(I could not find as much on the Toulmin argument in the book and used 3 online resources, which had some overlapping construction. I finally summed up the lacking information provided by the textbook, as well as the paragraph required.)
The point of the Toulmin argument is to take cacophony and jarring fights to turn into an effective argument divided into 6 specific parts. Those parts are divided into 2, the 1st 3 laying out the debate and the last 3 forcing the audience to agree.
Triad #1
"laying it down the line"
The Claim
The claim is your point.
It could be one of 3 of the following:
1. a fact
2. "passing judgment"
3. making a declaration of what should be or happen
Grounds
The grounds people love to come out, state the facts that prove your claim and introduce the beginning of a debate.
It could be one of 3 of the following:
1. statistics or facts
2. a reliable source
3. deductions
Warrant
The warrant is stating relevant significances.
It can be one of the 4 following:
1. Ethos - the ethics, like in relation to how credible and esteemed a person is
2. Logos - more impersonal credibility, facts, that can also deal with people
3. Pathos - the feeling emphasis, to appeal to an argument
4. Values - just what it says, things that people believe to be popular
Triad #2
The Fight/Debate
Backing
It simply helps your argument by answering a popular question.
Qualifier
This part of the argument is sincerity, saying how far the argument goes but saying how far it doesn't have to go.
Rebuttal
The author finally addresses the opposing views in question.
The Textbook
Claim - Stating the main idea of the debate.
Support - Proof of the claim.
Warrant - Stating why it is true.
Type of Claim - Being more specific and realistic in accomplishing something.
Paragraph Understanding
The Toulmin argument is a very effective way of delivering a debate, especially in the form of writing. It consists of usually 6 parts: the claim, grounds, warrant, backing, qualifier, and rebuttal. You state the made idea and back it up with facts and give the facts credibility by appealing to people. You start off proving yourself in the 1st 3 parts, and by the 2nd 3 parts you start the "fight" or persuasive lecture/speech. It may be confusing and unclear, but it is very amusing.