Here is an example of how to use this applet - [br][br]- set a goal number to reach - say 2345[br]- disable the 2,3,4,5,6,7,8, and 9 keys[br]- use only the remaining 0 and 1 keys along and the addition & subtraction keys to get a result of 2345.[br][br]How many steps do you need? Can you do it with fewer steps?[br]What about a goal of 9999? How many steps do you need? Can you do it in fewer steps?[br][br][b][size=85]This applet is a revised version of a program I wrote in the early 1980's entitled [br]"What do you do with a Broken Calculator". The program was widely imitated - [br]mostly by people with less flexible pedagogical views than I am comfortable with.[/size][/b][br][br]For some problem types as well as the underlying theory that drove the program's development read the essay on the Broken Calculator on the [url=https://sites.google.com/site/mathmindhabits/]MathMindHabits[/url] website.[br][br][color=#ff0000][i][b]What problems could / would you put to your students using this applet?[/b][/i][/color]

Are all calculators broken?[br][br]any calculator (or digital computer, for that matter) is a rational number machine - it cannot[br]represent real but irrational numbers numerically. Thus, there is a large[br]collection of problems that calculators must produce INCORRECT answers to - for[br]example, 1 divided by 3. [br][br]In this case one might suppose that the calculator might distinguish between .333...3 as a[br]truncated decimal which is incorrect and .3 with a line over (or under) the 3 to indicate the repeating pattern. [br][br]That would be a correct answer, but one has to consider how it is arrived at. [br][N.B. repeating decimals indicated with an underline, thus 1/6 = .1[u]6[/u], 1/3 = .[u]3[/u], 1/7 = .[u]142857[/u] etc.][br][br][br]Does the calculator ‘know’ that a pattern repeats -[br][br]-by calculating until the pattern repeats and then assumes it will continue to do so?[br][br]Or, [br][br]-does the calculator ‘know’ the way we humans ‘know’?[br][br]How do we humans know that 1/7 = .[u]142857[/u] ?[br][br][br][br][br][br][br]