#math problem solving strategies

[rankmymaths]

Website: https://www.rankmymaths.co.uk/

Rank My Maths specializes in comprehensive online math support for students of all ages, with a key focus on 11plus, KS2 SATs, GCSE, A Level Maths, and A Level Further Maths. Offering a range of services including mock tests, revision courses, and personalized tuition, the platform caters to diverse learning needs. Their approach combines problem-solving, non-verbal reasoning, and exam support, ensuring students are well-prepared for their academic challenges.

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[kidsinnowadays]

How to Help Your Child Excel in Math: Practical Strategies for Boosting Math Skills

Discover actionable techniques to guide your child towards mathematical proficiency, fostering confidence and success in the world of numbers. #MathMastery #MathSkills #ParentingTips #AcademicExcellence

Mathematics is a foundational skill that contributes significantly to a child’s cognitive development and overall academic success. Whether your child finds math enjoyable or challenging, there are practical strategies you can employ to help them excel in the subject. This comprehensive guide outlines effective approaches to boosting your child’s math skills while fostering a love for math that…

[abroadeducation]

SAT Math Tips: Best SAT Test-Taking Strategies for Math

Introduction

SAT math is one of the most difficult sections for most students. But it doesn't have to be! With these helpful tips and strategies, you can learn how to approach SAT math questions and boost your score.

Understand the SAT Math Test

The SAT Math Test is a standardized test that measures your math skills and ability to solve problems. The SAT Math section contains 60 questions in 75 minutes, for a total of 800 points (you get one point for every correct answer). This means you can expect to spend about 1 minute on each question.

The types of questions you'll encounter include:

Multiple Choice--pick an answer from five choices given in the text or diagram provided

Grid-In--fill in the blank with no multiple-choice options available

[Read More: A Complete Guide To The SAT Subject Test]

Don't Panic About SAT Math Practice Questions

You may find yourself in a situation where you do not know how to solve a problem, and panic sets in. This is normal, but it's important not to let this panic prevent you from making progress on the test.

There are several ways that you can figure out the answer:

Work through the problem step by step until you reach an answer (this is often easier if there is only one possible solution)

Look at other questions in this section that might have similar solutions or ideas

Look at other sections of the test, since they all have similar problems

Avoid These SAT Mistakes on Math Questions

Don't skip hard questions.

Don't rush through easy questions.

Don't get hung up on a difficult question. You may think that you'll be able to come back later and answer it, but don't wait too long; some of these questions have time limits, and if you don't finish them within the allotted three minutes (or two minutes for some), they will disappear from your screen forever.

Avoid guessing on SAT math tests! Guessing blindly is not an effective strategy because there's no way to know what choices are incorrect until after you've finished all of them--and even then, only one of those answers can be right!

To avoid guessing randomly or based on hunches alone when taking an SAT test question by using our strategies below instead! (And as always: Read directions carefully!)

Effective sat math test-taking strategies

Using test-taking strategies is one of the best tips to score in SAT exam Math problems.

Choose the right answer first and then work backward to see if it works.

Write down what you know and don't waste time on questions that are too difficult for you to solve in time.

-Solve problems that are similar to ones you've already done. -Read the problem carefully and make sure you understand it before starting to solve it. -Work backward from the answer choices to see if any of them work.

SAT math problem-solving strategies

Understand the question. The first step to solving any problem understands what you're being asked to do. Make sure you read each problem carefully and take notes if necessary.

Use the answer choices to help you. If a question has multiple parts, don't worry about them all at once--just focus on one part at a time until you get stuck or need help with another portion of the question. Then go back and work on another part of it!

Make a plan before working out solutions: This can be as simple as writing down your ideas on paper so they're clear in your head before starting to work through them mathematically (or even just mentally).

Tips to Score High on SAT math score improvement strategies

Practice as much as you can.

Learn from your mistakes.

Use the right strategies for solving problems, like plugging in numbers and drawing diagrams to visualize the problem.

Make sure that you understand all the math concepts tested in the SAT Math section, such as geometry, algebra, and other topics covered in high school courses like Geometry/Trig (Math 2).

Learn how to solve math problems quickly so that you don't waste time on any question that is too difficult for you or not worth answering in detail because it doesn't count toward your score anyway!

Conclusion

The SAT Math section is not easy, but it's also not impossible. If you're prepared and know what to expect, then you can do well on this section of the test. I hope these tips have helped you understand the best strategies and how to manage time effectively for SAT Math questions.

Author Bio:

Global Tree is a genuine company with an age of more than 15 years in the industry of Study Abroad and Immigration helping thousands of students and skilled professionals every year. Their customized approach for each client makes them stand as industry leaders and the most trustworthy consultants. They have a special division to handle Global Tree consumer complaints and solve the issues immediately.

[universalitgirlsblog2]

GROWTH MINDSET VS FIXED MINDSET

The Growth Mindset term was coined by American psychologist Carol Dweck . It is the belief that talent, intelligence and abilities can be cultivated through efforts whereas the Fixed mindset is the total opposite of Growth Mindset. Fixed Mindset is the belief that talent, intelligence and abilities are Fixed and cannot be changed.

A person with Growth Mindset sees efforts as a good thing and an opportunity to improve themselves whereas a person with a Fixed mindset will see hardwork as a bad thing . For example: Let's say Aria is bad at maths , she feels that math isn't her forte so she doesn't even try. She feels that she isn't intelligent enough. She believes that intelligence and math skills are Fixed. Aria has a Fixed mindset. Her mindset limits her. She will never improve or get good grades in maths with that mindset. Now let's say there is another girl Ariel , she believes that she can improve her maths by practice. She believes that if she needs to put effort to improve her math skills , it's not a bad thing and it doesn't mean that she is " dumb " . Ariel has a growth mindset. Growth Mindset is essential for success in any kind of field.

A person with Growth Mindset solve problems & persist despite obstacles. Neuroscientists believe Growth Mindset. They confirm that the brain grows like any other muscle in the body with training . A person with Growth Mindset believes we are in control of our abilities whereas a person with fixed Mindset believes that we aren't in control of our abilities. A person with Growth Mindset are focused on the process of getting better . They appreciate feedback and constructive criticism and use it to improve themselves whereas a person with fixed Mindset don't appreciate constructive criticism , they get defensive and take it personally.

Fixed mindset Growth Mindset

I'm not good at this ➔ I can get good at this with effort and practice.

I am not talented enough ➔I can improve with effort with practice .

