###### October 22, 2023

### How to Find the Base, Height, and Area of Triangles (Right, Acute, or Obtuse!)

Why can’t triangles all be the same? It’d be nice if isosceles, equilateral, acute, and obtuse triangles followed the same rules as right triangles, but unfortunately they do not. Don’t let the goofy shape names confuse you, every type of triangle has a simple formula for finding area, base, and height. Perhaps the easiest way to approach these formulae is to start with the most basic triangle form: The Right Triangle.

**Right Triangles**

A **right triangle** is characterized as having one 90° angle, a base, height, and hypotenuse. The base and height are the two adjacent sides to the right angle. The hypotenuse is the side opposite the right angle and is the longest of the three.

**Finding the Area of a Right Triangle**

In geometry, we often need to find the area of a triangle. We can only find the area of the triangle when we know two of the side lengths. It’s easiest to calculate the area when we know the length of the base and height. If we have this information, we can use the following equation to determine the area:

*A *= ½ *base* × *height*

Let’s use this formula to find the area of the triangle below:

*A* = ½ *base ×** height*

*A* = ½ (6 × 7)

*A* = ½ (54)

*A* = 27

Simple enough, right? However, in geometry we’re not always given both the base and height measurements. In this case, we have to take a few more steps to solving for the area of a right triangle. So, let’s go through the process of determining the base and height of a right triangle so we can perform the formula *A* = ½ *base ×** height*.

**Finding the Base & Height Using The Pythagorean Theorem**

We use the **pythagorean theorem** to determine the side lengths of a right triangle. The equation goes as follows:

*a ²* + *b ²* = *c ²*

Variables *a* and *b* represent the base and height of the triangle and variable *c* represents the hypotenuse. In this example, the shorter lengths of the triangle (the base and height) are on the left side of the equation whereas the longest side (the hypotenuse) is on the right side.

Let’s use the pythagorean theorem to solve for the base of the triangle below:

*a ² + b ² = c ²*

*a ²* + (12) ² = (15) ²

*a ²* + 144 = 225

*a ²* = 225 – 144

*a ²* = 225 – 144

*a ²* = 81

*a* = √81

*a* = 9

The base length of this triangle is the integer 9. Since all the side lengths of this triangle are integers (whole numbers with no decimals points) this combination of numbers qualifies as a **pythagorean triple**. Common examples of pythagorean triples are 3:4:5 , 6:8:10 , 9:12:15 , and 8:15:17.

Most combinations of side lengths do not result in all numbers being integers, however. Because the pythagorean theorem deals with square roots, one of the side lengths will usually be rounded to the hundredth decimal.

Let’s find the missing height of a triangle that doesn’t result in a integer:

*a ² + b ² = c ²
*(7) ²

*+ b ² =*(13) ²

*49 +*

*b ²*= 169

*b ² =*169 – 49

*b ² =*169 – 49

*b ² =*120

*b =*120

*b =*10.95

Now that we know the height of the triangle, let’s solve for the area:

*A* = ½ *base *×* height
A = ½ *(7 ×

*10.95)*

*A = ½*(7 ×

*10.95)*

*A = ½*(7 ×

*6.65)*

*A =*38.32

It’s as easy as that!

**Using Area to Determine the Base and Height**

How can you determine the base and height of a right triangle when you only know the area and one side length? You can’t use the pythagorean theorem because that requires two side lengths. Instead, you can rearrange the area formula to solve for the missing side length:

*A* = *½ base × height
2 × A = (½ base × height) ×2
2A = base × height
2A/base = height or 2A/height = base*

Let’s use the above formula to solve for the height of the triangle below:

Let’s use the same formula to solve for the base of this triangle:

**Finding the Area of an Acute Triangle**

There are two ways to determine the area of triangles without a 90° angle. The formula you use depends on what type of triangle we’re working with. If we’re looking to find the **area of an acute triangle**, we will have to implement one of these three sine formulas:

*½ ab sin(c)* = Area

*½ ab sin(a)* = Area

*½ ab sin(b)* = Area

In order to determine the area of an acute triangle, we must know two side lengths and the angle measurement opposite of the third side. The formula we use depends on which combination of sides and angles we know. In the triangle below, we know side lengths a and b. We also know the measure of angle c. Because of this, we can use the formula *½ ab sin(c)* to determine the area of this triangle:

*½ ab sin(c)* = *A
*

*½*(25 × 22)

*sin(40°)*=

*A*

½(25 × 22)

