Math & Logic Archives - Eva Varga


July 15, 2019

My daughter plans to take the SAT exam this summer. However, she feels that she is rusty and needs to brush up on her math skills. We thereby wanted to an SAT prep course to freshen her memory on concepts taught in algebra and pre-calculus.

As most of my readers know, my kids are dual enrolled at the local community college. I thereby spend more time in the role of chauffeur than as teacher. In fact, I do very little direct instruction with either of them anymore.

My daughter has been taking courses full time at the college for two years now and has just completed the first year calculus course. She has done very well and this fall, she will begin tutoring.

It was thereby a surprise when her first SAT scores came back last year. She took the exam twice (once in the fall and again in spring) and yet her math score remained the same. Though she surpassed the benchmark, she didn’t feel it was a true reflection of her ability. After all, math is her favorite subject (next to foreign languages) and she excels in the classroom.

She has thereby challenged herself to take the SAT a third time at the end of the summer. In order to brush up on the skills tested on the SAT, she wanted an SAT prep online program she could use at her pace – to set her own schedule and course plan to help her review and practice. Teaching Textbooks is a math curriculum designed for independent learners – perfect for her! Best of all, the first 15 lessons of any level are free. Try one level or every level with no obligation with this link, Teaching Textbooks.

I received access to this product in exchange for a review. I was compensated for my time and was not required to make a positive review.

Homeschool SAT Prep

One of the main features of Teaching Textbooks is that it provides step-by-step explanations for every single problem in a multimedia form. The lessons are written directly to the student and do not assume the presence of a teacher.

Students can thereby work through the material independently in just three easy steps: watch the video tutorial, do the practice problems, and if you error, an audio tutor explanations the solutions.  The explanations are clear and complete and plenty of practical examples are provided throughout the curricula.

The program is very easy to use. Teaching Textbooks is a particularly good choice for the student who might have struggled with other math programs and needs a less pressured pace and style of delivery. While my daughter does not struggle, she likes that she can move along at her own pace and even skip sections when she is comfortable with the material.

Though it is not considered a specific SAT prep course aimed at testing strategies and SAT question format, it provides practice with the content of high school level coursework. We opted for Pre-Calculus but the high school courses also include Pre-Algebra, Algebra 1, Algebra 2, and Geometry.

Her test isn’t until the end of August so we do not yet know her newest score. However, she is enjoying the program and has expressed that she feels more confident.

At the college, she has alternated between two professors and had become accustomed to their word choice and approach. She states that the vocabulary and the specific wording of the problems in Teaching Textbooks has challenged her to more carefully analyze each question. It has also given her practice with another approach to solving each problem.

Regardless of what her score may reflect, her comfort with the material is what is important. As a tutor, this flexibility and confidence will serve her well.

Online Learning Improved

Teaching Textbooks now works a little differently than previous 2.0 versions. The academic content is the same as always but the course is now delivered online as a 12-month subscription. Also, physical books have been replaced by eBooks. No more discs!

The 3.0 version of Teaching Textbooks course material is easy to access from computers, tablets, or phones. This makes it easy to access from anywhere! If you prefer a more traditional textbook, an electronic textbook is available and includes a printing option.

Because all of the content in 3.0 is available online, the price is significantly lower. With 3.0, you purchase a yearly (12-month) subscription for one child and one course. Large-family discounts (for families with four to eight students) are also available.

Teaching Textbooks Giveaway

You can find placement tests on the publisher’s website to guide you in selecting the appropriate course. The series is a college prep curriculum though it is not as rigorous as some other courses.

NOTE: The Free trial does not require a credit card and does work for the first 15 lessons with no time limit. You may try any level or all of the levels.

Because we were using the course to review for the SAT exam, we were not concerned with the grading options. However, I was intrigued to discover that grades can be accessed anytime from anywhere (even after a subscription has ended).

For additional study materials organized by exam type, visit Exam Prep Books, over 20 exams types from which to choose.



April 26, 2019

My son started dual enrollment at the community college this past fall. The assessment test placed him in Intermediate Algebra. I felt confidant that all would be well – after all, his sister had forged the same trail two years prior.

Things didn’t go quite as planned however. He struggled to manage his time well and follow through on the homework. We thereby decided that he should repeat the course. He improved the second term, particularly in the latter part of the term.

