How to apply tiered discounts to entire cart based on quantity

[TAS_SHMA]

What I'm trying to do is create an add to cart function that adds a tiered discount system depending on the quantity of an order.

For example,

I'm using the following variables:

discount_amount=0
discount_num=1
discount_amount2=10
discount_num=2
discount_amount3=20
discount_num=3

However, only discount amount 2 is achieved.  I want to make it so that when someone adds:

1 item = no discount

2 items - $10 off

3-5 items - $20 off

6 or more items - $40 off