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• Big Ideas Math Algebra 1, 2015
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• Big Ideas Math Algebra 1 A Bridge to Success
• Core Connections Algebra 1, 2013
• Houghton Mifflin Harcourt Algebra 1, 2015
• Holt McDougal Algebra 1, 2011
• McDougal Littell Algebra 1, 1999
• McGraw Hill Glencoe Algebra 1, 2012
• McGraw Hill Glencoe Algebra 1, 2017
• McGraw Hill Glencoe Algebra 1 Texas, 2016
• Pearson Algebra 1 Common Core, 2011
• Pearson Algebra 1 Common Core, 2015

Geometry Worksheets(pdf)

Free worksheets with answer keys.

Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Graphic Organizer on All Formulas
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• Area of Triangle
• Interior Angles of Triangle

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Math Courses

Math 1060q — precalculus (fall 2024).

• Supplementary Materials

Course Coordinator (Storrs): Erika Fiore

Description:  Precalculus is a  preparation for calculus which includes a thorough review of algebra. Emphasis will be on functions and their applications; in particular, polynomials, rational functions, exponentials, logarithms, and trigonometric functions.

Prerequisites: A qualifying score of 17 on the mathematics placement exam (MPE), unless you began attending UConn prior to Fall 2016 (in which case it is still recommended). Students who fail to achieve this minimum score are required to spend time on the preparatory and learning modules before re-taking the MPE or register for a lower level Mathematics course. Not open for credit to students who have passed MATH 1120, 1125Q , or 1131Q . Students may not receive credit for this course and MATH 1040Q .

General Learning Objectives:

• Use definitions, formulas, properties, identities, theorems, and basic algebra skills to solve problems.
• Identify, graph, evaluate, describe, combine, compose, transform, invert, and analyze different types of functions (including polynomial, piecewise, rational, exponential, logarithmic, and trigonometric functions)
• Solve different types of equations (including polynomial, rational, exponential, logarithmic and trigonometric equations).
• Use functions to model and solve real world problems.

Course Materials:

Textbook: Precalculus 10e , by Larson (ISBN 978-1-337-27107-3)

You are  not  required to have a physical textbook. You are only required to have WebAssign access.

If you are participating in the  Husky Book Bundle Program, you do not need to purchase anything. Please sign into HuskyCT to access course materials through the WebAssign link.

If you have opted out of the Husky Book Bundle Program, you can buy the textbook from the UConn Bookstore, or direct from Cengage. You will need a WebAssign access code to access your homework assignments. When you buy the textbook from the bookstore, the WebAssign code will come bundled with the textbook. You will have two weeks of free access  to WebAssign, which includes the e-book, so you can get started right away in case you need some time to arrange to buy textbook with the access code.

There is only ONE way to access WebAssign .  Once the semester officially begins, simply log into your HuskyCT account ( lms.uconn.edu ), navigate to the page for Math 1060Q, then follow the link  for WebAssign Homework.  When logging into WebAssign (through HuskyCT),  do not use Internet Explorer or Safari. Use Firefox or Chrome.

If you need help getting started with WebAssign, please visit this link for more information and support from Cengage representatives:  https://www.cengage.com/coursepages/UConn_MATH1060Q

WebAssign assignments will be due every Tuesday and Thursday night. The first WebAssign assignment is due Tuesday, September 3rd , so please get started ASAP!

Calculators : The use of calculators IS  NOT permitted on exams or quizzes.

Classwork Assignments:

Quizzes and Exams:

Grading Scale:

• If you’ve taken precalculus before, be warned —  this course is harder . We will likely cover more material, and it will be more in-depth, than what you’ve done before.
• Don’t miss class! Each day builds on the previous days, so if you miss class, you get behind very quickly. If you do get sick or have to miss class, talk to your classmates and instructor to catch up before the next class. The outline for the course that is available using the link above will provide you with information about the topics to be covered in lecture.
• Do not skip the WebAssign homework. Doing these problems will give you the practice you need in order to be successful on quizzes and exams.
• Seek help early if you think you may need it! Some great resources for help are your instructor’s office hours, the  Q-Center , a tutor, and other students.