½

*sin(40°) = A*

½(550) × 0.64

½

*= A*

275 × 0.64 =

*A*

176 =

*A*

**Finding the Area of an Obtuse Angle**

Finding the **area of an obtuse triangle** requires a different method. Instead of using the sine function right away, we will create a right angle by forming a straight line that extends out from both points C and A. The point at which these two lines intersect forms a right angle. Let’s label the new triangle DEF. For both of these triangles, the uppercase letters represent angles. The lowercase version of each letter represents the corresponding side length to each angle:

We can find the area of an obtuse triangle by creating an altitude line. The altitude of triangle ABC was created by forming the line labeled *h *(height). Since ACD is a right triangle, we can find it’s area with the equation *A* = ½ *base *×* height.* We can also determine the area of the larger triangle ABD using this equation. To find the area of obtuse triangle ABC, we must then subtract the area of ACD from ABD:

*Area of ABC = Area of ABD – Area of ACD*

Depending on the given information, we can use **geometric proofs** and perform sine formulas and to solve for the missing side lengths. Once we have enough information to find the areas of triangle ABD and triangle ACD, we can use subtraction to find the area of triangle ABC.

**Solving for Area Using Multi-Step Formulas**

Let’s apply the numerous methods we’ve learned about determining area to obtuse triangle DEF:

The first step to finding the area is solving for the missing lengths. You can determine the base length of the smaller right triangle by subtracting 28–20=8. To figure out the height of this triangle we must use the pythagorean theorem:

8 ² + (height) *² *= 172

64 + (height) *² *= 289

(height) *² *= 289 – 64*
(height) ² *= 289 – 64

*= 225*

(height) ²

(height) ²

*(height)*= 225

*= 15*

(height)

(height)

As you can see, this right triangle is a quadratic triple as all it’s measurements are integers. Let’s use the height and base to find the area of this right triangle:

*A* = ½ *base *×* height
A = ½ *(8 × 15)

*A = ½*(120)

*A =*60

Now let’s find the area of the larger right triangle:

*A = ½ *(15 × 28)

*A = ½ *(15 × 28)

*A = ½ *(420)

*A = 2*10

Finally, let’s subtract the two areas to find the area of triangle DEF:

Area of DEF = 210 – 60

Area of DEF = 210 – 60

Area of DEF = 150

If you’re still having a hard time grasping triangle areas, heights, and bases, don’t feel defeated. Tutor Portland is here to the rescue! At Tutor Portland, we specialize in finding tutors that will give you the extra help and assistance you need to keep up with your coursework and kick butt at your next test. Whether you need in-home or virtual assistance, we’ll find the perfect tutor to suit your academic needs and help you master concepts like finding the areas of triangles. **Sign up** today for your free intro session!

###### 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

**, where**

*b**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.

###### 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!

###### March 24, 2021

### How Tutoring Can Help Students Master Math in the Era of Virtual Learning

If your kids are taking math online right now, I can see why you might be worried. It’s hard enough to hope for As in math classes when kids are attending school in person, but 2020 made everything more complicated.

Now that class is online, it’s even easier for kids to find themselves falling behind. Students are more distracted and less engaged. Class discussions are virtually nonexistent. Getting individual attention from a teacher seems harder than ever. How in the world are students supposed to master complicated math concepts in this environment?

While the online format isn’t ideal, tutoring can help! For kids who are missing that one-on-one interaction, a math tutor can bring them the connection they crave, now from the comfort of their home. Classes are now almost always recorded, giving tutors a way to glimpse course material and work through it with students. Virtual pod-based tutoring can help kids supplement the social aspect they might be yearning for. So if you worry about your kid grasping the math curriculum, don’t give up just yet. Here’s how tutors can make a difference…

**Engaging Students**

Many parents worry that Zoom is less engaging than in person math class. There’s definitely some truth to that–it’s hard for kids to get invested in the material when they’re just another black square in a sea full of turned-off cameras. It’s tempting for kids to start playing Minecraft or scroll through Instagram during a lecture as there’s no teacher in the room. Discussions aren’t as fluid or active and it’s hard for kids to make themselves known. In this virtual environment, students are not as involved in the subject at hand.

However, getting a great tutor can help solve this problem. No longer will your kid be an anonymous member of a huge Zoom class. Tutoring gives kids a personal, individualized approach to learning, even through the internet.

At Tutor Portland, we give one-on-one tutoring that’s totally focused on engaging the student. Our tutors build a strong rapport with students, ensuring that kids feel safe to express their frustrations and explain their own way of thinking about problems. Tutors check back with students each week and give them the positive encouragement they need to strive for growth. Even though kids have to learn through a screen, with this approach, we can keep kids excited and interested in the material.

