what is a set up in an essay

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How to Format an Essay

Last Updated: April 11, 2024 Fact Checked

This article was co-authored by Carrie Adkins, PhD and by wikiHow staff writer, Aly Rusciano . Carrie Adkins is the cofounder of NursingClio, an open access, peer-reviewed, collaborative blog that connects historical scholarship to current issues in gender and medicine. She completed her PhD in American History at the University of Oregon in 2013. While completing her PhD, she earned numerous competitive research grants, teaching fellowships, and writing awards. There are 11 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 87,369 times.

You’re opening your laptop to write an essay, knowing exactly what you want to write, but then it hits you—you don’t know how to format it! Using the correct format when writing an essay can help your paper look polished and professional while earning you full credit. There are 3 common essay formats—MLA, APA, and Chicago Style—and we’ll teach you the basics of properly formatting each in this article. So, before you shut your laptop in frustration, take a deep breath and keep reading because soon you’ll be formatting like a pro.

Setting Up Your Document

• If you can’t find information on the style guide you should be following, talk to your instructor after class to discuss the assignment or send them a quick email with your questions.
• If your instructor lets you pick the format of your essay, opt for the style that matches your course or degree best: MLA is best for English and humanities; APA is typically for education, psychology, and sciences; Chicago Style is common for business, history, and fine arts.

• Most word processors default to 1 inch (2.5 cm) margins.

• Do not change the font size, style, or color throughout your essay.

• Change the spacing on Google Docs by clicking on Format , and then selecting “Line spacing.”
• Click on Layout in Microsoft Word, and then click the arrow at the bottom left of the “paragraph” section.

• Using the page number function will create consecutive numbering.
• When using Chicago Style, don’t include a page number on your title page. The first page after the title page should be numbered starting at 2. [4] X Research source
• In APA format, a running heading may be required in the left-hand header. This is a maximum of 50 characters that’s the full or abbreviated version of your essay’s title. [5] X Research source

• For APA formatting, place the title in bold at the center of the page 3 to 4 lines down from the top. Insert one double-spaced line under the title and type your name. Under your name, in separate centered lines, type out the name of your school, course, instructor, and assignment due date. [6] X Research source
• For Chicago Style, set your cursor ⅓ of the way down the page, then type your title. In the very center of your page, put your name. Move your cursor ⅔ down the page, then write your course number, followed by your instructor’s name and paper due date on separate, double-spaced lines. [7] X Trustworthy Source Purdue Online Writing Lab Trusted resource for writing and citation guidelines Go to source

• Double-space the heading like the rest of your paper.

Writing the Essay Body

• Use standard capitalization rules for your title.
• Do not underline, italicize, or put quotation marks around your title, unless you include other titles of referred texts.

• A good hook might include a quote, statistic, or rhetorical question.
• For example, you might write, “Every day in the United States, accidents caused by distracted drivers kill 9 people and injure more than 1,000 others.”

• "Action must be taken to reduce accidents caused by distracted driving, including enacting laws against texting while driving, educating the public about the risks, and giving strong punishments to offenders."
• "Although passing and enforcing new laws can be challenging, the best way to reduce accidents caused by distracted driving is to enact a law against texting, educate the public about the new law, and levy strong penalties."

• Use transitions between paragraphs so your paper flows well. For example, say, “In addition to,” “Similarly,” or “On the other hand.” [12] X Research source

• A statement of impact might be, "Every day that distracted driving goes unaddressed, another 9 families must plan a funeral."
• A call to action might read, “Fewer distracted driving accidents are possible, but only if every driver keeps their focus on the road.”

Using References

• In MLA format, citations should include the author’s last name and the page number where you found the information. If the author's name appears in the sentence, use just the page number. [14] X Trustworthy Source Purdue Online Writing Lab Trusted resource for writing and citation guidelines Go to source
• For APA format, include the author’s last name and the publication year. If the author’s name appears in the sentence, use just the year. [15] X Trustworthy Source Purdue Online Writing Lab Trusted resource for writing and citation guidelines Go to source
• If you don’t use parenthetical or internal citations, your instructor may accuse you of plagiarizing.

• At the bottom of the page, include the source’s information from your bibliography page next to the footnote number. [16] X Trustworthy Source Purdue Online Writing Lab Trusted resource for writing and citation guidelines Go to source
• Each footnote should be numbered consecutively.

• If you’re using MLA format, this page will be titled “Works Cited.”
• In APA and Chicago Style, title the page “References.”

• If you have more than one work from the same author, list alphabetically following the title name for MLA and by earliest to latest publication year for APA and Chicago Style.
• Double-space the references page like the rest of your paper.
• Use a hanging indent of 0.5 inches (1.3 cm) if your citations are longer than one line. Press Tab to indent any lines after the first. [17] X Research source
• Citations should include (when applicable) the author(s)’s name(s), title of the work, publication date and/or year, and page numbers.
• Sites like Grammarly , EasyBib , and MyBib can help generate citations if you get stuck.

Formatting Resources

Expert Q&A

You might also like.

• ↑ https://www.une.edu.au/__data/assets/pdf_file/0010/392149/WE_Formatting-your-essay.pdf
• ↑ https://content.nroc.org/DevelopmentalEnglish/unit10/Foundations/formatting-a-college-essay-mla-style.html
• ↑ https://camosun.libguides.com/Chicago-17thEd/titlePage
• ↑ https://apastyle.apa.org/style-grammar-guidelines/paper-format/page-header
• ↑ https://apastyle.apa.org/style-grammar-guidelines/paper-format/title-page
• ↑ https://owl.purdue.edu/owl/research_and_citation/chicago_manual_17th_edition/cmos_formatting_and_style_guide/general_format.html
• ↑ https://www.uvu.edu/writingcenter/docs/basicessayformat.pdf
• ↑ https://www.deanza.edu/faculty/cruzmayra/basicessayformat.pdf
• ↑ https://owl.purdue.edu/owl/research_and_citation/mla_style/mla_formatting_and_style_guide/mla_in_text_citations_the_basics.html
• ↑ https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guide/in_text_citations_the_basics.html
• ↑ https://library.menloschool.org/chicago

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The writer of the academic essay aims to persuade readers of an idea based on evidence. The beginning of the essay is a crucial first step in this process. In order to engage readers and establish your authority, the beginning of your essay has to accomplish certain business. Your beginning should introduce the essay, focus it, and orient readers.

