Money Fun

A recent trip reminded me of one practical way math serves as a useful tool–money conversion. On our trip, we saw prices listed in dollars, pounds, euros, forrents, and marks–and needed to use some quick math to figure out how much we were really spending : ). We employed addition, subtraction, division, and round/estimating at various times throughout the trip.

As you study different cultures in history, consider having your child learn about their money systems too. Simply search the Internet for “money” and the country’s name. You should be able to find some pictures and descriptions of the money in that country. Then search for exchange rates and see how the money compares to American money.

If your child is young and just getting used to American money and math facts, you could simply show your child the pictures of the money, explaining that different countries use different money systems just like they use different languages, and that math helps us compare prices. If your child is proficient with math, you could actually have your child pretend to go shopping in the foreign country and figure out how much something marked in that country’s currency would cost in American dollars. You could even set up a pretend shop!

Math is truly a useful tool!

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Free Workshop Invite, Book Update, Math Information Online

Things have been piling up to post, so this post will contain quite a few different things.

Free Workshop
First off, I wanted to invite you all to attend a workshop this afternoon (Tuesday, March 18, 2008) at 1:00 p.m. CST I’ll be giving on teaching math biblically. You can attend right from your computers–and it’s free! The workshop is being done through Cindy Rushton’s Ultimate Homeschool Expo as one of their free, pre-conference preview chats. The chat will be archived and available after the conference begins to attendees, but it’s only open to everyone this afternoon. To join, follow the instructions at the bottom of this post. (I apologize for the late notice.)

Math Book Update
Next, after several drafts and a name change, my math book is actually nearing completion! The book is now titled Revealing Arithmetic, and serves as a guide for teaching arithmetic concepts from a biblical worldview. Revealing Arithmetic will walk through teaching basic arithmetic concepts from counting clear through long division, offering an overview, example presentation, reinforcement ideas, and much more. Thank you all for your continual prayers.

Math Information Online
We recently posted an article adapted from Beyond Numbers to our site and reorganized some other math information. I hope you enjoy!

I also recently found an article on biblical math online I think you some of you might find helpful. Vern S. Poythress helpful, although more intellectual, essay titled, “A Biblical View of Mathematics” is available online at www.frame-poythress.org/poythress_articles/1976Biblical.htm.

Please Note: I’ve not had a chance to look at any of the other essays on this site or by Poythress to know their merit or theological content. I mention this particular article because it looked helpful.

Instructions for Joining the Workshop (from Cindy Rushton)

When you are ready to enter, you will enter your NAME or EMAIL ADDRESS in the first blank.

Add the following information when prompted:

Name of Room: Talk-a-Latte

Password: letschat (for Preview Chats)

Remember…your password is different for chats and other classes. It only works for the room when the room is open for the study.

The Golden Ratio – The Creator’s Mark Throughout His Creation

Updated 11/13/15

Some time ago, someone wrote and suggested I write something on the golden ratio. I hope to finally post something on the topic today (this post has been in progress now for QUITE some time).

The “golden ratio” is a special name given to describe a ratio that seems to relate indirectly or directly to many aspects of God’s creation. The ratio is approximately 1.618 (see Wikipedia for a more exact definition).

To understand how we observe the ratio 1.618 in God’s creation, we need to take a look at a special sequence called the Fibonacci numbers. This special sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…and continues, with each new number formed by adding the previous two numbers together (1 + 2 = 3, 3 + 5 = 8, etc.). The ratio between most numbers in this sequence is very close to the golden ratio. This means that if you were to divide two neighboring numbers in the Fibonacci sequence, you’d get a number close to 1.618!

Since we find neighboring Fibonacci numbers all over creation, it follows that we also find the golden ratio all over too. For example, the seeds in any given sunflower are arranged in two patterns of spirals. If one of the patterns has 55 spirals; the other will have either 34 or 89—the number of spirals in each pattern are always neighboring numbers in the Fibonacci sequence! This also means that the ratio between the two patterns is always very close to the “golden” ratio. No matter how large or small the sunflower, one spiral pattern always contains approximately 1.618 times the number of seeds as the other pattern. Guess what? This ratio allows for the most number of seeds to fit in any given sunflower! God sure thinks of all the details, doesn’t He?

If we were to look at plants, pinecones, or pineapples, we would again find Fibonacci numbers and the golden ratio and be awed again at the Creator (please see the websites listed at the end of this article for a more detailed explanation). Scientists have even found ways where things like the nautilus’ shell relates indirectly to the golden ratio. And artists and architects have discovered that rectangles based on the golden ratio are artistically pleasing (surprise!).

Many marvel over how the golden ratio (and numbers in the Fibonacci sequence) keeps popping up all over creation. As Christians, we know the ratio appears everywhere because God designed the golden ratio to have the properties it has, and then designed each part of His creation with infinite care and wisdom, using this ratio to give sunflowers, pinecones, and more just what they needed. He also created our minds to appreciate this same ratio as something “beautiful”—as testified to by the many buildings and paintings that incorporate this ratio.

