# Category Archives: Math

# I hate math…

I don’t really hate math, but that’s the title of my post because it’s going to be about someone who DID hate math and how that all played out. Feel free to apply the concept to any particular subject your child hates and your own struggles with that. 😉

Back when I was paving the way with my oldest (Emily), I worried about my children’s futures in the context of my homeschooling choices. There is a lot of responsibility placed on a homeschooling parent’s shoulders. Like, if you don’t get the BEST, PERFECT, MOST WONDERFUL curriculum, you will destroy your child’s love for learning and all her future college scholarships and she will end up pushing a shopping cart *only not at the store*. Yeah. That. Nevermind if it costs $159,897,657. You can afford it. Your children are worth it. What kind of mom would not mortgage her house for her child’s future!? The catalogs beckon. The siren call of a better math, writing program, history core, grammar workbook and everything else lures you as you go about your never-ending search for THE ONE. The one curriculum/program/workbook/video/online program/something that will teach your child perfectly. And she will love it. LOVE IT. Come bounding out in the morning with a smile wanting to do it. And her future will unfurl with sugar coated bunnies and baby chicks dancing in a field of yellow flowers and dollars – growing on trees. Because it’s her FUTURE we are talking about. Her earning potential. Her happiness. My future great-grand babies living situations! Generations could be affected by the wrong choice!

So, the point is that I worried about choosing the right thing. I wanted to find something that spoke to my daughter’s learning styles, was fun, something she loved, and would help her become everything that she had the potential to become. Oh, and it had to be something I could teach. That too. 😉 Every homeschooling parent’s dilemma.

So, picture me, with my lovely 3 children sitting around the table with our books cracked open and me teaching that when you are doing long division you bring down the number and some other mumbo-jumbo algorithm and then I assigned some practice problems and we all smiled and had a terrific day. Not.

The whining started. It was Emily. Whining. Again. Oh wait…was that a teeny, tiny tear sparkling in the corner of her eye? Tears? A flood? My kitchen pipes burst? Emily was crying AGAIN over math. “I hate math!!!!!!!!!!!!!!!!!!!!!!!!!” (That’s me quoting her.) “I can’t do it.” “I don’t get it!” Insert more tears and crying and at least whining. I just knew we were heading toward disaster. She had to learn math. If she didn’t learn math, well…how would she buy food at the grocery store and get good deals and pay her bills and and and…. succeed???!!! At anything??!!! You know, it all ends at the shopping cart. The one…not in the store. Little note: I’m not making fun of homeless people. I’m being sarcastic. Honest. I did worry though…I think we all do, to some extent.

I began the search for the perfect math curriculum. I researched. I studied. I looked up stuff online (when there wasn’t as much online as there is today). Then I started buying. Math stuff. Math workbooks. Math manipulatives. Math programs. Math curricula. Math. Math. And more math. Do you know I still have math workbooks from back then that have never been used?

And I worried (yes, I know I said that – but it must be *emphasized*!). What if I didn’t get it right? What if she never learned math the way she was supposed to? It would be my fault because I didn’t do a good enough job. Because I didn’t find the right thing. Because I didn’t spend enough, try hard enough, research enough. Etc.

And what if she kept on hating math?!! It would be a total tragedy because my job as a homeschooling parent was to light a fire in her heart for all learning. The last thing any homeschool parent wants to hear is, “I don’t like school.” The last thing a homeschool parent wants to think is that somehow future college math courses won’t be successful because math wasn’t learned well enough at home. The last thing a homeschool parent wants to see is a child not succeeding as an adult because of something that didn’t get taught properly in your homeschool setting. Well, that’s a lot of “last things” you wouldn’t want to think. I guess they can all crowd together at the last together.

Ok, so fast forward through the years (and plenty of tears – oh, and whining): Emily graduated from high school and guess what? She did not like math. She even had to REPEAT some really easy basics. Oh yes, I took her back to addition and subtraction. In the SIXTH GRADE. And she did algebra TWICE. There were glimmers of math-like, like when she tried Teaching Textbook’s Algebra II and Geometry and actually loved it (for a little while). But oh my goodness, Teaching Textbooks didn’t have a higher level math ready yet. And you’ve heard the stories on those super rigorous homeschooling boards about Teaching Textbooks, I’m sure. How non-rigorous it is. How….(let’s whisper here) *it will damage your child’s ability to do math at a higher level in college and hence destroy her future chances.* The math love petered out due to the unavailability of more Teaching Textbook levels… and horrors! Emily didn’t even take a math course during her 12th grade year.

Did I fail? Was Emily’s future destroyed?