Introduce the Essay.  The beginning lets your readers know what the essay is about, the  topic . The essay's topic does not exist in a vacuum, however; part of letting readers know what your essay is about means establishing the essay's  context , the frame within which you will approach your topic. For instance, in an essay about the First Amendment guarantee of freedom of speech, the context may be a particular legal theory about the speech right; it may be historical information concerning the writing of the amendment; it may be a contemporary dispute over flag burning; or it may be a question raised by the text itself. The point here is that, in establishing the essay's context, you are also limiting your topic. That is, you are framing an approach to your topic that necessarily eliminates other approaches. Thus, when you determine your context, you simultaneously narrow your topic and take a big step toward focusing your essay. Here's an example.

The paragraph goes on. But as you can see, Chopin's novel (the topic) is introduced in the context of the critical and moral controversy its publication engendered.

Focus the Essay.  Beyond introducing your topic, your beginning must also let readers know what the central issue is. What question or problem will you be thinking about? You can pose a question that will lead to your idea (in which case, your idea will be the answer to your question), or you can make a thesis statement. Or you can do both: you can ask a question and immediately suggest the answer that your essay will argue. Here's an example from an essay about Memorial Hall.

The fullness of your idea will not emerge until your conclusion, but your beginning must clearly indicate the direction your idea will take, must set your essay on that road. And whether you focus your essay by posing a question, stating a thesis, or combining these approaches, by the end of your beginning, readers should know what you're writing about, and  why —and why they might want to read on.

Orient Readers.  Orienting readers, locating them in your discussion, means providing information and explanations wherever necessary for your readers' understanding. Orienting is important throughout your essay, but it is crucial in the beginning. Readers who don't have the information they need to follow your discussion will get lost and quit reading. (Your teachers, of course, will trudge on.) Supplying the necessary information to orient your readers may be as simple as answering the journalist's questions of who, what, where, when, how, and why. It may mean providing a brief overview of events or a summary of the text you'll be analyzing. If the source text is brief, such as the First Amendment, you might just quote it. If the text is well known, your summary, for most audiences, won't need to be more than an identifying phrase or two:

Often, however, you will want to summarize your source more fully so that readers can follow your analysis of it.

Questions of Length and Order.  How long should the beginning be? The length should be proportionate to the length and complexity of the whole essay. For instance, if you're writing a five-page essay analyzing a single text, your beginning should be brief, no more than one or two paragraphs. On the other hand, it may take a couple of pages to set up a ten-page essay.

Does the business of the beginning have to be addressed in a particular order? No, but the order should be logical. Usually, for instance, the question or statement that focuses the essay comes at the end of the beginning, where it serves as the jumping-off point for the middle, or main body, of the essay. Topic and context are often intertwined, but the context may be established before the particular topic is introduced. In other words, the order in which you accomplish the business of the beginning is flexible and should be determined by your purpose.

Opening Strategies.  There is still the further question of how to start. What makes a good opening? You can start with specific facts and information, a keynote quotation, a question, an anecdote, or an image. But whatever sort of opening you choose, it should be directly related to your focus. A snappy quotation that doesn't help establish the context for your essay or that later plays no part in your thinking will only mislead readers and blur your focus. Be as direct and specific as you can be. This means you should avoid two types of openings:

• The history-of-the-world (or long-distance) opening, which aims to establish a context for the essay by getting a long running start: "Ever since the dawn of civilized life, societies have struggled to reconcile the need for change with the need for order." What are we talking about here, political revolution or a new brand of soft drink? Get to it.
• The funnel opening (a variation on the same theme), which starts with something broad and general and "funnels" its way down to a specific topic. If your essay is an argument about state-mandated prayer in public schools, don't start by generalizing about religion; start with the specific topic at hand.

Remember.  After working your way through the whole draft, testing your thinking against the evidence, perhaps changing direction or modifying the idea you started with, go back to your beginning and make sure it still provides a clear focus for the essay. Then clarify and sharpen your focus as needed. Clear, direct beginnings rarely present themselves ready-made; they must be written, and rewritten, into the sort of sharp-eyed clarity that engages readers and establishes your authority.

Copyright 1999, Patricia Kain, for the Writing Center at Harvard University

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College essays are an entirely new type of writing for high school seniors. For that reason, many students are confused about proper formatting and essay structure. Should you double-space or single-space? Do you need a title? What kind of narrative style is best-suited for your topic?

In this post, we’ll be going over proper college essay format, traditional and unconventional essay structures (plus sample essays!), and which structure might work best for you. 

