Power of fractions

5.NSBT.2B Decimals Multiplied by Powers of 10 & Fractions

Fed. 51: To the People of the State of New York: TO WHAT expedient, then, shall we finally resort, for maintaining in practice the necessary partition of power among the several departments, as laid down in the Constitution? The only answer that can be given is, that as all these exterior provisions are found to be inadequate, the defect must be supplied, by so contriving the interior structure of the government as that its several constituent parts may, by their mutual relations, be the means of keeping each other in their proper places. Without presuming to undertake a full development of this important idea, I will hazard a few general observations, which may perhaps place it in a clearer light, and enable us to form a more correct judgment of the principles and structure of the government planned by the convention. In order to lay a due foundation for that separate and distinct exercise of the different powers of government, which to a certain extent is admitted on all hands to be essential to the preservation of liberty, it is evident that each department should have a will of its own; and consequently should be so constituted that the members of each should have as little agency as possible in the appointment of the members of the others. Were this principle rigorously adhered to, it would require that all the appointments for the supreme executive, legislative, and judiciary magistracies should be drawn from the same fountain of authority, the people, through channels having no communication whatever with one another. Perhaps such a plan of constructing the several departments would be less difficult in practice than it may in contemplation appear. Some difficulties, however, and some additional expense would attend the execution of it. Some deviations, therefore, from the principle must be admitted. In the constitution of the judiciary department in particular, it might be inexpedient to insist rigorously on the principle: first, because peculiar qualifications being essential in the members, the primary consideration ought to be to select that mode of choice which best secures these qualifications; secondly, because the permanent tenure by which the appointments are held in that department, must soon destroy all sense of dependence on the authority conferring them. It is equally evident, that the members of each department should be as little dependent as possible on those of the others, for the emoluments annexed to their offices. Were the executive magistrate, or the judges, not independent of the legislature in this particular, their independence in every other would be merely nominal. But the great security against a gradual concentration of the several powers in the same department, consists in giving to those who administer each department the necessary constitutional means and personal motives to resist encroachments of the others. The provision for defense must in this, as in all other cases, be made commensurate to the danger of attack. Ambition must be made to counteract ambition. The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions. This policy of supplying, by opposite and rival interests, the defect of better motives, might be traced through the whole system of human affairs, private as well as public. We see it particularly displayed in all the subordinate distributions of power, where the constant aim is to divide and arrange the several offices in such a manner as that each may be a check on the other that the private interest of every individual may be a sentinel over the public rights. These inventions of prudence cannot be less requisite in the distribution of the supreme powers of the State. But it is not possible to give to each department an equal power of self-defense. In republican government, the legislative authority necessarily predominates. The remedy for this inconveniency is to divide the legislature into different branches; and to render them, by different modes of election and different principles of action, as little connected with each other as the nature of their common functions and their common dependence on the society will admit. It may even be necessary to guard against dangerous encroachments by still further precautions. As the weight of the legislative authority requires that it should be thus divided, the weakness of the executive may require, on the other hand, that it should be fortified. An absolute negative on the legislature appears, at first view, to be the natural defense with which the executive magistrate should be armed. But perhaps it would be neither altogether safe nor alone sufficient. On ordinary occasions it might not be exerted with the requisite firmness, and on extraordinary occasions it might be perfidiously abused. May not this defect of an absolute negative be supplied by some qualified connection between this weaker department and the weaker branch of the stronger department, by which the latter may be led to support the constitutional rights of the former, without being too much detached from the rights of its own department? If the principles on which these observations are founded be just, as I persuade myself they are, and they be applied as a criterion to the several State constitutions, and to the federal Constitution it will be found that if the latter does not perfectly correspond with them, the former are infinitely less able to bear such a test. There are, moreover, two considerations particularly applicable to the federal system of America, which place that system in a very interesting point of view. First. In a single republic, all the power surrendered by the people is submitted to the administration of a single government; and the usurpations are guarded against by a division of the government into distinct and separate departments. In