That being said, even if students remain involved, they might not be able to be able to keep up. Math is cumulative, meaning if students miss one concept, they can easily get behind. Working through recorded lectures with a tutor might be able to change that…

**Keeping Students From Falling Behind**

Fast-paced math lectures are so common, it’s a wonder how kids can keep up at all. This has been a problem long before online learning. It’s a byproduct of our tendency to teach math with little to no discussion among students, let alone individual questions and feedback. Now that many lectures are virtual, students might have even less opportunity to slow down the class and inquire about a tricky concept.

Luckily, in this new online educational environment, lectures are almost always recorded. These recorded lectures are made available to students at any time. This means students can go back and rewatch whenever they need to in case they get stuck on homework. They can pause and rewind or go to a specific section when they may have overlooked a detail. Plus, if they want to review for a midterm or a final, they have every lecture laid out for them online. Instead of having one chance to get the teacher’s lecture, they can access it any time.

This is a great tool that tutors and kids can use together. Previously, if a kid struggled to comprehend an idea, tutors would have to guess how the teacher taught it to them. Now, tutors can see exactly how the concept was explained to the student, so the tutor can more deeply understand their student’s learning process. Students and tutors can go through recorded videos and take a new look at any material the student doesn’t quite understand.

Beyond having relationships with teachers and tutors, students also need to relate to each other and work together. But, how can tutoring help kids get that experience without in-person classes?

**Incorporating the Social Aspect**

Although socializing with others may seem extraneous to learning equations, having discussions with others about material really helps struggling math students. Studies show that students understand concepts better when they’re able to verbalize their thinking and have back-and-forth exchanges with other individuals.

However, online school makes it impossible for kids to talk about material as they walk the halls, and makes forming study groups a lot more challenging. This is especially true if your student is new to the class or doesn’t have a group of classmates to collaborate with.

Tutoring can help by not only connecting students with a great tutor, but a network of their peers as well. My brother and I had this social component in mind when we created **Zoom Tutor**, a website made specifically to help kids through the online educational landscape. On Zoom Tutor, not only is one-on-one tutoring offered, but pod-based tutoring with a group of students as well.

This means students are organized into small groups that meet each week to go over material. Although they may not be able to gather in person (yet), these regular sessions give kids the ability to meet and work with an entirely new group of peers. Instead of working through problem after problem alone, they can have a community to share their frustrations and victories. This can fundamentally transform students’ attitudes towards math. Instead of stale repetition, these peer groups help make math fun and social.

**Get Your Kid Tutoring Today!**

Even though learning math online may seem like an impossible challenge, tutoring can help students make the most of it. When Zoom leaves kids uninvested, good tutoring can help them engage with material again. Working through recorded lectures with tutors can guide kids towards success if they find themselves falling behind. Incorporating group work into the online tutoring format can help students have meaningful discussions that allow them to get a grasp on complicated math subjects..

So if you want to help your kid make the most of learning math online, you can sign up for your first free Tutor Portland session **here**, free of charge. You can also check out Zoom Tutor **here**! If we can give students access to a meaningful learning experience despite the tribulations of the online format, we can help kids come out of this challenging time on top, ready to achieve their goals.

###### February 21, 2021

### One-on-One English Language and Writing Tutors

English is incredibly frustrating. We often underestimate it’s difficulty, since it’s such an integral part of our lives. However, when it’s time to sit down and write an essay, we find our grammer doesn’t sound right. We struggle to make our sentences flow. The word count seems impossible to reach and our whole argument feels inconsistent.

Writing is more than just a trivial part of high school academics. It’s central to passing any university course and remains relevant in the professional world. If a student finds English challenging now, they’re going to have trouble crafting a compelling college admissions essay or expressing themselves concisely in a cover letter. It could cost them job opportunities, promotions, research positions, and more.

At Tutor Portland, we understand the importance of helping kids master English now so they can excel later. Our tutoring focuses on helping students get the core principles of writing down, while also boosting comprehension and critical thinking skills. We offer tutoring for all kinds of writing, including college admissions essays, editing, research papers, standardized tests, descriptive essays and narrative work. Stick with us and we’ll have your kid reading and writing like a pro in no time.

**Mastering Writing Basics**

There are a lot of parallels between the high school English curriculum and communicating in the professional world. That’s because basics like thesis writing, crafting strong arguments, providing solid evidence and conducting thorough research are extremely relevant beyond grade school. Lawyers need powerful arguments to create contracts or defend clients. Business professionals must know how to present evidence to effectively share quarterly earnings. Scientists rely on strong research abilities to compile solid research papers.

Working with an English tutor to hone in on these basics is remarkably helpful. Tutors read through essays to make sure a students’ arguments are in line with their thesis. They can determine if the evidence in an essay is really proving a point, or simply distracting from the main idea. An English tutor knows what relevant and impactful research looks like and help students incorporate it correctly.