General College Essay Formatting Guidelines

How you format your essay will depend on whether you’re submitting in a text box, or attaching a document. We’ll go over the different best practices for both, but regardless of how you’re submitting, here are some general formatting tips:

• There’s no need for a title; it takes up unnecessary space and eats into your word count
• Stay within the word count as much as possible (+/- 10% of the upper limit). For further discussion on college essay length, see our post How Long Should Your College Essay Be?
• Indent or double space to separate paragraphs clearly

If you’re submitting in a text box:

• Avoid italics and bold, since formatting often doesn’t transfer over in text boxes
• Be careful with essays meant to be a certain shape (like a balloon); text boxes will likely not respect that formatting. Beyond that, this technique can also seem gimmicky, so proceed with caution
• Make sure that paragraphs are clearly separated, as text boxes can also undo indents and double spacing

If you’re attaching a document:

• Use a standard font and size like Times New Roman, 12 point
• Make your lines 1.5-spaced or double-spaced
• Use 1-inch margins
• Save as a PDF since it can’t be edited. This also prevents any formatting issues that come with Microsoft Word, since older versions are sometimes incompatible with the newer formatting
• Number each page with your last name in the header or footer (like “Smith 1”)
• Pay extra attention to any word limits, as you won’t be cut off automatically, unlike with most text boxes

Conventional College Essay Structures

Now that we’ve gone over the logistical aspects of your essay, let’s talk about how you should structure your writing. There are three traditional college essay structures. They are:

• In-the-moment narrative
• Narrative told over an extended period of time
• Series of anecdotes, or montage

Let’s go over what each one is exactly, and take a look at some real essays using these structures.

1. In-the-moment narrative

This is where you tell the story one moment at a time, sharing the events as they occur. In the moment narrative is a powerful essay format, as your reader experiences the events, your thoughts, and your emotions with you . This structure is ideal for a specific experience involving extensive internal dialogue, emotions, and reflections.

Here’s an example:

The morning of the Model United Nation conference, I walked into Committee feeling confident about my research. We were simulating the Nuremberg Trials – a series of post-World War II proceedings for war crimes – and my portfolio was of the Soviet Judge Major General Iona Nikitchenko. Until that day, the infamous Nazi regime had only been a chapter in my history textbook; however, the conference’s unveiling of each defendant’s crimes brought those horrors to life. The previous night, I had organized my research, proofread my position paper and gone over Judge Nikitchenko’s pertinent statements. I aimed to find the perfect balance between his stance and my own.

As I walked into committee anticipating a battle of wits, my director abruptly called out to me. “I’m afraid we’ve received a late confirmation from another delegate who will be representing Judge Nikitchenko. You, on the other hand, are now the defense attorney, Otto Stahmer.” Everyone around me buzzed around the room in excitement, coordinating with their allies and developing strategies against their enemies, oblivious to the bomb that had just dropped on me. I felt frozen in my tracks, and it seemed that only rage against the careless delegate who had confirmed her presence so late could pull me out of my trance. After having spent a month painstakingly crafting my verdicts and gathering evidence against the Nazis, I now needed to reverse my stance only three hours before the first session.

Gradually, anger gave way to utter panic. My research was fundamental to my performance, and without it, I knew I could add little to the Trials. But confident in my ability, my director optimistically recommended constructing an impromptu defense. Nervously, I began my research anew. Despite feeling hopeless, as I read through the prosecution’s arguments, I uncovered substantial loopholes. I noticed a lack of conclusive evidence against the defendants and certain inconsistencies in testimonies. My discovery energized me, inspiring me to revisit the historical overview in my conference “Background Guide” and to search the web for other relevant articles. Some Nazi prisoners had been treated as “guilty” before their court dates. While I had brushed this information under the carpet while developing my position as a judge, it now became the focus of my defense. I began scratching out a new argument, centered on the premise that the allied countries had violated the fundamental rule that, a defendant was “not guilty” until proven otherwise.

At the end of the three hours, I felt better prepared. The first session began, and with bravado, I raised my placard to speak. Microphone in hand, I turned to face my audience. “Greetings delegates. I, Otto Stahmer would like to…….” I suddenly blanked. Utter dread permeated my body as I tried to recall my thoughts in vain. “Defence Attorney, Stahmer we’ll come back to you,” my Committee Director broke the silence as I tottered back to my seat, flushed with embarrassment. Despite my shame, I was undeterred. I needed to vindicate my director’s faith in me. I pulled out my notes, refocused, and began outlining my arguments in a more clear and direct manner. Thereafter, I spoke articulately, confidently putting forth my points. I was overjoyed when Secretariat members congratulated me on my fine performance.

Going into the conference, I believed that preparation was the key to success. I wouldn’t say I disagree with that statement now, but I believe adaptability is equally important. My ability to problem-solve in the face of an unforeseen challenge proved advantageous in the art of diplomacy. Not only did this experience transform me into a confident and eloquent delegate at that conference, but it also helped me become a more flexible and creative thinker in a variety of other capacities. Now that I know I can adapt under pressure, I look forward to engaging in activities that will push me to be even quicker on my feet.

This essay is an excellent example of in-the-moment narration. The student openly shares their internal state with us — we feel their anger and panic upon the reversal of roles. We empathize with their emotions of “utter dread” and embarrassment when they’re unable to speak. 

For in-the-moment essays, overloading on descriptions is a common mistake students make. This writer provides just the right amount of background and details to help us understand the situation, however, and balances out the actual event with reflection on the significance of this experience. 

One main area of improvement is that the writer sometimes makes explicit statements that could be better illustrated through their thoughts, actions, and feelings. For instance, they say they “spoke articulately” after recovering from their initial inability to speak, and they also claim that adaptability has helped them in other situations. This is not as engaging as actual examples that convey the same meaning. Still, this essay overall is a strong example of in-the-moment narration, and gives us a relatable look into the writer’s life and personality.

2. Narrative told over an extended period of time

In this essay structure, you share a story that takes place across several different experiences. This narrative style is well-suited for any story arc with multiple parts. If you want to highlight your development over time, you might consider this structure. 

When I was younger, I was adamant that no two foods on my plate touch. As a result, I often used a second plate to prevent such an atrocity. In many ways, I learned to separate different things this way from my older brothers, Nate and Rob. Growing up, I idolized both of them. Nate was a performer, and I insisted on arriving early to his shows to secure front row seats, refusing to budge during intermission for fear of missing anything. Rob was a three-sport athlete, and I attended his games religiously, waving worn-out foam cougar paws and cheering until my voice was hoarse. My brothers were my role models. However, while each was talented, neither was interested in the other’s passion. To me, they represented two contrasting ideals of what I could become: artist or athlete. I believed I had to choose.

