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

Educreations

Price:  Free 

Purpose/Capabilities: 

Educreations is an interactive whiteboard with voice recording, the ability to import images, write on the screen with four different colored inks, add text, and share the video through e-mail, Facebook, Twitter, or upload it to a website.

Educreations can be used in the classroom by the teacher or the students.  It is a great way for teachers to preview material and have students watch it before coming into class, work through a homework problem that students had trouble with without spending class time on it, add commentary to an image, and provide extra help tutorials for difficult concepts.  Students can also use Educreations themselves to showcase and explain a problem they solved.

 Positive Aspects: 

This is what the blank screen looks like.

Educreations is very intuitive and easy to use.  It has great potential for both teachers and students.  Educreations does allow you to create multiple screens for one project and go back and forth between them.  You can record and write at the same time, or if you prefer, you can have it all written or drawn out and then record the explanation to go along with the different screens.  You can pause the audio and continue recording as well.

Negative Aspects: 

Educreations does not have an eraser feature, only an undo button that will delete the last move (you can use it multiple times in a row).  In addition, with this app, you cannot save your work unless it is recorded.  Once you record, you cannot go back and edit your recording.  If you make a mistake, you are forced to start again from the beginning.  Despite these negatives, Educreations is definitely a must try, especially since it is free!

Sample Activity:
In each of my Honors Algebra II classes, I had my students use Educreations to create a video explaining an application of exponential functions.  There were seven application problems and each group was selected to be the experts of a particular problem.  They were to solve that problem first and create a video explaining the problem and how to solve it.  After previewing the videos myself, I posted them on the class wiki and the rest of the class was able to check their work using the videos.  They were asked to comment on at least one other group's video.  Below you will find the link to the directions and rubric I used in my class, which can definitely be adapted for other activities.

Educreations Video Assignment