No. Emily has been successful in her college math classes and has even tutored high school math through a charter school. Take that Teaching Textbooks haters! Take that worries that plagued me! Not only has Emily received great grades in math, she actually teaches it to other homeschool students and gets paid to do so! Was it because I finally found Teaching Textbooks and helped her enjoy math for the first time? That might be a small part of it, but certainly is not the entire reason. I think it’s more about the fact that she was allowed to go at her own pace, repeat things when necessary and I taught her something more important than loving a school subject. I taught her to learn. I taught her to know how to figure something out *herself*, when she really needs to. I taught her to love God and depend on him when the going gets tough (or math needs to be learned, lol). That wasn’t in any curriculum or program or schedule. That was just in me, loving her, believing in her and encouraging her, even when she hated math.

So, next time you are panicking because your child hates a school subject, take a deep breath. No one has to love everything. And that’s ok. I promise.

Next time you are stressing over which perfect curriculum to buy, take a deep breath. You’ll teach it one way or another. If something doesn’t work out, you can try again. You can even start over. We did.

Next time you are tempted to spend money on something you probably don’t really need…put away your wallet and wait. Breathe. Decide if you really need to get something new or if that new curriculum love just wore off. It’s ok to switch and change gears because sometimes you really do need to. And sometimes you don’t. And you know it, but wish you didn’t. 😉

Next time you’re worrying that your current homeschooling choices might forever damage your children’s futures, take another deep breath! It’s not as much about what you choose or don’t choose, it’s about the life lessons you teach. It’s about the kind of person your child becomes. Those lessons don’t come in a package and they don’t cost anything. They are grounded in right choices and a dependence on God. Pursue Him first, and the rest *happens*. Yes, there may be detours and you may not even end up where you thought you were or wanted to go…but you’ll get where you’re *supposed* to be. And your kids will too, if they do the same thing. THAT is the important thing to teach.

Emily is a good (and successful!) person who has sought God first in her life and everything else has fallen into place. Even math.

Proverbs 9:10 – “The fear of the LORD is the beginning of wisdom…”

May God give you peace in your heart as you struggle to find “the right/best/most awesome curriculum”. 🙂 May He soothe the trouble in your spirit and wipe away your worries as you wonder how everything will turn out in the end.

Romans 8:28 – “And we know that all things work together for good to them that love God, to them who are the called according to his purpose.”

# Learning about ratios and proportions

Today Otter explored ratios and proportions using ETA’s Hands-On Math Standards book.

I handed Otter the bag of plastic square tiles and told him to pretend that each tile measures 1 square foot. I then asked him to build a pretend “porch” in the shape of a rectangle measuring 45 square feet. I told him it takes 3 pints of paint to paint his new porch.

I then asked him to figure out how much paint he would need for just 15 square feet. This is how he found the answer.

After that I asked him how much paint would he need if the porch measured 75 square feet! He figured he would need 5 pints.

After this activity and a worksheet from the ETA book we talked about changing proportions, like doubling a recipe for cookies. Proportions are now a crystal clear concept instead of a math term to be easily forgotten!

We’ll be doing a lot of hands-on math activities this year to really get ready for algebra next year. You can read about some of the resources I’m using this year in a previous post here.

# Making Math Fun with Hands-on Pre-Algebra

It’s not often that Otter asks to do MORE math. However, after incorporating some recent hands-on pre-algebra activities into our summer studies, I’ve been hearing that quite a bit!

Transitioning from concrete math to the abstract can be a little tough for some kids. It doesn’t have to be though! Below are some of the resources I’ve used to help make pre-algebra not only tangible, but also fun.

Exploring Algebra and Pre-Algebra with Manipulatives is one of Otter’s summer favorites. Chock full of lots of activities, this book even comes with tear-out tiles you can use for some of the games. You do need to copy some of the pages though for things like the algebra dominoes, game boards, and activity sheets.

Otter was having trouble solving equations like “40 – 2X = 6”. Looking at rows of problems like that in his math text just made his eyes glaze over. After playing a game with some math dominoes, he was solving these types of problems like a pro and then asking if he could do MORE. After I picked my jaw up off the floor we played for about an additional 45 minutes or so.

Another big hit is The Hands-On Equations Learning System. I honestly think this is Otter’s favorite math “program” he’s ever used. Every time I pull it out he’s enthusiastic and his math confidence soars.

Basically the program takes something that is usually thought of as abstract and makes it totally concrete, helping to lay a terrific foundation for algebra. I really wish I had had access to something like this when I was a kid.