And for a long time, I chose athlete. I played soccer, basketball, and lacrosse and viewed myself exclusively as an athlete, believing the arts were not for me. I conveniently overlooked that since the age of five, I had been composing stories for my family for Christmas, gifts that were as much for me as them, as I loved writing. So when in tenth grade, I had the option of taking a creative writing class, I was faced with a question: could I be an athlete and a writer? After much debate, I enrolled in the class, feeling both apprehensive and excited. When I arrived on the first day of school, my teacher, Ms. Jenkins, asked us to write down our expectations for the class. After a few minutes, eraser shavings stubbornly sunbathing on my now-smudged paper, I finally wrote, “I do not expect to become a published writer from this class. I just want this to be a place where I can write freely.”

Although the purpose of the class never changed for me, on the third “submission day,” – our time to submit writing to upcoming contests and literary magazines – I faced a predicament. For the first two submission days, I had passed the time editing earlier pieces, eventually (pretty quickly) resorting to screen snake when hopelessness made the words look like hieroglyphics. I must not have been as subtle as I thought, as on the third of these days, Ms. Jenkins approached me. After shifting from excuse to excuse as to why I did not submit my writing, I finally recognized the real reason I had withheld my work: I was scared. I did not want to be different, and I did not want to challenge not only others’ perceptions of me, but also my own. I yielded to Ms. Jenkin’s pleas and sent one of my pieces to an upcoming contest.

By the time the letter came, I had already forgotten about the contest. When the flimsy white envelope arrived in the mail, I was shocked and ecstatic to learn that I had received 2nd place in a nationwide writing competition. The next morning, however, I discovered Ms. Jenkins would make an announcement to the whole school exposing me as a poet. I decided to own this identity and embrace my friends’ jokes and playful digs, and over time, they have learned to accept and respect this part of me. I have since seen more boys at my school identifying themselves as writers or artists.

I no longer see myself as an athlete and a poet independently, but rather I see these two aspects forming a single inseparable identity – me. Despite their apparent differences, these two disciplines are quite similar, as each requires creativity and devotion. I am still a poet when I am lacing up my cleats for soccer practice and still an athlete when I am building metaphors in the back of my mind – and I have realized ice cream and gummy bears taste pretty good together.

The timeline of this essay spans from the writer’s childhood all the way to sophomore year, but we only see key moments along this journey. First, we get context for why the writer thought he had to choose one identity: his older brothers had very distinct interests. Then, we learn about the student’s 10th grade creative writing class, writing contest, and results of the contest. Finally, the essay covers the writers’ embarrassment of his identity as a poet, to gradual acceptance and pride in that identity. 

This essay is a great example of a narrative told over an extended period of time. It’s highly personal and reflective, as the piece shares the writer’s conflicting feelings, and takes care to get to the root of those feelings. Furthermore, the overarching story is that of a personal transformation and development, so it’s well-suited to this essay structure.

3. Series of anecdotes, or montage

This essay structure allows you to focus on the most important experiences of a single storyline, or it lets you feature multiple (not necessarily related) stories that highlight your personality. Montage is a structure where you piece together separate scenes to form a whole story. This technique is most commonly associated with film. Just envision your favorite movie—it likely is a montage of various scenes that may not even be chronological. 

Night had robbed the academy of its daytime colors, yet there was comfort in the dim lights that cast shadows of our advances against the bare studio walls. Silhouettes of roundhouse kicks, spin crescent kicks, uppercuts and the occasional butterfly kick danced while we sparred. She approached me, eyes narrowed with the trace of a smirk challenging me. “Ready spar!” Her arm began an upward trajectory targeting my shoulder, a common first move. I sidestepped — only to almost collide with another flying fist. Pivoting my right foot, I snapped my left leg, aiming my heel at her midsection. The center judge raised one finger. 

There was no time to celebrate, not in the traditional sense at least. Master Pollard gave a brief command greeted with a unanimous “Yes, sir” and the thud of 20 hands dropping-down-and-giving-him-30, while the “winners” celebrated their victory with laps as usual. 

Three years ago, seven-thirty in the evening meant I was a warrior. It meant standing up straighter, pushing a little harder, “Yes, sir” and “Yes, ma’am”, celebrating birthdays by breaking boards, never pointing your toes, and familiarity. Three years later, seven-thirty in the morning meant I was nervous. 

The room is uncomfortably large. The sprung floor soaks up the checkerboard of sunlight piercing through the colonial windows. The mirrored walls further illuminate the studio and I feel the light scrutinizing my sorry attempts at a pas de bourrée , while capturing the organic fluidity of the dancers around me. “ Chassé en croix, grand battement, pique, pirouette.” I follow the graceful limbs of the woman in front of me, her legs floating ribbons, as she executes what seems to be a perfect ronds de jambes. Each movement remains a negotiation. With admirable patience, Ms. Tan casts me a sympathetic glance.   

There is no time to wallow in the misery that is my right foot. Taekwondo calls for dorsiflexion; pointed toes are synonymous with broken toes. My thoughts drag me into a flashback of the usual response to this painful mistake: “You might as well grab a tutu and head to the ballet studio next door.” Well, here I am Master Pollard, unfortunately still following your orders to never point my toes, but no longer feeling the satisfaction that comes with being a third degree black belt with 5 years of experience quite literally under her belt. It’s like being a white belt again — just in a leotard and ballet slippers. 

But the appetite for new beginnings that brought me here doesn’t falter. It is only reinforced by the classical rendition of “Dancing Queen” that floods the room and the ghost of familiarity that reassures me that this new beginning does not and will not erase the past. After years spent at the top, it’s hard to start over. But surrendering what you are only leads you to what you may become. In Taekwondo, we started each class reciting the tenets: honor, courtesy, integrity, perseverance, self-control, courage, humility, and knowledge, and I have never felt that I embodied those traits more so than when I started ballet. 