I don't know how ➔ I can learn !

I don't like challenges ➔ Overcoming challenges helps me to grow !

I give up ➔ I can't succeed if I don't try / I will use a different strategy !

It's too hard➔ With more practice, it will get easier.

I can't do this ➔ I can do anything I put my mind to !

Plan A didn't work ➔ There is always Plan B

I failed and I embarrassed myself ➔I'm proud that I tried and I will try again !

Everyone is better at it than me ➔ I can learn from them !

Questions a person ask with Growth Mindset What can I learn from this ?

what support can I reach out to ?

How will I prepare myself to learn today ?

What will I do to challenge myself today ?

How do I learn ?

🤍Affirmations for growth mindset 🤍

- I can do anything I put my mind into !

- I focus on progress !

- I can get through anything !

- I am ready to ask for help !

- I am problem solver !

- I strive to do my best .

- I am not afraid of challenges.

[skamenglishsubs]

Subtext and Culture, Young Royals, Season 3, Episode 4

Last episode ended with Simon coming home to a smashed window, this episode starts the morning after, Simon takes the bus to school, while Wilhelm is anxiously waiting for him.

Culture: At a high school level in Sweden, there's national tests in Swedish, English, and Math. Like everywhere else, the purpose of these tests is not only to grade students, but to align all schools across the country to combat grade inflation.

Blink and you miss it: Vincent is trying to cheat by looking at Nils' answers.

Blink and you miss it: Vincent draws a dick in the gravel while waiting for the others to be done with the test.

Subtext: This entire episode is overflowing with examples of privilege. For Vincent, and many other rich kids like him, studying and learning doesn't matter, they'll graduate regardless, so he doesn't care about the exam, he only cares about the graduation party.

Cinematography: Even with Felice and friends being completely blurred out in the background, you can still see Stella and Fredrika turning to look at Sara, and then turning their backs on her.

Culture: In the US, a lot of people are using "socialism" as a catch-all phrase which means politics they don't agree with, regardless of its actual ideology. Likewise, in Sweden, a lot of people use "communist" in the same way about generally left-wing politics, which is what Vincent is doing here.

Subtext: Wilhelm asks Simon if he can reconcile the conflict of dating a royal while being anti-monarchy, but the real question is of course if Wilhelm can reconcile the conflict in himself.

Subtext: This is where the show's political stance shines through, and this argument, that Wilhelm wasn't allowed to choose his life for himself, is the main argument they're gonna use in the finale.

Subtext: Wilhelm is weakly defending the monarchy, but just ends up repeating what his mother told him; it's a privilege, not a punishment, but does he believe it himself?

Subtext: The letter-to-yourself plot is mainly there in order to help August along his redemption arc, but here the show is using it to reinforce the point of the previous scene. Who does Wilhelm want to become? Does he have a choice?

Culture: In Sweden, Säkerhetspolisen, SÄPO, is the government agency in charge of national security, which includes providing security and assigning bodyguards to the royal family.

Subtext: Note the great use of passive voice here by Farima to avoid taking responsibility for the decision to force August to join the birthday foundation event. She's also expertly bargaining with Wilhelm to get what she wants.

Subtext: We know it was the far-right assholes who posted comments to Simon's videos a couple of episodes ago.

Blink and you miss it: Jan-Olof really perks up when Linda talks about moving to Gothenburg, because that would probably mean the end to the relationship between Wilhelm and Simon, which would solve all of his current problems.

Subtext: Like Farima, he bargains with Linda and Simon to get what he wants, for Simon to stop posting things to social media. It's almost as if their strategy was to do nothing at the start, waiting for things to blow up so they could swoop in, help out, and start making demands in exchange...

Blink and you miss it: The option to inactivate and hide your social media account is right there, but of course Simon has to choose to delete everything, because it will cause more drama and anguish.

Blink and you miss it: Fencing! Woohoo! I did fencing for five years as a kid until 8th grade or something, but I only did foil, and not épée like these students. I have absolutely no idea where these two are coming from or going to though, where would they practice? Is there a hidden fencing hall somewhere on the grounds that we haven't seen yet? How many kids at Hillerska are fencing? Also, he's carrying a practice blade and not an electric competition blade, so that checks out. Of the three types of modern fencing, épée is unique in that the entire body counts as a valid target, while in foil only the torso counts, and in sabre only the upper half counts. Oh wow, it looks like the gear is now wireless and every fencer carries their own indicator lights. Cool! Back in my day you had to be strapped in with a cord for competitions.

This tumblr is now about French School fencing. Allez! Touché!

Subtext: The narrative is that it's perfectly ok for the crown prince to be gay, as long as he's not gay gay.

Culture: The show keeps saying this, but in real world Sweden it's no longer the case. Supporting los jibbities is viewed as a completely mainstream and inoffensive opinion, on par with supporting human rights in general.

Subtext: Another example of privilege is being in a position to do a lot of good, and then just not caring about it. Simon is fighting for the causes he believes in, so seeing Wilhelm just casually throw it away is extremely disappointing for him.

Subtext: Unlike Vincent, August is actually a natural leader, someone people listen to, which is why he manages to quiet down the room when Vincent is unable to. Maybe a good quality in a future king?

Subtext: Simon is continuing the argument from before. Wilhelm could have shown solidarity with mental health causes or LGBT causes, but chose not to. However, he immediately decided to join in solidarity with the other rich kids protesting the school rules, which is rather selfish.

Subtext: Colour theory! Sara in purple, because part of the reason she's back at school is that August asked her to? And Simon in yellow, because he sure isn't loving Wilhelm very much right now.

Subtext: Just a reminder that Sara has actually been completely out of the loop since the end of season 2. She has no idea about the school rules, what's happened at home, how it's going with Simon and Wilhelm, or what's happening at school.

Blink and you miss it: Fredrika is so close to stop striking as soon as she's threatened with repercussions.

Subtext: I keep hammering this point home: The culture is in the walls, it's not something some of the kids made up. The visiting alumni were also hazed as new students and kept it going as third years. Same for the parents of all these kids. They're all part of the system, they all kept the cycles of abuse going, because they want the school to be like that.

Subtext: Privilege is thinking you can get things your way with almost no effort. None of these kids have ever struggled or protested something for real and then not been given what they wanted, so they seriously believed they'd win immediately.

