Geometry Worksheet Middle School: Fill & Download for Free

When I skipped 7th grade math.During sixth grade, schools usually look at students with good math grades who also do well on the math sections of standardized tests. Students who do well in these areas are then given the opportunity to take the regular math class during 7th grade, or skip it and take “advanced math”, which is the math 8th graders take.I was given this opportunity to skip 7th grade math. And I took it.Why? Because I felt smart. Most of my middle school friends didn’t get the same chance to take 8th grade math, and I wanted something that “proved” I was more intelligent than them.I struggled with 8th grade math. It was a pre-algebra class, and I wasn’t used to working with variables. I had to go to a math-tutoring place where I could get help on homework and do some of their math worksheets to work on other areas I struggled with. I ended up getting B’s and C’s in the pre-algebra class.During 8th grade, I took algebra I. Yet again, I struggled. I still had to go to the math tutors, and I got mostly C’s throughout the year (the B I got for the first quarter was my only exception).Towards the end of 8th grade, I took a test to see which math class I would take during my freshman year of high school. I ended up being eligible for the geometry honors class. My parents warned me against taking the class; they knew I struggled with math, and the only reason I was making C’s in algebra I was because I worked my butt off. But once again, I wanted to feel smart. I went against their advice and wrote my name down for geometry honors.Freshman year came around, and geometry honors kicked my butt. One big change from middle school math to high school math was using a computer. In middle school, the teacher stood at the front and taught while writing on a board, and students took notes/did work with paper and pencil. In high school, the teacher puts their screen on the projector and stands in the back of the class while they go through notes/do problems.This was a big change for me. It was hard getting used to everything being done electronically, considering the only electronics I used for middle school were the old computers in the computer lab, iPads (they were occasionally used for research during class), and the second-hand computers we used a little during the 4th quarter of 8th grade.I also got lazy, and made low C’s and even D’s during geometry honors. Every time we had a test, all my classmates would gush about their A’s and B’s while I tried to hide my D’s and F’s under my elbow (the only reason I ever made a C some quarters was because my teacher made homework worth a lot of points, and I always did the homework). The teacher would then say the class average of the test, and my classmates would confusedly ask, “How is that the average? We all made good scores,” while I tried to keep a poker face. The only person in that class (besides the teacher) who knew of my poor scores was the girl who sat behind me. She was nice, and I always felt comfortable talking to her (she would end up becoming one of my best friends).On the final exam, I got an F. My teacher sent an email to my mom saying that she simply couldn’t recommend me for algebra II honors because it would be setting me up for failure.I took regular algebra II last year (my sophomore year) and didn’t do too great. I made C’s and possibly a D. The algebra II honors class and the regular class actually compared classwork, homework, and tests and we discovered that the regular algebra II class was actually MORE DIFFICULT than the honors class!!! It would’ve been better for me to be in the honors class!I’m taking trigonometry right now, and doing horribly. I made a C the first quarter and an F the second quarter. An F. I had never gotten an F in a class before. That makes my first semester average a D. I got another F for the third quarter. If I don’t get a C or higher this quarter, then I’ll have to go to summer school for the first time.I had my teacher ask administration if I could take algebra III next year instead of probability/statistics or calculus. Yep. That means I’ll be taking the “dumb kid” math class with other kids in my grade instead of being a math ahead. That means that all the stress and all the work I did in middle school… was for absolutely nothing.If I didn’t skip 7th grade math, then I’d be taking trigonometry next year instead of algebra III.The point I’m making here is that you don’t have to do something difficult just to look smart. You don’t have to set yourself up for failure because you’re too stubborn to do things at your own pace.At the end of the day, it never even mattered what math I took! I’m going to major in English in college, and I want to eventually become a writer. That means that I never had to be ahead in math. I never had to take honors geometry. In fact, it would’ve looked better if I took regular math classes and got good grades instead of making bad grades just so I could be “ahead”.Just because you’re ahead doesn’t mean that’s where you should be.For example, if you’re in first place during a race but you get tired and people pass you up, does it really matter that you were ahead for a bit? No, because you got passed up anyway.But what if you stay a little bit behind the others, wait for them to get tired, and pass them up? Yeah, you were behind, but now you’re ahead because you stuck to your own pace. And because you stuck to your own pace, you ended up being the real winner.Stick to your own pace. You’ll be more successful that way.

