Technology vs true proportionality.

Today was the first day of a local celebration called "Cultural Heritage" week.  It is a three day event in which students spend half a day listening to elders and others speak on important topics such as tobacco abstinence, environment, family, etc.  In the afternoon, students work on a local skill such as fish hooks, fish traps, mask carving, beading, crochet, or Kuspuk making.  Kuspuk is a simple dress or shirt that is put together using rectangular pieces.
   These are two examples of kuspuks worn by females.  The thing about making these outfits is that each one is cut individually to fit the person who is wearing it.  You actually hold the material up against the person to figure out how wide and long to cut the base part which is the main body of the kuspuk.  Two more rectangle are cut into trapezoids to make the sleeves.  Two small rectangles for cuffs.  The only pieces that are really cut with curves are the front pocket pieces and the hood.  Even the skirt is made of several rectangles sewn together and gathered.
One lady told me that when you sew like this, you are making the garment so it is proportional to the persons body and it will look good on them.

There is a series of math books out there called "Math in a Cultural Context".  Jerry Lipka up at the University of Fairbanks worked with many, many people to create some wonderful math units that could be used from lower elementary up to high school.  Topics include place value, probability, navigation, geometry, and other good topics.  I've used several in my classroom and they work well.

Bettermarks GmbH

I found a company, Bettermarks GmbH, who offers both online and apps for the iPad.  They make apps covering fractions, geometry, data and a few other topics in both English and German.





I stumbled across this company when I down loaded the 2nd app on fractions.  The app is set up with prerequisite topics and then has 3 "chapters" for the student to work through.  What I like is even if the student is correct, they can still get an explanation to make sure.  If they miss the problem, it provides an explanation.
Last night I downloaded almost every one of the free apps they offer because I would like to check them out to see how well they will fit into my class.
Their website indicates they have created adaptive mathematics for grades 4 to 10.  Honestly, I plan to spend time throughout the week, checking these products out and I will be happy to give a more indepth report later on. 
I just found out the only difference between the free and paid apps is that the paid apps have no apps.

Basic Fraction

I came across this free app called Basic Fraction.Although it is listed as 12 and under, I can see using in a middle school or high school class to re-mediate or scaffold learning.

If you notice it offers several different  ways to learn fractions. I like the find x because there is a fraction equation and the student is required to find the missing value to make the statement. 

You have a choice of working on only addition, subtraction, multiplication, division problems so a student can focus on the area they struggle in or you can have them do random which will mix problems.

The word allows someone to type in several words  and then you get a wheel of fortune type board with the words.  In order to uncover the letters, the student has to answer problems correctly.

Each problem is done on a chalkboard and you can use your fingers to do the work.  I plan to add this to my list of apps for next year.  I usually have Pre-algebra students who struggle with fractions.  I see this as a fun way for them to improve.

Ratios and geardoodleLT

I stumbled across an app that I can see using in the classroom even though it is more of an art app.  This is an app that has both paid and free versions but I'll be talking about the free version.  This app, GearDoodleLT, is very similar to the old spiralgraph but it is a virtual version of it.

If you look closely at the picture you will see that it is one gear inside another.  The outer gear is static but the inner gear can change size and the pen changes size.  You can caluclate the gear ratios to determine one set of values, you can also find the relationship between the radius of the inner circle and the outer circle and the size and type of design you get.  In addition, you can add in how the size of the pen point effects the number of repetitions needed to create one full design.
There is a native way of using Archimedes's n-gon to create a circle.  You start with a square and find the distance from the center to the side.  Use that distance on the diagonal to make a new fold/side  Do this to the four diagonals, then cut the folds to make new sides. and repeat till you get a circle.  I'll try to make a video this weekend and post it.