Subtext: Another theme of this season is bringing secrets out in the open. We've all seen August struggling with body dysmorphia and an eating disorder since season 1, but no-one has ever called it out and put words on it, until Simon immediately recognizes it and calls it out.

Subtext: ...while the rich kids are just stuck in denial, because eating disorders is for poor people or something, it's not something that happens to them. And if it did, you certainly wouldn't admit it to anyone else.

Subtext: August tries to jokingly fend off Nils because he doesn't want anyone to know that the letter actually meant something to him, until Nils pushes too hard, and August punches him.

Subtext: Vincent talked a big game about striking in solidarity, but when they're caught as hilariously unprepared as they are, they're not pooling their resources in solidarity with each other, and instead resort to selling them to the highest bidder. Capitalism in a nutshell, illustrated perfectly by the behaviour of spoiled rich kids. Also, pet peeve, the English word for the currency of Sweden is "kronor", not "crowns".

Lost in translation: They're actually repeating a single word in Swedish, "svikare", which is pretty hard to translate. The verb, "svika", is a bit worse than letting someone down, but not as bad as betraying someone. The adjective, "besviken" typically means disappointed. So "svikare" means a person who is letting other people down, disappointing them, or betraying them.

Subtext: The culture is in the walls of the place, but the kids are also pretty damn complicit in continuing all the shitty traditions. This looks like a game of strip poker or truth or dare that went off the rails and just resulted in more bullying, with everyone joining in.

Subtext: The other girls are upset with Felice because she broke the code. You don't snitch to outsiders, you don't tell the truth, you keep up appearances.

Blink and you miss it: Henry won the potato chip auction, happily ate the entire bag, and passed out in a chair, clutching the bag. Mmmm, sourcream and onion.

Subtext: Speaking of closing ranks towards the outside, this also applies to this strike. It would be bad PR for the school if anyone outside found out that it happened, so it's better to solve it quietly and discreetly. Vanessa can trust the kids not to snitch. Vincent is also right, the parents, who are paying the tuition fees, are on their side.

Subtext: Felice can't be seen talking to Sara, so she checks that the coast is clear, and then drags Sara into a private bathroom to have their conversation.

Subtext: Likewise, Sara was probably Felice's first real friend.

Subtext: Nice little foreshadowing. I would have loved seeing Simon's drawing though!

Subtext: Well, he could have just made his social media private, but the show has to maximize the drama, so here we are, piling on more examples of how Simon is losing himself to the monarchy, that maybe he can't reconcile the conflict.

Subtext: Erik spent three years living at Hillerska, of course he wouldn't have told his then twelve year old kid brother about all the shit going on at the school. August spent an entire year living with Erik at the school, seeing what went on first hand, so of course he knows a side of Erik that Wilhelm doesn't.

Subtext: August has been trying to keep his mouth shut and avoid Wilhelm, but since they have yet another fight, he decides to drop the bomb about Erik to hurt Wilhelm.

Subtext: Again, the culture is in the walls. This is not something that only Erik's class did, once. It's probably been happening to all the boys for decades. It happened to the current second-year students, it happened to Erik, and lots of students before him who kept this shitty initiation tradition going.

Culture: Let's talk about the gay porn hazing a bit more. To me, this is an urban legend. I heard about it when I was a teenager back in the 90's, but I don't personally know anyone it happened to, or anyone who did it to anyone else. It was always hearsay, it happened to a friend of a friend's brother, or a classmate's cousin's friend or something similar, as is typical of urban legends.

Let's also make one thing absolutely clear: It doesn't work. The homophobic idea behind this shit is that if you are forced to watch gay porn and get a boner, you are gay, and if you don't, you're straight. But that is actually not true, erections don't work that way, and the fear of being found out is quite the boner killer. Also, what if you like guys, but the guys in the porno aren't your type? There's just so many ignorant misconceptions behind this idea.

I've also seen a lot of fan comments that keep playing into this ignorance; that the only reason Nils decided to stop the tradition was because he obviously failed it. Or that the only reason August is against it is because he failed, and the only reason he failed is because he's secretly not straight. No. Remember that the test doesn't work. Nils probably passed, despite actually being gay. August might have failed, despite being completely straight. Regardless of what happened, they both found it humiliating, and that is why they made a pact to stop it.

[pinkacademiaprincess]

Hiii I’m so sorry to bother you!, hope your day goes well <3 I just want to ask, how can I improve in maths? I’m preparing myself for the sat and I have trouble with understanding it. Any tips would be very much appreciated, thanku !! ♡

Become a Math Whiz: Acing Math Class & the SAT 📈✏️📚👩‍🏫

ty for the ask & the kind words! you are never a bother, i'm happy to help 🥰 i can def give some tips as someone who went from struggling w/ math to being good at it. and i’ve taken the SAT so i know that experience as well! i hope this helps 💗

take accountability

it’s very easy to try to shift blame & avoid taking responsibility for your grades/ performance. i used to think things like “the teacher is just bad!” or “i’m just not a math person!” but this mindset is just deflecting. some things are out of your control, like what teacher you have or preferring other subjects, but you have to step up & work hard to create your own success! remembering this will help you stay motivated and disciplined.

find your learning style

i talked about this in a previous post too, but there are different styles of learning - visual, auditory, hands-on, & reading/writing - and not all of them work for everyone. if you spend a ton of time studying and don’t see improvement or results, that’s a big sign that you’re studying wrong. a method that works for your friend or that your teacher uses might not actually be effective for you. so do some research into learning styles and study methods, and find implement strategies that work for you.

never fall behind

okay, easier said than done. but one of the biggest reasons i used to struggle is math is that i would get stuck on a concept, never fully master it, and then i’d stay behind. in math, a lot of topics build on each other. if you get stuck on a topic, it’s crucial that you figure it out asap or your confusion will snowball. you can’t build a solid structure on top of a wobbly foundation. the moment you encounter a problem area, study it until you’ve completely understood.

practice makes perfect

i try to steer clear of recommending specific study methods b/c everyone has different learning styles. but math is so dependent on problem solving & applications that you really have to master this skill in order to succeed. beyond just reviewing your notes & reading over concepts, you need to practice applying topics by solving problems. do the homework questions & do them for accuracy, even if it’s just graded for completion. find extra problems in the textbook, workbook, online, etc. redo questions from class or the hw that confused you until you can do them correctly without your notes. drill it until you can solve them AND understand how the steps work!