Speaking as an aspiring mathematician, on a more ideological level, mathematics is not taught how a mathematician would do it. Mathematics is presented in a very dull and boring manner. The purpose of mathematics is not to simply solve problems, but understand them. Something which our education system does not seem to value.This isn't helped by a culture which assumes that it's okay to be bad at math. People say it almost pridefully! Imagine if people said with pride “oh yeah I SUCK at reading!” — somehow it's okay to say this for mathematics.Mathematics is truly about logic and creativity. The current public school system has taken it upon themselves to remove both components from a math education. Most students never get to see the beauty of simple geometry, or the amazing symmetries that elementary group theory models so well.Instead, students are left to solving polynomials, with no clue why they are doing it, and no clue why the method they have been taught works. They are not taught abstraction and reasoning skills. The concept of a proof does not exist. Yet since proofs are central to mathematics, what then are they learning? Equation solving. The mathematical education of the US is equation solving. There's not much else but a brief and disconnected stint in geometry, which entirely never fails to disappoint the student, as it becomes the subject of proving obscure results whose significance is never understood.As the mathematician Edward Frenkel says,“What if at school you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it...Of course this sounds ridiculous, but this is how math is taught.”How truly sad our mathematics education is! Our mathematical education “becomes the mental equivalent of watching paint dry.”One mathematician, Paul Lockhart, has given a very detailed criticism of the mathematical education system in the US in a document titled “A Mathematician's Lament” which can be found athttps://www.google.com/url?sa=t&source=web&rct=j&url=https://www.maa.org/external_archive/devlin/LockhartsLament.pdf&ved=2ahUKEwjfqoik59TbAhWpuVkKHeRPD1UQFjAOegQIABAB&usg=AOvVaw1-8EksPe3CjESJf4g-GoVETowards the end, he gives a paraphrase of the US math education. I will include it here, as it is quite clear:“LOWER SCHOOL MATH. The indoctrination begins. Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions. Children are expected to master a complex set of algorithms for manipulating Hindi symbols, unrelated to any real desire or curiosity on their part, and regarded only a few centuries ago as too difficult for the average adult. Multiplication tables are stressed, as are parents, teachers, and the kids themselves.MIDDLE SCHOOL MATH. Students are taught to view mathematics as a set of procedures, akin to religious rites, which are eternal and set in stone. The holy tablets, or “Math Books,” are handed out, and the students learn to address the church elders as “they” (as in “What do they want here? Do they want me to divide?”) Contrived and artificial “word problems” will be introduced in order to make the mindless drudgery of arithmetic seem enjoyable by comparison. Students will be tested on a wide array of unnecessary technical terms, such as ‘whole number’ and ‘proper fraction,’ without the slightest rationale for making such distinctions. Excellent preparation for Algebra I.ALGEBRA I. So as not to waste valuable time thinking about numbers and their patterns, this course instead focuses on symbols and rules for their manipulation. The smooth narrative thread that leads from ancient Mesopotamian tablet problems to the high art of the Renaissance algebraists is discarded in favor of a disturbingly fractured, post-modern retelling with no characters, plot, or theme. The insistence that all numbers and expressions be put into various standard forms will provide additional confusion as to the meaning of identity and equality. Students must also memorize the quadratic formula for some reason.GEOMETRY. Isolated from the rest of the curriculum, this course will raise the hopes of students who wish to engage in meaningful mathematical activity, and then dash them. Clumsy and distracting notation will be introduced, and no pains will be spared to make the simple seem complicated. This goal of this course is to eradicate any last remaining vestiges of natural mathematical intuition, in preparation for Algebra II.ALGEBRA II. The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects, simply because they have to be stuck in somewhere, apparently. The name of the course is chosen to reinforce the ladder mythology. Why Geometry occurs in between Algebra I and its sequel remains a mystery.TRIGONOMETRY. Two weeks of content are stretched to semester length by masturbatory definitional runarounds. Truly interesting and beautiful phenomena, such as the way the sides of a triangle depend on its angles, will be given the same emphasis as irrelevant abbreviations and obsolete notational conventions, in order to prevent students from forming any clear idea as to what the subject is about. Students will learn such mnemonic devices as “SohCahToa” and “All Students Take Calculus” in lieu of developing a natural intuitive feeling for orientation and symmetry. The measurement of triangles will be discussed without mention of the transcendental nature of the trigonometric functions, or the consequent linguistic and philosophical problems inherent in making such measurements. Calculator required, so as to further blur these issues.PRE-CALCULUS. A senseless bouillabaisse of disconnected topics. Mostly a half-baked attempt to introduce late nineteenth-century analytic methods into settings where they are neither necessary nor helpful. Technical definitions of ‘limits’ and ‘continuity’ are presented in order to obscure the intuitively clear notion of smooth change. As the name suggests, this course prepares the student for Calculus, where the final phase in the systematic obfuscation of any natural ideas related to shape and motion will be completed.CALCULUS. This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-based approach developed as a response to various analytic crises which do not really apply in this setting, and which will of course not be mentioned. To be taken again in college, verbatim.***And there you have it. A complete prescription for permanently disabling young minds— a proven cure for curiosity. What have they done to mathematics!”… Sigh…***EDIT***To address some of the remarks with regards to the importance of calculus and unimportance of more mathematicians, Lockhart does address this in his paper:“How many students taking literature classes will one day be writers? That is not why we teach literature, nor why students take it. We teach to enlighten everyone, not to train only the future professionals. In any case, the most valuable skill for a scientist or engineer is being able to think creatively and independently. The last thing anyone needs is to be trained.”—“But don’t we need people to learn those useful consequences of math? Don’t we need accountants and carpenters and such?How many people actually use any of this “practical math” they supposedly learn in school? Do you think carpenters are out there using trigonometry? How many adults remember how to divide fractions, or solve a quadratic equation? Obviously the current practical training program isn’t working, and for good reason: it is excruciatingly boring, and nobody ever uses it anyway. So why do people think it’s so important? I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them. It might do some good, though, to show them something beautiful and give them an opportunity to enjoy being creative, flexible, open-minded thinkers— the kind of thing a real mathematical education might provide.”—“But don’t you think that if math class were made more like art class that a lot of kids just wouldn’t learn anything?They’re not learning anything now! Better to not have math classes at all than to do what is currently being done. At least some people might have a chance to discover something beautiful on their own.”

