tag:blogger.com,1999:blog-83993892678150591122014-04-15T03:20:49.552-05:00Algebra's FriendMath is beautiful.Beth Fergusonhttps://plus.google.com/101031905836509369212noreply@blogger.comBlogger206125tag:blogger.com,1999:blog-8399389267815059112.post-79760753057287550012014-04-14T21:42:00.002-05:002014-04-14T21:42:36.207-05:00Writing in Math ClassWriting has been a big topic on our campus this year ... a school initiative. Our math coach has stressed improving upon our short constructed responses more than emphasizing the writing of essays.<br /><br />With that in mind our coach shared a few writing frames from science that can be used in math. <a href="https://drive.google.com/a/roundrockisd.org/file/d/0ByJ71RI_wBc7N2hfNDNualFyaHNJZkxWWUlIeWh5aGp0WEpz/edit?usp=sharing">Here are 3 samples!</a> These samples are simplistic but great for teaching structure of writing short responses!<br /><br />We incorporate writing in many activities and all of our tests. Again, our writing prompts are for short responses. Here are some examples from recent activities:<br /><br /><b>From our rational function unit,</b> What is the horizontal asymptote of this function? Show this on the graph. What does this value represent in terms of the prom tickets? Thinking about the cost of the tickets, why does your value for the horizontal asymptote make sense?<br /><b><br /></b><b>From our exponential unit:</b> You have a rich Uncle that gives you $5000 to invest. You have researched two different banks to see which you want to use to help you make the most money. Describe when it would be better to choose MK Federal Credit Union and when it would be better to choose MCB National.<br /><br /><b>From our square root unit: </b>Does doubling the length of the skid double the speed the driver was going? Justify your response using tables, symbols, and graphs.<br /><br /><b>From a recent project, one choice included:</b> Read an article about mathematics or a mathematician in the New York Times (http://topics.nytimes.com/top/news/science/topics/mathematics/). Create a mini-poster that illustrates the article. Include a “3-Part Source Integration” writing. A “3-Part Source Integration” is a three-sentence statement that includes the title of the text, the author’s name, author information, source material that is either paraphrased or directly quoted, and a brief statement explaining the significance of the paraphrase or quotation.<br /><br />We have also written responses on Edmodo to Math Munch postings. Here is <a href="http://algebrasfriend.blogspot.com/2013/10/math-munching-today.html">a blog post</a> where I share students' thoughts. <br /><br />I find that these short writing opportunities provide windows into students' thinking. How do you use short writing prompts?<br /><br />In the article, <a href="http://www-tc.pbs.org/teacherline/courses/rdla230/docs/session_6_brandenburg.pdf">"Advanced Math? Write!"</a> the author stresses to start small. She emphasizes journal writing. I have not tried journal writing with 150 students. Even when I had considerably fewer students I found keeping up with responses to journals challenging. How could I begin journaling with students without feeling overwhelmed?<br /><br /><br /><br /><br />Beth Fergusonhttps://plus.google.com/101031905836509369212noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-8737808981421180232014-04-10T18:03:00.000-05:002014-04-10T18:03:17.589-05:00Rational Functions ... how do you teach them?I thought I'd write about how we structure our rational functions unit. I'm curious what others do with it.<br /><br />(Background ... we are Texas - a non common core state; we have 90 minute classes <u><b>every other </b></u>day)<br /><br />We split the unit into two parts.<br /><br />Part 1<br />Day 1: Data Collection: How is the resulting graph like others we have studied? How is it different? (We start every function unit with a data collection day). For rational functions we used the spaghetti cantilever activity. <a href="http://180snaps.blogspot.com/2014/03/day-128-spaghetti-cantilevers.html">Find it here.</a> Students work in teams, collect data, answer questions about independent, dependent variables, discrete vs continuous functions, and domain and range. Then they try to find a function that fits their data.<br /><br />Day 2: Transformations: Transformations are a huge part of our curriculum and by this time of the year, students are very familiar with how "a," "h," and "k" affect functions. So we start with the basic rational function in transformation form. Students use Desmos to track transformations and describe them. With this day we talk about asymptotes and how they are a major attribute of this function. (Asymptotes were introduced in our exponential/logarithm unit). Last we express the domain and range of functions!<br /><br />Day 3 & 4: We start this day with a review of factoring and how to use factoring to simplify algebraic fractions. Then we being the work of dissecting the attributes of the rational functions based on the factored forms of functions. We start with discontinuities - the vertical asymptotes and holes. Then we discuss the horizontal asymptote; next we find the intercepts; and last we write the domain and range. <br /><br />Day 5: We review ... presenting the content in various ways. <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7MUVySW1qQ1luSms/edit?usp=sharing">Here is a sample.