This term, however, the instructor he wanted to take was not teaching the next course. He thereby opted to wait until Fall. Yet, I wasn’t comfortable skipping two terms of instruction time for fear he would slip back after the gains he has made.

I received access to this product in exchange for a review. I was compensated for my time and was not required to make a positive review.

Teen boy using CTCMath online math program with text overlay CTCMath & College Prep

CTCMath College Prep

When I discovered CTCMath I was immediately intrigued. I loved that the concepts were introduced with video tutorials. My son is a visual learner and excels when material is presented in this way.

CTCMath video tutorials are perfect because as my son puts it, “They are S cubed!” Simple – there is no gimmick designed to entertain which he finds annoying (let’s be honest, he often finds ME annoying!), Short – each video ranges between 4 to 9 minutes, andStep-by-Step – the problem solving method is explained succinctly and clearly.

The CTCMath video tutorials also use synchronized audio and animation which harnesses both audio and visual learning styles simultaneously.

He especially likes to skip forward or speed through the concepts he understands. Often, he’ll jump right to the practice problems and only refer back to the videos when he gets stuck.

We have been using CTCMath for a short time and I’m already seeing his confidence grow. Thus far, he has been skipping around and trying out concepts that he is both familiar with (polynomials and simplifying equations) and even challenging himself with higher trigonometry concepts.

Parental Support within CTCMath

I also like the detailed summary report that is provided. It’s broken down by course and can also be download as a PDF if, for example, I needed to provided documentation to a learning partner or charter school.

I like that there is also an optional worksheet that he can download and print out for extra practice. Upon entering his answers into the online portal, the solutions are shown to help him identify where he went wrong.

My son was interested in the Speed Skills activities. Unfortunately, these skills do not exceed level four, order of operations. As he played around with this, he decided it wasn’t as useful as he had hoped.

As we continue to progress, I am excited to try out the tasks (where I can assign specific problem sets). I want him to review concepts he struggled with previously and then also begin to work through the material he will encounter in the college course this fall. I am confident that his confidence will continue to grow and he will rediscover the joy of math he had in elementary school.

Want to try CTCMath in your homeschool?

If you have multiple children or simply want a budget friendly curriculum, CTCMath is perfect! As a homeschooler, you can receive a massive 60% discount off of the regular price.

Better yet, if you purchase any 12 Month Membership and receive a bonus 6 months for FREE! That’s a total of 18 months of online math instruction for under $7 a month!

Purchase a 12 Month Membership Here

Still not convinced? You can test CTCMath before purchasing. Simply sign up for the FREE CTCMath trial and check it out before you commit.

CTCMath Giveaway!

Right now, CTCMath is also doing a giveaway! One lucky family will have a chance to win a free one year membership for their homeschool. You can enter below. Best of luck!!

a Rafflecopter giveaway



December 11, 2017

A couple of years ago, I  shared an amazing new tech toy – Piper – which provided kids the opportunity to build their own computer from scratch all by playing Minecraft. What we love most about Piper is that the kids are involved in the construction at every level.PlayPiper

The Piper Computer Kit teaches kids engineering and computer programming through gameplay as well as the physical process of building a computer with hardware.

Piper’s mission is to empower the inventors of tomorrow by giving them the tools to build creatively today.

Piper Grows With Your Child

We have had such fun with Piper these past couple of years and are always impressed with how the company responds to our email queries as well as continually improves their product so that it can grow with the child.

PiperCodeRecently, they announced the biggest update in the company’s history … Programming!  Yes – computer programming code the kids write themselves! How cool is that?!

Kids can now learn to program and control electronics from their own Piper computer starting today! Each project contains step by step instructions to get kids engaged immediately in making awesome creations from the start. For example,

  • Make an LED blink at the touch of a button
  • Design a game to see who can set off a buzzer the fastest
  • Create a light show set to musicPiper allows you to be creative with coding from the very start.  All experience levels are welcome.

Unfamiliar with Coding Yourself?

Piper has us parents covered, too. They provide a multitude of lesson plans to ensure teaching PiperCode is simple and rewarding for students in grade third and above.  Even if you don’t know how to code yourself, you will have fun learning alongside your kids.

Check out the additional resources for educators at Piper to learn more, including how to disassemble Piper and reuse the components with new students. 

Already Own Piper? 

Existing Piper customers should follow these simple steps to download PiperCode:

  • Turn on your Piper Computer
  • Connect to the internet
  • A message will appear alerting you there is an update
  • Click on the UPDATE button
  • Say goodbye to Piper Classic and welcome to the new Piper!


