February 15, 2022

Best Books To Get Middle Schoolers Into Reading

Lots of middle schoolers say that reading simply isn’t for them. School is partly to blame for this, as reading often gets turned into a chore rather than something for enjoyment (though many teachers do try their best to make it fun–some successfully, others not so much.) But that doesn’t mean reading can’t turn back into something enjoyable. It’s simply a matter of finding the right book. This is just a shortlist of recommendations covering various genres and styles. If one of these sounds interesting, there’s a good chance there are more books by either the same author or similar ones that you’ll love too. Not to mention most of these have a movie or tv show adaption to watch after (or before, I won’t judge!) 

    • Ender’s Game by Orson Scott Card 
      • Ender’s Game is a book that every sci-fi should read and enjoy. It has everything: aliens, video games, adventure, and an extraordinary but complicated protagonist. Written in the 1980s but set in the very distant future, Ender Wiggins is a child genius selected to study in an elite school to train to fight the Buggers, the aliens that Earth is locked in war with. It’s a bit of a longer book at over 300 pages, but it’s packed with intense fight scenes set in zero gravity and interesting plots as Ender tries to figure out his place in the school–and in the war. Ender’s Game also got made into a movie starring Asa Butterfield and Harrison Ford in 2013. Orson Scott Card also wrote lots of spin-offs and sequels, so if you fall in love with the world and history, there’s plenty more to read!
    • Holes by Louis Sachar
      • This is a classic coming-of-age book (and also one of my favorite movies) that’s about friendship, cruelty, and good ol’ karma. It follows Stanley Yelnats, who is seemingly cursed with bad luck and gets falsely accused of stealing a pair of famous shoes that were donated to a homeless shelter. As punishment, he is sent out to Camp Green Lake (which isn’t green or a lake at all) and is forced to dig holes all day in the heat. There, he meets unlikely friends like Zero, another kid at the camp, and some enemies, such as the cruel Warden who has rattlesnake poison in her nail polish. The book is full of twists and keeps you hooked till the very last word. 
    • Wonder by R. J. Palacio
      • Now, I’m going to be honest–this book is a tear-jerker. My 6th-grade teacher Mrs. Bodenmiller read this to us during class sometimes and I never remember a classroom full of tweens being so quiet and attentive before (except for when Bill Nye was on.) Wonder is about a young boy named August Pullman starting his first day at middle school. That’s scary enough for any typical 10 year old, but August isn’t exactly normal; he was born with a facial deformity and needed several surgeries throughout his life, leading him to be homeschooled and to constantly wear an astronaut’s helmet on his head. While it’s clear this story is a sad one, it’s also a funny and profound one about love and humanity. And, like many great books, it got made into a Julia Roberts movie in 2017.
    • The Outsiders by S. E. Hinton
      • This is a classic book that your parents probably read in middle school. Lots of schools even assign it, but that doesn’t mean it’s just some boring old book. The Outsiders is about a group of greasers living in Oklahoma and if you enjoyed Grease or West Side Story, this is the book for you. The main character is Ponyboy, the youngest in the little gang he is in with his brothers and his friends, and it follows their misadventures and interactions with the kids from the other side of the tracks. At less than 200 pages, it’s a short but action-packed novel that proves why teens still read it 55 years later. The 1983 movie adaptation is also a star-studded masterpiece for fans of classic 80s movies. 
    • Inkheart by Cornelia Funke
      • This book is kinda like the Inception of books and it’s every bit as cool as its movie counterpart. This contemporary fantasy adventure novel is about a young girl and her father who is able to have things come out of books simply by reading it out loud. But there is a price to pay for this great power–something must go into the book in return. One day, Maggie’s father Mo is captured by strange people and she must go on an adventure to get him back. This book is critically acclaimed for a reason and got made into a movie starring Brendan Fraiser in 2008. With themes about family and pride, and great references to other famous books, this book is a great fit for anybody (especially if you find someone to read it out loud for you!) Not to mention, it’s also the first of a trilogy.
    • The Mortal Instruments series by Cassandra Clare
      • This is by far the biggest book, and biggest series, on this list but it’s a great one for fans of fantasy, romance, and action. With six books in the series, a prequel trilogy, a sequel trilogy, a movie, and a tv show, this franchise has enough content to rival Star Wars. But once you get sucked into this world of shadowhunters, Nephilim, demons, warlocks, and angels, it’s hard to get out of it. Clarissa Frey is our main character (of the main series, at least) and it chronicles her journey in discovering her family history and heritage that was kept hidden from her all her life. With lots of action, sarcasm, and romance, it’s a great middle school read (and worth a lot of AR points too!)
    • Mysterious Benedict Society  by Trenton Lee Stewart 
      • This quartet of books is perfect for those who are naturally curious and feel a bit like outsiders. This spy/mystery/adventure book follows for exceptionally gifted children under the tutelage of the mysterious Nicholas Benedict who need their help to save the world from his evil twin sister. It’s on par with the classic Jame Bond spy movies (and I mean the Sean Connery ones, not the new ones.) Disney even made a tv series based on the books in 2021 with the hilarious Tony Hale.
    • Roll of Thunder, Hear My Cry by Mildred D. Taylor
      • This is another one of those books that’s important for any teenager to read in America (and not surprisingly, it’s been banned in a lot of schools too.) Set in 1930s Mississippi, 9-year-old Cassie Logan tries to navigate the difficult and racist life of the Jim Crow south. It’s a powerful book about power, not just with people but with land too.  The 1978 movie is also definitely worth watching too, with Morgan Freeman playing Uncle Hammer. It’s one of timeless and brutal African-American fiction books. And its descriptions of deep southern living make its 250+ page count feel too short. 


