Archive for Algebra

Students Learning -AND having fun!

Today in class I passed out the Mobis!

I have had my students sitting in groups since the first day of class, but today I thought I would add more interaction and have them contribute to the board notes.   There were 8 groups, and I have 4 Mobis.    After putting a problem on the board (computer screen, writing with the Mobi and using software called Interwrite Workspace), I would give 4 groups each a Mobi and have someone from the group post their group’s solution.  At first no one wanted to try it, but after a short time, they were all wanting to have a chance to write with the Mobi!

Some of the students had more fun than others – drawing pictures and fooling around on the screen, but it was OK because they were ENGAGED!

The first four groups would hand off their Mobi to the other four groups and we would work another problem.


I have to admit, some students were able to write using the Mobi better than I can, and I have practiced longer!  You have to look at the screen while writing on the Mobi  – a little challenging at first.   For their first day, they did a great job!

They have really embraced the technology I use in class, starting with having 2 students take notes with Livescribe pens to share with the class on the website.

In a week or two I will introduce the clickers!

 

Off To A Great Semester With Technology!

A new semester has begun and I have added a few new ways to help my students succeed.

  1. I borrowed my colleague’s idea to have 2 students take notes during every class using a Livescribe smartpen.  I then upload the notes to their class website, and post a link  in the calendar on the day the notes were taken.

I created a webpage to house the daily notes for each chapter, starting with our first chapter:  Chapter 9

2.  I use a Mobi (from eInstruction) to present the lesson from anywhere in the room.   An especially nice feature of the Mobi software, called Workspace, is that I can save the board notes and export them to a PDF file.  I place on link in the calendar to the board lesson on the day the lesson was given.

*to see the actual board notes, you must go to the calendar and click on “board notes”, since they are an attached PDF file, I cannot link to it here.

3.  The students use an online program to do their homework, which sends me a screen shot when they need help on a particular problem.  Instead of trying to type back a response to them, I fully explain their solution using a Livescribe smartpen.  I then send them the link to the pencast, and I also created a webpage to house all solutions to student homework questions.

*here is the link to the page that contains all the homework solutions

Here is one of the solutions I wrote to my students just today:

This is just the first week of class, and the students have shown a positive reaction to these extra support features I have included on my website for them.   I look forward to seeing how the semester progresses!
*To see more of my college website go to:  Glascoe College Website .  I built the website using Dreamweaver.
*All screenshots were taken using TechSmith Snagit

 

Japanese Multiplication – How Does it Work?

I have come across some fun math problems (yes, math CAN be fun!) through the internet and friends.  Here is a video of Japanese Multiplication.  First watch the video, and then see if you can figure out how they are multiplying  before you read my explanation below!

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Well, did you figure it out?  Let’s take a closer look at the first example:

Now take it apart:

  • The first set of lines, the green ones in my image above, represent 2 sets of 10 , or 20
  • The second region with one line, which is orange in my image, represents 1 set of 1
  • Together these sets of lines, read top to bottom,  represent 2×10 + 1×1  which is expanded notation for 21

Let’s look at the next set of lines that were drawn perpendicular to these lines:

  • The first region that contains the 1 blue line represents 1 set of 10 or 1×10
  • The second set of lines that were drawn, the three red lines, represent 3 sets of 1
  • Together these 4 lines, read left to right, represent 1×10+3×1 = 13 in expanded notation.

Now for the tricky part!

Those of you who have ever FOIL-ed in Algebra will recognize the process of distributing the values by “First, Outer, Inner, Last”

Here is a quick Algebra example to remind you
(x+3)(2x+5) =

First = x * 2x = 2x^2
Outer= x*5 = 5x
Inner = 3*2x = 6x
Last = 3*5 = 15

Then,  2x^2 + 5x +6x +15 = 2x^2 + 11x +15 (the Outer and Inner were “like” terms, so could be added together)

Now back to the arithmetic.   If you look at the product 21×13 by separating out each factor by its place values, you have:

(20 + 1)(10 + 3)  and now you can FOIL out the values, just like in the Algebra problem!

First = 20×10 = 200
Outer =  20×3 = 60
Inner = 1×10 = 10
Last =  1×3 = 3

The 200 is represented by the 2 sets of crossing lines circled in yellow on the image above- that location on the paper represents the hundreds place value, so having a 2 in the hundreds location represents 2×100 = 200.  In the video a 2 is placed as the first digit of the product, which will be the hundreds place.

Next:

The 60 is represented by the 6 sets of crossing lines in green on the top right
The 10 is represented by the 1 set of crossing lines in green on the bottom left

Together the 60+10 gives 70.  In the video, the areas circled in green on the image above both represent the tens place value, so they are adding up the 6 crossed marks and the 1 crossed mark to get 7 sets in the tens place, or 7×10=70.    They then place a 7 to the right of the 2 in the product (placing it in the tens place)

Finally:

The 3 is represented by the 3 crossed marks in the lower right (circled in red on the image above).   This area of the paper represents the ones place, so we have 3×1 = 3.   They then place a 3 to the right of the 7 in the product, placing the 3 in the ones place.

This gives the final product of 200+60+10+3 or 200+70+3 = 273

~Now look at the second product in the video and see if you can figure out how it works!

 

I Made My First Interactive GeoGebra Applet!

Logo taken from the GeoGebra website – holiday version!

I have met several people in the past year (some only virtually) who have convinced me that learning GeoGebra would be a great addition to my tech tools for teaching mathematics. Since GeoGebra is FREE, it makes it an even better resource as a teacher and tech ed consultant, and also for student projects as well! Geometry is one of my favorite subjects to teach;  in the past I used Geometer’s Sketchpad, but in the future I plan on using GeoGebra!

I believe WordPress is not allowing me to directly embed the <applet> Javascript code for my first GeoGebra applet, so I created a new set of webpages on my Tech4MathEd site where I will be posting all of the GeoGebra applets I create.   I am just learning, so there is only 1 there now 🙂

To see my first interactive GeoGebra applet, which helps students understand graphing a line using the slope-intercept form of the line by interacting with the graph, go to  Slope Intercept GeoGebra Applet.

I am really looking forward to using GeoGebra, not only to create interactive applets for my Algebra students, but also to help my Math For Elementary Teacher classes learn more about Geometry!

To download  and start playing with GeoGebra, go to:  download GeoGebra

Image of my interactive applet:

 

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