?) \u00a0The power here comes from\u00a0the open-endedness of the puzzle–teams look for any\u00a0<\/em>features and patterns that look interesting. \u00a0In doing so, they’ll find many things they’ve seen before (e.g. curves and intercepts) and several unique features (e.g. a U-shape and a squared term), which will help them intuit how quadratics fit among the other function families.<\/p>\n\n\n\n

At the end of this stage, record the questions each team comes up with and pose them to the class.  If you like, add one or two questions of your own!<\/p>\n\n\n\n

Stage 2<\/strong><\/h3>\n\n\n\n

Teams answer as many of the questions as they can. \u00a0For this stage, you may choose to group the questions into checkpoints. \u00a0If you do, you’ll have the chance to stop and reflect as a group once you complete each checkpoint\u00a0throughout the class. \u00a0Alternatively, you may tell students you’ll have checkpoints… but never tell them which questions will fall into which buckets until the\u00a0end\u00a0<\/em>of the checkpoint. \u00a0This way, each team is\u00a0incentivized to answer as many questions as it can and has the autonomy\u00a0to begin with the questions it finds most interesting.<\/p>\n\n\n\n

Here’s a link to the activity: Sample Hack – Quadratics<\/a>.  By the end of one day, teams will have built a conceptual framework about what defines quadratics and what makes them work.  For an idea about the range of questions teams can answer together, see the teacher guide included at the bottom of the assignment.<\/p>\n\n\n\n

Extensions<\/strong><\/h3>\n\n\n\n

If you’re looking for a Stage 3<\/strong>, consider challenging each team to design a series of quadratics that meet certain specifications (e.g. opens down and has a vertex in the third quadrant) and letting them test their idea on a graphing calculator.  (If you don’t have graphing calculators or computers, project Desmos and let the class see each team’s results.)<\/p>\n\n\n\n

On Day 2<\/strong>, you can spend part of class opening the door to applications in a way that connects tables to the graphs and equations students learned on the first day.  Students can begin class by answering the question, “What kinds of things might quadratics model?” in as many creative ways possible.  Once the class (or each team) has a number of ideas, students can fill out blank xy data tables with hypothesized data (e.g. “I think <\/em>that this data would model how many people show up to a concert over time”) and then plot that data to see if it really looks like a quadratic (in the case of concert attendance, probably not because it would likely rise, stay fairly flat, and then drop).  At the end, students can look for patterns differentiating the tables that worked from those that didn’t.<\/p>\n\n\n\n

Let me know if you have any questions, suggestions, or requests!<\/p>\n\n\n","protected":false},"excerpt":{"rendered":"

A great first day activity for quadratics that let’s students analyze and define the key features of their graphs and equations… entirely on their own!<\/p>\n","protected":false},"author":1,"featured_media":161,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[37,12,16],"_links":{"self":[{"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/posts\/159"}],"collection":[{"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/comments?post=159"}],"version-history":[{"count":7,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/posts\/159\/revisions"}],"predecessor-version":[{"id":891,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/posts\/159\/revisions\/891"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/media\/161"}],"wp:attachment":[{"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/media?parent=159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/categories?post=159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/chalkdoc.com\/wp-json\/wp\/v2\/tags?post=159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}