Here’s the current cover.

And here’s the redesign we’re considering (note that the watermark in the background is just temporary).

I’d really love to hear your thoughts about the proposed new cover. What does it make you think of/what does it say to you? What do you/don’t you like about it?

Note: If the covers are not showing up, please click here to view them.

Here’s a quote from one of the opening pages:

Geometry is all about measuring lines, angles, surfaces, solids, velocities and their interrelationships. In this study, you will act as a consultant, designer-planner, and builder. The projects will range from designing a tree fort in your back yard to planning the construction of a sidewalk and home on the hilly streets of San Francisco to charting the path of the earth around the sun. In the process you will learn the principles as well as the vast usage of geometry in everyday life. Geometry is used by graphic animators, artists, photographers, interior designers, engineers, architects, builders, construction teams, surveyors and doctors just to name a few.

The draft copy online does not contain answers to the problems, nor is it an entire course, but you could certainly use some of the application ideas or concept presentations from the free download. If you do, I’d love to hear how you liked it–as I’m sure would the author.

I thought you might enjoy this interview I did a few weeks ago on HSLDA’s Homeschool Spotlight. It offers an overview of viewing and teaching math from a biblical worldview.

Spotlight on Math – Homeschool Spotlight with HSLDA from Paul Bass on Vimeo.

While working in the garden, you have a wonderful opportunity to have your child apply those math concepts he’s been learning! Graphing, multiplication, addition, measurement, area, perimeter–these and other concepts prove helpful in the garden. Why? Because math is a way of describing God’s creation! We can use math in real life because God created man with the ability to “subdue the earth,” and because He faithfully holds all things together in a consistent fashion.

Kidsgardening.org offers an entire section filled with ideas for teaching math while gardening. While written for school teachers, most of the ideas can easily be adapted to a home setting. Be sure to take a look at page 2, which offers a variety of simple ideas on how different concepts apply (you may want to print this page to consult throughout the summer). The other pages offer more detailed ideas.

The suggestions offered, as well as others you might think of, could be used or adapted for a wide variety of ages–a young child can help you count the number of earthworms in a section of soil (or the number of seed packets you need/the number of seeds to plant in each hole, etc.), while an older one can start a plant business or calculate the surface area of leaves.

Don’t let the ideas limit you. Even if you aren’t planning on growing a vegetable garden, you can still have your child grow some plants indoors or on the patio and measure their growth–or design a pretend garden on paper.

Speaking of designing on paper, you may want to use graph paper, letting each square represent a foot. The graph paper should aid in visually seeing how much area each plant needs.

Lastly, here’s a page with handy math formulas. It explains how to find the area of your yard, the amount of mulch and fertilizer you’ll need to cover it, and more.

Hope you have fun using math in the garden! Please let me know how your gardening applications go.

Math is used to help design airplanes, to find a plane’s capacity, to schedule flights, and more. See www.planemath.com for some engaging, interactive activities illustrating some of math’s aeronautical uses. NASA also has some more activities and lessons on aerospace topics, many of which show some of the math involved.

Whether your travels involve air or auto travel, this page titled “Mathematics on the Go” offers some simple ideas of how you can illustrate math’s usefulness while traveling. Some of the ideas would make great family games on your next car trip!

Math’s applications in traveling is just one example of how math serves as a real-life tool–a tool we can use because of God’s faithfulness in consistently holding all things together.

The series are secular series, and I do not agree with some of the examples chosen and ideas presented in the videos, but they do contain very clear, helpful examples of math in action if you discern through some of the conclusions. It might be wise to discuss them together with your students afterward, and explore together what the Bible says about the various topics (the environment, health, etc.)

If you’re interested in the videos, I would suggest watching them soon, as the site dropped another video series on math they used to have, and purchasing the DVDs are VERY expensive. I think they rotate the content periodically.

Anyway, here are the links!

Algebra in Simplest Terms
Against All Odds: Inside Statistics

Understanding how shapes respond to pressure–as well as lots of other math concepts–plays an important role in building bridges. Here are two bridge-building resources you could use with your children as a way to teach them to use math as a God-given, real-life tool.

Golden Gate Bridge – This section of the Golden Gate Bridge site offers lots of useful bridge-making links. There are links you could use with younger children, as well as ones for high schoolers.

Build a Bridge – While this interactive page doesn’t get into much of the math behind building bridges, it gives students an opportunity to explore the properties of different bridge designs and determine which design would be best suited for various situations.

What Is Pi?

Pi, symbolized π, is “A transcendental number, approximately 3.14159, representing the ratio of the circumference to the diameter of a circle and appearing as a constant in a wide range of mathematical problems.”[1]

As this definition explains, pi is a transcendental–a number that keeps going on and on. To get a better feel, take a quick look at the first 100,000 digits of pi–it’s a mind-boggling number!

Numbers such as pi defy our comprehension. As I mention in Revealing Arithmetic when looking at different types of numbers,

“The infinite nature of numbers reminds us of our limited knowledge. As James D. Nickel points out, ‘The infinite nature of the natural numbers has a way of telling man’s reason, ‘Under certain conditions, you can never know everything there is to know about me.’” Although our understanding is finite, God’s understanding is infinite. Psalm 147:5 tells us, ‘Great is our Lord, and of great power; his understanding is infinite.’ How foolish it would be not to trust Him!”[2]

When we look at pi, our minds should turn in awe and wonder at God’s greatness! Sadly, though, there “is almost a cultlike following that has arisen over the concept of π.”[3] It’s a reminder of Romans 1:20-23:

“For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse: Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things.”

Has Pi Always Been Expressed the Way It Is Today?

Hardly! The symbol π is just a symbol man chose to help express that real-life ratio–the symbol has actually been used to mean other things! Like most math symbols, it has been adopted within the last several hundred years [4].

Throughout history, men have tried to more precisely define pi. I found it fascinating to read in π: A Biography of the World’s Most Mysterious Number that, when you really dig into the text, it appears the Bible accurately uses pi to the fourth decimal place (1 Kings 7:23)–the book concluded that ”such accuracy is quite astonishing for ancient times.” [5] Not surprising considering the Bible’s Author!

Where Do We Use Pi?

Pi has a way of showing up all over the place–a testimony to the same Creator holding all things together. The most obvious use is when dealing with circles (for example, pi is used to find the area and circumference of a circle), but pi also proves useful in less-obvious places, such as in sound waves, general relativity, movements of the heavens, and probability, to name a few.

Why Are We Able to Explore Pi?

Because God created man in His image and gave him the ability to explore His creation! We’re thus accountable to Him for how we use that ability.

Where Can I Learn More?

There are lots of materials online that share more about pi (you might start with Wikipedia’s overview or this historical overview of pi). Your library may also have some books that could prove helpful. One I particularly enjoyed is π: A Biography of the World’s Most Mysterious Number by Alfred S. Posamentier and Ingmar Lehmanne.

The thing to keep in mind is to turn the wonder at pi itself into wonder at the Creator of all things–the one who understands what only baffles our comprehension.

[2] Loop, Katherine, Revealing Arithmetic: Math Concepts from a Biblical Worldview (Fairfax, VA: Christian Perspective, 2009), p. 125. Internal quote from James D. Nickel, Rudiments of Arithmetic: Foundational Principles in the Computation and Theory of Numbers, 1st ed. (preliminary draft) (U.S.: James D. Nickel, 2008), p. 294.

[3] Posamentier, Alfred S. and Ingmar Lehmann, π: A Biography of the World’s Most Mysterious Number (Amherst, New York: Prometheus Books, 2004), p. 13.

[4] It was “introduced in 1706.” Cajori, Florian, A History of Mathematical Notations: Two Volumes Bound As One (Mineola, NY: Dover Publications, 1993), vol. 2, p. 9.

[5] Posamentier, Alfred S. and Ingmar Lehmann, π: A Biography of the World’s Most Mysterious Number (Amherst, New York: Prometheus Books, 2004), p. 28.

Knowing this quality about arches helps us in designing buildings and bridges, many of which have an arch shape! It also gives us new appreciation for the design in our feet. If you run your finger along the bottom of your foot, you will feel multiple arches on your foot! God, the master engineer, designed the shape of our feet to support our body’s weight. Our feet are truly marvels of engineering!

If the foot were flat and rigid, fixed at right angles to the bone of the leg, walking would be difficult or impossible. The elastic arches also serve as shock absorbers to soften the jar resulting from walking on a hard surface.

The human foot is a miniature suspension bridge which is much more complicated than an ordinary bridge. Would anyone say that the Golden Gate suspension bridge just happened? Of course not, if he were truthful! But why do people assume that the even more intricate mechanism of the human foot could have just happened without intelligent cause or the workmanship of a master Engineer? [Allen L. Gillen, Body by Design (Green Forest, AZ: Master Books, 2001), pp. 43-44.]

The point? Learning about shapes doesn’t have to be confined to a textbook! As you teach your child shapes, you can be teaching him about the shapes all around us–and seeing the Creator’s wisdom and care in how He chose just the right shape for everything.

SCORE Mathematics Lessons – Check this site for some free, practical lesson ideas for grades K-12. Many of these lessons offer ideas on how to have children apply math for a specific real-life project, such as planning a trip or buying a car. Although written for a classroom setting, most of the lessons could easily be adapted to the home. It’s a site you may wish to bookmark and consult when you’re not sure how a specific concept serves as a useful tool or need an idea on how to actually have your child apply a concept. Please use your own discernment, as many of the lessons include Internet usage.

REMINDER! Next week is request week. Does anyone have a specific concept or question you’d like discussed?