Sketchpad Explorer for iPad

On the lookout for possible apps that can help you replace Smartboard activities?  Take a look at this math app that has a lot of possibilities!  App designers need to take a cue from this app as well as there are so many possibilities for developing better apps for iPads based upon this model.  Content can be added to this app!  Here is the description straight from the website itself;

"Drag, manipulate and animate visual mathematics to develop and generalize your understanding of fundamental concepts across elementary math, geometry, algebra, trigonometry, calculus, and beyond. Based on the award-winning software The Geometer’s Sketchpad®, the Sketchpad Explorer app allows you to interact with, and investigate, any document created in Sketchpad. With a simple, powerful multitouch interface, Sketchpad Explorer puts mathematical comprehension at your fingertips."

Sketchpad Explorer includes iPad®-specific activities and workbooks for:
• elementary mathematics (Grades 1-6)
• early algebra (Grades 7-9)
• geometry (Grades 9-10)
as well as full access to many mathematical documents hosted on the Sketch Exchange community site and across the web. Users of The Geometer’s Sketchpad can also create and share documents with and for their iPad using iTunes® File Sharing.

Thanks to my colleague, Helen Mowers (ADE) for mentioning this app ...

Review of Draw for iPad by Kathy Burdick

Name of App: Draw for iPad

Free or Fee: Free!

Rating: 5/5 stars

Why I like it: Draw for iPad offers more than just a medium for creating masterpieces (however, even my artwork looks decent and I am no Van Gogh!) There are also options for playing a basic game of Tic-Tac-Toe or a word game. The word game gives a word in the upper left hand corner leaving space for students to draw the given word or to write a sentence using that word. There is a dots option, which fills the page with rows of dots making it a perfect replacement for the geo board and all its rubber bands. The straightening toggle makes this a great app to use in a geometry class. When the toggle is turned on any line that is created is straightened making it easy to draw perfect shapes while still leaving room to write in equations and angles. Images on the screen can be emailed, added to a photo album (which I have yet to figure out how to access) or tweeted. I always appreciate when developers add the email feature so that students can email their end product to the teacher or in some cases vice versa. Draw for iPad offers many color options as well as an eraser (or a clear button to delete the whole page) for students to let their creativity run wild. Draw for iPad is loaded with uses for the classroom- elementary, middle school or high school!

Visit Kathy's website for more ideas on using apps in the classroom!

Geometry - (Mathomatix)

App Title: Geometry (Mathomatix)

Grade Level: Kindergarten

Purpose: A-   This app introduces shapes by tracing and matching, but misses the opportunity to associate the name of the shape with the shape.

Program Functionality: A-  The A is for the consistency within the Mathomatix series. I like the design and my first graders are big fans. They love that they are built the same way - it’s like an old friend when they open it up. The A- is for the ads. Oh, I’m so sorry that they have ads on this game! Several times I was trying to play this app and I was whisked off to the App store to download Google. On one screen, the ad actually covered the Play Again button!

Overall Educational Value: A-  If the standards just require Kindergartners to identify and describe common geometric objects, would it really be a bad thing to name the shape as they trace it? I’m all for standards, but I’m not about the minimum. Let’s see if we can stretch our students’ thinking!

Cost: Free, but has ads. At this time, a paid version is not available.

Recommendation: While the shape is being traced, have the voice state the name of the shape. If kids soak up a little extra learning - that’s great! The “praise” prompt could easily be replaced with the name of the shape.  

Classroom Use Examples / Ideas: A very basic introduction to shapes, very intuitive for children to use on their own.  

Developer Website: Punflay

iTunes Link: click here!

Reviewer Name: Carolyn Wojtera

Reviewer Blog: Teach with Tech 

Polar Sweep - free

 Polar Sweep

Polar Sweep reinforces relationships between rectangular coordinates, polar coordinates, and basic trigonometry with a dynamic educational interface. Users can sweep through the circle to see changing values and helpful diagrams of right triangles for common angles.

Radians - as an introduction to radians this app shows decimal values, common PI fractions, and degree equivalents.

For a solid understanding of cartesian plane quadrants and polar coordinates, spend some time playing with this app.

Version 1.1: Now with a keypad for direct entry of (x,y) or (r, angle) coordinates, this app becomes one of the best rectangular-to-polar converters available.

The Angle (Greek letter Theta) Slider and Arrow Keys

This central slider allows the user to explore the cartesian plane. The values of (x,y) for the end of the red line are shown dynamically as the angle changes with the slider. The horizontal axis for “x” is positive to the right, and the vertical axis for “y” is positive going up. Sweep through the quadrants to see the relationships in action. The arrow keys allow stepping through the common angles.

The r Slider

The “r” slider is located at the bottom left of the screen. When r = 1 (default), x is the cosine of the angle, and y is the sine of the angle. Polar Sweep effectively becomes a trig table. To make the numbers easier to think about, try r = 10. In each case, adjusting r does not change the look of the polar diagram since the angle is not changing; “x” and “y” grow or shrink proportionally as “r” is adjusted. The scales of the axes would change, but in this case the red line “r” always represents full scale.

Radians

Radians can be shown by toggling the blue button located at the bottom right of the screen. Radians are simply another way of making angular measurements. They are very powerful, since the radian value indicates the arc length of the swept angle (when r = 1, the full circumference of a circle is 2*PI. Half a circle (180 degrees) represents an arc length of PI. Half of that (90 degrees) represents an arc length of PI/2). These ratios are true for any value of “r”, since the radius and circumference are proportional. Polar Sweep can help students get more comfortable with radians.

Standard Angles

Understanding a few standard angles will give reference points to understand the entire plane (cartesian plane -- a slice of 3-D space). Using the arrow keys will step through some common angles, all based on only two right triangles.

Direct Entry

Touch the upper gray blocks to enter (x, y) directly. Touch the red blocks to enter (r, angle). Refer to the images below for more.

Angles larger than 360 degrees ( or larger than 2*PI radians)

If a large angle is entered, it will be reduced. For example, if 380 degrees is entered, the resultant angle shown will be 20 degrees (one full revolution + 20 degrees). If -380 degrees is entered, the resultant angle shown will be 340 degrees (one full revolution clockwise + an additional 20 degrees clockwise, finishing 20 degrees below the x axis).

Polar Sweep launch image

(x,y) gray blocks for Rectangular Coordinates

(r, angle theta) red blocks for Polar Coordinates

Polar Sweep Layout

The central slider allows sweeping through a circle. The blue arrow keys advance through standard angles.

A slider for r (1 to 20) and the Degrees/Radians toggle are at the bottom of the screen.

(x, y) entry

Touch one of the gray blocks to bring up the keypad.

The x block is ready for input.

Enter the first x value (e.g. 8.25)

Touch the y block or the large green arrow button.

The y block is now ready for input.

Enter the y value (e.g. 4.125)

To complete, press the large green arrow button.

After pressing the large green arrow button, this display returns.

The red radius line in the diagram is 9.22 long at 26.565 degrees from the x axis. Its x component stretches 8.25 in the x direction, and its y component stretches up 4.125 in the y direction.

Pressing the Degrees/Radians key converts the main angle display to radians (or back to degrees).

In this case, the angle swept from the x axis to the red line is 0.463648 radians. The arc length of the sweep would be this times the radius (this is easier to compute if r = 1 or r = 10).

Right Triangle Formulas

The “info” button reveals this formula sheet.

The general length and angle definitions are at the top, and then the specifics for two standard triangles are illustrated.