f. Modeling & Formulating

"It is more useful to know how to mathematize than to know a lot of mathematics", David Wheeler This collection is a potpourri of problems that require the formulation of measures, combining those measures into functions and relating those functions to one another to form equations and/or inequalities. Many of these problems are standard algebra word problems that are approached in non-standard graphical ways. In order to understand the problem of modeling in a broader context please read the essay on this web site entitled "Formulating Measures" If you have a particular interest in word problems as they are often presented  in traditional texts please read the essay on this web site entitled "Some thoughts on representing word problems graphically"   Word problems [with some suggested applet sequences] 1 Adult tickets & child tickets I  1 Coffee mixture Problem I 1 Hens and Rabbits I  1 Dimes & Quarters I   Coin problem workbench 1 Word Problem Duo Distance, Time,Rate 1 Combining rates - I Joe & Sam paint a wall 2 Combining rates - I Joe & Sam revisited 2 Adult tickets & child tickets II 2 Coffee mixture Problem II 2 Hens and Rabbits II  2 Dimes & Quarters II 2 Word Problem Duo Mass, Volume,Density A False Combining Rates Problem  Bagels or Donuts - a Balanced Assessment Task   Age Problem Calculator  3 Hens & Rabbits for Teachers  3 Dimes & Quarters for Teachers   Sales Optimizer   General word problem workbench  1 Combining rates - II upstream, downstream Part I  2 Combining rates - II upstream, downstream Part II "ness" problems & Formulating measures [with some suggested applet sequences] 1 'Squareness' of Rectangles   2 'Squareness' of Rectangles - revisited 3 'Squareness' of Parallelograms 4 Three 'nearSQUARES'     5 'Squareness' of Rhombuses Cubicality of Boxes   Steepness - a road up a mountain   Steepness - another road up a mountain 6 Rhomboidicity of Kites   Crowdedness  1 A Car & 20 Questions  2 A Car & 20 Questions - Part II   Disc-ness of cylinders  7 'EQUILATERAL-ness' of triangles   Smoothness of Spheres Motion problems   Two lap average   The Repentant Reader  The Princess and the Key   Keeping Pace - a Balanced Assessment Task   Planetary orbits in two frames   Meeting Up - on the road with Green & Blue  A puzzling problem   v = dx/dt Beyond Linear Functions   Going on a trip - a motion problem sandbox   Ship Rendezvous   Two lap average - revisited   The Repentant Reader - revisited   Projectile with Air Resistance   Recovering from a long lunch  Two Planets & a Sun - a digital triptych   A run for two  1 Horse on road and field   Jack & Jill   Carpe diem - a day clock   How a DVD player works   Two lap average - for teachers   Two Motions - One Path in Space   Gear train   Mary's round trip   Travel Optimizer   A run for two - revised 2 Gelfand's Horse       Modeling spatial relationships   Sum of Circle Areas   Sum of polygonal areas   Erehwon Coinage  The sliding ladder Problem   A different kind of analog clock   Bicycle chain math - a Balanced Assessment task   Optimally Locating Public Services   Fuel Consumption Calculator   Polygonal numbers     Rain Gutter   Shortest Ladder       Building a box     Monte Carlo Pi   Fill your oil tank - a sandbox for posing problems     About models   A Leaky Bathtub - a metaphor for equilibrium Two metaphors - one model   Weigh to go !   Another weigh to go !   How can f(x) equal f'(x)?   Gear train   Good fits - Bad Models   Linear & Parabolic  Function Sketcher   What do you now know more about? What surprised you? What would you like to know more about? Judah L. Schwartz mathMINDhabits by Judah L. Schwartz is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.