At Tutor Portland, we can help teens apply these basics in any subject–not just English. For example, if your student is interested in science, but needs a little help with writing, we can tailor lessons to stronger research papers instead of just book reports. Say history is a student’s weak spot. An English tutor from Tutor Portland can help them identify strong sources and construct a powerful thesis with compelling arguments that explain the causes of the War of 1812. No matter what the task, we’ve got you covered.

**Conquering Reading and Comprehension**

If kids are struggling to get through assigned readings, an English tutor can help with that as well. Being able to effectively read and extract the valuable information from a document is an exceptionally useful skill. Tutors can go through class readings line by line to help kids see what data is really critical. This ability will come into play when teens are expected to read a dense credit card contract or understand a complicated economics lecture.

Not only that, but reading can be a way for young people to increase empathy, think more critically about life, and reflect on their own emotions. Reading literature allows students to step into the shoes of others and empathize with characters from different times and situations. Understanding how to digest and process non-fiction, like news stories or texts about history, politics and economics will bring students a greater understanding of the world. By guiding kids towards becoming better readers, tutors help students explore new perspectives.

When it comes to comprehension, a good English tutor steps in where teachers might be lacking. Oftentimes, teachers are just concerned with making sure kids read the assigned works, quizzing them on what happened in chapter five. A tutor can help kids really break down the material and pull out the most important information. They encourage kids to think deeper and ask them challenging questions that actually engage them in what they’re reading.

**Cementing These Skills**

Any good English tutor knows that the key to truly mastering language arts is the same as studying for science or math: careful repetition and putting in the hours.

I dedicated time to writing every single day when I was in college. This discipline and structure helped me improve my writing immensely. It gave me the power to ace college classes and land jobs after graduating. Now, my writing skills play an integral role in running my business and maintaining my blog. If students really want to write strong material, they’ll have to put in the reps. Tutors can create practice prompts or go through exercises with students to give them the repetition they need to succeed.

Along with discipline, great writing requires a lot of trial and error. An A-scoring essay is not going to come easy. Students have to be willing to assess, rework and rewrite, no matter how much time and effort it takes. A tutor can guide students through this process and provide constructive feedback on every draft.

Additionally, an English tutor can apply a trained eye to students’ writing and identify how they can take it from acceptable to incredible. Even when the material in an essay is grammatically correct, that doesn’t mean it’s as strong as it could be. Ditching bland or overused words for more active, impactful language can elevate a piece of writing immensely. Changing sentence structure can make an essay much more digestible and persuasive. Tutors allow students to accelerate their writing skills beyond what they thought possible.

**English Tutoring at Tutor Portland**

At Tutor Portland, we know that tutoring isn’t one-size-fits-all, especially not for a subject as nuanced as English. We’ve got tutors from a wide range of backgrounds, ready to meet the needs of each individual student.

Our **English tutors** can help your student with focused, intentional practice in the language arts. As college students and professional writers, they know how to create written work that’s not only grammatically correct, but compelling. They’ll equip your student to impress professors, amaze college admissions officers and achieve their wildest dreams.

If you’re ready to unlock your full potential, sign up for a **free session** today.

###### January 20, 2021

### 9 Necessary Study Habits for Academic Excellence

Studying. Few of us like to do it, but it’s totally necessary for nailing exams and earning awesome grades. If you think you’re a bad test-taker, you might be super smart, but lack some of the best strategies for effective studying. Here are some tips for excelling at studying and doing everything you need to ace your next test.

**1. Plan a Study Schedule**

You might think you should focus on the hardest subjects first, but that can be a counterproductive study habit. Instead, create a plan that designates extra time to focus on more challenging subjects but still includes time to review everything that’s going to be on the test. That way you’ll be well versed in all the topics you need to know and won’t be thrown off by a test question that references a subject you forgot to study. For example, if you have three hours to study for a test that covers six chapters of your textbook, and you really struggled with chapter three, create a plan like this:

Review Chapter 1 & 2: **30 minutes
**Review Chapter 3:

**50 minutes**

Chapter 4-6:

**55 minutes**

Re-review Chapter 3:

**45 minutes**

This schedule prioritizes chapter 3 but still ensures that you review everything else at least once. So instead of assuming that you’ll be able to recall information, you’ll go into the test 100% sure that you’re prepared for anything that could be on it.

**2. Create Essay Outlines**

When you sit down to write a big essay for an end of semester project, it’s common to experience writer’s block. The weight of it’s importance can stir up so much anxiety that you feel totally out of ideas.