    • Scythe by Neal Shusterman
      • I’m going to level with you here—this is the only book on this list I haven’t read. It was recommended by a friend while I was doing research for this article. But after doing a little digging, I can see why. In a perfect future with no misery, no war, and no disease, this perfect utopia comes at a deadly price; select few called Scythes are chosen to kill others to keep the population and world in order. Crazy, right? Two teens, Citra and Rowan are chosen to be apprentices and learn about this deadly underside to their world. While this is the only one on the list without a silver screen adaption, it is rumored to be in the works.  It’s one of the few YA books that’s made my to-read list and I hope it will make yours too. 


    • Anything by John Green
      • I know this isn’t exactly a conventional entry is a list of books to read, but trust me on this: all John Green books are worth the read. My godfather actually got me all of his books in 7th grade (after asking his AP Literature class for help) and I finished all of them within 2 weeks. Out of all his books, the one I would recommend the most is Paper Towns, as I think it’s a book that every teen will relate to at some point in their lives. And for the rebels out there, Green’s book Looking for Alaska actually got banned in many schools and libraries.  I’m not going to give any summaries, unlike the other books, because I think these are best experienced going in blind. Just maybe have a few tissue boxes on hand.
February 1, 2022

This Portland Neighborhood May Be The Suburbia Oasis You’re Looking For

Ever wondered if Portland could be a home for you? Well, with their increasing popularity and diverse personality, there’s a fit for everyone!

America is home to so many cities with an individual energy like no others. Of course you know the infamous NYC and Los Angeles, maybe you’ve been to Chicago or took a trip to Denver. All of them have something refreshing to offer their residents just as much as their visitors. It’s super incredible to be able to absorb the wonderful communities + cultures that fortified the flourishing of these cities.

Of course, there are some that have ascended to be up and coming places to reside. With the constant evolution of humanity and its expanding experience, cities take on the personalities of those who enliven it with their own interests and values. A city to have become extremely popular within the last few years is located in the Pacific Northwest, a green haven for many.

It’s Portland, Oregon!


About Portland

Portland is quite a distinct city known for a variety of compelling characteristics such as their ecofriendliness, progressive demographic, and vast amount of outdoorsy outlets. 

It’s home to an assortment of fabulous storefronts, cuisine, live music, and microbreweries that appeal to many of its inhabitants. If you’re looking for things to do outside eating and shopping, there’s an assortment of art museums, luscious parks, and many MANY bicycle routes! Both outdoor and indoor enthusiasts can find something they’ll enjoy in Portland. For such a big city, it embodies a very tight knit, small town atmosphere to it.

Oregon’s largest city is home to quite a few special spots. Did you know that Portland is home to one of the largest urban forests in the United States? That’s right- Forest Park sits at 5200 acres and is THE place to enjoy nature if you’re visiting or residing in the city! And if nature isn’t your thing, no worries; the largest independent bookstore, Powell Books, is found right in the heart of the bustling metropolis!

An appealing living aspect of Portland is its comparably low living expenses; it’s one of the most inexpensive places to live on the West Coast! And because of Oregon’s state mandates, there’s no sales tax either! As for transportation, you do NOT necessarily need a car in Portland to enjoy what it has to offer! It’s one of the most bicycle friendly places in the world, and it also offers public transportation as well!

Regardless if you’re just passing through or making it your newest home, Portland is for sure able to accommodate your every need and satisfy every passion!


One of Portland’s GEM Neighborhoods

Like all major cities, Portland has a copious amount of neighborhoods. The city is split into five major regions dependent upon their cardinal placement, each containing unique neighborhoods. All of them possess specific perks; they vary depending upon your own demographic and what you’re looking for! 

If you’re a young professional looking for a great social life and freedom to explore on foot, you may enjoy a more central or downtown area compared to more family-oriented individuals! It’s always advised to do your research when finding your home in Portland!

Of course, there are some happy mediums that converge quiet with lively. One of the best places to live is the neighborhood known as Eastmoreland- not only is it a top ranked place to live in Portland, but also in the state of Oregon as a WHOLE!

Located in what many categorize as the southeast region of the city, Eastmoreland attracts many different people. It’s a mostly liberal demographic, home to young professionals AND families which constitutes a community that is both engaging and reliable.

As for living situations and options, most residents own their homes; HOWEVER, some rent, but it’s an almost entirely residential area. This neighborhood has its fair share of high-end residencies; if you drive down the winding roads of Eastmoreland, especially near its golf course, you’ll lay eyes on beautiful homes and fine greenery!

If you’re someone raising or starting a family, Eastmoreland definitely has some lovely schooling options! With 26 amazing options for public schooling, Some of these institutions include Le Monde French Immersion Public Charter School, Emerson School, and Winterhaven School. If you want a private school, you’ve got well over 100 options! Northwest Academy, St. Mary’s, and Central Catholic High School are just to name a few!

Outside of the more permanent long-term amenities, there’s so much fun to do, too! The Woodstock Farmer’s Market is open from June to November with bountiful yummy food! More year round activities include the Crystal Springs Rhododendron Garden, Oaks Amusement Park, Studio One Theaters, even Oregon Museum of Science and Industry.

Luckily, the public transportation can also help you out when exploring these enthralling experiences!


What Are You Waiting For?

If you’re thinking about relocating to somewhere exciting and new, look no further! Do your own research on the city of Portland; you can check out this city guide and informational site to learn more!

January 1, 2022

How To Get Into One of the Best Schools in the Portland Are

What makes Catlin Gabel School so incredible as an academic institution- and what it takes to be admitted as a student!


Education has proven essential to many states and their instituted curriculums. All grades of varying levels and parameters all have their important place in the greater cultivation of a comprehensive learned knowledge. More importantly, school curriculums also make for a wonderful opportunity to broaden and exercise crucial life skills.

A very particular, exemplary location that emphasizes education is located in Oregon- Portland, specifically. Within Portland is a school that rises above many others with progressive measures to ensure their student body experiences the same caliber of transformational growth. This school is known as the Catlin Gabel School!