June 10, 2017

For the past eight months there has been a constant click heard in my home. At the dinner table, while driving in the car, and even late at night when I am beginning to drift off to sleep, I can hear the subtle sounds of my son cubing. Cubing has become one of his passion projects and he spends every waking moment with a puzzle in his hands.

The Puzzling Impact of Erno Rubik @EvaVarga.netI had given him a traditional Rubik’s Cube a few years ago for Christmas but once it was scrambled, it sat in the corner of his bookshelf collecting dust. That was until he stumbled upon a recommended video on his YouTube feed of Collin Burns’ 5.25 world record solve. That was all it took. He was hooked.

As it is always in his hand, he gains a lot of attention and notoriety. He is now recognized around our community as the fastest cuber. Kids and adults alike bring him cubes that they “messed up” for him to solve.

His best solve time for the 3×3 is presently 7.22 seconds. He averages 13.09. Yet the 3×3 is not the only puzzle he enjoys. He also competes in 2×2, 4×4, 5×5, Megaminx, Pyraminx, and Skewb.

The Puzzling Impact of Erno Rubik @EvaVarga.netBiography

Ernő Rubik was born during World War II in Budapest, Hungary on the 13th of July 1944. His father, Ernő Rubik Sr., was a flight engineer at the Esztergom aircraft factory and a highly respected engineer of gliders. His mother, Magdolna Szántó, was a poet.

While Rubik has stated in almost every interview that he got his inspiration from his father, he also considers university and the education it afforded him as the decisive event which shaped his life. From 1958 to 1962, Rubik specialised in sculpture at the Secondary School of Fine and Applied Arts and later attended the Budapest University of Technology where he became a member of the faculty upon graduation.

“Schools offered me the opportunity to acquire knowledge of subjects or rather crafts that need a lot of practice, persistence and diligence with the direction of a mentor.”

In the 1970s, Rubik was a professor of architecture at the Budapest College of Applied Arts. It was during this time that he invented the Rubik’s Cube. The cube was originally designed to help Mr. Rubik explain spatial relationship to a class that he taught at the time. He soon realized the potential of the cube and began to get the cube mass produced, applying for a patent in 1975.

It was quickly a huge success. The cube was originally called ‘Magic Cube’ but after some discussion the name was changed to what it is known for today, Rubik’s Cube. In an interview with CNN, Rubik stated;

Space always intrigued me, with its incredibly rich possibilities, space alteration by (architectural) objects, objects’ transformation in space (sculpture, design), movement in space and in time, their correlation, their repercussion on mankind, the relation between man and space, the object and time. I think the CUBE arose from this interest, from this search for expression and for this always more increased acuteness of these thoughts…

In the nearly forty years the cube has been around, over three hundred and fifty million copies have been produced. Yet, only about 1.25% of the people who have purchased the cube can actually solve it.

The Puzzling Impact of Erno Rubik @EvaVarga.netErnő Rubik witnessed his creation blow up around the world. The cube became the Toy of the Year twice in a row, and the first world championship for The Rubik’s Cube was in 1982. At this competition the first world record was set at 22.95 seconds. Nowadays that is what most cubers average.

Today, there are a variety of speed cubes available on the market. Each is designed to turn faster and more efficiently without the lockups or pops that speed cubers abhor. The current 3×3 record is 4.737 seconds held by a 19 year old from Australia, Feliks Zemdegs.

Bring it Home

Learn to solve the original 3×3 puzzle using online tutorials; there are many to choose from.

Challenge yourself to get faster or learn to solve another puzzle type.

Visit the World Cube Association and find a competition near you to see what it is all about.

Science Milestones

Visit my Science Milestones page to learn more about scientists whose discoveries and advancements have made a significant difference in our lives or who have advanced our understanding of the world around us.

The bloggers of the iHomeschool Network have teamed up to create fun and original unit studies on fascinating people who were born in July.



June 8, 2017

Science with Harry Potter: Alchemy @EvaVarga.net Alchemy 

Alchemy is an elective taught at Hogwarts School of Witchcraft and Wizardry concerning the study of the four basic elements, as well as the study of the transmutation of substances. It is intimately connected with potion-making and chemistry but for purposes of clarity, this post will focus on transformation of rocks and minerals.

