Common Core Nuggets

Free apps, created by Larry Ottman using Geometry Expressions.
Each app is directly focused on a specific topic in the Common Core
Standards. Download directly here either as browser apps, as native Android apps (iOS coming soon), or as Lua apps for the TI Nspire.


Geometry Expressions 3.1 SP1 Released
 Geometry Expressions 3.1 SP1 has now been released. It is a free upgrade for any Geometry Expressions 3.0 or 3.1 user.


How to... Create an App with Random Inputs
 One of the new input types for apps created with Geometry Expressions 3.1 is random.
Whenever the page is refreshed, an input of type random is given a new, random, value.
To use random inputs in a testing app for the cosine rule:
 Draw a triangle and constrain two sides to have lengths a and b, and the angle between them to be theta.
 Create a measurement for the length of AC.
 Use
Draw/Expression to create output measurements for a, b and theta.
(these will be given random values in the app, but having outputs will
let the user see their values.)
 In the Variable panel,
set the range for each variable. In the app random values will be
generated within these ranges.
 Use File/Export/HTML5/JavaScript App to create your browser app.
 Set a, b and theta to have Input type Random.
 Select a Show/Hide button for the output type of the answer.
The resulting app may be viewed here.
A video showing how to create this model is here.
A tns file to load on the TINspire is here.

Problem of the Month

This one involves a little physics ...
Equal masses B and C are joined by equal length rods AB and BC of negligible mass.
A is fixed and C is constrained to lie on an inclined plane. Gravity acts downwards.
For a given angle of the inclined plane, what is the angle of AB.
Clearly if the plane is horizontal or vertical, the answer is that AB lies vertically. How about in between?
An app which lets you explore this problem is here.

May Problem Solution

Given a triangle ABC, parallelograms ADEB and BFGC are constructed.
H is the intersection of DE and GF, I is the intersection between HB
and AC. AJ and CK are parallel to HI. J lies on DH and K lies on
GH.
Show that the area of AJKC is the sum of the areas ADEB and BCGF.
Pappus of Alexandria presents this theorem as a generalization of the Pythagorean Theorem. Show that it is.
An app which lets you explore this problem is here.
The
Geometry Expressions Model above shows that the purple parallelogram
has an area equal to the sum of the other parallelograms. Setting
the triangle to be right and the parallelograms to be square yields a
diagram that in itself could constitute a visual proof of the
Pythagorean Theorem. The crucial issue here is to prove that BH,
which defines the directions of AK and CJ is in fact perpendicular to
AB. We can then show that the rectangle ACJK is in fact a square. Easy enough with Geometry Expressions. By hand proof left to the reader.