ask for help

i am clearly a big proponent of asking for help. in school, your teachers are gonna be one of the best resources you have. for one, they’re teachers for a reason, so even if you think they’re not too great at explaining stuff, they know the concepts. and besides that, your teachers the ones who are creating units, assigning your work, writing & grading your tests... they should be your go-to for questions. visit them during office hours or email to set up a meeting where you can discuss concepts. ask for extra practice problems, ask them to look over your work & let you know how it looks, talk through your work with them. aside from teachers, you can get help from a tutor, a classmate, whoever you can turn to. but pls don’t suffer alone! succeeding with help is still succeeding.

use the internet

so maybe your teacher truly sucks at explaining. maybe you don’t have classmates to help and can’t afford a tutor. or maybe you just wanna supplement your learning another way. i really really recommend utilizing free learning tools online!! khan academy is an obvious one for videos, practice problems, and more. you can also find tons of youtube videos explaining math topics. sometimes it helps to hear things explained another way. i also google “[math concept] practice problems” if i want extra questions to work through.

bonus: tips for SAT math

the SAT is a bit different b/c the math concepts aren’t actually too advanced. it’s all multiple choice so you don’t get to rely on partial points for showing your work. the SAT is testing your strategy & speed as much as it’s actually testing you on math concepts, so here are my best tips for that specifically:

use khan academy’s SAT prep tool - it’s free (!!!!!) and it links to your collegeboard account. it uses prior years’ SAT content so it’s very similar to the test itself. it helps you pace yourself, pinpoint your problem areas, learn & apply concepts, & track your progress. here's a screenshot from when i used it, as you can see my scores improved and i was able to ultimately get a superscore of 1450!

take practice tests - this helps you get familiar with the time constraint. khan academy has plenty!!

do a ton of SAT math practice questions - ideally, find a ton of questions used in prior SAT tests and just crank them out. the test's concepts are quite repetitive so if you just focus on the topics they usually test, you can master them

learn test-taking strategies - the SAT is multiple choice and has a tricky time constraint, so however you can save time will help. become good at using the process of elimination & other multiple choice test methods. you can find these sorts of tips online!

i hope this helps! know that you are completely capable of improving at math. i went from thinking i suck at it & doing poorly in math class to acing my calc courses & studying to enter a math-focused field. utilize your resources and figure out your best study style asap, and you WILL see improvements!

[psychicreadsgirl]

Pick a Picture: What are your strengths?

Pick the picture that draws you most. If you can't choose between two, then look at both readings. This is a general reading so take what resonates and leave what doesn't behind.

Also, I just stupidly realized that pick a pile/card readings are all related to tarot. For clarification, I don't use tarot so there are no "cards" to share with you or read. I place a picture there for you to choose for an intuitive reading.

I stress again that this is a general reading so take it with a grain of salt. These readings are for fun and entertainment and if they're helpful to you, then great.

#1

You are very resilient and determined. You are probably very independent and don't need much caring/hand holding.

You know what you want in life and generally have a plan to execute your goals/dreams.

You are pretty responsible and stay true to your words.

You are firm and you know when to stand your ground.

You excel in logic and probably are good with numbers/math/concepts/sciences. You are also probably good with directions and determining a strategy. You know how to solve problems.

#2

You have strong leaderships skills. People will generally listen to you or follow you.

You have good communication skills. You know what to say to make people listen to you. You're persuasive and probably eloquent.

You are confident and people generally believe in you. You have a strong presence and are memorable.

Even if you're unsure of things, you know how to fake it till you make it.

You don't shy away from confrontation. You are fearless and courageous. You are protective and will stand for your rights.

#3

You are a team player. You go with the flow and are pretty adaptable. You are sweet and cooperative. You are considerate and are attentive to details.

You are sensitive to other's feelings and generally people feel comfortable with you. You have strong empathy and people just feel like they can share their thoughts/secrets with you.

You are a good listener and have a lot of patience. You generally give good advice related to relationships/friendships.

You generally are quite lucky and things just easily come to you.

#4

You are probably quite athletic. You excel in many sports or many activities that require the use of your body. You might possess strength like you can lift many things. Perhaps you are very flexible or you have great balance. You might also have great control of your body.

You can endure a lot. You can go through a lot of physical training or other training and not complain. Generally you won't really complain much it seems.

You have strong physical endurance. You have a lot of stamina and energy. It's very hard for you to get tired. You might even have too much energy that you have issue sleeping. You are the type that can pull multiple all nighters without caffeine.

You also probably don't get sick very often. If you do get sick, you recover very quickly. You'll notice that even with injuries, you recover very fast like maybe it'll take someone several days to recover from some physical injuries but it'll just take you like 1 or 2 days max.

#5

You have a lot of creativity. You have interesting and unique ideas. You think outside the box.

You might fantasize a lot. You're very imaginative. You have a lot of innocence and naivety. You are very pure.

You are also friendly. People generally are attracted to you somehow. You have this aura that magnetizes others.

You can design a lot. You might excel greatly in the arts. If not, you are the type that can always give out ideas (i.e. you're in marketing and you create this very unique marketing campaign.)

It's possible that you have very vivid dreams too.

#6

You're excellent at figuring out the truth. You know when someone is lying. Somehow you also just know things. Perhaps you are very intuitive or maybe psychic. You have a strong 6th sense.

You might have talent in the occult, including tarot, astrology, psychic reading, etc. You're very intuitive and are hyper aware of what's not known to the human eye.

You are very spiritual. You can connect with others spiritually. You often have profound insights or epiphanies.

You're good at spotting opportunities too. You can also be good at predicting.

[rendy-a]

Chiming in~

Here to request a yandere! Rook (and/or Epel) with their darling in a P.E. setting? (Could be like a joint class or smth-)

Well, well. Here it is, my first attempt at a Yandere request. I hope you like it!

It was a strange day indeed when you, the magicless Prefect of Ramshackle dorm, were invited to join flying class.  You had questioned Coach Vargus when he gave you the news but all he told you was, “Cheer up!  If there are any problems, I’ll solve them with my prodigious muscles!”  The shiny smile he flashed you did not reassure. 

To your great surprise, this WAS a flying class you could participate in.  The topic of the day was carrying passengers while flying.  “While solo flying is a great way to hone your personal strength, there are times when you might be required to carry a passenger.  Medical emergencies, search and rescue operations, even certain thrilling Spelldrive strategies are all reasons you might fly double.”  Vargus smiles widely at the large crowd gathered.  It seems you were not to only participate in your first flying lesson, but it would be a rare joint class between first years and third years.