the compound republic of America, the power surrendered by the people is first divided between two distinct governments, and then the portion allotted to each subdivided among distinct and separate departments. Hence a double security arises to the rights of the people. The different governments will control each other, at the same time that each will be controlled by itself. Second. It is of great importance in a republic not only to guard the society against the oppression of its rulers, but to guard one part of the society against the injustice of the other part. Different interests necessarily exist in different classes of citizens. If a majority be united by a common interest, the rights of the minority will be insecure. There are but two methods of providing against this evil: the one by creating a will in the community independent of the majority that is, of the society itself; the other, by comprehending in the society so many separate descriptions of citizens as will render an unjust combination of a majority of the whole very improbable, if not impracticable. The first method prevails in all governments possessing an hereditary or self-appointed authority. This, at best, is but a precarious security; because a power independent of the society may as well espouse the unjust views of the major, as the rightful interests of the minor party, and may possibly be turned against both parties. The second method will be exemplified in the federal republic of the United States. Whilst all authority in it will be derived from and dependent on the society, the society itself will be broken into so many parts, interests, and classes of citizens, that the rights of individuals, or of the minority, will be in little danger from interested combinations of the majority. In a free government the security for civil rights must be the same as that for religious rights. It consists in the one case in the multiplicity of interests, and in the other in the multiplicity of sects. The degree of security in both cases will depend on the number of interests and sects; and this may be presumed to depend on the extent of country and number of people comprehended under the same government. This view of the subject must particularly recommend a proper federal system to all the sincere and considerate friends of republican government, since it shows that in exact proportion as the territory of the Union may be formed into more circumscribed Confederacies, or States oppressive combinations of a majority will be facilitated: the best security, under the republican forms, for the rights of every class of citizens, will be diminished: and consequently the stability and independence of some member of the government, the only other security, must be proportionately increased. Justice is the end of government. It is the end of civil society. It ever has been and ever will be pursued until it be obtained, or until liberty be lost in the pursuit. In a society under the forms of which the stronger faction can readily unite and oppress the weaker, anarchy may as truly be said to reign as in a state of nature, where the weaker individual is not secured against the violence of the stronger; and as, in the latter state, even the stronger individuals are prompted, by the uncertainty of their condition, to submit to a government which may protect the weak as well as themselves; so, in the former state, will the more powerful factions or parties be gradnally induced, by a like motive, to wish for a government which will protect all parties, the weaker as well as the more powerful. It can be little doubted that if the State of Rhode Island was separated from the Confederacy and left to itself, the insecurity of rights under the popular form of government within such narrow limits would be displayed by such reiterated oppressions of factious majorities that some power altogether independent of the people would soon be called for by the voice of the very factions whose misrule had proved the necessity of it. In the extended republic of the United States, and among the great variety of interests, parties, and sects which it embraces, a coalition of a majority of the whole society could seldom take place on any other principles than those of justice and the general good; whilst there being thus less danger to a minor from the will of a major party, there must be less pretext, also, to provide for the security of the former, by introducing into the government a will not dependent on the latter, or, in other words, a will independent of the society itself. It is no less certain than it is important, notwithstanding the contrary opinions which have been entertained, that the larger the society, provided it lie within a practical sphere, the more duly capable it will be of self-government. And happily for the REPUBLICAN CAUSE, the practicable sphere may be carried to a very great extent, by a judicious modification and mixture of the FEDERAL PRINCIPLE. PUBLIUS.

Q1. A teacher designs a lesson where students compute real-life percentages such as discounts and savings. 👉 A student calculates 15% of 200 to determine savings in a purchase. What is the correct result? A. 20 B. 25 C. 30 D. 35 Q2. In a classroom activity, learners compare numbers to find the highest common factor for grouping materials evenly. 👉 What is the GCF of 24 and 36? A. 6 B. 8 C. 12 D. 18 📘 FRACTIONS, DECIMALS, AND POWERS Q3. A learner converts fractions into percentages for data interpretation. 👉 What is 3/4 expressed as a percentage? A. 50% B. 60% C. 75% D. 80% Q4. A student models exponential growth using repeated multiplication. 👉 What is the value of 252^525? A. 25 B. 30 C. 32 D. 64 📘 ALGEBRA (EQUATIONS AND EXPRESSIONS) Q5. A teacher guides students to solve equations that represent real-life situations. 