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I'm teaching a quantitative reasoning course at a two-year community college and I'm endeavoring to be as inquiry-based as possible in my teaching. We have access to class sets of iPads, and I'd like to use them in a few class sessions, but I need to find the right apps. I'm looking for apps that do something like the Tile Pile exercise on proportional reasoning over at Desmos.

I've seen a few apps that are basically textbooks with interactive problems, and a few other apps that are just exercises disguised as games. What I really want is an app that allows students to explore the concepts on their own. The Tile Pile example is really perfect in this regard.

Here is a list of different topics I'll be covering to help you suggest different apps.

  • Proportional reasoning (ratios, percentages, rates)
  • Number Sense (place value, scientific notation, rounding, understanding big numbers)
  • Graphs and charts (creating, interpreting, and analyzing)
  • Inequalities
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    $\begingroup$ I'm teaching OCR quantative reasoning course this year. 16 year old C grade GCSE and would also be interested in ideas for explorative learning. Especially transparent tasks that have clearly identifiable goals and that are not frustrating. $\endgroup$ – Karl Oct 4 '15 at 1:55
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    $\begingroup$ This is not an app, but you may want to take a look at Mathalicious (mathalicious.com). It has a lot of pretty awesome lessons that need minor tweaking to do anything you want them to do. Additionally, you could use stuff from Dan Meyer's 3Acts stuff (docs.google.com/spreadsheet/…). That is also a lot of inquiry/applied math and some of it fits under the categories you have described (then use things like Desmos to do work). $\endgroup$ – Joey Kramer Oct 4 '15 at 5:39
  • $\begingroup$ @Joey Kramer a very useful resource thanks $\endgroup$ – Karl Oct 8 '15 at 17:39
  • $\begingroup$ iPads are expensive. Better look for stuff that runs on a generic Android tablet and/or a not-so-high-end smartphone, or can be used over the 'net from those devices. As a bonus, the later ones will work with the iPad too ;-) $\endgroup$ – vonbrand Jan 17 '16 at 21:41
  • $\begingroup$ @vonvrand an iPad is not nearly as expensive as a year's worth of textbooks, and can be used over the course of several years. As a student and a teacher, my iPad is invaluable. $\endgroup$ – Andrew Jan 18 '16 at 0:22
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Mandelpad plots the Mandelbrot set and associated Julia sets in the complex plane, and could spark a few interesting discussions (it has in my class), or even a "fractal art" project. In coordination with some other visual processing apps I've used it to create some very beautiful and intriguing images to use as cover photos, backgrounds, and the like on my class websites. I actually used it this year to make a "festive fractal" holiday greeting card.

festive fractal

Geometry pad is a fantastic iPad geometry platform. Students can construct geometric objects, and purchase additional features that make constructions easier. I've relied on this tool heavily for teaching and demonstrations in my geometry classes.

Good Grapher is hands down the best and most versatile graphing tool I've come across. It permits graphing in two or three dimensions, parametric and implicitly defined graphs, inequalities, and includes a scientific calculator, polynomial solver, and linear system solver. There is a free version, but I use the paid version with more features. It has been an indispensable for demonstrations in my multivariate calculus class.

I'll try to update this answer if I come across anything else I really like.

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