To describe partial products in a "laymans" term, you'd have to set up an problem with the 4th grader.
Set it up in a big format and even make a game out of it with tiles on the floor.
Explain to the 4th grader that the number on the bottom will be multiplied by each number separately and then eventually added. For more than one digit multiplication problems, they add a "0" for each number they are on. Example: One zero after the first number is multiplied. Two zero's after the second number is multiplied, etc...
Then, you just add like normal.
I have actually used the tile method to help my 4th grader learn how to do partial products.
I suggest making BIG 8x10 numbers. Then, tape them (gently) on the floor. Have the 4th grader stand on the first number they'd be multiplying. Example:
12 x 6
The student would stand on the number 6. You then ask them to jump (or hop-just be careful of slippery surfaces) on the number they have to multiply with next; which would be the 2. You'd ask them, what is "6 x 2?". They should reply with 12.
Next, have another set of smaller numbers where they can come back and place the numbers. 2 would go on the bottom and they hold the 1 so they can remember they need to add it to the next multiplication number.
So, now you'd have them stand on the number 6 again. Ask where they have to multiply again. They should move to the 1. Ask what is "6x1". Then answer should be 6. Then remind them they are holding a number and what they should do with it. The answer should be "add it to the answer of the multiplication". So, it should be 6+1=7. Then, they'd place the number 7 at the bottom of the problem.
Once they figure it out with single digits, move onto double digits at the bottom and work up from there.
This way, they are having to use BIG movements and will eventually gain muscle memory on which directions and how to multiple correctly.
GOOD LUCK!
