Sketchpad Explorer

Price:  Free

Purpose/Capabilities: 

Based on The Geometer’s Sketchpad software, the Sketchpad Explorer app allows you to interact with and investigate any document created in Sketchpad, allowing students to have hands-on experiences for investigating a variety of different concepts.  The teacher can create their own document using Geometer’s Sketchpad on their computer, or there is a large variety of pre-made materials available to use.  The students can then drag, manipulate, and animate the document to develop generalizations of the different mathematical concepts they are studying.

Geometer’s Sketchpad and Sketchpad Explorer are not only for Geometry related topics.  It is great for investigating elementary mathematics, algebraic concepts (such as slope, functions, understanding variables), trigonometry (unit circle, sine and cosine values and graphs, polar graphs and complex numbers), and calculus (limits, derivatives, and integrals). 

Positive Aspects: 

Sketchpad Explorer is a great, free way for students to visually see mathematical concepts in action by generalizing what happens when the visual is manipulated in different ways.  The app has a getting started tutorial that is helpful in learning the ins and outs of what the app is capable of.  It has several networked documents that can easily be accessed through the app.  This includes elementary mathematics, geometry constructions, ellipse constructions, dynagraphs, and slope.  It also has a link to the website for the app, which has many more already made activities to use in your classes that can easily be downloaded.  If you want to use this in your classes, you can save the document and upload it to your website/wiki.  Once the document is saved, students can access it at any time and refer back to what they learned.   Most of the documents take only seconds/minutes for the students to manipulate in order to make these generalizations.

Negative Aspects: 

Sketchpad Explorer was, for me, one of the more difficult apps to intuitively figure out how to use, at least initially.  However, once you have the documents already there, it is very easy to manipulate them to show the different concept.  It takes a decent amount of time creating different documents from scratch, but there are so many already made ones that this may not be necessary.

Geoboard

Price:  Free

Purpose/Capabilities: 

Geoboards are manipulatives that can be used by elementary, middle, and high school students to explore a variety of mathematical topics from shapes, perimeter, area, and congruence for geometry related topics to fractions, linear equations, and linear systems for algebra and pre-algebra related topics.  This app is the virtual version of the Geoboard with the same capabilities and more.  The app has what seems like an unlimited supply of eight different colored rubber bands and two different size boards, a 25-peg board and a 150-peg board.

Positive Aspects: 

The benefit of using Geoboards in class is to allow students the hands on experience of exploring a concept on their own and being able to make and see a visual representation.  The benefits of using the app over the Geoboards themselves are the convenience, having an unlimited supply of all the different color rubber bands, being able to switch between a 25-peg board and the expanded 150-peg board with just a swipe of the finger, and having the quick clean up without having to pick rubber bands off the floor or worry about them being flung across the room.  In addition, students have the ability to take a screenshot of their work so they can look back on what they previously did.

Different ways to use this app.

Negative Aspects: 

Some may feel that the iPad version of the app does not feel as hands-on, but in my opinion, the positives far out way the negatives with this app.  There are only a limited number of concepts that can be thoroughly explored using the Georboard, but for those concepts, I think this app is a great resource.

**These pictures were taken from iTunes Preview.  For more ideas see: https://itunes.apple.com/us/app/geoboard-by-math-learning/id519896952?mt=8.

Sample Activity: 

I worked with one of my colleagues in the math department to develop a sample activity for the Geoboard app.  The colleague of mine often uses Geoboards in his Geometry classes to have students discover concepts or formulas on their own.  He showed me one of his activities for investigating the formula for area of a parallelogram which I revised to fit the Geoboard app.  See the link below for a copy of this activity.

Geoboard Activity

Free Graphing Calculator

Price:  Free ($0.99 to remove ads)

Purpose/Capabilities: 

This free graphing calculator app has a scientific calculator which can take nth roots, find logarithms of any base, compute absolute value, factorials, permutations, combinations, select a random integer, and switch between fractions and decimals. 

The graphing calculator can graph up to four equations at one time (each graph is labeled for distinguishing purposes).  It can find the roots and points of intersection by simplify tapping on the point.  You can also hit the “table” tab on the bottom of the app to see a full table of values for the graph that you can determine the x-value in which the table starts as well as the increments it increases by.  The new update also allows the user to graph in polar coordinates and graph parametric equations.

There is a reference section that contains different formulas and information organized by subject content.  For example, the trigonometry section contains definitions of the different trig functions, a detailed unit circle, identities, laws of sine and cosine, angle addition/subtraction formulas, half angle and double angle formulas, and more.

This app also contains a unit converter and important constants such as the speed of light, gravity, etc..  The polynomial solver allows the user to put in a linear, quadratic, or cubic equation in standard form and it will find the real solutions.

Positive Aspects: 

The free graphing calculator app is one of my favorites to use with my students.  It is very easy to use and even easier than a hand held graphing calculator to adjust the graph and zoom in and out, done simply by dragging and pinching the graph (you can also do this by changing the settings).  Until I researched the app to write this review, I had no idea of how much this app was really capable of doing.  I downloaded the new version of this app to test out the polar graphing capabilities, something that you previously had to pay to use. 

This app is great for discovery activities where students can adjust an equation to determine how to transform a graph, checking answers, and referencing formula.  I always have my students use this to check their homework answers (when applicable) so they can try to fix their mistakes before coming into class.

Negative Aspects: 

In order to enter a function in the graphing calculator (or polynomial solver) it must be in standard form, similar to a hand held graphing calculator.  The polynomial solver only gives real solutions.  One ad usually appears on the top or bottom of the screen in the free version.  It costs $0.99 to upgrade to the ad free version. 

This is a great app.  One that should be on every math teacher or student’s iPad!

Sample Activity: 

The Free Graphing Calculator app is great for investigating how the graphs of different functions are affected by their equation.  Below you will find a graphing calculator investigation for absolute value functions that I have adapted for this app, including directions on how to use it.  Similar investigations can be made for any family of functions.

Absolute Value Function Investigation