Rather than starting off your writing session with no direction or plan, prepare an outline beforehand. This is a complete breakdown of *everything* you want to include in your introduction, body paragraphs, and conclusion. In the outline, you’ll want to include everything from clever hooks, transitional phrases, and quotations from outside sources. Outlining helps you determine the order of information you’re presenting and what ideas you want to focus on the most. That way when you sit down to write, all you have to do is transcribe everything into an essay format. If you need help getting started, use **Scribbr** to help you craft the perfect essay outline.

**3. Review Your Notes**

This might sound obvious, but reviewing your notes before starting any assignment, even homework, is imperative. Doing a quick re-read not only assures you understand every concept before diving in, it can also prevent you from making critical mistakes, which is especially important for writing assignments. Make sure to read a writing prompt in its entirety so you know exactly how many paragraphs you have to write, what topics you need to discuss, and the format it needs to be written in. Nothing is worse than spending two hours on a 1,200-word essay only to realize it only needed to be 800.

**4. Test Yourself!**

You don’t have to wait for the big exam to get into test mode. Create weekly quizzes for yourself so you can better absorb what you’ve been learning. Focus on identifying the main topics your teacher highlights, especially points that have been brought up multiple times, because they *will* be on the test.

To find material for your practice test, use questions from quizzes you’ve already taken as well as review sections located in textbook chapters. You can also use online platforms like **Complete Test Preparation** to find practice tests for math, science, reading comprehension, and more.

**5. Compare with Friends**

We’ve all had that one classmate who always seems to have the right answer and aces every test without even trying. Rather than seeing them as your biggest competition, use them as your greatest resource. Gather a group of your most prodigious classmates to do a weekly review of the lessons that’ll be on the test. Studying together helps you discover where you can improve, while you share your strengths to help others improve. This way, you’ll all become better students together!

**6. List Your Distractions**

Do you ever get distracted when you need to study? Not only by Netflix and phone notifications, but by chores too? Chores that your parents are harping about because they needed to get done *yesterday*? When other important tasks are competing with your studying duties, don’t ignore them. Instead, write them down and choose a time when you’ll be available to complete them. Set a timer that requires you to put in one hour of intense studying. When it goes off, allow yourself 10-20 minutes to get these chores done.

Let’s be honest—many distractions, like texting your significant other, are far less imperative than chores. Many of us are tempted to check Instagram likes on our latest post or scroll through news stories on Twitter, when we should be focusing on studying for a final. This can lead us to take constant mini-breaks that grow into all-day distractions. Putting off our work all day can lead to feelings of guilt or stress as we run over schedule and fall behind on studies.

The solution is to not deprive ourselves of study breaks. Instead, we can reward ourselves for an hour’s worth of intense studying with 10 minutes of free time. This way, we give our minds a break and can indulge in our favorite pastimes, guilt-free.

**7. Study Offline**

While we highly recommend using online platforms for study tips, time away from the computer allows you to purely focus on studying and not get distracted by the internet. Find a screen-free environment to study in, like the kitchen table, a comfy chair, or outdoors. This’ll give you a nice change of scenery and your eyes a break from the screen.

There’s also plenty of online tools you can use without internet access like **Desmos**, which is a website that provides a variety of calculators and graphing tools. Use these tools while your computer is in offline mode. That way you’ll have access to all the helpful resources Desmos offers without being distracted by email or social media alerts.

**8. Leave Your Friends on Read**

With instant messaging, friends are just a text away. But are group chats more important than grades? If you struggle to avoid text messages and Snapchats when you’re supposed to be studying, hold your friends accountable. Let them know that you have a big test to study for and won’t be reachable for the next few hours. If they know how important this test is, they won’t create unnecessary distractions to prevent you from succeeding. If they’re still hitting you up during studying sessions, put your phone on “Do not Disturb” and update your messaging settings so only emergency contacts can reach you while your studies are in session.

**9. Ask Your Teacher**

It’s good practice for students to regularly ask questions during class. It not only helps you better understand a subject but can provide clarity to other students who have the same questions. However, asking too lengthy of questions can monopolize your teacher’s ability to help other students, and can make you look inconsiderate of those who want to move on to the next lesson. Instead of disrupting other students’ time, pull your teacher aside after class and ask when they’ll have free time to help you with tougher subjects.

Oftentimes teachers’ have office hours where you can get one-on-one help. Going to office hours demonstrates your intentions to improve your schoolwork and shows that you don’t want to take away from their in-class time. Plus it puts you on their good side—they might even be more willing to boost you to an A- when your end of semester grade is 89.8%.

**…And if that Doesn’t Help**

Every good teacher should be willing to provide extra help to students that need it. However, you won’t always have the privilege of teachers who are willing to help us during their off-time. If that’s the case, don’t be afraid to seek tutoring in subjects that aren’t your strong suit. Here at Tutor Portland, we provide **in-home and online tutoring sessions** with first-class tutors throughout the Portland area. Each of our hand-selected tutors will provide you with the specialized attention you need to raise your grades, pass your tests, and get accepted to your dream school. Start your free online introductory session today!