My sixth-grade math teacher. Mrs. Day.Unlike many of the other answerers, I can’t point to single events of extreme meanness or even violence. She never said anything especially mean; she never insulted us; she never screamed or shouted or even raised her voice. She didn’t have to. She just had a personality like a rotten piece of raw chicken meat pickled in ice-cold ammonia.It didn’t help that it was sixth grade math. I don’t know what the curriculum is like now, but at the time, as near as I can recall, we’d learned simple addition and subtraction in 1st grade (i.e. at the age of six), simple multiplication in 2nd grade, addition and subtraction of 2-digit numbers in third grade, 3-digit numbers in fourth grade (and I think we started long division around that time, but it might have been later), 4-digit numbers in fifth grade. . . I remember thinking that my father, who was a math professor, probably taught his students to add and multiply 20-digit numbers, because I figured you just added one digit with every year of schooling.I’m sure I’m leaving stuff out; there was more content than that, including geometry and such. But by 6th grade, at that time and place, math class was an awful lot of drill-and-kill, a ton of worksheets with nothing but math problems—and as far as I remember, nothing that was conceptually new. In seventh grade we started preparing for algebra and learning some statistics. In sixth grade, it was all the same stuff we’d been doing for a couple of years—just more and more and more of it. It could not have been more effective at killing any interest we had in math if it had been deliberately designed for that purpose.So the curriculum was pretty damn joyless, but maybe a more human teacher could have made it bearable. Mrs. Day, however, was not that teacher. Every day there were worksheets in class and worksheets to take home, watched over by this grim, hatchet-faced middle-aged lady with a voice like the creak of a coffin lid, as much sense of fun as a roadkilled armadillo, and as much expressiveness, warmth and gentleness as an inukshuk, who rarely spoke except to lecture or to express disappointment. I don’t know if she deliberately turned the air conditioning down twenty degrees—but it felt like it in that classroom.Every time you forgot to do your homework—worksheets, always worksheets—she filled out something called a Discipline Sheet, which you had to show your parents, get them to sign it, and then return it the next day. I racked up seven of those that year. And some of you were little hellions in class, but I was a pretty conscientious kid. I hated getting a Discipline Sheet, and I hated the way her lips would purse and her eyes would narrow with even more disapproval than usual. I usually didn’t have trouble remembering to do the homework of the less repulsive teachers. But after a few weeks of sixth grade, every day, ten minutes before the bell would ring to send us to second period, I would always get this horrible sinking feeling in the pit of my stomach. Even if I wasn’t thinking about Mrs. Day’s class, my stomach would remind me like clockwork.I was later told that when she had her conference with my parents, she said, “Well, Ben may be gifted in other things, but he’s certainly not gifted in math!”To which my father said, “Bullshit.”Thank you, Dad.When I got As in two semesters of honors calculus, my freshman year at university, seven years after leaving Mrs. Day’s joyless tutelage, I wanted to go back to Edgar Martin Middle School, waltz into her classroom, and shove my transcript in her face. I didn’t. But I sometimes I still wish I had. She was the only teacher I’ve ever had, at any level, who ever inspired that level of vindictiveness in me.Maybe she had some deep personal sorrow or tragedy that had turned her that way. . . or maybe she was burned out (which I honestly wouldn’t blame her for; thirty years of teaching sixth graders would ablate anyone’s soul). I will never know. And I don’t care. She should not have been teaching.I hope she is enjoying her career in Malebolge. Bitch.