About Catlin Gabel School In Portland, OR

Catlin Gabel school is a private institution; they educate all grades from Preschool (PreK) up through the 12th grade. The grades themselves are separated into three distinct schools: Beginning & Lower School (PreK-5th), Middle School (6th-8th), and finally Upper School (9th-12th). Although the various levels of education are categorized based upon closeness in age & maturity, Catlin Gabel has a strong, tight-knit community fueled by consistent efforts of ethical and academic value.

This school has a very humanistic, enlightened approach to their schooling; they refer to it as “student-centered education”. According to their website, student-centered education was designed so that students “are encouraged to pursue their interests and exercise their natural curiosity”. By placing the student’s passions and skills at the center, they are able to “become active learners… to discover the pleasures and rewards of education and develop into adults for whom learning is a lifelong pursuit”.

What does this entail? Well, it’s an education dedicated to supporting original thinking skills, which overall strengthens self-awareness for real life scenarios. This fortifies the student body’s responsibility to take action in their communities, helps them with problem solving and creates space to “foster a curiosity” about life. Catlin Gabel teaches the WHOLE student, which means they develop learning modalities to best embrace the growth of their entire self. 

Educators have a BIG role to play in the deliverance of this powerful mission. Their communication with students is very responsive yet differentiated to reaffirm every individual’s own style of learning. Not only that, but educators inhabit a professional curiosity about the wholeness of the students; for instance, they don’t just focus on their academic skills but their interpersonal, physical, emotional, and ethical sense of selves. 

An empowering approach to Catlin Gabel’s education is their prioritization of discourse about power and privilege. This aids in the embodiment of diversity and inclusion within the curriculum and sees all backgrounds of the students as valid!


How To Get Into This Reputable School

Because Catlin Gabel School is an independent and private institution, admission is entirely based on a selection process. However, Catlin Gabel has provided an integrative application process combining forms with events.

First, there’s an official Admission Inquiry Form for the family of the prospective student to complete; this gains them access to an important admissions portal. Then, they are granted the steps to learn more about the parameters of the admissions and school in its entire entity.

Access to the online portal is integral, being that it’s where you can register for events and complete the official Catlin Gabel application. There are admissions events, both in-person and virtual, for the applicants interested in attending the coming school year. 

Now, there are a few different kinds of admissions events, depending upon the school you’re applying to. There are general information sessions, which are a GREAT chance to speak to Catlin Gable faculty. By creating an opportunity for educators to speak about the Catlin Gabel experience, families will  effectively learn about important school aspects such as curriculum, scheduling, extracurriculars, grading, resources, even financial assistance!

The earlier grades have a slightly more individualized session. There are drop in Q&As for specifically the beginning and Lower School. Being that this school offers education for much younger ages, there’s an opportunity for those who have particular questions to ask the personnel working at the school to answer them transparently. 

Once the events are attended, all the families have to do is complete an actual application. This encompasses varying assessments such as confidential teacher evaluations, prompted questions for both students AND their parents, school records, notes about the student’s visit. Catlin has a web page designed to share the detailed answers to common questions about the enrollment process

Catlin Gabel makes it quite easy to schedule a convenient visit to the school so the families are impassioned by the school’s environment to know they’re making the right choice. The careful consideration of the families also delves deep into processes that occur after the initial enrollment; financial assistance is one of them. More than a quarter of the student body receives need-based tuition as well as merit scholarships as forms of financial assistance (given a qualified application for it).



All in all, Catlin Gabel conducts a personable experience from the moment a family peaks interest in them. They sure live up to the tedious application process with great community engagement and consistent performance as a whole. If you’d like to learn more about this school or make a call to visit, check out their website.

December 26, 2021

The Beaverton Academy of Science and Engineering

Portland’s Passion for Specialized Education: The Beaverton Academy of Science and Engineering


An especially rigorous and specialized academy located in the greater Portland area, the opportunities they provide, and what it takes to get in

It’s no secret the past couple of years have been WONDROUSLY revolutionary in Portland’s education system. They’ve taken measures in revitalizing their take on education by unlearning ideologies that hinder the future of our society from breaching the societal confines of race & ethnicity to instill unity. 

Portland has received quite the amount of attention for taking a progressive stance on converging ethnic studies within schooling. They believe that EVERY and all students of varying backgrounds deserve an unbiased chance at pursuing their passions and achieving great success. 

A prominent example of this motif is the wide acceptance and enthusiasm some of Portland’s niche schools inhabit. A great example lies in Hillsboro, OR; in the Beaverton school district is a school known as the Beaverton Academy of Science and Engineering (BASE).


What is BASE?

Ranked as both Niche’s TOP public AND magnet high school in the entire state of Oregon, BASE strives to provide diversified community opportunities to succeed in innovative and collaborative work so they’re best prepared for the world beyond secondary education.

The BASE is a magnet program rooted in math, technology, and life science. It’s a learning option for grades 9 through 12, however, they do have a middle school curriculum for grades 6 through 8. Their middle school program was crafted to introduce many of the topics offered in the high school; they formulated a nine-week rotational system for the sixth and seventh-grade students to explore Computer Science, Engineering, Biomedical Studies, and Art. Eighth grade is when they start to partake in semester-long classes so they have a more solidified idea about their passions to fully embark on in high school.

In the high school program, there are three pathway options: Biomedical Studies, Engineering, or Computer Science. All in all, despite the chosen pathway, the institution has an Expeditionary Learning (EL) approach. This means students “experience expeditions (real-world, in-depth studies both inside and outside the classroom), share their learning and achievements with authentic audiences through public exhibitions, and belong to a Crew (EL’s advisory vehicle for fostering relationships and the habits of scholarship that every student needs to be successful)”.

The BASE does have quite intensive educational avenues. Aside from their foundational pathways of learning and core curriculum, coursework such as Advanced Placement and AVID are offered to align with the specialty of their magnet program. They even have intensive summer programs for those who want to move at a quicker pace and prepare for the next course!