“Carrying an incapacitated passenger is more difficult than flying with a conscious person.  Third years pair up with a first year and practice your medical carry!  I expect you’ll give your juniors lots of tips for when it is their turn to fly!”  You are nervous but also pleased that you were all to be ‘dead weight’ in this exercise.  You laugh a bit to yourself, knowing you had worried about putting your partner at a disadvantage but with this assignment, your lack of flying knowledge wouldn’t matter at all.  Only now you had to find a partner.  Even though you were only to be carried, you worried no one would want to pair up with a magicless partner.

As you stand there, unsure of your position in this joint class, you jump as you feel a hand on your shoulder.  “Ah!” you yell in surprise, turning to look at the smiling face behind you.  Although you’d never met him before, Rook Hunt had such a reputation around campus that you’d certainly heard OF him.  From the very first moment you set eyes on his smiling face, you’d felt that reputation was well earned.  He looked at you with that easy smile fixed on his face, his sharp eyes taking in your reaction as though it was a most fascinating study and he the researcher.

When your reactions stilled, he deepened his smile and spoke, “Bonjour!  How fortunate I am to reach your side before you’ve been chosen.  Certainly, I implore you to accept my request to be my partner.”  Then he holds out his hand in a flourish.  You are rather embarrassed by this display of dramatics in PE class, but you do need a partner, so you smile awkwardly and place your hand in his own, “Sure, I’ll be your partner.”  He grasps your hand, and you think he takes a sudden inhale of breath but before you can process that Coach Vargus is shouting instructions for your activity. 

It turns out there is a surprisingly complex method to determine how to fly double.  It involves a disappointingly large amount of math.  You hadn’t anticipated the need to measure your height and pop it into a formula to determine the minimum length broom to bare your weight safely, but you were willing to give it a shot.  “So, Hunt sir, my height is,” you began before seeing Rook had appeared at your side holding a broom.  He smiles at you coyly, “Non, there is no need to say.  Of course, I have already determined your height and computed the proper broom length.”  You look at him startled for a moment and then flash him an impressed look, “You can tell how tall I am from just this little bit of time standing together?  That’s some skill you have there!”  He returns you a mysterious smile and holds out the broom for you to mount.

You do toss a leg over the handle but then look questioningly back at your partner, “Should I be riding like this?  Aren’t I supposed to be, I don’t know, like…” and you finish your statement by making a gesture indicating a flopping posture.  He laughs heartily at your pantomime, “My, your performance is très bon!  I thought for a moment you were truly knocked out.  What a trickster you are!”  You laugh a forced chuckle, embarrassed at his overreaction and the attention it was pulling to your group, “Yup, that’s what all my friends call me.  Hey, Trickster, show us that one again.  Ha ha ha.”  His gaze sharpens and he asks carefully, “Why then I shall call you that too.  Oui?  Mon Trickster?”  You give him a shrug as thought to say, ‘do what you want’ and place a hand behind your head as you laugh awkwardly.  You feel the pleased smile he returns is far more than the silly nickname deserves but hey, whatever makes him happy. 

“In turn, Mon Trickster, won’t you call me by name?” the senior asks you with a fox sharp smile, “We are partners now, are we not?”  You again give another shrug and hold out your hand to shake his, “Sure thing, Rook.  Partners it is.”  He returns your handshake with vigor and at the end, squeezes your hand unusually long with an appraising look.  “What are you doing?” you ask curiously.  “Why I’m taking measure of your hand size, of course.” Rook replies.  You can’t tell if he is joking or not.  “What could you possibly need to know my hand size for?” you laugh off the situation.  Rook gives you a mysterious smile and only replies, “Oh, you’d be surprised how things become useful.”

---

A whistle blows and Rooks eyes travel easily to Coach Vargus where he stands.  “Time to switch tasks!” he yells from below.  Rooks sighs and pulls his dear Trickster (a pet name! très magnifique!) tighter in his arms.  He’d easily convinced his naïve dove to allow him a bridal carry as a convenient way to complete their task.  Coach Vargus had even praised the choice (Builds muscles in the arms!), to his amusement.  Rook couldn’t have cared less about workout efficiency or learning life-saving rescue techniques; all that mattered was squeezing one more second into this flight, one more moment where he could keep you in his arms and imagine you were his own. 

Alas, seconds do not last.  He settles you both on the ground and smiles at your nervous expression.  Were you embarrassed to be seen in such an intimate hold by your classmates or had you instinctively sensed the danger of having a predator so close at hand?  Either answer was beautiful in its own way.  Rook would like to have asked you for the answer but knew such a question would only create unwanted distance between you.  He’d bide his time and observe, it was in his nature to do so.  You believed so innocently that this class was your first meeting, and for you, it was.  He though, he’d been watching you for weeks.  When the time was right, well, he’d already taken your measure.  He now had a good idea what size ring you’d need.  Or shackle.  Either way would bring its own enjoyment; just you, him, and the hunt.

“Second task!” Coach Vargus bellows.  “Being carried as dead weight is a great workout for a flyer but it does nothing to build your own strength!  In task two, we will be doing something that requires effort from both participants!”  With a flourish of his hand, Vargus summons a large obstacle course from the ground.  A second flick of his wrist sets it in motion.  It is immediately obvious to you what he meant about effort being needed from both parties.  You could tell by the path of the course how you’d have to shift your weight together or in counterpart to navigate certain obstacles.  Moving on your own would only cause you both to be caught up in the traps and knocked from the broom.  At least you had Grim.  While he wasn’t exactly what you’d call cooperative, at least you were familiar enough with each other to be relatively in sync.

“Grim!” Vargus bellows, “You are excused from this exercise.  As much as I’d like to have you hone your small body, your lightweight will make it impossible for a partner to balance with you.”  Your mouth falls open in shock but Grim has no such trouble, “Mwrahaha!  The Great Grim wins again!  See you later suckers!”  His parting remarks earn some return jibes from your fellow first years but Grim remains unbothered as he departs.