Below are four sites that offer more details about the golden ratio. The first two approach the ratio from a biblical perspective; the last two do not have a biblical perspective, but contain some fascinating information and easy-to-understand explanations of the Fibonacci sequence and the Golden Ratio you might find helpful.

Note that one of the sites uses the name “golden mean” instead of “golden ratio” to refer to this ratio. The sites also refer to the “golden rectangle” or “golden section”—this is a rectangle whose sides follow the proportion of the golden ratio (one side is approximately 1.618 times the other side). Most of the sites also discus the Fibonacci sequence—remember that neighboring numbers in this sequence have a ratio that approaches the golden ratio.

I hope you enjoy!

Table Math

“How many math concepts could you teach using just the objects on this table?”

The question came from my brother. We had just finished eating dinner, and I was brainstorming with him about some decisions I needed to make regarding the layout and content of Unveiling Math

I looked at the objects on the table—our leftover food and an assortment of dirty dishes. These were hardly objects one would ordinarily think to use to teach math concepts.

Yet as I began to answer the question, I realized that one could really teach nearly every math concept using just the items on that table. Addition, a method of recording the way God causes objects to add together can be demonstrated by “adding” the forks or cups on the table! Subtraction, multiplication, and division could be taught in a similar fashion by subtracting, multiplying (adding in sets), or dividing (splitting up) the silverware or plates. Fractions could be presented as one way of recording partial quantities by cutting up the left over food and demonstrating how each part could be represented. Decimals would follow in a similar line. The table itself presented the perfect springboard for presenting shapes and geometry. Since algebra is just a way of generalizing about quantities, we could really use an a or an x to represent the various objects on the table—or about the height of the table. Economics and statistics, as well as linear graphing and calculus, would come into play if we began to talk about the process of growing the food and selling it to the restaurant…

I finally had to stop myself in amazement. Who would have thought that just a simple dinner table could prove the perfect classroom?

The Masterpiece in Math

The other day, I had an opportunity to look at an Impressionist painting. Up close, the painting looked like globs of paint on a canvas. But from a distance, those very strokes of paint transformed into boats, shadows, and buildings—objects that simply would get mistaken for meaningless swirls of color unless the viewer took the time to step back and look at the big picture. Then, and only then, would he see a masterpiece.

As you teach math to your child, remember to step back and behold God’s masterpiece. Don’t get so lost in all the mechanics of writing and solving problems that you forget their purpose. Just like the brush strokes in a painting, they’re just the means by which we attempt to record on paper the beautiful and faithful way God holds this universe together. There is a beautiful masterpiece to behold in math.

Online Worksheets/Activities

Wanted to share with you all a math site I found the other day that offers a whole collection of free math worksheets on a variety of different math concepts. The worksheets are pretty much just paper drills, but those of you who are trying to assemble your own curriculum using an assortment of different resources may find this helpful. You could use a problem or two from here to provide the “drill” part of your curriculum, using practical math resources/real-life settings to do the majority of your teaching. http://www.math-drills.com

And since writing the above, I found another site, http://score.kings.k12.ca.us/lessons.html, that offers a variety of mock situation suggestions you can use to help bring math into real-life. Don’t forget to point out to your child that math really is just a way of recording God’s creation, and as such is useful in helping us with the tasks He has given us to do.

Oh, no! I’m Out of Ideas/Fall Suggestions

Have you ever looked at your child’s math lesson and thought, I have no clue how to teach this. I’m clean out of ideas? If so, you’re not alone. We all face times when we’re simply not sure what to do or how to present something.

A few weeks ago, I knew I needed to write a blog entry on this blog, but I just couldn’t think of anything helpful to say. After a staring at my monitor blankly for a little while, I got up and headed out on a walk. While I walked, I prayed. What was something fall-related parents could do with their children? A leaf just starting to turn colors caught my eye. I wonder if there’s any way to integrate math with the falling leaves? I wondered.

Coming home, I decided to do a little search online on “changing leaves.” I later refined the search to “leaves math.” I found a wide variety of websites offering suggestions for ways to use leaves and math. Although I didn’t like many of the ideas as they were, they inspired other ideas.

For example, http://content.scholastic.com/browse/article.jsp?id=11901 had some interesting facts about leaves, such as that maple trees lose about 600,000 leaves each fall! I thought of how fun it would be to have a child try to count all the leaves that fall in your yard, pointing out that while this is impossible for man it’s not impossible for God. Surely the God who calls each star by name and knows the number of hairs on every person’s head also knows the number of leaves that are on (and falling off) each tree. He is truly MUCH greater than us!!!

In the end, other ideas came, and I didn’t even end up using my leaf idea for my blog. As I hit the post button on my finished blog entry, I thanked the Lord for giving me the ideas that I needed.

If you’re feeling out of ideas, I’d encourage you to take heart. God has the ideas you need. Seek Him. Ask Him. And watch Him give you the inspiration you need in His timing and way.