I’m particularly interested in Transfiguration, you know, turning something into something else, of course, it’s supposed to be very difficult.” —Hermione Granger regarding transformation

There are many myths and legends about the formation of the rocks of the Earth or about the rocks themselves. Every culture has its own beliefs about specific stones and those beliefs are often tied to that culture’s history, geography, and spiritual practices.

For this class students are required to become familiar with the many magical properties of common stones. Begin by writing the definitions for igneous, metamorphic, and sedimentary rock in a notebook. Include a detailed sketch of the rock cycle.

Additionally, create a two-page spread for each stone studied. Include the following information for each:

  1. photo or sketch
  2. list any historical or literary references to the gemstone
  3. describe the process by which it is formed
  4. list its magical properties

Some stones to consider are:

  • Agate
  • Quartz
  • Ruby
  • Opal
  • Flint
  • Moonstone
  • Jade
  • Obsidian

Put together a collection of rocks and minerals. Identify and label each as igneous, metamorphic, or sedimentary.

Take it Further

Learn to play Marbles, generally a Muggle game. Wizards play a variant known as Gobstones, where the enchanted marbles spit a putrid fluid into the face of the loser.

Science with Harry Potter: Potions @EvaVarga.net Astronomy & Divination

At Hogwart’s, Divination is an elective course that teaches methods of divining the future, or gathering insights into future events, through various rituals and tools. For the purposes of this course, we will focus on the ancient tools used by early navigators particularly in regards to the study of astronomy.

Generally out-of-bounds except for classes, the Astronomy Tower is the tallest tower at Hogwarts Castle. It is where students study the stars and planets through their telescopes with Professor Aurora Sinistra.

A Star chart is a written document used to represent the positions and movements of the stars, much like a map. Astronomers usually use these for research or study. An O.W.L. level wizard should be able of fill in a blank star chart based on some hours of sky gazing.

Similarly, a Moon chart is used to represent the position, movement and phases of the Moon. However, it is difficult to interpret and thus a Lunascope is often preferred.

Begin by researching the constellations common in your hemisphere and/or those referenced in the books.

Illustrate each cluster of stars in your notebook and make note of when the constellation was first discovered and how it was named. Include the names of the distinct stars (if possible).  Constellations to consider include:

  • Orion
  • Bartholomeus
  • Lupus
  • Leo
  • Ophiuchus
  • Canis Major
  • Scorpius

Create personal chart (also referred to as a birth chart) showing the relative positions of the planets at the time of an individual’s birth.

If possible, obtain a telescope with which you can observe the planets and distant stars.

Take it Further

Create a model of our solar system. Include the moons of Jupiter, Saturn, and other major planets.

Make an illustrated wall timeline of geologic time.

Draw maps of the earth at various times in history, showing movements of the tectonic plates. Include time periods that show Pangaea, Laurasia and Gondwanaland, and the modern arrangement of continents.

Illustrate the layers of the atmosphere in a poster. Label and describe each layer.

This post is part of a five-day hopscotch. Join me each day this week as we dive into each course.

Herbology (Botany)

Care of Magical Creatures (Zoology)

Potions (Chemistry)

Alchemy & Divination (Geology) – this post

Magical Motion (Physics)



May 15, 2017

When I heard that Prince had passed away, I was substitute teaching in a kindergarten classroom. My mother-in-law had texted me and I immediately pulled out my phone to confirm. It couldn’t be true.

It was the first time the death of a celebrity hit me in a real and immediate way. There was first disbelief, followed by dread and nausea. I struggled to keep it together until the dismissal bell released me. Then the tears that wrung out of my body were so strong it gave me stomach cramps.Prince Lessons

I drove home and immediately crawled into bed. I got a call from my mom asking if I was okay. She knew my heartache for she had experienced a similar loss when Elvis passed.

I am very grateful that my mother recognized his impact on my life very early. She purchased my first concert ticket for his Lovesexy tour in 1988 and drove seven hours one way to assure I could see him perform live.

“I’m a musician. I am music.” ~ Prince 

I would see him perform once more in Portland in 2004 for Musicology. I had hoped to see his Piano & a Microphone tour in 2016 but missed my chance.

Since his death on April 21, 2016, I have watched numerous video clips of his live performances, interviews, and amateur tour footage that have been shared online. The explosion of material now available have provided his #PurpleArmy with the solace we seek, an opportunity for one more connection with him.