You shake your head sadly but not that surprised.  These things just always seem to happen to you.  “Um, he.hello.” You turn around to find a lilac haired boy trying to gain your attention.  “If you don’t have a partner yet, would you like to pair with me?” he asks in a sweet voice and smiles at you cutely.  You are surprised to find such a gentle boy in a school like NRC.  And also, quite a bit charmed.  You smile at him gratefully, “I’d love to be your partner.”  You introduce yourselves and you give Epel some of the tips you’d learned from Rook in your first task.  For a moment, you imagine you see Epel glare over at where Rook stands in the distance with the third-year class, engaged in their own second task.  It was an intense look, but you couldn’t quite place it; was he jealous of the third year’s skill?  Before you can quite puzzle it out, his gaze returns to you.  He gives you a cute tilt of his head, causing his tied back hair to sway gently, “We should get practicing, Prefect.”

It was great to have a partner who had chosen you.  You had secretly feared standing there alone at the end and having Coach Vargus force someone to pair up with you.  Now, you had Epel, and he was such an attentive partner too!  Though he was the mage and you were just a magicless student, Epel was constantly asking your opinion on things and taking your advice.  “What do you think about that section?  We could…just push through.  Go full throttle!  Or…or we could be safe and do it slow.  Wha..what do you think?”  You turn to your partner.  Epel is trying to look as though he is focused on the course, but you can see the way he watches you intently out of the corner of his eye.  You smile to yourself, pleased that he is so considerate and yet not putting you on the spot.  “I think we should take it easy.  Slow and steady wins the race, right?”  You beam back at him and the corners of his mouth fall for a moment before a charming smile settles on his face.  “That’s just what I was thinking.  We are so in tune!” 

The obstacle course is difficult, but you know, if you are honest with yourself, that Vargus set a fair course for your beginner’s level.  You especially enjoy flying with Epel.  There are times when you think he is getting frustrated, watching the aggressive flying of other students but you are quick to reassure him.  “Don’t worry,” you say as you lean back and pat his hand, “Our method is just as good as that wild, show-off one.”  He gives you a tight smile; worried, you think.   Not you though, you have confidence in your partnership!  In the end, you are fine.  You don’t pass each obstacle without effort, but you only end up dumped from the broom a few times at each obstacle before you managed to suggest a good strategy to work your way though.  And Epel always takes your suggestions.

Finally, your feet touch the ground, the task being finished.  You jump off the broom and give Epel a little sideways hug.  “That was so much fun!  It really is great being able to fly.  I’m glad I had someone like you for a partner to do this with me.”  Epel gives you a dreamy smile back, “Yeah, I’m glad to have been able to be with you too.”  You smile and wave before setting off towards the main campus and your next class.

---

Epel watched you go sadly.  That was…well actually, it was a rather mixed experience.  There were times when Epel had nearly lost his cool.  When a Savanaclaw student made a mocking copy of the cute smile he’d given the Prefect, he’d nearly flown over to throw hands at him.  BUT! he’d caught himself in time, maintaining his sweet and cute persona.  If that was what the Prefect wanted from him, that is what he’d be for them.  He’d change himself in any way to please them.  For now.  Next time, he’ll start working on changing them.  Not a lot!  But over time, he was sure he could mold the Prefect into the perfect partner for a macho guy like him.  Afterall, he’d changed for you so its only fair that you change for him.

[for-my-mind-to-run-around-free]

Do you know what’s so fucking irritating ?

Having adhd and growing up forced into nt coping strategies. So much so that you have to talk yourself out of it every single fucking time.

Do you struggle to pay attention to your homework and stare into space for no reason for and unknown amount of time ?

You need to remove all and every possible distraction. Stop reading number plates. Stop reading grave stones. Don’t even try listening to any music. Remove EVERYTHING that’s on your desk.

Like. No. Please shut up.

Listen to songs that you’ve memorised while solving maths problems because it’s just stimulating enough that you can focus and enjoy the maths.

Have ALL the equipment you need at the reach of your hand because searching for them means you get nothing done.

My brother watches the tv shows he memorised while doing maths because that’s the level of stimulation he needs. I can’t stop myself from advising him to not do it because it’s bad for him. -I know I’m probably wrong. I say it anyways. I hate me for it-

Why are you soo messy? I’ve spent my life cleaning up and tidying your room your —- years old you should be organised now!

Put this here. And put this there. And you can’t have anything but your glasses on your dressing table, everything must be out of sight in drawers so it looks tidy. You can’t have anything on your desk it’ll distract you, make sure everything is put away.

No. Stop. Please. Stop.

I don’t remember things/ tasks that I can’t see. I won’t remember to read the book if I can’t see it on the bedside table. I won’t remember to grab my keys if they’re not staring at me.

I will procrastinate any task that requires me to do two more additional steps of actually finding the object and taking it out of the drawer.

I can’t use a completely empty bedside table/dressing table or whatever because I need to be able to see stuff.

My room isn’t untidy if I know EXACTLY where everything is. It might look unorganised to your nt eyes because you’ve been conditioned to see catalogue perfect rooms, but I know where everything is in this room and that means I can function.

[ardinwriter]

A particularly annoyingly evangelizing vegan colleague of mine got me wondering what exactly the end plan for these people is.

Presumably they want everyone on the planet to go vegan.

Okay, did the math and growing the world's densest (most calories per acre) crop, potatoes, on every acre of the world's arable land you could more than achieve the majority of the nutrition side of things.

You'd still have to deal with the B12 issue (the required human nutrient that potatoes lack), which depending on your level of veganism could be a problem since there are only three sources of B12: meat, dairy, and pills and the contents of the pills is bacterial cultures so that might be a no go, I don't know. Maybe that's fine.

We'll ignore for the moment the distribution issues of getting those spuds to people in non-arable areas.

So say you've completely solved the nutrition problem of being vegan.

How do you plan to open up the arable land currently used for animal production (roughly 75% of currently arable land is currently used for grazing) and what do you plan to do with the existing animals? Being vegan, you can't kill them or harm them in any way, so you can't sterilize them either. So they're just going to keep breeding with no culling other than natural deaths.

In the US alone, we have an estimated 308 million commercial laying hens. Each producing roughly an egg a day. At the moment, with the majority of those eggs going to stores to be consumed as eggs, the US has a fertilization rate of 13%. Even if that didn't climb after egg eating was stopped, that means 40 million fertilized eggs a day. If even 5% of those hatch, that's 2 million chicks after the first 20-21 days of this.

If we aren't eating or killing them, that's a problem.

And since the larger the predator, the longer the gestation time and smaller the number of offspring in a breeding period is a general reality, we are hosed on chickens alone if everyone just stops eating them because there won't be enough predators in the food chain without humans to stem the the chicken tide.

And that's just one livestock animal. It'll be a problem with the others as well.