The thing about change is that it eventually stops making things so different. After nine different schools, four different countries, three different continents, fluency in Tamil, Norwegian, and English, there are more blurred lines than there are clear fragments. My life has not been a tactfully executed, gold medal-worthy Taekwondo form with each movement defined, nor has it been a series of frappés performed by a prima ballerina with each extension identical and precise, but thankfully it has been like the dynamics of a spinning back kick, fluid, and like my chances of landing a pirouette, unpredictable. 

This essay takes a few different anecdotes and weaves them into a coherent narrative about the writer’s penchant for novel experiences. We’re plunged into her universe, in the middle of her Taekwondo spar, three years before the present day. She then transitions into a scene in a ballet studio, present day. By switching from past tense to present tense, the writer clearly demarcates this shift in time. 

The parallel use of the spoken phrase “Point” in the essay ties these two experiences together. The writer also employs a flashback to Master Pollard’s remark about “grabbing a tutu” and her habit of dorsiflexing her toes, which further cements the connection between these anecdotes. 

While some of the descriptions are a little wordy, the piece is well-executed overall, and is a stellar example of the montage structure. The two anecdotes are seamlessly intertwined, and they both clearly illustrate the student’s determination, dedication, reflectiveness, and adaptability. The writer also concludes the essay with a larger reflection on her life, many moves, and multiple languages. 

Unconventional College Essay Structures

Unconventional essay structures are any that don’t fit into the categories above. These tend to be higher risk, as it’s easier to turn off the admissions officer, but they’re also higher reward if executed correctly. 

There are endless possibilities for unconventional structures, but most fall under one of two categories:

1. Playing with essay format

Instead of choosing a traditional narrative format, you might take a more creative route to showcase your interests, writing your essay:

• As a movie script
• With a creative visual format (such as creating a visual pattern with the spaces between your sentences forming a picture)
• As a two-sided Lincoln-Douglas debate
• As a legal brief
• Using song lyrics

2. Linguistic techniques

You could also play with the actual language and sentence structure of your essay, writing it:

• In iambic pentameter
• Partially in your mother tongue
• In code or a programming language

These linguistic techniques are often hybrid, where you write some of the essay with the linguistic variation, then write more of an explanation in English.

Under no circumstances should you feel pressured to use an unconventional structure. Trying to force something unconventional will only hurt your chances. That being said, if a creative structure comes naturally to you, suits your personality, and works with the content of your essay — go for that structure!

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Prewriting is just getting all of your ideas on paper. There are many ways, and maybe prewriting deserves an instructable of its own. For the purposes of writing an essay all you need to do is write down your ideas somewhere until you have a good idea what you'd like to do your essay on.

Step 2: The Thesis Statement & Set Up

The Thesis Statement is hugely important to your essay. It's the point you want your essay to drive home. A good thesis statement is strong. A good example of a thesis statement is: Twain uses the growth and development of Huck Finn to show readers what is morally right. The thing that is most important about a thesis statement is that it needs to be about what you're going to write about. If your thesis statement is about the relationship between Shakespeare and Scooby Doo, then you better stick to it. You can't throw in a paragraph about how Velma relates to Charles Dickens, because it does not fit with your thesis. Everything in your essay should work towards proving your thesis. Note: If writing about a book you might want to include the title and author in your them statement. Otherwise you can include that info in another sentence before it. Also multiple sentence theme statements are possible, but can mucky up the point. Set Up Before I write my Essay I use the following set up. 1. Attention Getter 2.Thesis Statement. 2. Evidence for body paragraphs 5. Tie in to attention getter. I find it helps when writing to have these before i get too far into it. However, it is completely up to you.

Step 3: The Introduction

The introduction should have the follwing construction: 1. Attention Getter 2.Thesis 3. Plan of Development 4. Transition Somewhere in there you need to include any other information that is necessary, such as the title and author (if your essay is about a book), or the time period (if about a certain event). You need to include the setting. 1The Attention Getter Write whatever you need to get attention as long as it relates to the essay. Warning: Contrary to popular belief a question is not a very good attention getter. A reader simply answering no to a question can ruin one of these questions very easily. Good ideas for an attention getter are short anecdotes or a quote (if writing about a book it's best to use a quote that is not from this book). It's important that the attention getter has some relation to the rest of your essay. 2. The Thesis Usually a sentence or two you need to state your thesis. Let the purpose of this essay be known to the reader. 3. The Plan of Development For the pl an of development you need to go over what your essay will be showing/explaining. You want to tell what the purpose is of each of your body paragraph. You can use anywhere from 1-5 sentences. I tend to keep mine short, and use the topic sentences of my body paragraphs to help me write my plan of development. 4.Transitions. You want your essay to flow. One idea leads to the next. An essay without transitions will be chunky and unappealing. There's not much advice to give you on transitions except that you need to connect your paragraphs together.

Step 4: Body Paragraph

Most Body paragraphs consist of. 1.Topic Sentence 2.Lead to evidence 3.Evidence 4.Explanation of Evidence 5.Short Recap 6.Transition *note: steps 2-4 can be repeated multiple times in the same paragraph as long as it all relates and proves the topic sentence. 1. The topic sentence is like a mini thesis for this paragraph. What point is this paragraph proving? 2. You have to lead into the quote you can't just plop a quote randomly in the middle of a paragraph. example: At a sad time for his family Bobby said, " 3. The best evidence is a quote in my opinion. Specific examples can also work. Make sure your evidence really does prove what you need it to, and that it comes from a reliable source. 4. Explain what the evidence shows. This should probably be at least 2 sentences. Make sure the reader knows how it supports the topic sentence. 5. The short recap is probably a sentence explaining what this paragraph said. 6. Once again you'll need to smoothly flow into the next paragraph.