Academic Integrity and Honesty:

This course expects all students to act in accordance with the Guidelines for Academic Integrity at the University of Connecticut. UConn defines academic misconduct as “dishonest or unethical academic behavior that includes, but is not limited to, misrepresenting mastery in an academic area (e.g., cheating), failing to properly credit information, research, or ideas to their rightful originators or representing such information, research, or ideas as your own (e.g., plagiarism).” Below is a list of examples of academic misconduct in this course:

• Cheating or helping others cheat on a quiz or an exam. Using unauthorized materials on quizzes or exams including looking at your neighbors’ papers, your notes, books, or electronic devices is cheating. Communicating with any other human being (besides the instructor) during a quiz or an exam is cheating.
• Cheating or helping others cheat on homework.  It is okay to receive help from a classmate or tutor on homework, but all work submitted should represent your honest understanding of the material.
• Distributing your instructor’s materials to students’ outside of this course, including posting materials on the internet. You are forbidden from sharing or posting exams, quizzes, and homework problems created by your instructor. You are also forbidden from sharing or posting solutions to exams, quizzes, and homework, and other assignments.

Any student who commits an act of misconduct will be reported to the university. Violations of this policy may range from a zero on the assignment to a grade of F in the course. If you have questions about academic integrity or intellectual property, you should consult with your instructor.

For more details, click here: Policy on Academic, Scholarly, and Professional Integrity and Misconduct

Students with Disabilities:

The University of Connecticut is committed to protecting the rights of individuals with disabilities and assuring that the learning environment is accessible.  If you anticipate or experience physical or academic barriers based on disability or pregnancy, please let me know immediately so that we can discuss options. Students who require accommodations should contact the Center for Students with Disabilities, Wilbur Cross Building Room 204, (860) 486-2020, or  http://csd.uconn.edu/ .

To provide students with disabilities the appropriate accommodations, CSD must send an official letter to your instructor. If your accommodations require you to take quizzes and/or exams in a separate space, it is your responsibility to schedule an appointment with CSD’s testing center through MyAccess at least one week before each quiz/exam date.

Resources for Students Experiencing Distress:

The University of Connecticut is committed to supporting students in their mental health, their psychological and social well-being, and their connection to their academic experience and overall wellness. The university believes that academic, personal, and professional development can flourish only when each member of our community is assured equitable access to mental health services. The university aims to make access to mental health attainable while fostering a community reflecting equity and diversity and understands that good mental health may lead to personal and professional growth, greater self-awareness, increased social engagement, enhanced academic success, and campus and community involvement.

Students who feel they may benefit from speaking with a mental health professional can find support and resources through the Student Health and Wellness-Mental Health (SHaW-MH) office located in Storrs on the main campus in the Arjona Building, 4th Floor. Through SHaW- MH, students can make an appointment with a mental health professional and engage in confidential conversations or seek recommendations or referrals for any mental health or psychological concern. Mental health services are included as part of the university’s student health insurance plan and partially funded through university fees. If you do not have UConn’s student health insurance plan, most major insurance plans are also accepted. Please visit https://studenthealth.uconn.edu/ or call (860) 486-4705 if you have questions.

Quizard AI: Homework Helper 4+

Instant math problem solver, quizard ai, inc., designed for iphone.

• #34 in Education
• 4.7 • 34K Ratings
• Offers In-App Purchases

iPhone Screenshots

Description.

Homework & AI Answers Solver. Are you struggling to keep up with your homework and studying? Don't worry, Quizard is here to help! Quizard is a revolutionary AI answer app designed to help students at all levels conquer their studies. Now introducing our new feature - AI answers for math questions! Just snap a photo of your math problem, and Quizard's AI will deliver the solution, along with a comprehensive explanation. This makes Quizard the perfect tool not only for general studies but also for math homework help. Whether you’re a college student, high school student, or even an adult looking to brush up on your knowledge, Quizard is the perfect tool to help you succeed. With Quizard, you can quickly and easily get help with multiple-choice questions and short answer problems. You can quickly and easily prepare for quizzes, tests, and exams, allowing you to confidently ace them. Quizard is free to use! With Quizard, you can get the help you need to understand the material and gain a better understanding of the subject. Quizard is the perfect homework helper and personal tutor, providing you with the answers you need to succeed. With Quizard, you can get help with your homework and studying, so you can get better grades and have more free time. Stop struggling with your homework and start using Quizard today! Fine print: • Payment will be charged to your Apple ID account at the confirmation of purchase. • Offers and pricing are subject to change without notice. Terms of Use: https://lovely-vault-f15.notion.site/Terms-of-Use-18a469738fd74c9bb7c919981de4bbcd Privacy policy: https://lovely-vault-f15.notion.site/Privacy-Policy-4fe9e56db4a04d88af6e1b78f2874a7d Suggestions or questions? Email us at [email protected] TikTok: @quizard.ai Instagram: @quizard.ai

Version 1.9.9

Quizard is ready for back to school!