And all this is ignoring all the other non-food products we get from animals. What are we replacing those with? And don't say plastic (or vegan leather or it's equivalents, cuz those are just plastics), I'd say relying even more heavily on fossil fuels isn't a good strategy here.

So, really, what's the end game here?

[skwpr]

A simple representation of images does not offer enough for proper memorization.

Study Faster And Retain More With This Quick Tip

I don’t know a single student who doesn’t want to study faster and retain more at the same time. I usually get a little nervous when trying to use quick fixes to make this happen, but today I have an actual quick tip to help you do just this!

Being a problem solver by nature, I dug into the situation and tried a few new approaches. Some worked, and some did not.

One of my best strategies was to sort the information into two categories:

facts to be memorized

concepts to be understood

You can use this strategy for any course. No matter the subject, there are things you have to memorize (terminology, dates, names, equations, etc) and concepts you need to master. Identifying this creates a clear, drama-free path, meaning you actually study faster and retain more because you are working on the right information in the right way.

How To Memorize Facts

I used to hate memorization work. It seemed tedious and hard and I sucked at it. Or so I thought!

Turns out I just didn’t have good skills. now I have some strategies in my toolbox and I love fact work. It’s easy and you can master it quickly. The key to mastering memorization is to:

Keep a list of what you need to memorize.

Schedule time every day to work on it. You must have the daily repetition if you want new facts to stick in your short-term memory. Start with just 10-min each day and you will see results.

Vary your memorization strategies. If you use only one strategy it becomes less effective.

How To Master Concepts

How you approach concept mastery is going to vary a lot based on the subject you are studying. There are two strategies to help with every subject:

1. Hands-On Practice

You will never fully master a concept through reading about it. You learn the concept through reading, but there is a big difference between learning something and mastering it.

The basics of hands-on practice for any subject are to come up with an applicable problem and solve it. Then come up with another problem and solve it too. Here are a few ideas, by subject, of how you might practice:

literature – Read a book or short story and write an analysis of whatever focus you are working on.

computer science – Come up with a problem and solve it with real code.

graphic design – Imagine a client asked you to design something, and create 3 different solutions for them.

math – Pick an equation, make up some starting numbers, and solve it.

science – Define a hypothesis, create a simple experiment, get in the lab and execute it!

2. Explain Or Teach It To Someone Else

Want to be certain you have mastered and fully understand a concept? Teach it to someone else.

As a teacher myself, I can tell you there have been plenty of concepts I thought I knew really well until I tried explaining them to someone else. You need a thorough understanding yourself before you can help someone else understand it.

Enlist the help of a friend or family member and try to explain a major concept in a few minutes. If you struggle, make note of the sticky spots. They are exactly what you need to work on next.

If you have no problem explaining it and your friend understood everything, mark it off your list and move on to the next concept.

I hope this quick strategy helps you dig out of confusion and take the right action in order to study faster and retain more.

Try It Yourself: 20-Minute Challenge

Grab your notes, a fresh piece of paper, and a timer.

Set the timer for 15 minutes.

Go through your notes and sort every piece of information into one of the two categories: concept or fact Challenge yourself to do this before the timer goes off. Go with your first instinct if you aren’t sure.

Spend the next 5 minutes and map out your next steps.

How and when will you work on the memorization each day?

How will you approach the first concept?

[squeakadeeks]

Transient lore overview

Figured at this point I have enough separate OC verses, let alone actual OCs themselves that its worthwhile to make big overview pages that describe all of their settings, characters, themes, connections, etc.

Transient is a OCverse i've been working on for a few years now ft. Sulu, Function, Felis, Splish, and Alpha in a fantasy space setting. In my head the intended format is an episodic cartoon comedy series, akin to things like regular show, futurama, adventure time, etc with no overarching ""plot"" per se, just following characters as they interact and develop.

Sulu:

Sulu is the main character, he travels throughout sea-space solving problems and helping people however he can. He is very competent and gives things his all until a problem is solved.

He spends a large portion of his time alone, but he frequently links up from his friends Felis and Splish when the need arises. He has a warm, comforting, friendly personality but doesn't often stick around long enough to form deeper bonds. Hes akin to a benevolent trader joes staffer that gives you a soothing sense of ease as he guides you where to the munster cheese is stocked, but like two ships passing never again will your two paths meet.

Sulu as a character is very dedicated and compassionate, and is genuinely motivated in helping others. That being said, there is a deeper layer to his unwavering dedication. Its a two-pronged coping strategy and distraction from his own struggles. He often ignores any ill that happens to him as a result of obsessively working and puts off addressing his own problems to an extremely problematic degree. His struggles with depression and self neglect end up devolving into the primary conflict.

Function:

Function is the closest thing to an antagonist the series has. Function is an entity originally from the realm of pure math that got wedged in what he refers to as "the meat world" (ie the physical world). By nature his intent is to increase disorder without bound. He's still adjusting to being stuck in the physical world and doesnt always understand the harm he's causing by driving chaos into systems. Although most of the time he is still uncomfortable in having a physical form, he adores thematics and getting attention from others. He has an expressive, energetic, rambunctious personality.

At first he poses a serious risk as a genuinely harmful figure in a cotton-candy marshmallow world, and Sulu has to frequently neutralize his actions. This causes a comical nemesis-esc relationship between the two, but in time as he adjusts and copes with his situation he settles down more into a goofy, campy 90's anime rival archetype and the two form a more genuine bond. He becomes great friends with Alpha, forming a "chaos crew" as the two largely goof around and make the most of things. He has a significantly hard time processing emotional turmoil as he's still trying to wrap his head around basic day-to-day functioning, let alone complicated interpersonal conflicts.

Alpha, Felis, Splish:

The other core cast consists of Felis, Splish the fish, and Alpha.

Felis is Sulu's current best friend, as they spend the most time together and work in tandem often. Felis is genuinely an out-of-place-astronaut, as all the other denizens are aquatic creatures. Felis has a classic goofy cat-like personality, they like to be entertained and pal around, but can struggle with serious matters and completing long-form tasks.

