2 vessel brewing - sparge questions

So I am new to all grain and getting ready for my first all grain brew (5 gallon ipa batch).  However, I have a question about sparging.  I have a 8 gallon brew kettle and 52 quart cooler mash tun.  (no pump, ball valve with silicone hose)
1.) Heat 4 gallons of water to 163 so I can mash at 148 (I anticipate a 15 degree temperature loss)
2.) Transer 4 gallons of water to the cooler
3.) Add the grain to cooler
4.) Stir the mash to make sure no lumps/dough balls
5.) Once that is mixed, close the lid of the cooler for an hour
6.) While that it is happening, heat up 3 gallons of water to 170 degrees to use as sparge
7.) After an hour, open the ball valve a little bit and let the wort come out and use the hose to pour it over the top of the grain bed. Doing this for 5 minutes
8.) Then pour the 170 water over the grain bed
9.) Transfer from cooler back to kettle using the ball valve hose until I have 6 and a half gallons of wort in my brew kettle
10.) Proceed with boil as I’m used to.

After reading  a few things, I think my sparging technique is wrong. I have a quart pitcher Id be using for pouring the water onto the grain.  Should I just do no-sparge and use more water to start with? Any and all info would be appreciated.

What you’re proposing sounds like batch sparging.  You can read more about it here…www.dennybrew.com

I don’t see any draining step before steps 7 and 8, so you aren’t doing a sparge.

Two approaches to sparging, drain the mash tun before sparging and you are batch sparging.  Simultaneous draining and sparging, you are fly sparging.

In step 7, you should vorlauf by recirculating wort from the mash drain top back to the top of the mash tun.

so I cant sparge with just my kettle and my mash tun. I need another vessel to either hold the sparge water or hold the wort that comes out of the mash tun?
should I just do no sparge and add more water to the mast tun at the start?

i had someone explain it to me on the phone and it makes sense now. im all set. thanks

You can either do a full no-sparge or a modified one in this fashion (kind of like a single batch sparge…).

Heat strike water in kettle to desired temp and transfer to mash-tun with grain. Conduct mash rest.

Meanwhile, heat remaining water needed to reach full kettle volume pre-boil and add to mash -tun to reach a desired mash-out temp. Let rest for 15 min, vorlauf (if desired) and drain into kettle for boil.

With this process you only need a mash-tun and boil kettle.

What is you grain to water ratio for the mash? Are you aware of the quarts per pound ratio?