whats the cheepests laptop for an 11yr old

A netbook could be a good choice. Inexpensive, and really lightweight so he/she could bring it anywhere. So if he/she wanted to install games and other applications I wouldn't go that route. For netbooks Asus and Acer make some good ones. Dell and HP have some very small type computers too.

Laptops are not cheap. To get a good deal on a laptop it takes some week by week browsing the circulars and checking the internet for the deals that are out there and which deals include what you need and so on. Dell is an awesome choice but when you hit their site and start customizing your machine the price is going to start rising. Longevity is there however. I included some choices below. I prefer Best Buy as they have deals on laptops and they come fully loaded with the essentials your child will need to get started.  Check it out:

HP Laptop / AMD Turion™ II Processor / 15.6" Display / 3GB Memory / 500GB Hard Drive

• 6-cell lithium-ion battery
• 65W AC adapter
• Software: Adobe Reader; Cyberlink Power DVD and more
• Owner's manual

• VISION Premium Technology by AMD
  For every detail to jump right off the screen when you're viewing high-definition movies and videos, playing games, converting MP3 tracks or video chatting online.
• AMD Turion™ II dual-core mobile processor P540*
  With a 2.4GHz processor speed for enhanced performance.
• 3GB DDR3 memory
  For multitasking power, expandable to 8GB.
• Multiformat DVD±RW/CD-RW drive with double-layer support
  Records up to 8.5GB of data or 4 hours of video using compatible DVD+R DL and DVD-R DL media. Also supports LightScribe direct-disc labels using compatible LightScribe media.
• 15.6" LED high-definition display
  With BrightView technology and 1366 x 768 resolution showcases movies and games in stunning clarity.
• 500GB Serial ATA hard drive (5400 rpm)
  For fast read/write times.
• ATI Mobility Radeon HD 4250 graphics
  Feature up to 1405MB total video memory for lush images. HDMI output for an easy connection to your HDTV.
• One-touch launch and Action keys
  Allow for easy navigation.
• Built-in webcam with microphone
  Makes it easy to video chat with family and friends.
• 5-in-1 digital media reader
  Supports Secure Digital, MultiMediaCard, Memory Stick, Memory Stick PRO and xD-Picture Card formats.
• 3 high-speed USB 2.0 ports
  For fast digital video, audio and data transfer.
• Built-in wireless LAN (802.11b/g/n)
  Connect to the Internet on the go.
• Built-in 10/100Base-T Ethernet LAN with RJ-45 connector
  For flexible wired Web connectivity options.
• Weighs 5.5 lbs. and measures just 1.4" thin
  For easy portability.
• Long battery life
  Of up to 4 hours to give you more time away from an outlet.
• Textured HP Imprint finish
  With a prism design in biscotti for a stylish look.
• Microsoft Windows 7 Home Premium Edition 64-bit operating system preinstalled
  Provides a stable platform for word processing, Web navigation, gaming, media storage and more.
• Software package included
  With Adobe Reader, Cyberlink Power DVD and more. Microsoft Office Starter 2010 also included (product key required for activation; sold separately).
• ENERGY STAR qualified
  Designed to use less energy and meets strict energy efficiency guidelines set by the Environmental Protection Agency and U.S. Department of Energy.
• AMD, AMD Arrow logo, AMD Turion, AMD PowerNow!, HyperTransport and combinations thereof are trademarks of Advanced Micro Devices, Inc.
  
  *Model number indicates relative mobility and performance among this AMD processor class.
• **AMD's Enhanced Virus Protection provides additional protection against buffer overflow viruses. AMD and its partners strongly recommend you continue to use third-party anti-virus software as part of your total security solution.

Awesome and priced right at $429.99. Enjoy!