Step 5: Conclusion

A conclusion should have the following steps. 1.Restate the Thesis. 2.Go over what you have already talked about. 3. Tie in with Attention getter. 1. just as it says 2. It's kind of like the plan of development. 3. This is where your essay gets that nice feeling because it starts in a similar way it ends. Sometimes a tie in can be hard to think of, but if you do it can pay off big time.

Step 6: Things to Remember Throughout Writing.

When writing an analytical or informative essay you should remain impersonal. Stay away from You's and I's. The only time I would recommend using I's and You's might be in a persuasive essay to a certain audience that knows you. When writing keep the same tense. If you're writing in the past tense stay in it. Here's an example of someone who doesn't keep in the same tense. Billy had a ball. The ball is nice. Too bad he popped it. See how awkward that sounds. Don't do that. It should read: Billy Had a ball. The ball was nice. Too bad he popped it.

Step 7: Revision and Rewriting.

I suggest rereading a printed copy of your essay and marking it up. Then you can make the changes print it out. For the best results you should let someone else read it. When you go back to make the changes again, feel free to rewrite whole sections of the essay that sound like they could be improved. Don't be afraid of changing your essay too much during the revision process. The whole point is to change it.

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Sat / act prep online guides and tips, how to format a college essay: 15 expert tips.

College Essays

When you're applying to college, even small decisions can feel high-stakes. This is especially true for the college essay, which often feels like the most personal part of the application. You may agonize over your college application essay format: the font, the margins, even the file format. Or maybe you're agonizing over how to organize your thoughts overall. Should you use a narrative structure? Five paragraphs?

In this comprehensive guide, we'll go over the ins and outs of how to format a college essay on both the micro and macro levels. We'll discuss minor formatting issues like headings and fonts, then discuss broad formatting concerns like whether or not to use a five-paragraph essay, and if you should use a college essay template.

How to Format a College Essay: Font, Margins, Etc.

Some of your formatting concerns will depend on whether you will be cutting and pasting your essay into a text box on an online application form or attaching a formatted document. If you aren't sure which you'll need to do, check the application instructions. Note that the Common Application does currently require you to copy and paste your essay into a text box.

Most schools also allow you to send in a paper application, which theoretically gives you increased control over your essay formatting. However, I generally don't advise sending in a paper application (unless you have no other option) for a couple of reasons:

Most schools state that they prefer to receive online applications. While it typically won't affect your chances of admission, it is wise to comply with institutional preferences in the college application process where possible. It tends to make the whole process go much more smoothly.

Paper applications can get lost in the mail. Certainly there can also be problems with online applications, but you'll be aware of the problem much sooner than if your paper application gets diverted somehow and then mailed back to you. By contrast, online applications let you be confident that your materials were received.

Regardless of how you will end up submitting your essay, you should draft it in a word processor. This will help you keep track of word count, let you use spell check, and so on.

Next, I'll go over some of the concerns you might have about the correct college essay application format, whether you're copying and pasting into a text box or attaching a document, plus a few tips that apply either way.

Formatting Guidelines That Apply No Matter How You End Up Submitting the Essay:

Unless it's specifically requested, you don't need a title. It will just eat into your word count.

Avoid cutesy, overly colloquial formatting choices like ALL CAPS or ~unnecessary symbols~ or, heaven forbid, emoji and #hashtags. Your college essay should be professional, and anything too cutesy or casual will come off as immature.

Mmm, delicious essay...I mean sandwich.

Why College Essay Templates Are a Bad Idea

You might see college essay templates online that offer guidelines on how to structure your essay and what to say in each paragraph. I strongly advise against using a template. It will make your essay sound canned and bland—two of the worst things a college essay can be. It's much better to think about what you want to say, and then talk through how to best structure it with someone else and/or make your own practice outlines before you sit down to write.

You can also find tons of successful sample essays online. Looking at these to get an idea of different styles and topics is fine, but again, I don't advise closely patterning your essay after a sample essay. You will do the best if your essay really reflects your own original voice and the experiences that are most meaningful to you.

College Application Essay Format: Key Takeaways

There are two levels of formatting you might be worried about: the micro (fonts, headings, margins, etc) and the macro (the overall structure of your essay).

Tips for the micro level of your college application essay format:

• Always draft your essay in a word processing software, even if you'll be copy-and-pasting it over into a text box.
• If you are copy-and-pasting it into a text box, make sure your formatting transfers properly, your paragraphs are clearly delineated, and your essay isn't cut off.
• If you are attaching a document, make sure your font is easily readable, your margins are standard 1-inch, your essay is 1.5 or double-spaced, and your file format is compatible with the application specs.
• There's no need for a title unless otherwise specified—it will just eat into your word count.

Tips for the macro level of your college application essay format :

• There is no super-secret college essay format that will guarantee success.
• In terms of structure, it's most important that you have an introduction that makes it clear where you're going and a conclusion that wraps up with a main point. For the middle of your essay, you have lots of freedom, just so long as it flows logically!
• I advise against using an essay template, as it will make your essay sound stilted and unoriginal.

Plus, if you use a college essay template, how will you get rid of these medieval weirdos?

What's Next?

Still feeling lost? Check out our total guide to the personal statement , or see our step-by-step guide to writing the perfect essay .

If you're not sure where to start, consider these tips for attention-grabbing first sentences to college essays!

And be sure to avoid these 10 college essay mistakes .

Ellen has extensive education mentorship experience and is deeply committed to helping students succeed in all areas of life. She received a BA from Harvard in Folklore and Mythology and is currently pursuing graduate studies at Columbia University.

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How to Write an Essay Introduction (with Examples)   

The introduction of an essay plays a critical role in engaging the reader and providing contextual information about the topic. It sets the stage for the rest of the essay, establishes the tone and style, and motivates the reader to continue reading. 

