Here is a selection of apps that represent cause and effect. Here is a good link for more apps, some of which move beyond cause and effect into targeting: Teaching Learners with Multiple Special Needs. Note: I think this might be coming from the UK. As a result, some of the apps mentioned are not available in the U.S.
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Cause and Effect
Sensory Light Box
App was created for teens with significant disabilities including visual impairments,
autism and developmental disabilities. It features 21 different activities that
respond to various actions including multi-finger gestures.
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Little Gems Visual
Scene
App has pentagon shaped gems that appear magnetized when you touch the screen.
Hold your finger down and they spin. Release and they separate. Move your finger and the gems follow.
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Koi Pond
Peaceful pond scene with fish, music and turtles. Water responds to touch and fish dart away as if it were real.
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BuzzBack Cause
& Effect with Vibration
This simple app was created for students who are deaf/blind. It uses vibration as the reinforcer and is best used with and iPhone not an iPad. It provides training for three different touches: any touch, holding or distinct taps.
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Draw with Stars
Touch the screen and a star appears. Touch and move a string of spinner stars appears. Tap the stars and they shoot away. Good sound effects and some options available.
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Baby Finger HD
Tap the screen for shapes with noises, numbers or a mixture. Tap the shape or number again and they disappear.
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iBaby Buttons
Tap the screen and a button appears. Tap the button and it flips to reveal a photograph and sound or label. You can customize and create your own buttons. Even though it's called iBaby, the customization feature lends itself to using with older kids. Tap twice with 2 fingers to return to the home screen.
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Heat Sense
Set the background color and special effects. Tap or move on the screen for a kaleidoscope of color.
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Hidden Grid
App has a black background that lights up with shapes and fabulous tones. Can be used with multi-finger or single finger. As soon as the finger is removed, the music or sound stops.
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Finger Paint with Sounds
This app is a an intro to using the touch screen. It provides colors and sounds or music. 6 colored bubbles are located on the sides and one erasing bubble at the top. Child selects the bubble and paints on the screen. As soon as the finger is removed, the music or sound stops. App accepts multi-touching.