Repeating decimals

I consider myself to be pretty good at math...I have a thorough math background, I've homeschooled my kids in math (so it's currently in my thoughts!), I am a math tutor, and I am learning calculus through self-study.

SO -- I would've thought that I would know how to do this already, but it's new to me!  I learned it actually when I was tutoring a student (haha!!)--and then I came home and taught it to my kids :)

The question is how to convert a repeating decimal into its fraction. Now we probably all already "know" some repeatig decimal conversions (like .3333... and .6666....) but at least for me, I did not know how to convert them to their fraction--so here it is!

If you have a repeating decimal, we'll use .333... first (sorry I'm not writing it with the line over top, I can't figure out how to type it that way on blogger!)

We will set x=.333...

Okay, so you look at the decimal and see how many digits are repeating. In this case, it is one. You will now multiply both sides of the equation by a multiple of ten with that many zeroes after it (so for one repeat, you multiply it by 10).

so now we have

x=.333...
10x=3.333...

now we will subtract the original from the multiple of ten one.

          10x = 3.333...
    -         x= 0.333....
             9x=3

Okay, so now we solve for x by dividing both sides of the equation by 9, which gives us the fraction
3/9, which we reduce to 1/3!

Cool, huh?

Let's try a number with a longer repeat. How about .512512...

We'll  look at the repeat, and it is three digits, so our multiplier will be 1000.

so x=.512512... and 1000x=512.512...

subtract:

1000x=512.512...
 -      x=   0.512
   999x=512

divide both sides by 999 and you get 512/999. 

Pretty easy, huh? :) So there's your math lesson for the day :) :)

High school :)

What does homeschooling your high schooler look like? When I look at blogs and other media posts of other people homeschooling high schoolers, they look so interesting, exciting, sophisticated. Here's what my days recently include, with homeschooling my 12th grader.

       

Ahh, calculus and advanced physics. Just trying to stay a day or two ahead of my student. Doing homework (mine!) at 11 pm when the house quiets down. It's an exciting life I lead... ;)  Like literally, I am up doing homework five nights a week, so I can be prepared to teach/explain/help him! I never took calculus, so this is all fresh to me :)

I'm not complaining:) Every life stage is different and big picture it is a joy to be a mom, and a homeschooling mom, at that.

It's sometimes I just look at others' beautiful pictures of their homeschooling lives and wonder why they're so picture-perfect when some days ours is more like...work.

Is it because what is being shared is the prettiest parts of the day? Or is it real life and our real life is just different? 

SO, I'm curious...those of you homeschooling high schoolers, what do your days look like?

PSA ... ticks :/

Don't forget that even though it's winter...if you have unseasonably warm weather and go for a hike...those awful ticks are still around and looking for a good meal from you. Don't forget to do tick checks!!

(I HATE those things!!! This one was on my belly after a walk in the woods today).

Ultimate PreK-12 Annual Membership with SchoolhouseTeachers.com -- my REVIEW

Disclaimer: I received a FREE copy of this product through the HOMESCHOOL REVIEW CREW in exchange for my honest review. I was not required to write a positive review nor was I compensated in any other way.

Every year our homeschool life evolves a little more. Many of the courses and curricula that we used with my oldest daughter are still a part of my youngest daughter's school day, though some have been changed or replaced--and some new materials have been added!  Today I want to mention to you a homeschooling resource that homeschoolers with any age child will want to check out. That resource is an online subscription to  SchoolhouseTeachers.com and their Ultimate PreK-12 Annual Membership. This is a website which is filled with different online or offline content and curricula to assist you with your home schooling.



I write a post about this program every year, and still never can really do it justice! It is such a compilation of courses on different subjects that you can use with your preschooler, your elementary student, your middle schooler, your high schooler, and even for yourself!  (Here are some of my past posts about this great homeschooling resource, from 2017, 2018, and 2019).  My family has used different parts throughout the years, and it is really a great site to have access to for so many reasons!