Table of Contents

What is an essay introduction , what to include in an essay introduction, how to create an essay structure , step-by-step process for writing an essay introduction , how to write an introduction paragraph , how to write a hook for your essay , how to include background information , how to write a thesis statement .

• Argumentative Essay Introduction Example: 
• Expository Essay Introduction Example 

Literary Analysis Essay Introduction Example

Check and revise – checklist for essay introduction , key takeaways , frequently asked questions .

An introduction is the opening section of an essay, paper, or other written work. It introduces the topic and provides background information, context, and an overview of what the reader can expect from the rest of the work. 1 The key is to be concise and to the point, providing enough information to engage the reader without delving into excessive detail. 

The essay introduction is crucial as it sets the tone for the entire piece and provides the reader with a roadmap of what to expect. Here are key elements to include in your essay introduction: 

• Hook : Start with an attention-grabbing statement or question to engage the reader. This could be a surprising fact, a relevant quote, or a compelling anecdote. 
• Background information : Provide context and background information to help the reader understand the topic. This can include historical information, definitions of key terms, or an overview of the current state of affairs related to your topic. 
• Thesis statement : Clearly state your main argument or position on the topic. Your thesis should be concise and specific, providing a clear direction for your essay. 

Before we get into how to write an essay introduction, we need to know how it is structured. The structure of an essay is crucial for organizing your thoughts and presenting them clearly and logically. It is divided as follows: 2  

• Introduction:  The introduction should grab the reader’s attention with a hook, provide context, and include a thesis statement that presents the main argument or purpose of the essay.  
• Body:  The body should consist of focused paragraphs that support your thesis statement using evidence and analysis. Each paragraph should concentrate on a single central idea or argument and provide evidence, examples, or analysis to back it up.  
• Conclusion:  The conclusion should summarize the main points and restate the thesis differently. End with a final statement that leaves a lasting impression on the reader. Avoid new information or arguments. 

Here’s a step-by-step guide on how to write an essay introduction: 

• Start with a Hook : Begin your introduction paragraph with an attention-grabbing statement, question, quote, or anecdote related to your topic. The hook should pique the reader’s interest and encourage them to continue reading. 
• Provide Background Information : This helps the reader understand the relevance and importance of the topic. 
• State Your Thesis Statement : The last sentence is the main argument or point of your essay. It should be clear, concise, and directly address the topic of your essay. 
• Preview the Main Points : This gives the reader an idea of what to expect and how you will support your thesis. 
• Keep it Concise and Clear : Avoid going into too much detail or including information not directly relevant to your topic. 
• Revise : Revise your introduction after you’ve written the rest of your essay to ensure it aligns with your final argument. 

Here’s an example of an essay introduction paragraph about the importance of education: 

Education is often viewed as a fundamental human right and a key social and economic development driver. As Nelson Mandela once famously said, “Education is the most powerful weapon which you can use to change the world.” It is the key to unlocking a wide range of opportunities and benefits for individuals, societies, and nations. In today’s constantly evolving world, education has become even more critical. It has expanded beyond traditional classroom learning to include digital and remote learning, making education more accessible and convenient. This essay will delve into the importance of education in empowering individuals to achieve their dreams, improving societies by promoting social justice and equality, and driving economic growth by developing a skilled workforce and promoting innovation. 

This introduction paragraph example includes a hook (the quote by Nelson Mandela), provides some background information on education, and states the thesis statement (the importance of education). 

This is one of the key steps in how to write an essay introduction. Crafting a compelling hook is vital because it sets the tone for your entire essay and determines whether your readers will stay interested. A good hook draws the reader in and sets the stage for the rest of your essay.  

• Avoid Dry Fact : Instead of simply stating a bland fact, try to make it engaging and relevant to your topic. For example, if you’re writing about the benefits of exercise, you could start with a startling statistic like, “Did you know that regular exercise can increase your lifespan by up to seven years?” 
• Avoid Using a Dictionary Definition : While definitions can be informative, they’re not always the most captivating way to start an essay. Instead, try to use a quote, anecdote, or provocative question to pique the reader’s interest. For instance, if you’re writing about freedom, you could begin with a quote from a famous freedom fighter or philosopher. 
• Do Not Just State a Fact That the Reader Already Knows : This ties back to the first point—your hook should surprise or intrigue the reader. For Here’s an introduction paragraph example, if you’re writing about climate change, you could start with a thought-provoking statement like, “Despite overwhelming evidence, many people still refuse to believe in the reality of climate change.” 

Including background information in the introduction section of your essay is important to provide context and establish the relevance of your topic. When writing the background information, you can follow these steps: 

• Start with a General Statement:  Begin with a general statement about the topic and gradually narrow it down to your specific focus. For example, when discussing the impact of social media, you can begin by making a broad statement about social media and its widespread use in today’s society, as follows: “Social media has become an integral part of modern life, with billions of users worldwide.” 
• Define Key Terms : Define any key terms or concepts that may be unfamiliar to your readers but are essential for understanding your argument. 
• Provide Relevant Statistics:  Use statistics or facts to highlight the significance of the issue you’re discussing. For instance, “According to a report by Statista, the number of social media users is expected to reach 4.41 billion by 2025.” 
• Discuss the Evolution:  Mention previous research or studies that have been conducted on the topic, especially those that are relevant to your argument. Mention key milestones or developments that have shaped its current impact. You can also outline some of the major effects of social media. For example, you can briefly describe how social media has evolved, including positives such as increased connectivity and issues like cyberbullying and privacy concerns. 
• Transition to Your Thesis:  Use the background information to lead into your thesis statement, which should clearly state the main argument or purpose of your essay. For example, “Given its pervasive influence, it is crucial to examine the impact of social media on mental health.” 