###### November 3, 2020

### Classical Music for Studying

School can be intense, especially during exam season. You find yourself spending all your free time studying, working on projects, reviewing assignments, pouring over practice tests, and doing everything you can to prepare yourself. But have you really tried everything? What do you listen to when you study––a favorite playlist, a babbling brook, nothing at all? A wealth of scientific research has found a new way for you to boost your academic performance: listening to classical music for studying!

This simple practice can boost your grades and help you retain information, so give classical music a try and see if it becomes a helpful habit for life! You might find that you finally get the exam scores you’ve been craving, and feel healthier and happier in the process. Here’s why classical music for studying works for so many people:

**Scientifically Significant Study Benefits**

You may be familiar with the rumored brainpower phenomenon called the “Mozart Effect.” A 1993 linked the effects of listening to Mozart with an increase in IQ, spurring an increase in the popularity of classical music for studying. The study demonstrated that participants who listened to Mozart tended to score higher on subsequent IQ tests. While this specific research is now **widely discredited**, it has been replaced by a plethora of well-respected studies demonstrating that there are definite academic effects derived from listening to classical music for studying.

**Research conducted in a French university** found that when students listened to classical music for studying, their academic performance improved. In this study, two groups of students watched a lecture, one with classical music in the background and one without. The students who listened to the music scored higher on a lecture quiz than the other group.

**Another study** suggests that students are able to focus better and study longer with classical music playing in the background, leading them to perform up to 12% better on exams than their peers. The absence of words in classical music might decrease distractions and could account for the improved focus amongst listeners.

Classical music for studying can boost academic performance in creative classes as well because it increases divergent thinking. Divergent thinking, or the ability to come up with new and innovative concepts, is the backbone of creativity. A **2017 study from Goethe-Universitat** in Frankfurt, Germany, tied listening to “happy music” to enhanced divergent thinking, meaning happy music makes you more creative. Classical music is commonly **considered both positive and energetic**, and thus encourages creativity. Working on a final project for an art or film class? Trying to find a new way to approach a complex calculus question? Or just feeling stuck in general? Find a classical playlist. Classical music for studying gets your creative juices flowing and puts you in a mindset open to innovation and discovery.

Turn on some Mozart, because studying with classical music has also been shown to increase productivity. A **UK-based experiment** paired a classical radio station with a psychologist to see if British office workers would be more productive while listening to artists such as Beethoven and Bach. They found a 15% increase in productivity when participants completed a task listening to classical music, versus working in silence. By blocking out noises and distractions, classical music can increase your focus, leading to improved productivity. Apply these findings to your own study habits and get more done in less time!

Plus if you find yourself losing sleep due to exam stress, listen to this. **Researchers at the University of Toronto** found that classical music can combat insomnia and improve sleep. With 60% of college students habitually getting less than 7 hours of sleep, finding ways to improve sleep quality is of paramount importance. Improving sleep quality is a tried and true strategy to increase cognitive performance, paving the way for better understanding of school subjects.

A **study conducted by Baylor University** found evidence that listening to classical music for studying both during lectures and while sleeping can trigger targeted memory reactivation (TMR). During this process, the music triggers the brain to move the concepts learned during studying to more permanent memory storage. The students exposed to classical music for studying both during lecture and sleep performed **18% better** on the test than the control group. So try turning on classical music to help you study and sleep! But that’s not all, listening to classical music for studying offers a number of physical and emotional health benefits too!

**Physical Benefits**

When you listen to classical music, it improves your overall health quality by reducing stress. Researchers at the Duke Cancer Institute found that **blood pressure actually decreases** as individuals enjoy music. However, this effect was only observed in participants who listened to *classical* music, not jazz, pop, or other genres tested in this study. So, if you like to read with the music in the background, but feel it hasn’t helped you improve exam scores or relax, you may want to try switching to calming classical music for studying.

Music with too many dynamic changes, unpredictable rhythms, lyrics, or jarring instruments will serve to distract rather than calm, so be intentional in your music choices. Classical music has been found to reduce stress as a result of its specific, unique musical qualities: **the slow, rhythmic tempo of classical music is similar to the natural pace of the human heartbeat**, encouraging your body to calm down, lower your heart rate, and de-stress. Its patterns and textures allow your brain to expand as you listen, without over exciting your body.

Not only do these physical benefits help you study better, but decreased blood pressure and lowered anxiety contribute to a healthier lifestyle for years to come. Making classical music a part of your daily routine, even on the days you take a break from studying, will certainly pay off in the long run.

