Monday, October 17, 2016

Pan Balance 1: Cats and fractions

Usually in elementary mathematics, teaching pan scale balances are used only for display them at the time of equilibrium, to verify that two quantities are equivalent.

In this case, apart of this use, it is also useful imbalance in the balance. 

Many years ago (2003), Wendy Petti of and me, we developed the "MathCats Balance":

" choose from a wide range of objects to place on this scale - from electrons to galaxies!
" So how can we balance thin cats with fat cats? You might try multiplying each side by the number shown on the opposite side of the balance. Will 2 x 6 thin cats balance with 5 fat cats? Yes, 12 thin cats do balance with 5 fat cats".

MathCats Balance App (Google Play)
MathCats Balance (Amazon) 

Many years after this, I developed under the same idea a pan balance of fractions.
Inspired in a old photograph of Maria Montessori and his son Mario:

 ( from Getty Images: )

Pan balance to weigh fractions:

This imbalance, when the imbalance ratio under certain conditions is proportional to the ratio of content of the dishes, is also the result of the division. The slope of a straight line. In this case, the result of the division of fractions.

To view it, you can multiply the contents of each dish, until the balance is obtained, the numbers for which has multiplied each dish are in turn the result  fraction of the division.
The program only multiply by prime numbers, because any number can be built with them.

 This is the "Fractions Balance" Android App:

1/2 + 1/3 + 1/6 
with: 1/3 + 1/5 + 1/6 + 1/8 + 1/10 + 1/12
And with: 1/3 + 1/4 + 1/5 + 1/8 + 1/12

I hope it helps on teaching division of fractions.

Wednesday, October 5, 2016

Place Value Time

After the experience of my old "Time Calculator" (for 2004) I tried to develop an app that explains how this webpage subtract time.

Over the years I have received all kinds of comments on how to make this calculation.
This time, I tried to explain graphically how the original application does.

And I think I've managed to build what should have been the original application.
What was missing was to be able to modify the difference between the two dates.

(and save last configuration) 

I must thank all those who have been making comments over many years

Here you can find the new: "Place Value Time"  (for Android devices) 
(  ) 

 Here is the video of the 'Place Value Time' Android app:

 In the video:
  • - From countdown to elapsed time.
  • - my age.
  • - when I should have celebrated my 500,000 hours of life.

The app is available on Google Play, Samsung Galaxy Apps and Amazon.
Place Value Time - Google Play
Place Value Time - Amazon
Is a paid app.(the paid version of the previous 'Time Calculator' (Android)