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The bill of rights is a list of the rights of american citizens, this list continues to have rights added on to it. These additions are called amendments.
Below is a picture listing the original ten amendments in the bill of rights

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Federalism, in america's case, is the way we govern our country, there is a federal government and 50 state governments. State governments have certain powers the federal government doesn't have, vice versa for the federal government, and there are certain powers they both have, these are called concurrent powers.

Below is a venn diagram of the powers of the federal gov. state gov. and the shared powers between the two.

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Checks and balances are a bunch of things that the branches can do to make sure the other branches cannot be too powerful.

Below is a graphic organizer that shows all of the checks and balances between every branch of government.

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Legislative:
This branch makes laws, prints money, declares war, confirms appointments, and ratifies treaties. The leaders of the branch are the members of the two chambers of congress, members of the senate and the house of representatives
Judicial:
This branch determines if a law or an act by another branch is unconstitutional, this branch contains the courts. The leaders of this branch are the supreme court justices
Executive:
This branch enforces the laws and commands the military, the leader of this branch, the president appoints cabinet members and justices.

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How to choose a president:

Immediately after the presidential election of 1876, it was clear that the elections were unfair based on populations of the bigger states overpowering smaller states. So there was a debate on how to elect the president. Two proposals were made, one of them were that the people should elect the president, the other was that representatives should. The founding fathers came up with a perfect idea, the next thing you know, the electoral college was made, no matter how many votes came from florida, the candidate would just get the electoral college votes from florida.

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3/5 compromise:
The 3/5 compromise was founded upon the idea that the population of slaves would be counted as three fifths when electing Representatives, as well as Presidents and taxes. This was proposed by James Wilson and Roger Sherman. This compromise was made after the dispute between the northern and southern states.

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Great Compromise:
Problem:
There were two big disagreements over a very important issue, what type of government to have. There were two major plans that came to the convention. The Virginia Plan was a proposal by Virginia delegates for a bicameral legislative branch. The plan was drafted by James Madison. The New Jersey Plan was one option as to how the United States would have the congress. The Plan wanted each state to have one vote in Congress instead of the number of votes being based on population. It was introduced to the  Convention by William Paterson on June 15, 1787.
These were both very controversial and debated a lot, so then came the Connecticut plan/ The great compromise. This compromise  was an agreement that large and small states reached during the Convention that defined the legislative structure and representation that each state would have under the Constitution. It retained the bicameral legislature along with proportional representation in the lower house, but required the upper house to be equal between the states. Each state would have two representatives in the upper house.

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Definition:
The Continental Congress made and used the Articles of Confederation, in 1777. This was replaced by the current constitution.
Weaknesses:
A very major weakness was taxes and the ability for the government to get money.  This was the cause of the very infamous shays rebellion, the uprising that made the fact that the necessity of the remake of the articles very high and very noticeable by the government. Daniel shays was not being paid enough, being a rev war vet and being taxed too much,  apparently he had much in common with another 4k farmers. Under the articles, the federal government could not form an army.
Strengths:
The Articles of confederation did have strengths though. The Northwest ordinance is a perfect example of this! The Northwest ordinance of 1787 was an expansion made from the original 13 colonies to make new states, these being ohio, minnesota, wisconsin, michigan, illinois, and indiana.