**Emotional Benefits**

Listening to classical music for studying produces a wealth of emotional benefits on top of the physical benefits. When the “Mozart Effect” was debunked, researchers replaced it with a new theory. They determined that while listening to Mozart didn’t necessarily cause increases in IQ, it did improve mood. Listening to Mozart’s music **causes the brain to release more dopamine**, a hormone known for improving mood and producing a ‘feel-good’ effect. These increased dopamine levels were tied to improved feelings of happiness among listeners. Happier participants tended to perform better on evaluations.

Increased dopamine also makes classical music a tool for fighting the symptoms of depression. If you tend to feel discouraged while tackling a difficult class, classical music for studying can help improve your mood and keep you on track for success. And not only that: by improving your emotional state, classical music actually makes your brain **more receptive to new information**. By getting you into a good headspace, classical music for studying prepares you to tackle any academic challenge.

**Recommendations**

Ready to pop in your headphones and play some classical music for studying? There is an endless variety of classical music playlists online to choose from! From hours long YouTube videos to specially curated Spotify playlists, your options are inexhaustible. Taking a bit of time to find the perfect blend for you is definitely worth it.

A good general rule to follow is: **skip the big orchestral selections**! Pieces with huge dynamic changes that range from whispers to crashes are too busy and distracting for your purposes. *The 1812 Overture*, for instance, will probably have the opposite of the intended effect and increase your heart rate and anxiety.

Try to stick with simple pieces to avoid inadvertently distracting yourself. Classical radio station producer **Alan Chapman recommends** solo piano pieces by Mozart, Poulenc, Debussy, or Fauré, gentle guitar music, Bach lute suites, and Elizabethan consort music written in the 16th century.

To help you get started, here’s a list of classical pieces to study to that we recommend:

- Goldberg Variations, by Johann Sebastian Bach
- The Four Seasons, by Antonio Vivaldi
- Für Elise, by Beethoven
- Canon in D, by Johann Pachelbel
- Clair De Lune, by Claude Debussy
- Piano Concerto No. 23, by Wolfgang Amadeus Mozart
- Salzburg Symphony No. 1 (‘Divertimento in D major’), by Mozart
- Gymnopédie No. 1, by Erik Satie
- Academic Festival Overture, by Johannes Brahms
- Etudes, by Frédéric Chopin
- The Hours, by Philip Glass
- Moonlight Sonata (I), by Beethoven
- Organ Concertos, by George Frideric Handel
- The Blue Danube Waltz, by Johann Strauss II

Exam season is challenging, exhausting, and stressful, but now you have another tool to get through it. Listening to classical music for studying has been proven to have a wealth of benefits on your mental, physical, and emotional health. It decreases your stress and anxiety, brings down your heart rate and blood pressure, and helps your retention skills by enhancing memory capabilities. Further, it releases dopamine to improve your mood and fight depression, increases your creative capacity, and improves productivity. The scientific studies point to classical music as the perfect study companion, so crack open that textbook and turn up the Bach!

###### March 29, 2020

### The Benefits of Active Tutoring

I always struggled trying to learn math and science. It wasn’t natural for me. Some students “got it.” They understood math. But I never did. I “got by.” Friends helped me with assignments, or I copied off my neighbors. I never really took the time to learn and invest in my mathematics abilities. This was because I had a **fixed mindset** when it came to math. I thought—well I always do poorly at math—I must **be bad** at math. In a weird, sort-of-rational way, I believed that I was permanently bad at math. I didn’t have any successes to prove otherwise!

Many other students and families feel this same way. These families are frustrated because they know their student is bright and smart. She is just having a hard time learning math. I believe this is more about the way that math and science are currently being taught in schools than it is about the learner. Math is being taught as a lecture. Teachers have a strict agenda of what they want to teach. They give their lecture, pass out a worksheet, and then expect the students to learn the ideas. This is outdated and simply doesn’t work.

This style of teaching doesn’t hold its ground when compared to the new research being published on math and science education. The research today shows that students learn math and science **when they hear themselves verbalize their own mathematical and scientific thinking.** *This is a huge finding.* Up until now, teachers have been relying mainly on lecture-based teaching. They lecture during class, maybe assign some worksheets to keep the students busy, and they send them home with work to complete.

I grew up taking math courses centered around lecture. They were all about one person presenting the ideas. The problem with lecture-based mathematics and STEM courses is that students often think they understand what is going on, but in reality they are missing a few small distinctions on how to complete the problem or activity. These small misunderstandings compound on each other until eventually the student is so far behind that they need massive assistance in order to catch up. *But these small misunderstandings don’t have to compound! *We can stop them in their tracks!