The school’s emphasis on academic intensity requires quite an amount of academic integrity to support it. They encompass the importance of understanding plagiarism and how it negatively affects one’s education both in and out of the classroom. Not only that, they do require a certain level of dedication and consistency in attendance; the coursework is so accelerated compared to traditional education, a student’s presence is key to maintaining optimal learning retention.

But not to worry, BASE has loads of resources for students like academic support & counseling to ensure they receive all they can for success. Upperclassmen have the luxury of being offered College & Career based counseling so they feel validated and encouraged to make the decisions best for themselves and their future.

Outside of their academic life, BASE is a very tight-knit community. There’s an assortment of student clubs & organizations to allot time for extracurricular interests! Because this is a magnet school, there are no athletic teams for the students to join. Instead, they are allowed to try out and/or join their neighborhood teams! They must contact or research their neighborhood school’s athletic department for more information on how they can participate in sports.

Contrary to popular belief, this school does have an artistic side. There’s a program known as BASE Productions where students can explore their curiosity in art and film production! Celebrating and applying their creative skills serves as a great outlet to strengthen their communication as well. The film aspect of this program ties into the focus of technology at BASE, too!

If you want to explore everything BASE offers, check out their website..


How to Enroll in BASE

Due to the competitive nature of being a magnet program, BASE encourages all prospective students to go through their application process.

The application process is only open for a certain amount of time and involves different due dates for parts of the application.

A selection committee requires information and exemplification of the well-roundedness and the prospective student has to offer. They aim to make this just as beneficial of a match for the school as they do for the student themselves. 

To apply, a student must provide previous transcripts, grades, basic information, and answer a series of questions. There is also a possibility of requiring letters of recommendation from educators who interact with the student candidly and constantly.

It’s beneficial to attend, or in the case of COVID-19, watch the open house BASE offers to fully encompass their mission and who they are as a school. They also have a virtual tour of the school grounds to get a sense of what the future of the prospective student may hold!

If you have particular questions about BASE, you can contact them!

December 10, 2021

A Universe of Education

The Top Public AND Private Institutions in the Portland, OR Area

Amidst the years of educational evolution, the Pacific Northwest has become a centralized hub of wealthy knowledge and activism for a revolutionized approach to schooling. One of their more popular focal locations exemplary of this movement is Portland, Oregon!

Portland has proven to be more on the progressive side. They prioritize a positive relationship with nature, the people, and most importantly the deep understanding of diversity to establish comprehensive inclusion efforts. Historically, Portland has become a home for a multitude of unique schools that signify this mission.

There are private, public, boarding, and even religious institutions that all strive to give their student body the best resources and learning possible for a fulfilled life.

Who are some of these outstanding schools? Well, take a look!

Ten of the BEST Schools in the Portland Area

Catlin Gabel School: Catlin Gabel is an exceptional, nationally recognized, progressive, independent day school; it was declared as Niche’s 2022 Top School in Oregon! They defy the traditional academic standard by utilizing an inquiry based style of learning, which means they foster creative thinking through the deliverance of experiential learning. They do this through They claim that they “educate for democracy” and incorporate discussions about power and privilege into their classwork.

Oregon Episcopal School: Much like Catlin Gabel, OES offers an inquiry-based education to “prepare students for lifelong learning”. As a K-12 school located in Southwest Portland, they’re very much a “learning-by-doing” institution; they believe action is the best way to retain knowledge! With small-sized classes and year-long research projects, OES cultivates a seamless and connected education for their pupils.

Jesuit High School: This is a nonprofit coed college prep school a part of a 450-year Jesuit educational tradition! They combine their holistic view of learning with educational philosophy focusing on the WHOLE of the student rather than just their intellectual talent. They do use the seven themes of Catholic Social Teaching as well as the Four  Universal Apostolic Preferences to guide their devout Jesuit work.

Beaverton Academy of Science and Engineering: BASE is a specialized academy passionate about creating a collaborative learning environment for real-life innovation. They’re focused on biomedical, engineering, and computer science education for future expertise! They craft pathways for each of the subjects taught to ensure the student receives the most integrative education possible so they enter their desired fields with profound life skills and advanced knowledge!

Northwest Academy: NWA is also ranked as a Niche 2022 Top School in Oregon! They emphasize the cultural impact of various influences, particularly their urban location AND expression through the arts. They have an entire corridor dedicated to showcasing Portland’s cultural resources! The school also exemplifies a passion for performing and visual arts; their academics consistently incorporate artistic disciplines to nourish more balanced and creative thinkers.

St. Mary’s Academy: St. Mary’s is Oregon’s oldest continuously operating secondary educational institution! It’s a Catholic all-girls college prep school in the hub of Portland that nurtures both the spiritual and cultural development of every student. Because of their close proximity to a number of popular locations in the city, including Portland State University, the young ladies are encouraged to utilize their surroundings to apply their education grounded in the Catholic faith.

Valley Catholic School: This is another, more religious option for schooling within the greater Portland area! They offer education from PreK through grade 12, but begin college preparatory efforts beginning in the middle school grades. A particularly interesting and unique education Valley Catholic offers is a music school! They offer private lessons for both children and adult amidst the school year!

International School of Beaverton- High School: ISB centers their education our intercultural respect as well as intellectual rigor for the most prepared of pupils for their future lives. They are recognized by the International Baccalaureate Organization as an IB World School, which means they have a worldwide curriculum able to cater to all diverse backgrounds. They offer both Middle School (grades 6-10) and High School (grades 11-12) programs.

Central Catholic High School: Integrating a Catholic worldview with an arduous education creates a strong community for learning and faith. Aside from their 14 honors courses and 13 AP courses, theology is deeply ingrained into the experience. Students partake in courses such as Scripture, Church History, Sacraments, Liturgy & Prayer, Moral Theology, Social Justice, and Christian Relationships.

Lakeridge High School: Ranked in the Top 5 PUBLIC High Schools near Portland, Lakeridge is a comprehensive four-year secondary academy crafted to strengthen and nurture college-bound students. They have an alternating schedule with lengthy allotments for fewer courses in a day to give them the attention and rigor necessary for optimal retainment! They do provide extracurriculars and subjects beyond the norm to ensure all passions of the student body are recognized and validated.