UPDATE: You can now get the Hands-On Equations Learning System via a set of apps and save a TON of money:

Hands-on Equations is so easy to use and understand. In the above picture, Otter is solving the equation 5X – 3X + 2 = X + 5. In this particular lesson he is learning to take away pawns as part of the set-up process. So, the first thing he needs to do is get rid of 3 pawns from the left (that’s the 5X – 3X part). Once he’s done that, he has things set up and is ready to solve the equation.

The next thing he would do is subtract one blue pawn from each side (because it’s a balance whatever you do to one side you must do to the other!). Finally, he would subtract 2 from both sides (get rid of the red 2 cube and replace the 5 cube with a 3) and come up with the final answer of X=3.

Afterwards he has to check his work. He checks it by looking at the original physical setup, NOT the original abstract equation. This way he understands the concrete meaning of the abstract equation.

The program comes with 3 levels of books and each step is spelled out visually to help you easily teach each concept. There is also the option to purchase DVDs, but the books were enough guidance for me.

I also order the Verbal Problems book that goes with the program. Using this book, he’ll be able to solve problems like the following by using hands-on methods that really help make the meaning and problem solving clear:

Dave had one package of cookies in his bag. Ed received 4 cookies from a friend on the bus to add to the 2 packages that his mother had packed for him. Andy did not eat breakfast that morning, so he had already eaten 2 cookies from his one package of cookies. Each package of cookies had the same number of cookies at the start. When the boys were ready to eat the cookies, they counted a total of 10 cookies. How many cookies were originally in each package?

You can purchase Hands-on Equations from Amazon or Rainbow Resource for around 35.00. It’s one of the best supplementary math purchases I’ve made.

Another hands-on pre-algebra resource I bought is ETA’s Hands-On Standards Math Online for grades 7-8. You can order physical copies, but I found it easier to use the online version which is basically PDFs you can print out as needed.

Each lesson has full-color lesson pages as well as black and white student pages to print out and work on. You can look at some of the sample lessons online for free. The only downside to the program is that you have to purchase a lot of manipulatives. Fortunately I already had some of the required items, but I had to search all over the ETA website for the rest of the ones I needed and the cost added up pretty quickly (over $100 bucks for the program and the manipulatives!). I also had to put in a special request for a single order of some algebra manipulatives as they only had a classroom sized set listed on the website. Because of this, I would recommend the other two previous resources, if you are looking for something that is **inexpensive**, quick and easy to implement your math studies. However, if you really need more, the ETA program is well put together with lots of different “things” to play with while you are learning math that help keep the interest level high.

Just because you’ve got a middle schooler or a high schooler doesn’t mean you have to stop using manipulatives! In fact, for some kids (like Otter), they really help foster a true understanding of higher level math. Pre-algebra doesn’t have to be boring and it doesn’t have to be hard!

# Free 30-Day Trial for “Gizmos”

courtesy of ExploreLearning Gizmos™

ExploreLearning.com has a free 30-day trial where you can have full access to their entire library of 450 Gizmos. The Gizmos are interactive math and science simulations that really help make learning concepts clear and easier to understand. ExploreLearning has a variety of Gizmos for grades 3-12 that cover topics like:

- Number and Operations
- Algebra
- Geometry
- Measurement
- Probability
- Precalculus
- Earth and Space Science
- Biology
- Chemistry
- Physics
- Physical Science
- Life Science

Once you choose a grade range and category, you get to choose specific Gizmos to play with like some of these:

courtesy of ExploreLearning Gizmos™

When you choose the Gizmo you want you then have the option of choosing some of the available printables to use with it like a student exploration sheet, teacher’s guide, vocabulary sheet, assessment questions, etc. (each Gizmo will not necessarily have every option available). In the screenshot below you can see that this Gizmo on pollination has a printable student exploration sheet as well as a vocabulary sheet available. Available printables are highlighted in blue.

courtesy of ExploreLearning Gizmos™

The student exploration sheets are a terrific help. This particular one is 5 pages long with various questions, activities and specific directions to help your student get the most out of the Gizmo. They are totally optional though. Sometimes your student may just want to plunge into the Gizmo and “play”. Other times he may need more assistance or you may want him to get a bit extra out of the lesson. The student exploration sheets offer both. They also look good in a notebook and/or give mom some tangible evidence of the kiddo having done some actual work and gained some understanding.

courtesy of ExploreLearning Gizmos™

The Gizmos themselves are interactive. In this demonstration of cross pollination I’m moving some pollen grains from one flower to another. The activity continues with animation and more opportunities for interaction.

courtesy of ExploreLearning Gizmos™

I’ve used Gizmos in the past with Otter and found that they are excellent in making various concepts clear and easy to understand. Some of my favorite Gizmos are in the math section. Gizmos take abstract concepts and help make them concrete – something your student can “touch” and manipulate. I’ve found them to be a big help in supplementing Otter’s middle school math lessons.