</a><br /><br />Day 6: We test ... this test is short and could be combined with a introductory activity to the second half of the unit. I chose to give my students time to work on their <a href="http://180snaps.blogspot.com/2014/04/day-140-141-short-test-allows-time-to.html">Desmos Creative Art unit</a>.<br /><br />(This is where we are now)<br /><br />Part 2<br />Day 1: Students use their understanding of simplifying algebraic fractions to multiply and divide fractions. This is a skill practice day. We also solve simple rational equations - the factors cancel leaving simple linear equations to finalize. Students play Tic Tac Toe after doing some routine work.<br /><br />Day 2: Students use rational functions in introductory problem solving. This year I am using <a href="http://illuminations.nctm.org/Lesson.aspx?id=1968">Illuminations, "Light It UP" unit</a>. Students will work in groups ... I may help them get started - use leading questions - but then I want them to grapple with the problems themselves as much as possible. I will set up the experiment ... maybe in 2 - 3 stations so that students can do the experiment as well.<br /><br />Day 3: I have to get pumped up for this day ... we will add and subtract algebraic functions and simplify complex fractions. My students are so squeamish about fractions. I would really like to talk with their previous teachers about how fractions were handled in middle school, algebra 1, and geometry. This will be a skills practice day! I'm thinking I will give every student a rational function on an index card. They will partner up with another student - find the sum and difference. Then I'll play a few seconds of music. When the music stops, they partner up again - find the sum and difference again. We may do this 4 or 5 times.<br /><br />Day 4: We solve rational equations. I haven't thought this far yet ... but I'd like to create some form of partner practice that is self-checking.<br /><br />Day 5: We will tackle the more traditional word problems that involve rational functions like rate of work problems.<br /><br />Day 6: I will use this as a catch up day. I know 90 minutes sounds like a long time but it's every other day ... and so often skills that I think we master in our 90 minutes need reviewing.<br /><br />Day 7: This will be our official test review day.<br /><br />Day 8: We will test!<br /><br />This about 5 school weeks! The only other unit that we spend this much time on is the quadratic unit.<br /><br />So ... how do you address rational functions? Do you have any activities that help students with adding and subtracting? What are your favorite application problems for rationals?<br /><br /><br /><br />Beth Fergusonhttps://plus.google.com/101031905836509369212noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-67138025152625625082014-04-07T22:15:00.000-05:002014-04-07T22:15:04.693-05:00Creative Art Project Introduced!Yes, some students were ho-hum ... but others ...<br /><br />... explored all the trig functions to see what shapes they would make<br />... imported a picture into Demos to see if he could outline it with equations<br />... discussed the virtues of a single drawing versus a scene<br />... asked if abstract drawings were acceptable<br />... tried a few basic functions and how to limit the domain and range<br /><br />I wish now I hadn't given students 3 whole weeks to complete the project ... I can't wait to see their art!<br /><br />So what is expected and why?<br /><br />Our algebra 2 curriculum is structured around a series of parent functions. We introduce the concept of functions at the beginning of the year. And then we start marching through seven of them! With linear functions we explore systems of equations. Then we look at absolute value functions and how they are related to linear functions. We end our first semester with an intensive study of quadratic functions ... first examining the graph, transformations, and using graphs to solve problems. And then we solve quadratics and problem solve some more.<br /><br />In our second semester we jump into radical equations first since they are inverses of quadratics ... and then we take a detour to study rational exponents. Next up are exponential functions and logarithms. And last we learn about rational functions. That's where we are now. We are finishing our first unit on rationals which is the graphing unit. Then we will simplify, solve, and apply rational functions to word problems.<br /><br />So this creative art project is planned with the purpose of reviewing these seven functions, their transformations, domain, and range. Students must use at least five of the seven studied to create art. Their artwork must have at least 12 equations total but as we discussed today, most will have many, many more.<br /><br />In the past I would have students create this work on paper. BUT oh my, <a href="https://www.desmos.com/">DESMOS</a> to the rescue! How much nicer to have the art online, equations clearly identified, easy to see what students did! Now the focus is on transformations, limiting domain and range ... not on their ability to graph the functions by hand. The thinking process is different ... better from my perspective!<br /><br />Here is <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7bFE0eGlJbGc0VlE/edit?usp=sharing">a link to the handout</a> I gave students. I can't wait to share their work with you all! Check back after April 28!