August 18, 2021

Is zero a rational number?

If you are currently studying integers in your math class, you may find that rational numbers are the next topic addressed by your teacher. They may ask the class “is zero a rational number?” Although you know the definition of a rational number, this question can stop you in your tracks.

Knowing basic properties regarding integers and rational numbers may seem like a one-time lesson in your mathematics career, but being able to fully comprehend the purpose and the rules of rational numbers can directly help you with other complicated math concepts. Instead of just thinking the old narrative that learning a math lesson will only pertain to your specific lesson, quizzes, and tests, truly understanding rational numbers can help you learn how to solve multi-step problems in the future.

In addition, learning rational numbers and mastering integers helps you to understand how these math concepts all relate to one another as you progress in your education. Learning the relationship between rational numbers makes mathematics easier to understand as a whole.

By using critical thinking skills to find answers to questions such as “is zero a rational number?”, you can help simplify complicated equations and find the solution. 

First – what is a rational number?

Before you can determine if zero is a rational number, we need to brush up on your definition of rational numbers. A rational number is any number that can be presented as a over b, where b is not equal to zero. Like this:

Therefore, practically every fraction that you have worked with in the past can be defined as a rational number. The only condition is that the “bottom” number in the fraction – also known as the denominator – cannot be equal to zero. Therefore, all whole numbers are rational, since any rational whole number can be expressed as a fraction with 1 in the denominator slot.


But how can you identify rational numbers from irrational numbers? Irrational numbers are not able to follow the rule that it can be presented as a over b, where b is not equal to zero. 


In this case, you might come across irrational numbers that look like the following: 

When looking at a fraction, sometimes the numerator can be zero. This means that a can equal zero, but b is not equal to zero. For new learners, just seeing a zero in the equation can sometimes throw off their thought process. However, keep in mind that a rational number with zero as a numerator can easily be simplified as such: 

Since the greatest common denominator between 0 and 12 is 0, you can simplify a rational number fraction with a zero in the numerator by dividing both integers by zero. If you see a fraction with zero in the numerator, the answer will ALWAYS be zero.  

Examples of rational numbers 

Some examples of rational numbers include ¼, ⅔, 0/1, 8/6, and so on. As you can see, one of the numbers included here was 0 over another number – this is considered a rational number since the denominator is either a positive or negative number and is not equal to zero. 

Operations on rational numbers

Just because a number is a fraction or contains a zero within the fraction, this does not mean arithmetic operations are impossible. Arithmetic operations are the basic processes of functions you can use with integers, including addition, subtraction, multiplication, and division. 

  • With addition, you can add two fractional rational numbers by making the denominator the same value. 
  • When carrying out subtraction, make the denominator the same number before subtracting one rational number from the other one. 
  • In the case of multiplying two rational numbers, make sure you multiply both the numerator and the denominator of the rational numbers.
  • When it comes to dividing a fraction, you must calculate the inverse of the rational number. In this process, switch the numerator and denominator. 
  • For example, 2/4 will then switch to 4/2. You can double-check your work by multiplying the two values together to see if they equal 1, with the equation being (2/4)x(4/2)=1.


What are irrational numbers?

There are clear differences between rational and irrational numbers. Now that you know rational numbers are any type of integer that can be expressed as a/b where b does not equal zero, you can narrow down all integers that do not follow this formula to be considered irrational numbers. 

Rational numbers are either positive numbers, negative numbers, or equivalent to zero. However, irrational numbers cannot be written in the form of a/b, but must be written as a decimal. 

One of the most common irrational numbers is Pi (), which has endless digits after the decimal point. If you have studied geometry in the past, you know that Pi is the ratio of the circumference of a circle to its diameter – a number that comes out to approximately 3.14. However, this solution is just an approximation, but not accurate enough to be written as a fraction or classified as a rational number. Since the decimal digits of Pi are nearly infinite, you cannot use a simple fraction that represents Pi. 

Furthermore, Euler’s number () is another irrational number that cannot be simplified or written as a fraction. This number is the base of natural logarithms and is an important concept used in the exponential function. Euler’s number is typically written as 2.718, but contains over 1 trillion digits in the decimal – making it impossible to compose in fractional form. 

Another common irrational number is the Golden Ratio (), a ratio called “divine proportion”. This unique ratio is a common number that is found in various aspects of our life and culture, not just in mathematics. Appearing in paintings, artwork, sculptures, and buildings, the Golden Ratio is known for being aesthetically pleasing. This number is typically approximated as 1.618, but cannot be expressed in simple fraction form. 

So – is zero a rational number?

Now that you know the difference between rational and irrational numbers, you may still be asking yourself – is zero a rational number? You know that zero cannot be the denominator of a rational number, since this would classify the rational function as undefined. However, zero can be the numerator in a fraction, which qualifies zero as an eligible rational number. 

Since zero is an integer, it can be written as A in the formula A/B (ex: 0/1, 0/3, 0/6, etc.). Writing zero as the numerator over a positive or negative denominator confirms that zero can be considered a rational number (ex: 0/2, 0/-2, etc.). 

Keep in mind that 0 cannot be used as a denominator in a rational number equation. If this was the case, any number divided by 0 would result in infinity – as we learned earlier, irrational numbers cannot be written as a fraction with integers as both the numerator and denominator. Any integer divided by 0 is an irrational number. 

Why is it important to know if zero is a rational number?

If you are struggling in your math class and you have finally cracked the code to the rational vs. irrational number debate you might still be wondering how this will help you understand difficult math concepts.

Knowing that zero is a rational number can give you deeper insight as to how integers can be calculated and how they function within different equations. Being able to distinguish between rational and irrational numbers can help you understand more difficult concepts that you previously had a difficult time understanding. 

Learning rational numbers, understanding how to interpret rational numbers, and identifying rational vs. irrational numbers can help students understand how to represent rational numbers when composing equations, how to determine which fractions are greater than others, and how to simplify rational numbers in fractional form.

July 23, 2021

How To Find A Statistics Tutor

“As with almost anything, you benefit most by being taught by someone who has a solid knowledge of the fundamentals, has real world experience in the area, and has the ability to communicate effectively.” 
― Ron Glaser, P.H.D., retired US Government statistician and retired UC Davis Statistics Professor, on finding the right statistics tutor.

If you are looking for a statistics tutor, there is a good probability you are looking at a math syllabus full of unusual words: biostatistics, linear models, regression analysis, data mining, survey sampling—that kind of thing.

Statistics isn’t like algebra or geometry, it’s a whole other animal. Even calculus professors can be lousy when it comes to statistics. And if you need help, you may find your math tutor doesn’t make the best statistics teacher either. So, where do you find the elusive statistics pro? Craigslist? The local college career office? Is there a young, fun descendant of the Father of Modern Statistics Sir Ronald Aylmer Fisher living in Portland?

If you actively seek out a statistics specialist, there’s a ninety-nine percent chance you will find what you’re looking for. But if you want a 100% guarantee, here’s what you need to do…

Where to Find a Statistics Tutor

If you sense you need help in statistics, you are already ahead of the curve. Many struggling students can be too stubborn to get help and end up tanking their grade point average by attempting to take on statistics on their own. If they pursue a career that uses statistics, such as sales or computer programming, they might be at a loss, frantically searching the internet for a review course. But it doesn’t have to be that way!

It’s important for anyone seeking a career that involves statistics to find a statistics tutor with a well-rounded understanding of both statistical computations and how it relates to a career in data science or statistics. The best place to find private statistics tutors is online. Don’t be overwhelmed with all the tutoring websites out there because there are ways to trim the fat and find the perfect fit.

Look for websites that have been around for a while, have helpful contact information, and use official email addresses or phone lines (as opposed to tutors’ personal contact information, which can be a sign of inexperience as a business). Another trait of a trustworthy tutoring site is a review section where users can provide feedback on their tutoring experience. This way you can validate a good reputation within your local tutoring community.

What Qualifications Should Your Tutor Have?

According to Ron Glaser, a retired Lawrence Livermore Lab statistician and university statistics professor, it’s ideal to find a tutor who has a degree in math or statistics, or a college student with marked success in statistics coursework. Glaser would not recommend engineers or scientists who have not had formal statistics training as tutors, because they tend to bluff on knowing lessons students need, but don’t actually know themselves. 

You will need someone who can prepare you for college-level coursework in statistics, which translates to someone who has at least a B.S. in statistics or a closely-related field, such as biostatistics, applied mathematics, or computer science. If you are searching on the Internet, think grad student. If a tutor is actively working toward a Masters or PhD in statistics, they will have the necessary experience to teach course material and apply it to everyday life.

However, having academic experience isn’t always enough. Consider finding someone who has experience applying statistics in the workforce or has experience teaching or tutoring. The combination of education and experience in the field will be your best bet for a statistics tutor.

To take the search one step further, here is a checklist for just some of the key elements we look for when hiring statistics tutors at Tutor Portland

  • Can this tutor explain tough concepts in five different ways?
  • Can this tutor use metaphors that relate to the student’s life?
  • Can this tutor adopt an active approach with in-depth discussions about statistics?
  • Does this tutor embody integrity and virtue? 
  • Can this tutor effectively teach us, the Tutor Portland team, before we hire them?

How much does a good statistics tutor cost and how to ask?

Okay, so you found yourself a qualified tutor named Sir Ronald Aylmer Fisher Jr. and he’s fabulous, but you need to know how much he charges per hour. Here’s a statistic for you: The cost of living in Portland is 29 percent higher than the national average. On a college student’s salary of $21,000 per year, with a meal card from the folks, can you afford a tutor?

Here’s the rundown on the costs: 

At Tutor Portland, for instance, we offer online and in-home tutoring backed by a Better Grades Guarantee for our Portland peeps with different budgets. Let’s say you need a statistics tutor for your coursework at Portland State University. We charge $96 per hour for our Silver Plan academic coaching or $384 monthly for one hour per week. Your hours never expire, rolling over to future months, and the more hours you book, the more discounts you receive. 

If you decide to hire an independent tutor without such payment models, you should consider asking their rates upfront. The more education, work experience, and overall skills the tutor has, the higher the rates may be. And don’t be shy— after all, statistics tutors are used to talking numbers.

How to Get the Most out of a Tutoring Session

It’s all about your personal needs. So the key to maximize your time with a tutor is to study between sessions. By being observant (and hopefully excited) about how statistics play out in the news, in school, in work-life, and at home, you will be mastering the subject in a meaningful way. Then when you meet with your tutor to review the lessons, you can have a deeper understanding of the course material in less time.

Now that You’ve Aced Statistics …  

If statistics clicks with your brain after a tutoring course, you may even choose it as a career. Among the industries that hire statisticians, the median wages range from $70,000 to more than $100,000 per year.  Statisticians are in high demand, and according to Northeastern University, employment for mathematicians and statisticians is expected to grow 30 percent from 2018 to 2028.

Now that you found your tutor who is qualified, affordable, and can get you ahead in your statistics class, what’s next? Maybe another class! TutorPortland offers tutoring in test prep, science, Spanish, and English, so contact us if you’re looking for some extra help.

June 1, 2021

How Tutors can Help Students with English Comprehension

English and reading comprehension is a critical skill that every child needs to learn during their education. Without comprehension, reading, learning, and speaking can be a frustrating task for students. As a teacher, all children must learn the proper skills to understand what they are reading and truly digest the information. 

However, all children learn differently. Some students are auditory learners, whereas others need to see physical examples to fully grasp the concept in the lesson. Due to the wide range of learning styles, public schools and current educational institutions often do not provide the classroom with enough variety for every student to comprehend all topics. 