Ratings and Reviews

34K Ratings

Trivia Meets Kaleidoscopic Chaos!

Quizzard might just be the hidden gem in the app store, assuming you like your learning served with a heaping spoonful of whimsy and a side of technicolor mayhem. The interface could be described as a unicorn's dream, painted in every hue of the rainbow and then some. It's so cheerfully bright, you'll forget whether you're here to learn or to play a round of digital laser tag. But it’s not all about looks; Quizzard delivers content with a zesty twist that keeps you on your toes. Trivia questions that make your brain do somersaults are the norm here. Ever wanted to decode the molecular structure of caffeine in under a minute or guess Shakespeare's favorite cheese? Quizzard makes such intellectual gymnastics delightful, and you’ll chuckle as much as you'll ponder. Plus, the ads, while frequent, are an adventure in themselves, offering you snippets of the outside world at the most unexpected moments. It’s like getting commercial breaks during your personal game show—annoying but part of the fun. So, strap in for a quiz experience that’s as entertaining as it is enlightening, where every question is a surprise party for your neurons!

GREAT LEARNING TOOL MADE BY A GENIUS DUDE!!! Quizard reads your question and like searches the web for similar information to come up with an answer. Quizard provides a paragraph explanation along with the short answer. READ THOROUGHLY bc it is a computer and sometimes the wording makes it come up with “the wrong (short) answer” even though throughout the (longer paragraph) explanation you can figure out the true answer that Quizard happened to word incorrectly or chose a similar but wrong multiple choice option for. If you’re not trying using it for just the short answer not bothering to read and check the answer and dont read the paragraph then ya.. some of your answers are gonna be wrong. But if it doesn’t give you the right answer it’ll at least provide some explanation to put you on the right path.

DO NOT GET THIS APP!

So, I’m in 4th grade, 4TH GRADE! & IT COULDN’T HELP ME CORRECTLY! So, you know in elementary school papers, & the printer will add these little pictures to the side, well, when i took a picture of this paper, quizard told me that “ I’m sorry, there’s a object in this paper, i cannot tell you the correct answer unless you cover it” ….. IM SORRY! IS A SMALL PICTURE DISTRACTING YOU!? & HOW IS PUTTING SOMETHING OVER IT GOING TO HELP!? Mm!? Well, i cover it, & it is so stupid! It can’t even proofread! It told me that the words that were “incorrect” (by the way, i fact checked it, & the words were correct) & it tells me that the correct answer for gymnasium is “gymnasuim” …i’m sorry, did you just make up a word? WHAT KIND OF AI ARE YOU!? So, i tell it that it’s incorrect, it’s actually “gymnasium” & it tells me, “ I’m sorry for the inconvenience, but can you explain the answer’s to me?” ….. WHY DO YOU THINK I GOT THIS APP!? I mean like, it’s not like I wanted YOU to explain it to me! So, yeah, I'm not going to sit there & waist my time trying to explain a ELEMENTARY SCHOOL PAPER TO AN AI! So, I definitely DON’T recommend this app. ( it’s not even worth 1 star )

App Privacy

The developer, Quizard AI, Inc. , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

Data Used to Track You

The following data may be used to track you across apps and websites owned by other companies:

Data Not Linked to You

The following data may be collected but it is not linked to your identity:

• Identifiers

Privacy practices may vary, for example, based on the features you use or your age. Learn More

Information

• Unlimited answers weekly $6.99
• quizard pro - monthly $9.99
• Quizard Pro Yearly $59.99
• quizard pro - monthly $19.99
• Yearly Quizard Pro $39.99
• Quizard Pro Yearly $89.99
• Yearly Quizard Pro $29.99
• Quizard pro 6 months $49.99
• Quizard pro 6 months $69.99
• Quizard Pro $39.99
• App Support
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Generative AI Transformed English Homework. Math Is Next

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ChatGPT has already wreaked havoc on classrooms and changed how teachers approach writing homework, since OpenAI publicly launched the generative AI chatbot in late 2022. School administrators rushed to try to detect AI-generated essays , and in turn, students scrambled to find out how to cloak their synthetic compositions. But by focusing on writing assignments, educators let another seismic shift take place in the periphery: students using AI more often to complete math homework too.

Right now, high schoolers and college students around the country are experimenting with free smartphone apps that help complete their math homework using generative AI . One of the most popular options on campus right now is the Gauth app , with millions of downloads. It’s owned by ByteDance, which is also TikTok’s parent company.

The Gauth app first launched in 2019 with a primary focus on mathematics, but soon expanded to other subjects as well, like chemistry and physics. It’s grown in relevance, and neared the top of smartphone download lists earlier this year for the education category. Students seem to love it. With hundreds of thousands of primarily positive reviews, Gauth has a favorable 4.8 star rating in the Apple App Store and Google Play Store .

All students have to do after downloading the app is point their smartphone at a homework problem, printed or handwritten, and then make sure any relevant information is inside of the image crop. Then Gauth’s AI model generates a step-by-step guide, often with the correct answer.

From our testing on high-school-level algebra and geometry homework samples, Gauth’s AI tool didn’t deliver A+ results and particularly struggled with some graphing questions. It performed well enough to get around a low B grade or a high C average on the homework we fed it. Not perfect, but also likely good enough to satisfy bored students who'd rather spend their time after school doing literally anything else.

The app struggled more on higher levels of math, like Calculus 2 problems, so students further along in their educational journey may find less utility in this current generation of AI homework-solving apps.

Yes, generative AI tools , with a foundation in natural language processing, are known for failing to generate accurate answers when presented with complex math equations. But researchers are focused on improving AI’s abilities in this sector, and an entry-level high school math class is likely well within the reach of current AI homework apps. Will has even written about how researchers at Google DeepMind are ecstatic about recent results from testing a math-focused large language model, called AlphaProof , on problems shown at this year’s International Math Olympiad.

To be fair, Gauth positions itself as an AI study company that’s there to “ace your homework” and help with difficult problems, rather than a cheating aid. The company even goes so far as to include an “ Honor Code ” on its website dictating proper usage. “Resist the temptation to use Gauth in ways that go against your values or school’s expectations,” reads the company’s website. So basically, Gauth implicitly acknowledges impulsive teenagers may use the app for much more than the occasional stumper, and wants them to pinkie promise that they’ll behave.

Prior to publication, a spokesperson for ByteDance did not answer a list of questions about the Gauth app when contacted by WIRED over email.

It’s easy to focus on Gauth’s limitations, but millions of students now have a free app in their pocket that can walk them through various math problems in seconds , with decent accuracy. This concept would be almost inconceivable to students from even a few years ago.

You could argue that Gauth promotes accessibility for students who don’t have access to quality education or who process information at a slower pace than their teacher’s curriculum. It’s a perspective shared by proponents of using AI tools, like ChatGPT, in the classroom. As long as the students all make it to the same destination, who cares what path they took on the journey? And isn’t this just the next evolution in our available math tools? We moved on from the abacus to the graphing calculator, so why not envision generative AI as another critical step forward?

I see value in teachers thoughtfully employing AI in the classroom for specific lessons or to provide students with more personalized practice questions. But I can’t get out of my head how this app, if students overly rely on it, could hollow out future generations’ critical thinking skills—often gleaned from powering through frustrating math classes and tough homework assignments. (I totally get it, though, as an English major.)

Educational leaders are missing the holistic picture if they continue to focus on AI-generated essays as the primary threat that could undermine the current approach to teaching. Instead of arduous assignments to complete outside of class, maybe centering in-class math practice could continue to facilitate positive learning outcomes in the age of AI.

If Gauth and apps like it eventually lead to the demise of math homework for high schoolers, throngs of students will breathe a collective sigh of relief. How will parents and educators respond? I’m not so sure. That remains an open question, and one for which Gauth can’t calculate an answer yet either.

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

By Bill Whitaker

Updated on: September 1, 2024 / 7:00 PM EDT / CBS News

This is an updated version of a story first published on May 5, 2024. The original video can be viewed  here . 

For many high school students returning to class this month, it may seem like 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 two thousand years. 

We met Calcea Johnson and Ne'Kiya Jackson, at their all-girls Catholic high school in New Orleans. And, as we first reported this past spring, 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 convent 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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