Tag: algebra

“Wow” Moments with Wolfram|Alpha

Post author By Bob Lochel
Post date March 21, 2013
1 Comment on “Wow” Moments with Wolfram|Alpha

The Siemens STEM Academy offers great resources for teachers, from lesson plans, to blog posts from teachers, to fantastic free webinars. Full disclosure: I have written for the STEM Academy blog, and been a part of the Academy summer program…but I am but a small fish in a cool ocean of resources!

This week, the Academy hosted a free webinar featuring a demonstration of the dynamic knowledge provided by Wolfram|Alpha. Having used Wolfram Demonstrations before in my classroom, I was looking forward to learning more about this search tool. Crystal Fantry provided an hour-long overview of this exciting resource, and ideas for classroom uses. It’s amazing how many “wow” moments I have these days with the new tech tools our students can have in their hands, but this one goes beyond that. Knowing that students have access to resources like this should cause us all to think about our roles as math teachers / facilitators….this is a game-changer!

So, just what is Wolfram|Alpha? The site is simple, just enter what you want to search for, and off you go…but this tool is so much more than that. The “about” from their website provides some insight:

Wolfram|Alpha introduces a fundamentally new way to get knowledge and answers—not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods.

So, what the heck does that mean exactly? Let’s learn by diving in. And while you can use Wolfram|Alpha for far more than math, this is a math blog so let’s focus in on some math….

Try this: “y=2x +3”. Let’s start with something simple…what does Wolfram|Alpha give us?

WA1

Fun stuff. A nice graph, the domain, and alternate form.

How about this: “3x+5=2x-9”

Also nice, a plot of the the functions. And the equations’s solution..but what’s this…a “step-by-step solution”? If you are logged in (free accounts) you can step through the solution:

WA2

So, what happens now when you give that worksheet of equations to solve for homework?

There are a lot of other neat computations to explore, try some of these as starters:

“y=(x+2)(x-3)”
“inverse y=x^2+3x+1”
“sin(x)+cos(x)=1”
“Integrate x^2 dx from 0 to 5”

WA3 But Wolfram|Alpha goes beyond quick lists and computation. How about “Pascal’s Triangle mod 5”. Or “triangle sides 3, 6, 8”, or try the elusive 17-gon, and see the many facts to check out.

A TOOL FOR RESEARCH AND GENERALIZATION

I have only scratached the surface of the many features, and there are also lots of nooks, crannies and links for you to explore. I’m eager to use this tool with students as a means to research new ideas, and make some sense of their characteristics. For example, let’s think about domain and range, as I ranted about in a previous post. I like that Wolfram|Alpha expresses domains using set notation, and this is a great opportunity to have students research new functions. Most of what we do in Algebra 1 deals with linear functions, so we get a lot of “all real numbers” domains. Expose your students to non-linear functions, once they know how to make their x,y tables. Try these:

y = 5 / x
y = rt (x-2)
y = 1 / (x^2 – 9 )
y = 2^x
y = x^2 – 4

And what to do with these new functions? Let’s place them into categories, share our findings, and communicate our ideas. Give each group 2 or 3 new functions to look at and share their findings on www.padlet.com. This site, formerly called WallWisher, allows everyone to contribute their ideasd and move them around the canvas. Here’s a sample of my function domain wall, click the link to contribute your own, play around the wall, and double-click in any empty space on the canvas to contribute. Or sign up for a free account and create your own wall.

Padlet

Thanks to Kyle Schutt (@ktschutt) and the gang at Discovery Education for providing these great webinars. Be sure to check out the Siemen’s STEM Academy blog for more great resources, blog posts, and archived webinars.

Tags algebra, wolfram

Algebra Technology

TI Publish View – Bringing Interactive Lessons Home

Post author By Bob Lochel
Post date March 19, 2012
No Comments on TI Publish View – Bringing Interactive Lessons Home

In the past few years, Texas Instruments has been aggressive in developing and marketing its Nspire product line. I recall the first time I shared the (now) old blue click pad product, and the oohs and aahs from my students when I showed them how you could trick out the keyboard with an 84 keypad. This was soon followed by the touchpad, and now we have the CX, with its thin design and color screen.

Along with the improved hardware, TI has also improved its software options, providing an opportunity for teachers to create their own lessons and demonstrations on the software. Files can be easily traded and shared with students, or used on a whiteboard as a classroom manipulative. Last month, I had the opportunity to attend a free morning of professional development on the TI Publish View feature. This feature of the Nspire software allows teachers to embed some of the interactive features of Nspire CX files into documents. The TI-Nspire document player then allows students to open these files and navigate the lesson.

In the short example I created below, the coefficients of a polynomial can be adjust using “elevator buttons”, which are sliders used to change the values. Students can then observe the value of the discriminant and look for patterns in the values. Click the link to join in the discriminant insanity!

http://education.ti.com/go/nspireplayer?nspirefile=http://dl.dropbox.com/u/68005919/Discriminant.tnsp

Additional files to try can be found at the TI Activity Exchange. What an interesting way to have students explore on their own. Thanks to Mike Darden from TI for the great session, and Doyt Jones for his continued hard work in bringing these sessions to the Philly area.

Tags algebra, technology

Algebra

Slope and the ADA

The middle school in the district where I work is quite old. Dedicated in 1959, and once serving as the district high school, the building is a Frankenstein of aging classrooms, newer additions, and inconsistent heat. One feature of the building is the network of ramps used to shuttle students from wing to wing, and supplies in and out.

Recently, I worked with a team of 8th grade algebra I teachers to develop an activity which would utilize the many ramps, get kids moving and measuring, and reinforce slope as a measure of steepness. The teachers had great ideas for leading students through measurement activitites. My initial idea of having students choose points along the ramp, then measuring the rise and run between points, was discussed and improved. The teachers used blue painter’s tape to create guiding triangles along the bricks on the walls along two of the ramps. Another teacher noted that railings could be used to connect parallel lines to slopes, and triangles utilizing the railing were also provided.

Students measured the slope of two ramps using the provided triangles, then were led outside, where both a pedestrian ramp and a custodian’s ramp were measured. The outside ramps were additional challenges, as no guiding tape marks were provided. Wacthing student reactions and approaches to these ramps was intriguing. Some students attempted to use the bricks on the building to trace their own triangles, while another group discovered that the level ground along the freight ramp could be used as the “run”.

After the activity, the class discussed and compared their results. In one class, the unusual steepness of one ramp in our building was questioned, and related to the legal limits of handicapped ramps. The class agreed that the ramp seems to be an original part of the building, and that an elevator had been installed alongside the ramp for our disabled friends. Further discussion could include the requirements of the Americans with Disabilities Act, which contains the following requirements for ramps:

The least possible slope shall be used for any ramp. The maximum slope of a ramp in new construction shall be 1:12. The maximum rise for any run shall be 30 in (760 mm) . Curb ramps and ramps to be constructed on existing sites or in existing buildings or facilities may have slopes and rises as allowed in 4.1.6(3)(a) if space limitations prohibit the use of a 1:12 slope or less.

As a follow-up, students found pictures of objects or places which they felt represented interesting slopes. Geometer’s Sketchpad was then used to measure and compare the slopes in their pictures: