Thursday, March 19, 2020

Of Mice and Men Summary

Of Mice and Men Summary Of Mice and Men is John Steinbeck’s best-known work. The 1937 novella tells the story of George Milton and Lennie Small, two migrant workers who travel from farm to farm in search of work in Depression-era California. Chapter 1 The story begins with two childhood friends, George Milton and Lennie Small, who are traveling through California in search of work. Lennie is drinking from a puddle of standing water, and George reproaches him. When Lennie stops drinking the water, George reminds him that they only have a little way to go until they arrive at their next farm. George notices that Lennie isn’t really listening; instead, Lennie has been focusing on petting a dead mouse that’s in his pocket. George mentions that Lennie picked up the habit from his Aunt Clara, then reminds Lennie that he always used to kill the mice. George angrily tosses the mouse into the woods. The two men settle down in the woods for the night. They eat a dinner of beans and talk by the fire about their dreams of making enough money to buy land of their own, with rabbits to care for. Chapter 2 The next morning, George and Lennie arrive at the ranch and meet their boss (referred to only as the Boss). The Boss tells them that they were supposed to arrive the night before; thanks to their delayed arrival, they will have to wait until the next day to start working. During the conversation, George speaks for both himself and Lennie, which frustrates the Boss. However, once Lennie finally speaks, the Boss agrees to hire the men. Next, George and Lennie meet Curley, the son of the Boss. Curley tries to intimidate them- especially Lennie- but once he leaves, they learn some gossip about his character from Candy, one of the ranch hands. Candy explains that Curley is a good fighter who made it to the finals of the Golden Gloves, but that he is mad at [big guys] because he aint a big guy. Curleys wife briefly appears and introduces herself to George and Lennie. Lennie cant take his eyes off of her, but the farm hands warn him against talking to her and describe her as flirtatious and a tart. Lennie frets about having to fight Curley, but George reassures him and instructs him to go to their predetermined hiding place should a fight begin to brew. Lennie and George also meet two other ranch hands- Slim and Carlson- and learn that Slims dog has recently given birth to a litter of puppies. Chapter 3 In the bunk house, George and Slim meet up. George thanks Slim for allowing Lennie to take one of the puppies. As the conversation continues, George tells Slim the truth about why he and Lennie left their previous farm: Lennie, who loves to touch soft things, tried to pet a woman’s red dress, leading people to think that he had raped her. George explains that Lennie is a gentle person and that he never raped the woman. Candy and Carlson arrive, and the conversation turns to the topic of Candys elderly dog. Candy clearly loves the animal and doesnt want to let him go, but he also recognizes that the dog is suffering; plus, according to Carlson, we cant sleep with him stinkin around in here. Candy finally agrees to let the dog go, and Carlson takes the dog away with a shovel to end its life. Later, George and Lennie discuss their plan to save up some money and buy land of their own. With childlike fascination and hope, Lennie asks George to describe more and more elements of the imagined farm. Candy overhears the conversation and says that he wants to join in using his own savings. George is skeptical at first, but he eventually agrees to let Candy in on the plan, convinced by the fact that Candy has considerable money saved up already. The three men agree to keep the plan a secret. As they make this pact, an annoyed Curley appears and starts to pick a fight with Lennie. Lennie doesnt want to fight and begs George for help. Curley punches Lennie in the face and, going against his own promises to protect Lennie, George encourages Lennie to fight back.  In nervous retaliation, Lennie grabs Curley’s fist in his own and squeezes; as a result, Curley starts â€Å"flopping like a fish on a line.† Lennie and Curley are separated, and it becomes clear that Curley’s hand is shattered. He is rushed to the doctor, but not before he and the others agree not to say a word about what has happened to anyone else. Once Curley has been taken away, George explains that Lennie only acted that way because he was scared. He then tries to calm his friend by telling him that he didn’t do anything wrong and that he can still tend the rabbits on their land. Chapter 4 That night, after everybody else has gone into town, Lennie is out on the farm visiting his puppy. He walks past the room of Crooks, the African American stable-hand who lives in separate lodging because the other farm hands wont allow him in the bunk house. The two men start talking, and Crooks asks him some probing questions about his relationship with George. At one point Crooks suggests that George won’t return that night, which frightens Lennie, but Crooks settles him down. Lennie lets slip that he, George, and Candy are planning on saving up for their own piece of land. Upon hearing this, Crooks calls the idea â€Å"nuts,† and says that â€Å"ever’body wants a little piece of lan’†¦nobody gets no land. It’s jus’ in their head.† Before Lennie can respond, Candy enters and joins in the conversation, also talking about their plan to buy some land. At this, Crooks once again expresses his skepticism, though Lennie and Candy remain unconvinced. Unexpectedly, Curley’s wife appears, mentioning that she is looking for Curley and drawing the attention of the three men as she flirts with them. The men tell her that they don’t know where Curley is. When she asks how Curley hurt his hand, the men lie, saying that it got caught in a machine. Curleys wife angrily accuses the men of covering up the truth, and Crooks tells her to leave. This response angers her even further; she hurls racial epithets at Crooks and threatens to have him lynched. Powerless, Crooks averts his gaze and apologizes flatly to her. Candy tries to come to Crooks’ defense, but Curley’s wife retorts that nobody would believe them over her. Before slipping out, she says she’s glad Lennie crushed Curley’s hand. As  soon as Curleys wife exits, the three men hear the other farm hands. Lennie and Candy return to the bunk house, leaving Crooks to himself once again. Chapter 5 The next afternoon, Lennie sits in the barn with his puppy, which has died as a result of his indelicate touch. As he buries the body, Lennie worries that George will find out and that the revelation will cause George to forbid Lennie from tending rabbits on their farm. Curley’s wife enters the barn. Lennie blurts out that he is not supposed to talk to her, but they converse nevertheless. Curleys wife describes her youthful dreams- now crushed- of becoming a Hollywood actress, as well as her resentment towards her husband. Lennie then tells Curleys wife about how he likes to pet soft things, like rabbits. Curleys wife lets Lennie stroke her hair, but Lennie clasps her too tightly and she squirms in his grip. Lennie shakes her - so hard that â€Å"her body flopped like a fish†- and breaks her neck. He runs off. Candy discovers the body of Curleys wife in the barn. He runs to get George, who, immediately recognizing what Lennie did, decides that they should walk away and let the others find the body. Once Curley learns the news, he quickly decides that Lennie must have killed her. Curley and the other farm hands set off to kill Lennie in revenge- only they can’t locate Carlson’s Luger pistol. George is supposed to join the search party, but he sneaks away, knowing that Lennie has gone to their pre-established hiding spot. Chapter 6 Lennie sits by the river, waiting for George and worrying about how he might react. He begins to hallucinate; first, he imagines that he is talking to his Aunt Clara, then, he imagines a conversation with a giant rabbit. George arrives at the hiding spot. He reassures Lennie that he wont leave him and describes the land theyll own together, which calms Lennie down. As the two men are talking, George can hear Curleys search party closing in. He raises Carlson’s Luger pistol to the back of Lennie’s head, so that Lennie cannot see it. George hesitates at first, continuing to calmly tell Lennie about their farm, but just before Curley and the others arrive, he finally pulls the trigger. The other men take in the scene. Slim tells George that he did what he had to do, and Carlson remarks to Curley, â€Å"Now what the hell ya suppose is eatin’ them two guys?†

Monday, March 2, 2020

Lines and Angles in SAT Math Prep and Review

Lines and Angles in SAT Math Prep and Review SAT / ACT Prep Online Guides and Tips Knowing your lines and angles is crucial for mastering SAT and is one of the foundational steps of geometry. Before you can tackle some of the more complex multi-shape problems that often appear towards the end of the test, you’ll need to know just how to solve for all your missing angle measures. Almost without fail, there will be exactly two problems on any given SAT on lines and angles (note: these problems are distinct from questions on lines and slopes, which are covered in a separate guide). Though this is a small percentage of the test in and of itself, line and angle knowledge provides the backbone for other geometry problems and so should be ranked high on your studying priorities. This will be your complete guide to lines and angles on the SATwhat they are, how you’ll see them on the test, and how to solve these types of questions to maximize your points on test day. Properties of Lines and Angles Before we get into how lines and angles function, let’s take a second to define what these terms mean. A line is a completely straight marker, meaning it has no curvature. It can either have termination points (and will be called a â€Å"line segment†) or go on infinitely. Its degree measure is always 180 °. Parallel lines are two or more lines that are a set distance apart (equidistant) and never meet. They travel in the same direction continuously. Perpendicular lines meet each other at 90 degree angles. An angle is the meeting of two lines. The measure of how they meet is expressed in degrees, and the point at which they intersect is called the angle’s â€Å"vertex.† Line and Angle Equalities Most of what you’ll need to know about lines and angles on the SAT is when and how they will be equal or supplementary to one another. Equal angles (or lines) are angles (or lines) that have the same measurement. Supplementary angles are angles that add up to 180 degrees. Because all these angles form a straight line and a straight line equals 180 degrees, the three angles are supplementary. Opposite Angles When two (or more) lines intersect, they form a series of opposite angles. Angles that are exactly opposite will always be equal to one another. Now let’s look at an opposite angle SAT problem. Here, you can see that the lines l and k intersect such that the sum of angles p and x make an angle that is exactly opposite angle m. This means that, when we add together angles p and x, their sum will be equal to angle m (because opposite angles are equal). 25+x=40 x=15 So our final answer is A, 15. Opposite Interior Angles When there are two parallel lines that are crossed by another line (called a transversal), the angles on alternate interiors will be equal to one another. And the angles on the same side of the transversal line and the same side of their respective parallel lines will also be equal. That may be difficult to picture, so let’s look at a diagram: (Note: when you are told that two lines are parallel on the SAT math section, the problem will almost always involve opposite interior angles in some way.) Now let’s look at an opposite interior angle SAT problem. We are told that lines l and m are parallel, so that means the three vertical lines are transversals. We can see that the angle to the far left is marked as 89 degrees and it is an opposite interior angle to angle r only. This means that r=89 degrees, as opposite interior angles are equal. So our final answer is A, r. Typical Line and Angle Problems Almost every line and angle problem is given to you as a diagram problem. You will be presented with a series of givens and then told to find a missing value of some kind. Almost always, this requires multiple steps and the use of multiple pieces of line/angle knowledge. For instance: This is a very typical line and angle problem, so let’s go through it. We are told that angle f is 85 degrees. This means we know that angle b is also 85 degrees because it is opposite f and opposite angles are equal. We are also told that c is 25 degrees. This means that g must also be 25 degrees because it is opposite angle c. And finally, we know that a line equals 180 degrees. This means that, in order to find angle a, we can say: a+25+85=180 a+110=180 a=70 So our final answer is C. As we said before, this question is representative of most line and angle problems you’ll see on the test. Based on your givens, you must use your knowledge of opposite angles (opposite angles are equal) and your knowledge of the degree measure of a line (a line is 180 degrees) in order to put together all the clues and solve your problem. The other kind of line and angle problem you may see will involve triangles. In these questions, you must not only put together multiple pieces of angle knowledge, but triangle knowledge as well. Generally, you will not need to know more than the fact that all the interior angles in a triangle add up to 180 degrees, but check out our guide to SAT triangles if you are rusty on your triangle geometry(coming soon!). Because we are told that lines l and m are parallel, we can guess that our answer likely has something to do with opposite interior angles. We also know that, to equal 180 degrees, our angles must either complete a triangle or a straight line. With those clues in mind, let’s go through our answer choices. Option A gives us k,n, and r. We know from our opposite interior angles that k and r are equal, and that n, s, and t are equal, but this information helps us complete neither a triangle nor a straight line. We can eliminate answer choice A. Answer choice B gives us k,p, and s. Again, from our opposite interior angle knowledge, we know that k and r are equal, and that n, s, and t are all equal. Because s=n, we can form a triangle with our given angles. And because s=t, p is given, and opposite interior angle equalities means that k is equal to the unknown angle counterclockwise above t, then our known values can also form a straight line of 180 degrees. Whether they are forming a triangle or a straight line, we can find 180 with the given angles of k,p, and s. We can stop here; we found our solution. Our final answer is B. You can see here that the lynchpin for solving the problem was in your understanding that opposite interior angles are equal. And though you could have also found your required 180 degree measurement using a straight line (as we did above), it was faster to use the triangle. For both ease of problem solving and knowing how to solve the more complex geometry problems, your knowledge of lines and angles should definitely be supplemented with triangle study. So don’t forget to brush up on your SAT triangles!(coming soon!) Let's take a look at the tips for unlocking SAT angle problems. Tips for Solving a Line and/or Angle Problem As you saw in the earlier examples, most line and angle problems require you to go through multiple steps before you find the right answer. And most of the time, you must solve the question piece by piece in order to unlock the final solution. As you go through this process, keep in mind these three tips: 1) Write in your givens If you are given a diagram in which your givens are NOT written in, then write them in yourself! Sometimes, seeing the numbers on the page can make all the difference in the world between a difficult problem and an easy one. You’ll also be far less likely to mix up your numbers and variables if you keep your work on the page instead of in your head. 2) Work from your givens to find the next puzzle piece Sometimes, it can be tricky to know where or when or in what order to work through a problem. Take a moment to find what you can before you worry about how to go forward. If you have opposite angles, write in the measure of the angle opposite you're given. If you have angles that make a straight line, find the value of the missing variable. Immediately find the missing pieces that you can, and that information will often lead you straight to your solution. 3) If necessary, use plugging in answers or plugging in numbers If you find yourself stuck (or there is literally no other way to solve the problem), then whip out your PIA or PIN knowledge. Sometimes the process can be slower than a straight solve, but these strategies will almost always get you where you need to go and so can be worth the extra seconds. Ready, set...go! Let's test that newfound knowledge! Test Your Knowledge 1) 2) 3) 4) Answers: A, D, A, D Answer Explanations: 1) This is a question that cannot be solved without using plugging in answers. We can see that x, y, y, and y all make up a straight line (which equals 180 degrees). So let us express that as an equation. x+3y=180 Now, we have no other information (other that that x and y are both integers), from the problem, so now we must look to the answers. Let us start with the answers that end in 0 as those are easiest to work with. If these do not work, then we can eliminate them and try the answers that end in 5. Let’s begin by plugging in our middle value, C, in place of x. If x=40, then: 40+3y=180 3y=140 y=46.67 140 is not evenly divisible by 3, so we can eliminate answer choice C. Let us now try answer choice A, x=30. 30+3y=180 3y=150 y=50 When x=30, both x and y are integers. This fulfils our question premise and so is our correct answer choice. Our final answer is A, x=30 2) Let us solve this question by finding the values of all the angles we can. Angle a is opposite the 60 degree angle, and so angle a=60. We can also see that angles a and b are supplementary, as they form a straight line. This means that: a+b=180 60+b=180 b=120 We can also see that angle e is supplementary with the 70 degree angle. So: e+70=180 e=110 Now, we need only find angles c and d. From our knowledge of triangles (coming soon!), we know that the interior degrees of a triangle add up to 180 degrees. So angle c must be: c+60+70=180 c=50 And because c and d form a straight line and are therefore supplementary, we can find angle d by saying: c+d=180 50+d=180 d=130 Which means, that of all the degree measurements that we found (a=60, b=120, c=50, d=130, and e=110), angle d is the largest. Our final answer is D, d. 3) Because we are told that lines l and m are parallel, we can guess that this problem likely involves opposite interior angles. Because we are familiar with our opposite angles and our opposite interior angles, we can see that angles s, u, and t are all equal. We can also see that angles r and s are supplementary, as they form a straight line. And if r=91, then let us find angle s: r+s=180 91+s=180 s=89 We already said that angles s, u, and t are equal, so they are all equal to 89 degrees. For the final step, we must add t and u. So: t+u = 89+89=178 So our final answer is A, 178. 4) In this question, we are working with multiple variables. Luckily, we can find our value for x and then use it to find our y value. The angle measures 4x and 2x make a straight line, so they are supplementary. This means that: 4x+2x=180 6x=180 x=30 Now, we can find y by using our x value in one of two wayseither because angle y is opposite (and therefore equal) to angle 2x or because angle y makes a straight line with 4x (and is therefore supplementary). So we can say that: y=2x y=2(30) y=60 Or, we can say that: y+4x=180 y+4(30)=180 y+120=180 y=60 Either way, our answer is y=60. So our final answer is D. Whoo! Your brain is on fire (in a purely metaphorical and non-lethal way, of course). The Take-Aways Lines and angles are often simpler than you may think. The tricky thing about these types of questions is generally in the number of steps it takes to get to the final answer. Just remember your equalities, keep your work organized, and do your best to avoid careless errors. Once you’ve locked down lines and angles, you will be well equipped to take on the more and more complex geometry problems the SAT can put in front of you. What’s Next? Raring to go and learn more about the many SAT math topics you'll see on the test? Well you're in luck! We've got guides upon guides on all the topicsyou'll need to know in order to rock the SAT math section, including probability, ratios, advanced integers, and more. Don't know where to start? Make sure you have set a realistic goal for yourself and understand how your scores currently stack up. Think you need a tutor? Check out how to find the right tutor for your needs, whether online or in person. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial: