Spiders, Math, & the Creator

It’s hard to watch a spider spinning its web without being awed at how carefully he engineers something so fragile, yet so strong.

When we look at spider webs using math, the awe simply compounds. Did you know that “the spider web is actually comprised of numerous radii, a logarithmic spiral (given by the polar equation r=ae^{bθ} ) and the arithmetic spiral (given by the polar equation r = a+bθ )”1?

(Video courtesy of Julie G.; used with permission.)

Nature worded it this way: “Spider webs themselves are characterized by a highly organized geometry that optimizes their function.”2

Spiders are yet one more example of how as we use math to explore God’s creation, we’re awed at the Creator’s wisdom and care. God designed spiders to spin these marvelous structures!

And we should be grateful He did. While spiders can certainly be spooky, they serve an incredible purpose. In his video Spiders! Ogres, Allies & Architects3, creation speaker Mike Snavely points out that if spiders were to take a vacation, the world would be overrun with insects. He actually uses math to better help us appreciate this fact.

In the video, Snavely looked with the viewer at the results of a study of how many ounces of insects one specific type of spider eats on average per day, and at another study done in Holland estimating the average number of spiders in each square yard. Then using basic arithmetic and some more facts (such as the size of Holland, the size of the world compared to Holland, the average weight of a person, etc.), he walks through how one could arrive at an estimate that spiders consume bugs that would equal the weight of 10,000,000 people per day! [Note: There’s no way to perfectly estimate something like this, but, as Snavely points out, “even if this number is exaggerated by a factor of 3 or even 4, that’s still a staggering number of bugs per day.” And other research indicates that the 10,000,000 number may even be a conservative estimate. It’s safe to say that spiders eat a LOT of bugs…and math helps us get a better idea of the magnitude of how much these little creatures eat!]

Now aren’t you glad God made spiders such incredible engineers? He knew that in a fallen world, we’d need these little creatures to keep the insect population down.

I loved how Snavely actually walked through the math (which was simple arithmetic) behind the estimate of how many bugs spiders eat. While many times science books or resources only quote a final number on a topic, know that math is involved in calculating the numbers you encounter in science. Math is truly the tool we use to explore God’s creation.

Here are a couple of ideas you can use to use math to explore God’s handiwork in spiders:

  • Have your student draw a spider web. (You can find various instructions online; here are 3 Ways to Draw a Spider Web.) As they draw, point out that we call what they’re drawing “line segments,” “angles,” etc. Depending on your student’s ages, you could also talk about the names we use to describe different types of angles (such as acute and right) that they are drawing. Math helps us name God’s creation. You could also have them pull out a protractor and measure some angles.
  • With older students, have them take a look at the spirals in many spider webs.
  • Head for a walk and find a spider web. Use a protractor to estimate some of the angles (being careful not to disrupt the web).
  • Read this article by Institute for Creation Research about God’s design on display in spider webs, and take a moment to thank God together for His wisdom and care over each detail.
  • Watch Mike Snavely’s Spiders!. You’ll be wowed by these amazing little creatures…and the even more amazing God Who created them. Plus, you’ll get to see an amazing example of math in action.

Reminder:  If you’re looking for a math curriculum that incorporates real life examples (including spiders!) so students see math in connection with God’s creation, be sure to check out Principles of Mathematics.
Principles of Mathematics


References:

[1] Alicia Bautista, “Spider Webs: Creepy or Cool?” (Math Projects, 2015), http://recursiveprocess.com/mathprojects/index.php/2015/06/09/spider-webs-creepy-or-cool/ (June 17, 2015 update).

[2] S.W. Cranford, et al., “Nonlinear Material Behaviour of Spider Silk Yields Robust Webs,” Nature. 482 (7383), 72-76. Quoted in Brian Thomas, “The Masterful Design of Spider Webs” Acts & Facts. 41 (4): 16. 2012, http://www.icr.org/article/masterful-design-spider-webs/

[3] Mike Snavely, Spiders! Ogres, Allies & Architects (Mission: Imperative!, 2015).

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Solar Eclipse, Math, & Praising the Creator

This upcoming Monday, August 21, 2017, be prepared for a period of darkness in the middle of the day as we experience a solar eclipse.

While solar eclipses occur periodically, it’s rare that the entire United States can view it. According to Time and Date, the last time “a total solar eclipse was visible from coast to coast was almost 100 years ago, on June 8, 1918.”

This short article by Kahn Academy offers a brief overview of a solar eclipse. NASA’s website on the eclipse is complete with information, along with a page of math challenges.

Math challenges? Yes. Math is the tool that we use to explore God’s creation—including the movement of the heavenly bodies overhead. While we can easily read online dates and times that the eclipse will occur in different parts of the world, it’s worth noting that math was used to predict those dates and times. You see, God governs creation so predictably and reliably that we can use math to know ahead of time when something like an eclipse will take place.

It is fascinating to go back and read the works of Johannes Kepler, known for discovering the Laws of Planetary Motion (i.e., mathematical ways of describing the consistent way God causes planets to orbit the sun). His work (which contains a lot of math, by the way) is interspersed with praises to the Creator, such as this one:

Crying out with the royal Psalmist: Great is our Lord and great His virtue and of His wisdom there is no number…To Him be praise, honour, and glory, wourld without end. Amen.[1]

As we experience the eclipse Monday, may we pause and praise the great Creator, exclaiming with the Psalmist:

The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard. Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun, Which is as a bridegroom coming out of his chamber, and rejoiceth as a strong man to run a race. His going forth is from the end of the heaven, and his circuit unto the ends of it: and there is nothing hid from the heat thereof. Psalm 19:1-6 (KJV)

I hope you’ll have fun learning a little about the eclipse (see the links above to get started) and how we use math to help us describe the movement of the sun, earth, and moon (look for words like angles, elliptical, etc., as you read). And then as you’re wowed by the ellipse Monday, remember how much greater the Creator is…and that, though our sin earns us His wrath, He took that punishment upon Himself (1 Peter 2:24) and offers us eternal life with Him forever (John 3:16; John 17:3). Is there someone you know with whom you could share that incredible news?

Reminder: If you’re looking for a curriculum that teaches math in such a way that students leave math praising the Creator and using math as a real-life tool to describe His creation, be sure to check out Principles of Mathematics. We also have resources available to help you bring that perspective for other grades.


[1] Stephen Hawking, ed. On the Shoulders of Giants: The Great Works of Physics and Astronomy. Philadelphia: Running Press Book Publishers, 2002, pg. 1157.

Math and Traveling (Includes Word Problems)

Math & Traveling

Math & TravelingOn a recent flight, I was reminded of how often we use math when traveling without even thinking about it. Below are a few examples (complete with example word problems) of math in action while on a flight–many of the same ideas would apply to car trips as well.

So if you’re traveling this summer, you can use the trip to remind your children how math isn’t a mere textbook exercise. It’s a way of describing the quantities and consistencies God created and sustains around us–and as such, it’s a useful, real-life tool.

Happy traveling!

  • How Much Will This Airplane Ticket Cost? There’s the ticket price…and then there are the taxes, fees, baggage cost, etc., that get added on top. How much is the ticket really costing altogether? To answer that, you need–drum roll please–math! Simply add all the costs together to find the total. Example Word Problem: An airplane ticket costs $119.98, plus $5.50 and $4.78 in taxes and fees. You also need to check 1 bag, which costs $20. What is the total cost? Answer: $119.98 + $5.50 + $4.78 + $20.00 = $150.26
  • What Time Should I Get Up to Make My Flight? How early should we set that alarm for? Math can help us decide!
    Example Word Problem: If it takes you 1 hour to get ready and 30 minutes to get to the airport, and you want to be at the airport 2 hours before your flight leaves at 9 am, what time should you wake up? Answer: You need to get up 3 hours and 30 minutes before your flight (1 hour + 30 minutes + 2 hours = 3 hours and 30 minutes), which would be at 5:30 am.
  • How Much Longer Do we Have Left? At the beginning of the flight, the pilot will often announce how long the flight will be. But after an hour goes by, how long is left? Again, you can use math to figure it out. Example Word Problem: If the flight is 2 hours and 45 minutes long, and you’ve been in the air now for 1 hour, how long in the flight do you have left? If it’s 3 pm right now, at what time should the plane land? Answer: Since you’ve completed 1 hour out of 2 hours and 45 minutes, you still have 1 hour and 45 minutes left, so that would mean the plane should land around 4:45 pm.
  • What Time Is It Back Home? Now that you’ve reached your destination, you want to call back home and let them know you’re safe. What time is it back there? Use math to figure it out! Example Word Problem: If it’s 5 pm in California and you want to call back home to Maryland, what time is it in Maryland if Maryland is 3 hours ahead of California? Answer: 8 pm

Tip: If the example word problems given are too advanced for your child, round the numbers used. For example, in the first word problem, change the cost of the ticket to an even $120, the fees to $6, etc., so as to avoid any decimals. By rounding or changing prices, you can simplify real-life situations so that younger students can begin applying math at their level.

Why Do I Have to Learn That?

Photo credit: Ignacio Sanz via Visual hunt / CC BY-SA

I recently looked at various college math materials, and they reminded me why so many students hate math. If I didn’t know better, I would have thought math was a meaningless set of rules I had to memorize—a subject designed to give me a headache.

However, nothing could be further from the truth! While math does have a lot of rules, there’s a purpose to it! Those rules help us describe and explore God’s creation.

As one example, consider the branching pattern of trees. Did you know that math helps us describe it? Well, it does! Fractal geometry helps us describe the branching pattern of trees, as well as many other aspects of God’s creation. (To learn more, check out the blog post I recently wrote about fractal geometry and trees over on the Creation Club website.)

Many students grow up thinking they hate math because they’ve never really been taught what math is. They’ve not seen it as a practical tool that helps us explore God’s creation and complete the tasks He’s given us to do.

If you have a student(s) that dislike math, try stepping back from the mechanics for a bit and showing math in action. Help them understand why what they’re learning matters. If you need some ideas, check out the sample pages from Revealing Arithmetic, Principles of Mathematics 1, and Principles of Mathematics 2. While the samples are designed to give you a flavor for the materials, some of the ideas can be used on their own with students even if you don’t purchase the materials.

Along those lines, here’s a simple challenge: make a list this week with your student(s) of all the ways you see math used (including simple ways, such as the numbers on a clock or microwave). You both might be surprised.


Principles of Mathematics

Need help teaching students math with a purpose?
Check out the Principles of Mathematics curriculum!

We just started using Principles of Mathematics 1 with our 7th grader. This particular 7th grades despises math. The previous years have been filled with tears, frustration and always asking the question “why do we need math?”. After hours and hours of searching, I found Masterbooks and Principles of Mathematics. I picked it because IT EXPLAINS WHY WE DO MATH!!! YAY!!! Our 7th grader was skeptical at first but after just a couple days he CHOSE to switch from the year schedule to the accelerated schedule. Woo Hoo! He enjoys doing math. So thankful!

 

Back-to-School Math Encouragement and Free Resources

Transforming Math

It’s the time of year again where many of you may be heading back to school after a summer break.

Here are some free resources to help encourage/equip you to teach math from a biblical worldview as you go.

  • Free Transforming Math Video – Watch this 18-minute video to get a glimpse into how biblical principles really can transform math, making it an exciting exploration of God’s creation. When you sign up for the video, you’ll also get a free read-aloud story that illustrates how often we really do use numbers, and a series of emails with other information and reminders to help you teach from a biblical worldview.
    Transforming Math
  • Math, Lightning, & Thunder – I recently blogged over on The Creation Club about how we can use math to help us approximate the distance to a lightning strike. Even a summer thunderstorm gives us an opportunity to explore God’s creation and marvel at God’s greatness (after all, He’s the one who makes the lightening and brings forth the wind – see Jeremiah 51:16).
  • Upcoming Articles – I have articles coming out this fall/winter in both the Old Schoolhouse Magazine and Homeschool Enrichment. If you get either of those magazines, be sure to take a look.
  • Sample Lessons – Watch a free preview of a lesson on place value, one on fractions, and one on lines and angles.
Note: If you’ve found these resources helpful, please share with a friend.

Geometry and Sounding Boards

Sounding Boards

Sounding BoardsDid you ever wonder how sound was projected before the days of microphones? I found it fascinating to learn at a historical church that sometimes they used “sounding boards” like the one shown here. Sound waves would bounce off this sounding board at different angles, causing the preacher’s voice to reach different parts of the church.

Room acoustics is a fascinating example of geometry in action. And it’s all possible due to the underlying order God has placed within sounds. You see, sound waves reflect off surfaces in a consistent fashion, making it possible to design buildings to reflect sounds where we want them to go.

P.S. The sounding board shown is from the church George Washington attended (Christ Church in Alexandria, VA). Here’s a link to a prayer Washington wrote for our nation and his inaugural address, both of which are filled with reminders of God’s sovereignty.

(For more examples of angles in action, see Book 1 of Principles of Mathematics: A Biblical Worldview Curriculum.)