If students were allowed the opportunity to simply discuss the concepts every day, then they would learn them much quicker. This is because when we discuss ideas we are better able to see the small holes in our own understanding. This allows learners to ask questions and fill in the gaps. Specifically, in active learning class rooms students spend the majority of the class discussing concepts, ideas, and working together on practice problems. This is the ideal way to learn math and science. But these courses require professors who invest a significant amount of time and energy into planning their courses and their course structure.

In college, I was fortunate enough to study under such a teacher. She not only knew mathematics, but also had a Ph.D. in mathematics education. She knew **how** to teach math. The entire course was centered around small groups. This is where everything started. We sat at a small table of 3-4 people and we discussed ideas *before* she taught us what the core concepts were. Most of the time we were able to figure things out in our small group!

Learning like this was difficult. It was challenging to learn this way because we weren’t simply spoon-fed the answer. We had to find it ourselves. We had to discover it. I took algebra 1/2, and algebra 3/4 this way. I also took pre-calculus and even two discovery-based calc I and calc II courses.

In my calculus classes, we spent weeks at our table discussing the concept of “rate-of-change.” We looked at graphs and got a good feel for what rate of change was. We learned that when you look at a graph, you can determine at what rate it is changing at any certain moment. Imagine zooming in on one small square of a graph. How fast is the line changing in that moment? **That is what a derivative is.** We learned that before ever hearing the word “derivative.” By the time she wrote the equation for a derivative on the board, we had already learned what it was. It was as if we built the meaning with our own hands. We felt as if we owned that word. We knew it inside and out.

Most people walk away from calculus course not learning anything. I’ve asked many people what they learned. (Try asking people yourself)! People generally say that calculus was useless and that they didn’t learn anything. “I can’t remember anything from that class,” they say. **And that is a total shame! **Because the concepts of calculus are so incredible. These concepts are fundamental to our lives. I think about rate of change all the time. You can apply it to the stock market, to human psychology, to climate change. What I find really fascinating, is that **you can even apply rate of change concepts to your own learning.** Think about it: *every course moves at a certain rate.* And each chapter moves at a different rate. It is also important to be able to think about your own rate of learning in each moment. How fast are you improving? Is your rate of change fast enough to learn all the material? If you aren’t learning at a fast enough rate, then you simply won’t do well in the course. If you realize you aren’t currently learning things at a fast enough rate, then you have to come up with a new plan or strategy. It’s all about having the right approach and mindset when it comes to learning.

One method we use with our clients—to increase their rate of learning—is to use **active tutoring** strategies. This means that we engage with out students. No longer are these students simply passively learning new knowledge. We believe that passive education is demoralizing. It reduces students’ confidence. It erodes their belief in themselves and their own ability to learn. Because essentially the message of lecture based STEM education is that: *we are the intelligent people with all of the answers, and all you can do is sit down in front of us and diligently take notes and learn. *Active learning flips this around and empowers students.

**Why is active learning so powerful?**

Active learning is inherently engaging. It gets students involved in the process of their own education. They cease to be passive observers of knowledge and become actively engaged in their own learning. This is empowering. It teaches them that they have control over what and how they learn. Active learning teaches kids to have a GROWTH MINDSET. It helps to **shatter** the fixed mindset which is inherently limiting. The whole idea of active learning is built around the growth mindset–that if you apply yourself, you can grow, you can improve, you can become better. And you do this by rolling up your sleeves and getting to work…. NOT sitting back and watching.

Importantly, active learning has been shown to do two main things: 1) it **increases students’ overall academic achievement** and 2) it **improves students’ attitude towards math and science**. It does all of this while also reducing misunderstandings about science and improving students’ understanding of big ideas and concepts.

Active learning works so well because it shifts learning from a one-size-fits-all approach to one that is inherently personalized and tailored to each student.

At Tutor Portland, we use an active approach to tutoring. Instead of simply giving answers or showing students how to solve problems, we ask them questions. We engage our students in critical thinking and in-depth discussions about concepts and topics. We ask questions and try to get students to connect the ideas they are currently learning to ones they learned last term or last chapter.

**This is often the first time they have *ever* thought critically about the ideas they are learning in school.** It’s a dramatic difference once students become engaged with the material. It changes from something abstract to something up-close and personal.

**We follow a few “active tutoring” rules very closely:**

- The tutor is simply
*a guide*, a facilitator — the tutor is not a teacher. - We give students time to
*think.* - We create a comfortable and relaxed learning environment.
- We ask open-ended questions.
- Curiosity is a quality which we embody, and which we attempt to bring forth within our students.
- Teach ethical behavior and thinking.
- Focus the session on the student. Not on the tutor or the parent or anyone else.

These are guidelines which help us create a positive and active tutoring environment.

*Updated March 2020.*