Prince Rogers Nelson

Prince Rogers Nelson was born June 7, 1958 in Minneapolis, Minnesota. His parents, Mattie Della and John Lewis Nelson, and grandparents were from Louisiana.  His parents separated when he was ten years and he subsequently repeatedly switched homes often as a teen. Yet music was always a strong element in his life.

Prince first began recording in 1975 with 94 East. A year later he signed a recording contract with Warner Bros whereupon they agreed to give him complete creative control.

His talent was limitless. He was a master composer, musician, and revolutionary artist. I dare say there is not a single artist in my lifetime who has influenced the sound and trajectory of music as much as he.

“I’m no different to anyone. Yes, I have fame and wealth and talent, but I certainly don’t consider myself any better than anyone who has no fame, wealth or talent. People fascinate me. They’re amazing! Life fascinates me! And I’m no more fascinated by my own life than by anyone else’s.” ~ Prince

A Legacy of Equality

I first discovered Prince while watching Night Tracks on TBS. They had aired two performances by him back-to-back, Little Red Corvette and 1999. I was immediately attracted to the music and his individuality. He was like no one else. He was different.

“I don’t really care so much about what people say about me. It usually is a reflection of who they are. For example, if people wish that I would sound the way I used to sound, it says more about them, than it does me.” ~ Prince

As the years progressed, his style evolved. Through it all, strong female musicians were an integral part of his band. They were not solely backup singers or dancers (though he did have those as well) but his partners – Wendy Melvoin, Sheila E., Rosie Gaines, and Candy Duffer amongst others.

Emma Garland recently stated that women are generally portrayed as passive objects in music, which is to not exist at all. “With Prince, they were addressed with awe and empathy. He wrote about women as real, powerful, complicated, sensitive, and sexual beings that he could learn from, and who enriched his life.”

Prince_FreeA Legacy of Freedom

He caught the media’s attention early in his career with his stage presence and outrageous costumes. Many of his songs were overtly sexual. Yet, Prince never made any apologies for who he was and always preached that the most important thing is staying true to yourself.

“Despite everything, no one can dictate who you are to other people.” ~ Prince

He showed me early the power of living one’s life by one’s own rules and no one else’s. He empowered me to walk my own path and to not be persuaded by others to follow the crowd.

Throughout every emotionally difficult time in my life, I’ve sang the lyrics to his songs in my mind. Repeating stanzas like a mantra. The song that had the biggest impact on me was most assuredly Free (lyrics shown above).

A Legacy of Compassion

Prince was also a secret philanthropist, supporting causes including youth empowerment, animal rights, racial justice, and clean energy for all. His compassion for the others was an important part of his legacy.

“Compassion is an action word with no boundaries.” ~ Prince

The legendary musician was renowned for speaking out on behalf of those who were vulnerable and voiceless. According to federal tax forms, his charity, Love 4 One Another, gave more than $1.5 million between 2005 and 2007 alone.

A new mural of Prince has been unveiled from 10:10 on Vimeo.

The climate charity 10:10 recently commissioned a new mural in honor of Prince’s contributions to environmental causes in Camden, north London. The mural kicks off their six-week campaign to provide solar panels to food banks and charities – groups that reflect the commitment to community, creativity and humanity that Prince demonstrated in life with his secret philanthropy.

“If you ever lose someone dear to you, never say the words, ‘They’re gone.’ They’ll come back.” ~ Prince

When he gave, he made only one request, to not publicize it. He wanted no publicity or accolades for the gifts he bestowed. Many of those who were impacted by his generosity only began sharing of his compassion after he had passed.

A Legacy of Love

Throughout his career, he brought cultures together. Uniting sexes and working to instill his message of love for one another. His fans or #PurpleArmy continue to share his vision.

Spirituality has always been a part of his music. Prince’s musical and lyrical explorations of spiritual themes are evident in each and every album he released. More importantly, he embodied and lived by his spiritual principals.

So many reasons why
There’s so many reasons why
I don’t belong here
But now that I am I
Without fear I am
Gonna conquer with no fear
Until I find my way back home

~ Prince, “Way Back Home”

When I think of Prince, both his music and his life overall, I don’t so much think about religion. When I think of him, I think of love—not romantic or sexual love—but unconditional, human love. A love that transcends gender, race, or religion. A love not limited to one’s family, social circle, community or nation. A love we are most in need of cultivating if we are to grow and evolve.

Prince logo.svg