👉 Solve: 2x+8=202x + 8 = 202x+8=20 A. x = 4 B. x = 6 C. x = 8 D. x = 10 Q6. Students simplify expressions to understand relationships between quantities. 👉 Simplify: 3(x+4)−2x3(x + 4) - 2x3(x+4)−2x A. x + 12 B. x + 4 C. 5x + 4 D. 5x + 12 📘 FUNCTIONS AND GRAPHING Q7. A student analyzes a linear equation to determine its rate of change. 👉 What is the slope of y=3x−5y = 3x - 5y=3x−5? A. -5 B. -3 C. 3 D. 5 Q8. A learner evaluates functions to predict outcomes. 👉 If f(x)=2x+3f(x) = 2x + 3f(x)=2x+3, what is f(4)f(4)f(4)? A. 7 B. 9 C. 11 D. 14 📘 GEOMETRY Q9. Students explore geometric shapes and their properties through visual models. 👉 What is the sum of interior angles of a triangle? A. 90° B. 180° C. 270° D. 360° Q10. A student calculates the area of a classroom table with dimensions 8 cm by 5 cm. 👉 What is the area? A. 26 sq cm B. 30 sq cm C. 40 sq cm D. 48 sq cm 📘 MEASUREMENT AND FIGURES Q11. A learner determines the volume of a cube used in a science experiment. 👉 What is the volume of a cube with side 4 cm? A. 16 cubic cm B. 32 cubic cm C. 48 cubic cm D. 64 cubic cm Q12. Students identify shapes used in design projects. 👉 How many sides does a hexagon have? A. 5 B. 6 C. 7 D. 8 📘 STATISTICS AND PROBABILITY Q13. A teacher helps students interpret data sets using measures of central tendency. 👉 What is the mean of 4, 6, 8, 10, 12? A. 6 B. 8 C. 10 D. 12 Q14. A class experiment involves flipping a fair coin. 👉 What is the probability of getting heads? A. 1/4 B. 1/3 C. 1/2 D. 2/3 📘 WORD PROBLEMS (APPLICATION) Q15. A car travels 180 km in 3 hours during a learning task on speed. 👉 What is its average speed? A. 45 km/h B. 60 km/h C. 75 km/h D. 90 km/h Q16. Students analyze work efficiency in a project. 👉 If 5 workers complete a task in 12 days, how long will 10 workers take? A. 3 days B. 6 days C. 8 days D. 12 days Q17. A student solves a problem involving ratios in a classroom population. 👉 If the ratio of boys to girls is 3:2 and there are 30 students, how many boys are there? A. 12 B. 15 C. 18 D. 20 Q18. A learner determines the duration of a scheduled trip. 👉 A journey starts at 8:30 AM and ends at 11:15 AM. How long is the trip? A. 2 hrs 15 mins B. 2 hrs 30 mins C. 2 hrs 45 mins D. 3 hrs 15 mins Q19. A student computes simple interest for financial literacy. 👉 What is the simple interest on ₱1000 at 5% for 2 years? A. ₱50 B. ₱75 C. ₱100 D. ₱150 Q20. A learner solves a perimeter problem involving a rectangle. 👉 A rectangle has a length of 12 cm and perimeter of 34 cm. What is the width? A. 5 cm B. 7 cm C. 10 cm D. 11 cm ✅ ANSWER KEY (BASED ON YOUR REVIEWER) (All verified from your uploaded file) [ilide.info...002acd4e5a | PDF] QAnswer1C2C3C4C5B6A7C8C9B10C11D12B13B14C15B16B17C18C19C20A

GRADE 4 Module 6 Lesson 3. Interpret Remainders This PowerPoint file contains instructional aids for teachers who have purchased Into Math. It is intended to be projected to students and used in conjunction with the Student Edition and manipulatives as needed. These slides can be used to move the conversation forward in the classroom, but they should not serve as a replacement for student-centered, collaborative conversations in which students have the space they need to find an entry point, construct meaning, and build understanding. About the Slide Presentation Presenter View: Use the Presenter view to see notes while presenting. Customization: Add or delete content or notes to get the best learning experience for your classroom. 1 Problem of the Day. Which equations can be used to solve the following problem? Rita makes 40 bracelets and gives an equal number to 8 friends, including Veronica. Veronica gives 2 of the bracelets that she received to her sister. How many bracelets does Veronica have left? A. 40 – 8 = 32 32 ÷ 2 = 16 B. 40 ÷ 8 = 5 5 + 2 = 7 C. 8 + 2 = 10 40 ÷ 10 = 4 D. 40 ÷ 8 = 5 5 – 2 = 3 2 I Can. I Can solve a division problem and interpret the remainder in the context of the problem. 3 Spark Your Learning. Aiden is building solar toy cars in his science club. The cars collect and use energy from the sun for power. Aiden buys 18 wheels. Each car needs 4 wheels. How many cars can Aiden build? Show your thinking. 4 Turn and Talk. What is the remainder in this problem? What does the remainder mean? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 5 Build Understanding • Task 1 ACTIVITY. There are 57 students going to the science museum. Each van can take 5 students. How many vans are needed to take all the students? Use a visual model to show how the students are divided into groups of 5. 6 Turn and Talk. How can you use the whole-number quotient and remainder to answer these questions? How many vans will be full? How many students will ride in the van that is not full? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 7 Step It Out • Task 2 ACTIVITY.. Amanda has 73 inches of wire for a science experiment. She needs to cut all the wire into 8 identical pieces. How many inches long will each piece be? 8 Turn and Talk. Why is this problem a good situation to write the remainder as a fraction? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 9 Check Understanding. 1. Maya needs 44 batteries for smoke alarms. The batteries come in packs of 6. How many packs does Maya need to buy? For 44 ÷ 6, the whole-number quotient is ____ and the remainder is ____. Maya needs to buy ____ packs. Circle how you interpreted the remainder to solve the problem. 10 I Can Scale. 4 I can explain how to solve a division problem and interpret the remainder in the context of the problem. 3 I can solve a division problem and interpret the remainder in the context of the problem. 2 I can solve a division problem and identify the whole-number quotient and the remainder. 1 I can solve a division problem with a remainder. 11 Exit Ticket. Mr. Jenkins’ class is giving speeches during a 46-minute class. Each student will be able to talk for 4 minutes. How many students can give speeches? Justify your answer.