Without the resources needed to help every individual student, some children fall by the wayside – a dangerous side effect of universal learning that can impact their educational trajectory. 

One solution to helping individual students who may have different needs than what they can find in the classroom is using individual tutors. To better understand a difficult concept and comprehend a book, poem, or story, an English tutor can help students work through the learning blocks in their minds.

What comprises ‘good’ reading and comprehension?

You may have heard your teacher in school talk about ‘good’ reading vs. absent-minded scanning the words on the page without really taking in any of the information.

  • Studies have shown that good readers use various skills while analyzing content that helps them comprehend and retain the information on the page. 
  • Good readers use active processes and skills before, during, and after reading text.

Before reading, active readers will set goals for their assignment, analyze the sentence structure, organization of the text, and outline the text to see what they may be looking for in their analysis and comprehension.

During reading, good readers will ensure they understand each word without skipping words or sentences, as this can change the intended message of the passage. They will simultaneously calculate the meaning of the phrases, sentences, and paragraphs as a whole, while piecing together this information into a comprehensive concept. 

When they are reading, they will focus their attention on the sections of text related to their pre-set goals. For example, if they must look for similes in a body of text, they will focus on scanning for the words ‘as’ or ‘like.’ 

After reading, good readers will analyze what they have just read. They will summarize the major points of the text, tie these major events back to their pre-reading goals, and research any extra information if needed to clarify the content.

What are the advantages of improving English comprehension?

You may think you can skate by without having perfect reading or English comprehension. Like other school subjects, you may think this subject becomes obsolete as you get older and only applies to certain professions and businesses. However, English comprehension is a must-have skill for every member of society. 

Reading comprehension is a crucial part of English literacy, being an important aspect of education, business, and communication. Understanding what is written in front of you gives people the skills to succeed in any occupation. 

Children who properly develop their reading skills can read quicker, absorb information, memorize essential facts, and understand written information higher than those who have fallen behind in school.

Why should I use a tutor for English comprehension?

Tutoring still has a stigma of being for children who are not as smart as others or falling behind in class. However, many children have various learning styles which may not be met through traditional classroom settings. If you find your child is a tactile learner, requires multiple repetitions of the same concept, or enjoys writing down new concepts, hiring a tutor can help your child best retain information and improve reading comprehension. 

Tutoring provides students with individualized attention they cannot receive in a busy classroom. This helps children who feel like they aren’t seen by the teacher or those who want even more school work get the attention they need.

What are the benefits of tutoring?

Tutoring programs help children learn how to study, analyze information, and improve reading comprehension to grasp concepts and stay current with their classwork.

Individual learning experience

By using a tutor, your child will not have to wait to get called on in class or spend time after school visiting each teacher to ask questions about the coursework. Instead of spending their time just trying to play catchup in class, tutors help the student fully understand the current concept in a timely manner.

One-on-one attention

Not only will a tutor help your child learn concepts quicker than in a traditional classroom setting, but the individual attention could be exactly what your child has needed all along. Some children can be easily distracted in class or may just need to ask one or two questions to understand a new topic – but in a crowded classroom, this can become virtually impossible.

Giving your child the ability to work one-on-one with a professional lets them ask questions, discuss topics with the tutor, and be unafraid to say they are struggling with reading comprehension.

Improved academic scores

Tutoring helps your child prepare for their English exams, feel confident going into a test, and understand the test material before sitting down to take the exam. Your child’s grades will subsequently improve from increasing their reading comprehension, bettering their confidence, and feeling ready to handle their current course load. 

Encourages self-directed learning

By teaching life skills and studying methods, tutoring can help your child take the initiative in their school work. You can help control the pace with tutoring to ensure your child is not moving too fast or too slow compared to the other kids in school. Your child will have a say in the speed of the learning program, ensuring he or she fully understands the concept before moving on to the next subject. 

Improves self-esteem

If you are constantly behind in school, your confidence will suffer. Classmates may make fun of you for always struggling, while you may feel embarrassed to constantly be asking questions. With tutoring, your child will never have to feel like they are the only one having trouble in school. 

Instead, having an individualized learning program will increase your child’s confidence by providing them with the necessary resources to better their English comprehension.

Improves work habits

Nothing helps a lazy kid more than having a one-on-one session with a professional who demands attention, focus, and hard work from their student. To improve your child’s work ethic and study habits, you can hire a tutor so they can’t shy away or hide from adult direction to do their work and focus on the task at hand.

Positive work environment

Working in loud classrooms or a busy library can cause students to become unfocused and not understand what they are supposed to be doing. By providing a calm, serene, and trusting environment, tutors can help make a space conducive to learning.

Encourages independence

Your child will learn the skills necessary to do schoolwork on their own. Once the child begins to understand how tutoring works, the tutor will often let the student do classwork independently, with the tutor just being there to supervise or if any questions are needed. This independence can help the student in all facets of life.

Trying A Tutor for Free!

Hiring a tutor can help your child fully understand a concept without having to feel embarrassed or shy to ask questions in a busy classroom. By providing the student with the necessary resources and tools to improve their English comprehension in a one-on-one setting, they will learn precious skills like independence, study methods, and self-directed learning to increase their overall aptitude.

Sign up for a free session with Tutor Portland today!

May 13, 2021

Summer Academy

Welcome to the Tutor Portland Summer Academy. The Summer Academy is a program which allows our members and new clients to enroll in private courses over the summer. For example, we offer courses such as Algebra 1 and Geometry. Your student will work privately with a tutor. With this one-on-one instruction, your student will move through the course material very rapidly. This is a great idea for students who are struggling with a subject or simply want to get ahead. For example, we offer families the ability to enroll in an Algebra 1 course over the summer as a way to prepare them for the next year. Imagine that. Picture having Algebra 1 in the fall, after already having taken the entire course in the summer! Of course you are going to do well in the course, likely even ace it. 