P.S. If you live in a part of the world where the leaves are changing colors, you may want to do your own search for “leaves math.” Then head out and enjoy the fall weather while you teach your children to use math to explore God’s creation!

Going Back to the Source

I had read so many works on math’s history that I thought for sure I had learned all I needed to learn. But as I was trying to finalize a few concepts late last week, I realized that I needed to do more research. I needed to go back and read the original writings of antiquity so I could see for myself what I’d read so many summaries about.

Fortunately, we live ten minutes from a university, so I was able to pack up my computer and head to the university library. Still, finding original works wasn’t easy, but as I got my hands on a few mathematic source books I felt well rewarded. There was something special about seeing those actual writings. The Lord also used the experience to remind me of a spiritual principle.

Just like I had nearly settled for summaries, we’re often tempted to settle for intellectual knowledge or summaries others make of God’s truths. Yet we continually need to go back to the Source–God Himself. God is the true Source of knowledge in all areas. There’s no substitute for hearing directly from Him in His Word.

In my past couple of blogs, I’ve tried to offer some practical resources to help you teaching math biblically, and I’ll try to keep posting practical ideas as I can. But it’s my prayer that you will keep going back to the Source yourself so that God Himself can give you the ideas and inspiration you need. There’s such a joy in letting Him teach us–in letting Him step in where we thought all was hopeless. As the Creator and Sustainer of all the order around us, His ideas and wisdom are infinite! What a wonderful privilege we have to keep going back to the ultimate Source.

Rejoicing in His Care,

Katherine

P.S. As you may have picked up on in this post, I’ve been spending some time lately finishing up some research for Unveiling Numbers. I wanted to ask you all to pray. There is a LOT of finalization of concepts and decisions that still need made in order to get it off to the editor. Please pray that I’ll have the wisdom and discipline to both know what needs done and to get it done.

Practical Math Resources

I’ve recently found out about a few practical math resources, and I thought I’d share them with you in case you might find them helpful.

1. http://www.livingmath.net/. This website looked like it had a lot of fun and helpful ideas on integrating math into everyday life.

2. Math on the Level. This new homeschool curriculum, although it doesn’t attempt to present a biblical world view towards math, it does a great job teaching math from real-life settings. It’s format was also very unique and more flexible/easy to modify than others I have seen. I posted my thoughts on https://www.christianperspective.net/math/reviews

3. Arithmetic for Parents. This book by Israeli math teacher Ron Aharoni came recommended to me, and I’ve been enjoying reading it. The book offers a lot of practical ideas about how to teach various concepts as useful tools. It’s available at http://www.sumizdat.org/.

Organizing

A few weeks ago, I had the opportunity to attend a workshop on organization. Now, slowly but surely, I’ve been organizing my office. The first weekend after the workshop, I tackled all my math notes by organizing them into sets. This organization process reminded me of something I wanted to share here with you all.

As a student, I always used to struggle when my math book began talking about counting numbers, whole numbers, real numbers, irrational numbers, and other number groups. Who determined that these numbers were real numbers, while these other numbers were irrational ones? And what did it matter?

After I began to grasp the biblical worldview in math, I went back and looked at these different number groups and discovered that they, too, were really useful ways of recording God’s creation!

Whole numbers, real numbers, etc., are just fancy names we gives to numbers with certain characteristics. Just like Adam used names to describe the animals, we use these names to describe and sort the quantities God placed around us. Now, we could have used different names. We could have used whole numbers to refer to numbers with different characteristics. These names in themselves are not absolutes; they’re just names that we’ve adopted to help us easily refer to different types of numbers.

Referring to different types of numbers comes in handy. There’s no way any human being could ever remember every single number that can’t be divided by two. But if we refer to all these numbers as odd numbers and learn the characteristics of odd numbers, then we’ll be able to recognize whether or not a number can be divided by two fairly easily. We group numbers into sets because we can’t memorize or keep track of every single number and its properties–only God can do that!

One way you could help your child really see number sets as a way of sorting quantities is to have him organize his closet/bedroom. As you help your child organize his room you could teach math! Tell your child about how, when organizing, we sort objects based on their properties. Have him sort things in his room. For example, we might sort clothes by color (red shirts will go in this drawer, blue shirts in this one, etc.) or by type (long sleeve shirts go in this drawer, short sleeve shirts go in this one, etc.).

Explain to your child that, just like we put like things together to organize, mathematicians have organized numbers based on their properties. Whole numbers, real numbers, etc., all have properties that make them different and unique. We can therefore put them in different “sets”—the mathematical name used to refer to the different “piles” used to organize numbers. Having these “piles” or sets helps us easily refer to numbers with specific attributes, much like the name “long sleeve shirt” helps us easily refer to a certain type of shirt.

There are also a lot of household chores that you can use to teach the concept of sets to your children. Setting the table, folding the wash (by child or by item), or even, putting away the groceries (canned goods, refrigerator goods, freezer goods, etc). Just think–your math class can actually help you get caught up on your housework this week! More importantly, it can help your child see each aspect of math–even number groups/sets–as a way of sorting/recording God’s creation.