Hello, welcome to FixYa.
Based on your description, the problem is likely worn agitator dogs/gears. The new dogs alone part # 3109 or what I'd recommend, part #8537434 as a kit with new hub too. An example is shown here...(double check with your complete model number to be certain)
These are very common and available at most brick & mortar parts depot's as well as on-line vendor's such as "repairclinic.com" or "searspartsdirect.com" to name a couple.
You`ll need to remove the top of the agitator to replace them.
To remove the top cover of the agitator, it should lift off by prying up gently with a flat screwdriver or puddy knife.
Under this cap there actually is a screw/fastener,( bolt ) it just may or may not look anything like a typical screw.
It could be a plastic piece with a square center and with the aid of a large flat screwdriver inserted in this location pressed into one of the corner`s in the square center (as to hold it still or turn it,I usually hold it still while turning the agitator) at the same time as holding the bottom of the agitator, turn it counter-clockwise and it will come loose. It may be the bolt style and in that case just remove the bolt and lift it out.
On Whirlpool washer (this is who built your Kenmore) throughout the years there are several types, ones with a 7/16", 1/2" or 9/16" bolt holding it in place, and the type I described. Based on the model number (11024966300) you provided yours will be the 7/16" bolt.
This is a link to a helpful "how to" video...it may have slight differences to your washer, and may refer to a different part number but essentially the same...it is still Whirlpool/Kenmore.
http://www.youtube.com/watch?v=0GQh8JLqVv8&feature=related
Thank`s for visiting FixYa. Good luck and let me know if I can assist you further.
Regards,
Macmarkus :)
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Thank You. I have ordered the kit (not that much more, so fix it right once instead of twice) and it arrives in two days. I will report back when I have finished the repair.
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