How did the framers of the Constitution try to limit the power of the national government? Separation of Powers: a key constitutional principle that divides the functions of government among three branches (legislative, executive, and judicial) to prevent any one branch from gaining too much power How did the framers of the Constitution try to keep one branch of the government from dominating the others? A system of checks and balances Checks: allow one branch to block the actions of other branch Congress can pass laws, but the president can check this power through veto. Congress can check the president’s veto power by a two-thirds majority vote in each house. Judicial branch can check the actions of both Congress and the president through its power of judicial review and so declare a law, a treaty, or an executive action unconstitutional. Balances: allow each branch of the government to have some role in the actions and power of the other branches Judges, ambassadors, and cabinet members are appointed only if the president nominates them and the Senate approves the nomination. President can sign treaties, but they only take effect if the Senate approves them. Powers of judicial branch are also balanced by the other branches. -- The Supreme Court can declare laws unconstitutional, but the president chooses federal judges, and the Senate must approve the appointments. Congress can impeach federal judges.

Of the 7 billion people on Earth roughly 0:02 6 billion own a cell phone which is 0:05 pretty shocking given that only 4 and2 0:07 billion have access to a working toilet 0:09 so how are these popular gadgets 0:11 changing your body and brain If you're 0:13 looking down at your phone right now 0:15 your spine angle is equivalent to that 0:17 of an 8-year-old child sitting on your 0:19 neck which is fairly significant 0:21 considering people spend an average of 0:23 4.7 hours a day looking at their phone 0:26 this combined with the length of time 0:28 spent in front of computers has led to 0:30 an increase in the prevalence of myopia 0:32 or nearsightedness in North America in 0:34 the 1970s about one quar of the 0:36 population had myopia where today nearly 0:39 half do and in some parts of Asia 80 to 0:41 90% of the population is now nearsighted 0:44 and it can be hard to put your phone 0:46 down take for example the game Candy 0:48 Crush as you play the game you achieve 0:50 small goals causing your brain to be 0:52 rewarded with little bursts of dopamine 0:54 and eventually you're rewarded in the 0:56 game with new content this novelty also 0:58 gives little bursts of dopamine and 1:00 together create what is known as a 1:01 compulsion Loop which just happens to be 1:04 the same Loop responsible for the 1:05 behaviors associated with nicotine or 1:07 cocaine our brains are hardwired to make 1:10 us novelty seeking and this is why apps 1:12 on our phones are designed to constantly 1:14 provide us with new content making them 1:16 hard to put down as a result 93% of 1:19 young people aged 18 to 29 report using 1:21 their smartphone as a tool to avoid 1:23 boredom as opposed to other activities 1:26 like reading a book or engaging with 1:27 people around them this has created a 1:29 new term nomophobia the fear or anxiety 1:32 of being without your phone we also see 1:35 a change in brain patterns Alpha rhythms 1:37 are commonly associated with wakeful 1:39 relaxation like when your mind wanders 1:41 off whereas gamma waves are associated 1:44 with conscious attentiveness and 1:46 experiments have shown that when a cell 1:47 phone is transmitting say during a phone 1:49 call the power of these Alpha Waves is 1:52 significantly boosted meaning phone 1:54 Transmissions can literally change the 1:56 way your brain functions your smartphone 1:58 can also disrupt your sleep the screen 2:00 emits a blue light which has been shown 2:02 to alter our circadian rhythms 2:03 diminishing the time spent in deep Sleep 2:06 which is linked to the development of 2:07 diabetes cancer and obesity Studies have 2:10 shown that people who read on their 2:11 smartphone at night have a harder time 2:13 falling asleep and produce less 2:15 melatonin a hormone responsible for the 2:17 regulation of sleep wake Cycles Harvard 2:20 medical school advises the last 2 to 3 2:22 hours before bed be technology free so 2:24 pick up a book before bed instead of 2:26 course smartphones also completely 2:28 change our ability to access information 2:30 most notably in poor and minority 2:32 populations 7% of Americans are entirely 2:35 dependent on smartphones for their 2:37 access to the internet a 2014 study 2:40 found that the majority of smartphone 2:41 owners use their phone for online 2:43 banking to look up medical information 2:45 and searching for jobs so while phones 2:47 are in no way exclusively bad and have 2:50 been part of a positive change in the 2:51 world there's no denying that they are 2:53 changing us but many successful people 2:56 have now decided to take smartphone 2:58 vacations in order to increase 3:00 productivity in our new ASAP thought 3:01 video we break down the top six reasons 3:04 you should take a smartphone vacation 3:06 and how it could benefit your life right 3:08 now and subscribe for more weekly 3:09 science videos

