It is always a good idea to keep your receipts. However, it is not necessary to have them to enter the amount on your return if you know for a fact you paid it. In the unlikely event you are audited, you would need them.
As stated by leeloo, it is always a good idea to have backup documentation for deductions you are claiming as part of your tax return.
As you may know, you are allowed to claim up to $300 in unreimbursed expenses for books, supplies, and equipment used in the classroom.
To go to the section of the tax return to enter this information, use these steps:
On the top row of the TurboTax online screen, click on Search (or for CD/downloaded TurboTax locate the search box in the upper right corner)
This opens a box where you can type in “educator expenses deduction” (be sure to enter exactly as shown here) and click the magnifying glass (or for CD/downloaded TurboTax, click Find)
The search results will give you an option to “Jump to educator expenses deduction”
Click on the blue “Jump to educator expenses deduction” link and enter your information