The site is not stagnant or old, it is constantly being updated, with new material added all the time. If you have used it in the past, check it out again! I'll bet there are new parts that you have not had the opportunity to use yet! And if you have never used it, DEFINITELY check it out and consider an Ultimate PreK-12 Annual Membership. For a year's access, the price is amazing.

So let me tell you about some things I'd like to highlight this year :) . I have said that the site contains courses for all different ages. My children are high school age now and we are kind of set in our curricula, but still like to use some parts of SchoolhouseTeachers.com.

Some of the things that I appreciate about this resource are the comprehensive course outlines and lesson plans for the courses.

(yes, I scribbled on it--didn't want to give away their info!) 

This information is so helpful to help you decide which courses your students will utilize--it's also helpful with planning and REALLY helpful at end of the year time if you have to submit summaries to your state department of ed (or whatever you do to summarize your schoolyear).

There are additional planning resources, such as suggested lesson schedules and transcript helps.

(oh, since I said "transcripts" I will quickly mention that there are ideas and tips for transcripts as well, complete with ideas for creating a transcript and downloadable samples!) 

My children have used many of the courses in the past, some of their favorites were economics and geology. Though we have a "book" science curriculum that we use, I checked out some of the science courses offered on SchoolhouseTeachers.com just for fun and was impressed with what I saw. The advanced chemistry looks like a thorough course, with videos and worksheets, practice problems, tests (and answer keys, yay!) and more! The two-semester course looked very comprehensive and the videos were easy to listen to and understand (lots of explaining!).

Recently, the sections that we are using the most are the videos (brought to you through Right Now Video) and the World Book Encyclopedia.  

There are so many videos, lectures, studies, courses in the video area. We have watched some leadership videos, some funny videos, some Bible study and theology videos. My husband is even planning to watch a series or two with them.  

(I can even watch the videos on my phone!)

My daughter's favorite thing currently is the World Book Encyclopedia section. She asked to be able to write her thoughts on that--so here's what she says:

"The student part of World Book is easier to use this year. It's pretty easy--you type into the search bar and it brings you to different articles, videos, tables, sounds, pictures, etc. They also have different sections on the main page that are cool. There are timeline things and interactive maps too!"

There are many things to love about this great resource. It has so many classes, some shorter than others, that you can easily use some to grab an area of interest or excitement with your child and help them learn more deeply about it. It is the kind of resource that you can use in the way that YOU want to!

Something that I haven't used (because my kids already read!) is the literacy center found on the site. It is full of great ideas and courses for a struggling reader or special needs reader (and their parents!) One part I checked out was some of the phonics lessons, which have an audio portion alongside worksheets. There are also some "Focused Learning Areas" which help students who are struggling in areas other than reading. I am just amazed at the scope of the offerings on this site!

Another thing you might want to check out (especially if you have middle/high schoolers) is the career exploration course! Fun, interesting, and educational!

The format of each course is different. Some are mostly videos with worksheets accompanying them. Some have powerpoints. Some are just worksheets or course outlines. They are easy to use, easy to jump right in without needing a lot of hand-holding.

Well, I've said a lot, but have just barely scratched the surface. I suggest you go over to SchoolhouseTeachers.com and look around a little--and seriously consider the Ultimate PreK-12 Annual Membership--right now they're running a special through the end of January 2020 of only $99 for a year!! There truly is something for everyone on it!

If you'd like to read some more review on this great product, please click on the link below!

Back from vacation? :)

We're back! Back from the vacation!

What vacation? Well, no vacation, really...but I've been pretty slack on the blog this holiday season :) Spending time with the family and not online has been our theme.

The total favorite family game this season is Ticket to Ride :) I posted about this game before, and now that we've had a couple of weeks with my family all together, I can definitely say it is a WINNER!!!! We have played it with age ranges from 5 to 75 and it's always a blast! It's a fast moving game, and everyone enjoys it!

A bonus is that our library also has a copy of the game for lending, so if we have more than the five of us, we can borrow the extra set from the library and have two games going on simultaneously, side by side! :)