This strategy is actually something I used myself in my own learning. In college one year I had to study organic chemistry. Organic chemistry is widely considered to be the most difficult course offered to undergraduate students. I was a little worried about my ability to do well in the course because “o-chem” was so hyped. I really wanted to do well in the course. One day I happened to read through the course catalog at Portland State University. I discovered that they offered a rapid – full year of organic chemistry – over the summer months. It was divided into three terms, each four weeks in length. I told myself I was going to sit in on those lectures, learn some o-chem, and get a head start on next year. My goal was to sit through the entire course, to even take the exams if possible. I wanted to do the homework. I was going to simulate taking the course, to practice before the scores started to really count. 

I showed up in the summer and started taking o-chem. It went fast. But I started picking a lot of things up. For some reason, I was a bit busier than I had expected and so I didn’t quite live up to my entire goal. I didn’t complete the homework. I just showed up to class – which was about three hours per day – and took notes. I ended up learning an incredible amount from this. I knew what organic chemistry was about. I had a solid framework in my mind for exactly what we were going to study. It was like I had this giant picture of the material in my mind. 

The strategy worked very well for me. When fall rolled around – even though I hadn’t made it through the full three terms in the summer – I was very ready. I was so confident because I knew exactly what they were going to be teaching us that first term. I knew the direction we were headed. I knew about arrow pushing and electron movement. Other people had no idea this was coming. I remember sitting in class and looking all around me. They have no idea what we are about to learn, I thought. When the lectures started, some students began asking questions. I was quickly able to pick out which questions were irrelevant or lacked importance. Since these students didn’t know where the overall course was headed, they were getting bogged down in the details and asking questions about things that weren’t relevant to the core of the course. 

May 4, 2021

The Most Amazing Scientists from Portland, Oregon

In our rapidly advancing world, the need for scientists of all fields is increasing every day. Scientists all over the world do amazing, world changing work in the hopes of improving and advancing our planet and our futures. Everyone from microbiologists and chemists, to data scientists and astrophysicists are questioning the world around them to provide a better future.

As the need for scientists grows, our need for people to fulfil those roles grows also. With so many careers opening up in STEM (Science, Technology, English, and Mathematics), parents encourage their children to pursue careers that could one day change the world. Getting a tutor to help aid children and push their skills to the next level could make the difference. Getting into better schools and better jobs is something all parents want for their children, and a science tutor in Portland is a great way to make that happen.

To show what a difference scientists make in our world, we’ve put together a list of famous, world-changing scientists that have come from the local Portland area.

Sheperd S. Doeleman

Arguably one of the biggest scientists in the world of astrophysics, Sheperd S. Doeleman has made a name for himself and his hometown, Portland. Named as one of Time magazine’s 100 Most Influential People of 2019, Doeleman’s popularity has blown up in recent years for his work on super massive black holes. The multi-award winning scientist got his PHD from MIT in 1995. Since then has grown in leaps and bounds, becoming a senior research fellow at the Harvard-Smithsonian Center for Astrophysics and being a founding director of the Event Horizon Telescope project.

As his work in black holes progressed, Doeleman became an important figure in astrophysics and eventually went on to lead the international team of researchers that produced the first directly observed image of a black hole. From the local streets of Portland, to snapping a photo of a black hole, Doeleman has become a true leader in his field and a role model for any budding stargazers.

Roberta Rudnick

Instead of looking off into space, Roberta Rudnick decided to focus on the ground beneath our feet. This award winning earth scientist, and processor of geology at the University of California, has spent most of her life being a strong female role model for aspiring girl scientists everywhere. Roberta is a world expert in the continental crust and lithosphere, is a member of the National Academy of the Sciences, and has won over five awards for her work, including the Dana Medal by the Mineralogical Society of America.

Rishabh Jain

At the age of thirteen, Rishabh Jain was named America’s Top Young Scientist for his research to improve radiotherapy for pancreatic cancer. By the age of seventeen, he had become a world renowned researcher, developer, inventor, and YouTube influencer. With all that under his belt, it’s crazy to think that he was just two years into his education at Westview High.

Beyond his numerous awards and recognitions, Jain spends a lot of his free time being an inventor and developer, developing AI software based around medical research. In his spare time, Jain has managed to become a highly followed Youtube influencer and he is an avid activist in a number of passions. At such a young age, it’s clear Rishabh Jain is going to go far.

Ann T. Bowling

Ann T. Bowling was one of the world’s leading geneticists in the study of horses. Throughout her life she became a major figure in the development of testing to determine the parentage of animals, first with blood typing in the 80s, then DNA testing in the 90s. Her passion has all been around her love of horses, and in her career she made ground-breaking developments in genetics and hereditary diseases.

Michael Li

Another young man of many talents, Tianhui Michael Li has made a name for himself as an entrepreneur, data scientist and businessman. Originally attending Oregon Episcopal School, Li went on to become the youngest person ever, at eighteen, to build a desktop nuclear fusion reactor and won second place and $75,000 at the Intel Science Talent Search. As a result of the competition, he has since had an asteroid named after him, 15083 Tianhuli.

In addition to rocking the science world as a mere teenager, Li went on to become the CEO of The Data Incubator, a data science education company aimed at helping students in Master’s and PhD degrees. For all young, aspiring scientists, Li is truly a role model.

Paul Hugh Emmett

Emmett was one of the physics giants of his day. As a trailblazer in the nuclear physics world, he spearheaded research to separate isotopes of uranium and to develop a corrosive uranium gas. He was a pioneer of catalysts and went on to work on the Manhattan project, working alongside world-renowned scientists like J. Robert Oppenheimer. Emmett also authored over 160 publications, some of which are still cited to this day.

Want to Learn More from Science Tutors in Portland, Oregon?

As you can see, Portland has produced some amazing scientists. Luckily, anyone can become a scientist with the right attitude and the right science tutor. With the help of one of the many high school science tutors Portland has to offer, any student might become a scientist that can change the world.