A thesis statement is a concise summary of the main point or claim of an essay, research paper, or other type of academic writing. It appears near the end of the introduction. Here’s how to write a thesis statement: 

• Identify the topic:  Start by identifying the topic of your essay. For example, if your essay is about the importance of exercise for overall health, your topic is “exercise.” 
• State your position:  Next, state your position or claim about the topic. This is the main argument or point you want to make. For example, if you believe that regular exercise is crucial for maintaining good health, your position could be: “Regular exercise is essential for maintaining good health.” 
• Support your position:  Provide a brief overview of the reasons or evidence that support your position. These will be the main points of your essay. For example, if you’re writing an essay about the importance of exercise, you could mention the physical health benefits, mental health benefits, and the role of exercise in disease prevention. 
• Make it specific:  Ensure your thesis statement clearly states what you will discuss in your essay. For example, instead of saying, “Exercise is good for you,” you could say, “Regular exercise, including cardiovascular and strength training, can improve overall health and reduce the risk of chronic diseases.” 

Examples of essay introduction 

Here are examples of essay introductions for different types of essays: 

Argumentative Essay Introduction Example:  

Topic: Should the voting age be lowered to 16? 

“The question of whether the voting age should be lowered to 16 has sparked nationwide debate. While some argue that 16-year-olds lack the requisite maturity and knowledge to make informed decisions, others argue that doing so would imbue young people with agency and give them a voice in shaping their future.” 

Expository Essay Introduction Example  

Topic: The benefits of regular exercise 

“In today’s fast-paced world, the importance of regular exercise cannot be overstated. From improving physical health to boosting mental well-being, the benefits of exercise are numerous and far-reaching. This essay will examine the various advantages of regular exercise and provide tips on incorporating it into your daily routine.” 

Text: “To Kill a Mockingbird” by Harper Lee 

“Harper Lee’s novel, ‘To Kill a Mockingbird,’ is a timeless classic that explores themes of racism, injustice, and morality in the American South. Through the eyes of young Scout Finch, the reader is taken on a journey that challenges societal norms and forces characters to confront their prejudices. This essay will analyze the novel’s use of symbolism, character development, and narrative structure to uncover its deeper meaning and relevance to contemporary society.” 

• Engaging and Relevant First Sentence : The opening sentence captures the reader’s attention and relates directly to the topic. 
• Background Information : Enough background information is introduced to provide context for the thesis statement. 
• Definition of Important Terms : Key terms or concepts that might be unfamiliar to the audience or are central to the argument are defined. 
• Clear Thesis Statement : The thesis statement presents the main point or argument of the essay. 
• Relevance to Main Body : Everything in the introduction directly relates to and sets up the discussion in the main body of the essay. 

Writing a strong introduction is crucial for setting the tone and context of your essay. Here are the key takeaways for how to write essay introduction: 3  

• Hook the Reader : Start with an engaging hook to grab the reader’s attention. This could be a compelling question, a surprising fact, a relevant quote, or an anecdote. 
• Provide Background : Give a brief overview of the topic, setting the context and stage for the discussion. 
• Thesis Statement : State your thesis, which is the main argument or point of your essay. It should be concise, clear, and specific. 
• Preview the Structure : Outline the main points or arguments to help the reader understand the organization of your essay. 
• Keep it Concise : Avoid including unnecessary details or information not directly related to your thesis. 
• Revise and Edit : Revise your introduction to ensure clarity, coherence, and relevance. Check for grammar and spelling errors. 
• Seek Feedback : Get feedback from peers or instructors to improve your introduction further. 

The purpose of an essay introduction is to give an overview of the topic, context, and main ideas of the essay. It is meant to engage the reader, establish the tone for the rest of the essay, and introduce the thesis statement or central argument.  

An essay introduction typically ranges from 5-10% of the total word count. For example, in a 1,000-word essay, the introduction would be roughly 50-100 words. However, the length can vary depending on the complexity of the topic and the overall length of the essay.

An essay introduction is critical in engaging the reader and providing contextual information about the topic. To ensure its effectiveness, consider incorporating these key elements: a compelling hook, background information, a clear thesis statement, an outline of the essay’s scope, a smooth transition to the body, and optional signposting sentences.  

The process of writing an essay introduction is not necessarily straightforward, but there are several strategies that can be employed to achieve this end. When experiencing difficulty initiating the process, consider the following techniques: begin with an anecdote, a quotation, an image, a question, or a startling fact to pique the reader’s interest. It may also be helpful to consider the five W’s of journalism: who, what, when, where, why, and how.   For instance, an anecdotal opening could be structured as follows: “As I ascended the stage, momentarily blinded by the intense lights, I could sense the weight of a hundred eyes upon me, anticipating my next move. The topic of discussion was climate change, a subject I was passionate about, and it was my first public speaking event. Little did I know , that pivotal moment would not only alter my perspective but also chart my life’s course.” 

Crafting a compelling thesis statement for your introduction paragraph is crucial to grab your reader’s attention. To achieve this, avoid using overused phrases such as “In this paper, I will write about” or “I will focus on” as they lack originality. Instead, strive to engage your reader by substantiating your stance or proposition with a “so what” clause. While writing your thesis statement, aim to be precise, succinct, and clear in conveying your main argument.  

To create an effective essay introduction, ensure it is clear, engaging, relevant, and contains a concise thesis statement. It should transition smoothly into the essay and be long enough to cover necessary points but not become overwhelming. Seek feedback from peers or instructors to assess its effectiveness. 

References  

• Cui, L. (2022). Unit 6 Essay Introduction.  Building Academic Writing Skills . 
• West, H., Malcolm, G., Keywood, S., & Hill, J. (2019). Writing a successful essay.  Journal of Geography in Higher Education ,  43 (4), 609-617. 
• Beavers, M. E., Thoune, D. L., & McBeth, M. (2023). Bibliographic Essay: Reading, Researching, Teaching, and Writing with Hooks: A Queer Literacy Sponsorship. College English, 85(3), 230-242. 

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Watch CBS News

Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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