Look at this Gizmo where you get to learn about square roots:

courtesy of ExploreLearning Gizmos™

Suddenly square roots aren’t just some abstract concept! You can SEE what a square root is instead of having it be scary, weird looking math term.

Anyway, I thought I’d pass on that ExploreLearning has a free trial. I know a lot of you are still ironing out curriculum choices for next fall and perhaps this might help a few looking for a boost in science and math. It also would make a great resource for some “summer learning fun”.

Click here to visit ExploreLearning’s website (www.explorelearning.com). You can also contact them toll-free at 1-866-882-4141. If you decide to order a subscription, be sure to ask them about a home account.

# How to Convert Metric Numbers Help Sheet

# Pre-algebra Math Schedule

I recently finished scheduling out Otter’s 7th grade math (pre-algebra). For each lesson I linked to various videos, books, games, Khan Academy lessons, BrainPOPs and more to make things more interesting and fun! If you’d like to take a peek or use it as a template for your math, click on the one of the links below to download the Microsoft Word document.

math.doc (older versions of Microsoft Word)

math.docx (Microsoft Word 2007)

# Math Help Sheet

I’m in the process of making Otter a mini office to help with a variety of subjects. Today I made him a math help sheet and am sharing it here with you.

Click here to download the PDF.

# Math Mammoth Fractions

One of the challenges of homeschooling is finding a program that works for each child. Years ago, we used to plan things out like this: buy a program for the oldest, save it for the middle child and then pass it on down to the youngest. It was a good plan. A money saving plan! Something where I could count on having books on the shelf ready-to-go and milk every penny’s worth! However, that plan crashed and burned because, *gasp*, all three of my children have different learning styles and preferences. What worked for one, simply did not work AT ALL for the other. So, I have a lot of different programs. Bad for the pocket book, but good for when my youngest hits a wall and needs a new approach. It’s like a lovely buffet of homeschool curricula to choose from. A veritable catalog ensconced in pine shelves that I can pick from at the first sign of a mental obstruction.

However, even with a plethora of materials to choose from, sometimes, even still, NOTHING works. Like lately. Otter doesn’t understand fractions. Teaching Textbooks didn’t work. Math-U-See didn’t work. Singapore didn’t work. Life of Fred – nope, didn’t work. Websites – worked for a while, but very inconvenient. I tore through math curriculum, workbooks, worksheets, pdfs, online lessons, videos… trying to find the perfect program that didn’t rely on Otter memorizing rules. I needed something that took a visual approach since he’s not ready for the cognitive leap to the abstract. Yes, some of the programs I tried started out with a visual approach. However, they dropped it too quickly and left Otter confused. He needs lots and lots of practice with visual reminders of what he is doing and why. He also, for some goofy reason, seems to get it when fractions are presented as circles much better than when they are presented as bars. (????) Maybe imaginary cookies are more motivating? Oh wait, yesterday he was calling them “Star Wars shields”…

Finally, I found an answer: Math Mammoth Fractions. For just $9.50, I was able to instantly download 2 full size workbooks in PDF form with exactly the kinds of lessons Otter needs. The workbooks contain clear, self directed lessons with visual models of pie(s) all throughout the pages. There are also printable manipulatives at the ends of the books for kids who may need a more hands-on component.

Now Otter is successfully going through his fraction lessons without feeling frustrated. All is well in the land of homeschool math again!

You can check out more Math Mammoth workbooks and even sign up to download 300 free worksheets. There are all sorts of sample pages to look at, as well as videos and other helps.

# Free Linear Algebra Textbook

I hardly ever blog about Bear. He’s such a big kid that there aren’t a lot of projects to take pictures of. However, I thought I’d share a gem that I found recently, in case it helps anyone else.

Bear “ran out” of homeschool math courses last year when he completed Calculus. While I waited for Life of Fred’s Linear Algebra book to become available, he messed around with various Art of Problem Solving books.

I was finally about to order Life of Fred, when I came across a textbook written by Dr. Jim Hefferon, a Professor of Mathematics at Saint Michael’s College. Not only can you download the entire text for FREE, but it comes with answers to the exercises. I also found some linear algebra video lectures from MIT. I’m really thankful that people share their hard work with others online. It’s such a blessing to our family.