Splish is a space safety ranger and works hard to keep everyone safe and happy and within the rules. He employs Sulu's help on the very frequent occasion when he is out of his depth. He doesn't really comprehend serious matters at all, as he belongs squarely to the "marshmallow head" class of sea-space critters. (Felis is capable of processing serious things, but often elects to not engage)

Alpha is a character from Sulu's past, in particular his former closest friend. She and Sulu were incredibly close in their teens and early 20s, but she eventually lost contact as he splintered off and isolated. Alpha gets frustrated with his lack of care towards his own health and functioning, especially how it affects others around him, seeing it as not taking proper responsibility for himself. She clicks with Function not just because they both have very similar bombastic personalities, but also because she admires how dedicated Function is to adjusting to his new circumstances and improve himself. She is wickedly driven, she loves new experiences and exciting things and is overall incredibly active, but can be somewhat introverted. sort of a "i want to do cool things, but only with the 2 people i have allowed into my inner circle". Holds grudges like the dickens.

Setting:

The setting itself is supposed to be a fusion between underwater and space, there are lots of fish, whales, coral formations etc scattered throughout open space. The various planets act more reefs, collecting lots of life and activity. From afar things look more like ""space"" with planets, stars, galaxies, etc, but the actual deinzens tend to resemble either fish or cartoony space aliens. The overall palette is very bright, colorful, and pastel tones to reflect the cheery, cotton-candy environment.

Concept:

Most of the types of problems Sulu, Felis and Splish work on are lighthearted or comical in nature, such as chauffeuring constellations around, babysitting in a stellar nursery, fishing for asteroids, a mediating in a break up between a binary star system, trying to fix the cowlic generated by the hairy ball theorem, cleaning up a milk spill in a galaxy, a magnetar that keeps demagnetizing people's credit cards, things spontaneously gaining more degrees of non-trivial rotational symmetry, neutron star bowling, and other sorts of whimsical space/math problems.

Every so often something more serious pops up, like a quasar posing a legitimate threat or instability in the laws of physics such as a power on a spatial dependence term flickering back and forth, but 90% of the time its cartoony situations, a la regular show. Another equally descriptive statement would be "Cyberchase but with 30-40yr old queer anime people."

Elephant in the room, Sulu is indeed intended to be an outlet/projection/expression of my own struggles with depression and how severe depressive episodes get entangled with my work and social life, but on a more surface level I also enjoy working on this thing because 1) i like drawing fish, 2) i love using vivid colors, and 3) I love being obnoxious about math and physics jokes while stuck in the throes of a physics phd myself.

[kyarori]

All my life, I loved maths. Studying for math exams? FUN! You have a type of problem and a logical way and structure of solving it and it works every time. Sometimes you have to think about it a little bit, solve it like a puzzle. But since I got to university, math isn't so fun anymore. Often times, the problems seem to be solvable with the same strategy as the last 24 problems of the same kind, but then it just doesn't work anymore. You get nowhere for hours until you finally are frustrated enough to look at the solution and it's some shady trick some mathematics professor pulled out of his ass, which is only applicable with this exact problem. It's so frustrating.

[dangeroustimetraveldonut]

One thing that has been making me feel truly miserable is my lack of will to study/work. Working I kind of understand due to my discontent with my career paths, but when it comes to studying I don’t really have that many excuses. I hate my university, but I love my major. So, it makes me downhearted to see how unmotivated I am nowadays to read about economy and related contents. I decided to change this. Everyday for the next weeks, I’m going to be studying for 30 minutes, at least or at most. And the strategy is: no fun pomodoro. I used to think that “Animedoro” was the best study technique out there, but recently I noticed how it’s a tricky trail for me. Since I have been lacking motivation, what I do is work for 20/30 minutes then grab my phone and do infinite scrolling or get lost in a Sex and the City episode. And I cannot make me stop. Today I stumbled into a video that talked exactly about this problem. Instead of doing something fun when you end a focus cycle, do something boring, that makes studying or working seems fun next to it. Or, and here’s my perception, something that doesn’t stimulate your brain in the wrong way. Here are the things that I believe requires thinking, so I don’t lose my focus flow (they are not necessarily boring to me, but some of them tires me quickly which makes me give up on them even quicker):

Reading the news.

Watch someone that motivates me to study/work.

Watch/listen to a podcast about something useful.

Sudoku video.

Math problems videos.

Solve a sudoku problem.

Read a few pages of one of the dense books I’m probably reading at the moment (I'm a slow reader so I know it won't fully distract me heheh)

If working, read an econ paper or something related to.

Or just do nothing. Go for a walk. Make some pancakes. Grab water and contemplate it.

<3 and if doesn't work, that's okay. I'll try something new <3

Here's the video in question:

[jkzmathodysseyquest]

Mathematics plays a crucial role in elementary education for several reasons:

Foundation Building: It lays the groundwork for understanding more complex mathematical concepts in higher grades.

Problem-Solving Skills: Math teaches children how to think logically, analyze situations, and solve problems systematically.

Critical Thinking: It fosters critical thinking skills by encouraging students to evaluate situations, make connections, and draw conclusions.

Real-Life Application: Math concepts such as counting, measuring, and geometry are applied in everyday activities like cooking, shopping, and building.

Preparation for Future Learning: A strong foundation in elementary math prepares students for advanced math topics they will encounter in middle school and beyond.

Certainly! For more comprehensive information on the importance of math in elementary education, you can visit the website https://jkzmathodysseyquest.com/. This resource may offer additional insights, strategies, and resources to enhance math learning experiences for elementary students.

[grepfrutmeat]

misc shane headcanons + my silly drawing of him

-his hair is greying and starting to fall out

-big eyebrows!!

-autistic (the pickles hatred is a texture thing)

-transmasc (I also hc the kid in note 11 is him)

-he wanted to go into teaching or something similar but couldn't handle school after highschool

-he loves science, especially biology.

-he's great at math and loves solving practical problems. be that coding or a random carpentry project.

-has a special interest in game strategy. for gridball and videogames :3

-former sneakerhead, sold his collection to take care of Jas before Marnie offered him a place to stay. Marnie actually offered him a room after Shane casually let it slip out he had to sell all his shoes.

-his parents were addicts who moved around a lot, so he never made any long term friends until he moved out and he had to provide for himself most of the time. he didn't do well in highschool because he was balancing jobs and his schoolwork.

-he can handle change a little better as a result but still hates moving.

-aro/ace (although I do enjoy some romantic pairings with him Sometimes but like. mostly harvey)

-lived in zuzu city for years with some help from Jas' parents. When they died it definitely broke him and he felt very lonely. He definitely still had issues before then but it exacerbated them and he sunk lower and lower.

-used to come to Marnie's ranch during the summer. She regrets not doing more to help Shane when he was younger, but has ultimately forgiven herself.