Today we began by reviewing the goals of the Constitution: to form a more perfect union, to establish justice, to insure domestic tranquility, to provide for the common defense, to promote the general welfare and to secure the blessings of liberty. We discussed the major principals which are: popular sovereignty, republicanism, limited government, federalism, separation of powers, checks and balances and individual rights. We then looked at how our nation's founding historical documents: the Declaration of Independence and the U.S. Constitution are housed for public display at the National Archives in Washington, D.C. They are kept in tightly secured chambers to preserve the documents and to protect them from damage or theft. The systems in place sound like something out of a movie - but it's true! We viewed how the documents are displayed and protected in the National Archives by viewing spectacular scenes from the film, "National Treasure," filmed on location in Washington, D.C. Bella was absolutely intrigued.

Algebra 1 Concepts – We began to take an end-of-course cumulative exam.

9-7 Solving Systems of Linear and Quadratic Equations – We learned to describe a linear-quadratic system of equations and solve this system of equations by graphing, elimination, or substitution. For any system of two equations in two variables the solution consists of the ordered pairs that satisfy both equations. Then we began a Review and Test on Topic 9 Solving Quadratic Equations.

Yesterday, we covered how delegates called for a Bill of Rights to be part of this new and stronger federal government being revised at the Constitutional Convention in 1787. Today we looked at some other impressive compromises to come from this convention that impact the structure of our unique democracy and America's democratic republic to this very day. The Articles of Confederation, or the first federal government of the United States, was far too weak because it did not accord enough power over the states to the federal government. At the convention, "The Great Compromise" produced a system of government that both large and small states could ratify. The Great Compromise combined elements of both the VA Plan and the NJ Plan by including two legislative bodies, or a bicameral government, one with proportional representation and the other with equal representation. The Constitution was ratified on June 21, 1788.
Participants in the Constitutional Convention also compromised by creating the electoral college and the three fifths compromise. The electoral college is a process in which state electors decide the winner of presidential elections. The three fifths compromise determined that enslaved people would be counted as less than free people in a state's political representation.

During the Constitutional Convention, several delegates proposed a bill of rights to be added to the Constitution. This way, a new national gov't couldn't abuse its power. However, most of the delegates believed the Constitution provided adequate individual rights. The Constitution was ratified in 1787 and the Bill of Rights was added in 1791. The Bill of Rights is the first 10 amendments to the U.S. Constitution. They are: Amendment I
This guarantees the freedom of religion, speech, press, and peaceable assembly, to petition the gov't. Amendment II
Guarantees the right to bear arms. Amendment III Guarantees no quartering of soldiers, without the consent of the home owner. The third amendment is hard for us to understand today because of the rights we all enjoy. No one has ever made an American in the 21st century put up a soldier for the night, but housing the military was something colonials had to do before and during the revolution. This amendment guarantees you will not have to feed and house soldiers against your will. Amendment IV This amendment guarantees the freedom from unreasonable searches and seizure. Amendment V - The right to due process of law, freedom from self-incrimination, double jeopardy. This means you can't be tried twice for the same crime. Amendment VI concerns the right to a speedy and public trial and the right to have an attorney. Under the 6th amendment you aren't guaranteed a good lawyer, but at least they should know the law better than most. Amendment VII
is the right of trial by jury in civil cases. Amendment VIII -
The freedom from excessive bail, cruel and unusual punishments.
Amendment IX says that rights not listed may exist, and just because they are not listed doesn't mean they can be violated.
Amendment X - The powers not given to the federal government by the Constitution are retained by the states. The first 10 Amendments to the U.S. Constitution are The Bill of Rights. As of 2022, there are now 33 total amendments.

On September 17, 1787, the Constitutional Convention submitted its proposal for a new constitution to Congress. Federalists (supporters of the Constitution) and Anti-federalists (against the Constitution) in the various states debated this new, proposed Constitutional government. In New York, the Federalists Alexander Hamilton, James Madison, and John Jay wrote a series of essays supporting the Constitution, later published as the Federalist Papers. One of the major concerns of the Anti-federalists was the absence of a ''bill of rights'' which would guarantee certain human rights. The Federalists argued that such a bill of rights could be added later. (And it was.) The new Constitution was ratified when New Hampshire became the ninth state to do so in June 1788. In May 1790, Rhode Island was the last state to ratify the Constitution after first rejecting it. Once ratified, the U.S. Constitution quickly alters American democracy and elevates the American federal government.

9-6 The Quadratic Formula and the Discriminant – We learned that the quadratic formula can be used to solve every quadratic equation and is particularly useful for those that cannot be easily factored. Then we learned to use the discriminant to determine the number and type of solutions to a quadratic equation. Next we began to review for an end-of-course cumulative exam.
Assignment: Complete the assigned problems for homework.

9-3 Rewriting Radical Expressions – We practiced finding square roots of whole numbers. Then we practiced finding square roots of variables with exponents. Next we practiced simplifying radical expressions with whole numbers and variables with exponents under the same radical. Then we took a quiz on Simplifying Radical Expressions. Then we moved on to multiplying radicals. We multiplied radicals under the square root and simplified the answer. 9-4 Solving Quadratic E and equations Using Square Roots – We learned that when the quadratic equation is in the form ax2 + bx = c, it can be solved by isolating the ax2 term, simplifying to remove the coefficients, and then taking the square root of each side of the equation. We practiced several of these type of problems where we take the square root and have two possible solutions. Next we reviewed completing the square to find the answers to a quadratic equation that is not able to be factored.
Assignment: Complete the assigned problems for homework.

For the first 11 years of its existence, the new United States of America were governed by a central government called the Articles of Confederation. Under the Articles, the new states gave up little of their power. Under the Articles, there was only one branch of federal government: a Congress that was so overwhelmed that it didn't accomplish much. We spent time reviewing many other weaknesses of the Articles of Confederation. By 1786 many Americans observed that the Confederation was not working. Even George Washington agreed the new U.S. govt. was insufficient. Therefore, in the spring of 1787, Washington joined delegates from all 13 states who gathered in Philadelphia to address this issue. Their intent was to amend the Articles of Confederation. Instead, they wrote an entirely new, brilliant document and format of government called the U.S. Constitution.

https://www.youtube.com/watch?v=2YpE4_HIAn8&list=PL0G-Nd0V5ZMp53jELWvQp4KFgD-pLmQ0Q sqrt 48x2y5
https://www.youtube.com/watch?v=lbzNKQnpVVs&list=PL0G-Nd0V5ZMp53jELWvQp4KFgD-pLmQ0Q&index=38 sqrt 144x4y3
https://www.youtube.com/watch?v=loHF2p1eNQw&list=PL0G-Nd0V5ZMp53jELWvQp4KFgD-pLmQ0Q&index=5 5*sqrt 200
9-3 Rewriting Radical Expressions – We practiced using the properties of exponents to rewrite radical expressions. Then we multiplied radical expressions. Next we learned to write a radical expression to model or represent a real-world problem. We practiced writing radical expressions in simplest form which is where there are no perfect square factors other than one in the radicand.
Assignment: Complete the assigned problems for homework.