What is a crime A crime is generally defined as an act or omission that is prohibited by criminal law Two critical ingredients of a crime are: 1) the commission of an act (Actus reus) 2) the mental intent to commit the act (Mens rea) A crime occurs when a person Commits an act or fails to commit an act when under a legal responsibility to do so Has the intent or mens rea to commit the act Does not have a legal defence or justification for committing the act and Violates a provision in criminal law The Social construction of crime Important to distinguish between behaviours that may be considered deviant by society and crimes Deviance is behaviour that is contrary to the norms and values of the larger society Crime is behaviour that breaks the law Deviance includes: Criminal behaviour and Wide range of other behaviours not against the law: May be frowned upon by the larger society What is viewed as deviant changes over time Crime includes: Social construction of crime Legal status of behaviours is not determined by behaviour itself but result of social response to the behaviour/persons/groups engaged in it Criminologists often conduct historical analyses to understand how social, economic and political environments may influence legislation Moral entrepreneurs Often play a key role in criminalizing certain activities Individuals, groups or organizations, seek action against certain groups of people/behaviours and bring pressure on legislators to enact criminal statutes The Origins and Application of the Criminal Law Differing perspectives on where criminal laws come from/ applied via the criminal justice system are reflected in two models 1) Value consensus model 2) Conflict Model Value consensus model Behaviours are defined as criminal/punishment imposed, reflect opinions/limits of tolerance Application of law, society reaffirms acceptable behaviours/social cohesion Conflict Model Crime and punishment reflect the power some groups have to influence, formulation/application of criminal law rich/privileged have an advantage in influencing law reform/criminal justice system The Canadian Legal System Is a common law system, with exception of Quebec which has a civil law system (Based on the French Code Napoleon) Common law is law based on custom, tradition, practice and generally unwritten Precedent is a judicial decision may be use as a standard in subsequent similar cases Canadian Courts Canadian courts organised in a hierarchy Supreme court of Canada is the highest court Stare decisis- principle whereby higher courts set precedents that lower courts must follow “To stand by what was decided” Like cases should be treated alike All courts below SSC bound to apply that same ruling in subsequent cases Criminal Law Body of law deals with conduct considered so harmful to society as a whole that it is prohibited by statute and prosecuted and punished by the government Functions of the Criminal Law In Canadian society, Criminal law provides the following functions Acts as a mechanism of social control Defines the parameters of acceptable behaviour Reduces the risk of personal retaliation Assists in general and specific deterrence Prosecutes criminalized behaviour Protects groups interests Principles of Canadian Law The Rule of Law The requirement that governments as well as individuals be subjected to Traced back to the English Magna Carta The essence of the rule of law is that No one person is above the law All persons are bound by the law All are entitled to protection by the law The law should be observed and enforced equally There is a standard to which criminal justice officials must adhere and will be held accountable Criminal Law Vs. Civil (Tort) Law Summary Crime is a social construction and is a reflection of changing time and mores Criminal law is not static and what behaviour legislatively defined as criminal can change overnight There are instances in which controversy arises when the criminal law is applied to issues of ethics, morality and religion The criminal law was identified as one type of public law and the functions of the criminal law were set out The rule of law and the charter of rights and freedoms are two key parts of the foundation of the criminal justice system There are several principles that also provide the foundation for Canadian law The role, principles origins and application of the criminal law were examined and a number of case studies were presented to illustrate the dynamic nature of the criminal law in a diverse society

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