God Knows the Measure – And We Don’t!

God knows not just the measure of the things easy to measure, but the measure of things we can’t possibly measure, such as the dust of the earth and the measure of all the waters in the oceans. Our inability to measure aspects of creation reminds us again of how much greater God is than we are!

Who hath measured the waters in the hollow of his hand, and meted out heaven with the span, and comprehended the dust of the earth in a measure, and weighed the mountains in scales, and the hills in a balance? Isaiah 40:12

The above quote is a little reminder included amid a section of the curriculum I’m writing focusing on measurements and geometry. As always, please leave your thoughts in a comment! I look forward to hearing from you.

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Review: Make It Real Volume 2 – And a 25%-Off Coupon Code at Make It Real Learning

Some time ago, I reviewed Make It Real Activity Library, Volume 1. Recently, they released a volume 2. Volume 2 is very similar to volume 1; once again, I appreciated how the series, designed as a curriculum supplement, provides numerous, stand-alone, real-world application problems for students. The series does not claim to be Christian, so Christian parents/teachers will want to discuss some of the lessons with their students, examining how we interpret the results or topic in a biblical worldview. Again, please see my previous review for more thoughts, as well as for a 25%-off coupon code good on all of the publisher’s products through the end of 2012.

Note: I received a free copy of this product to review. See my review policy disclosure.

Make It Real Learning Activity Library

Make It Real Learning Library

11/28/2012 Update: Make It Real Learning now has a Volume 2 as well. This post was originally a review of Volume 1, but I have added information on Volume 2, as they are very similar. Look at the bottom of the post for a 25%-off coupon good at Make It Real Learning through the end of December 2012!

I recently had the opportunity to review the Make It Real Learning Activity Library–a collection of e-books filled with practical worksheets that truly give students the chance to use math in real-life scenarios. While they do not come from a biblical worldview, their format lends itself to the parent picking and choosing which scenarios to use as well as discussing them further and could be a resource for those wishing to bring in practical examples.

I’ve put my entire review below. If you’ve used the product, please feel free to leave your thoughts in a comment!

Review of  Make It Real Learning Activity Library

Publisher: Make It Real Learning
Grade Level(s): K-College (Volume 1)/K-Grade 3 (Volume 2); see first paragraph below.
Price: $39.99/each volume of e-books (11 in each volume). Note: The publishers have offered a 25% discount (good through the end of 2012) for readers of this blog; this is not an affiliate code, and I do not get any commission on it. I am just passing it along in case any of you wanted to use it. To use the discount, enter christianperspective25 as the code during checkout at www.makeitreallearning.com.
Where to Obtain: www.makeitreallearning.com

Like its name implies, the Make It Real Learning series by Frank C. Wilson seeks to make math real for students, answering the question of “when am I ever going to use this?” Each volume in the series consists of 11 e-books, each one of which contains 10 real-world scenarios. The e-books range from one on fractions, percents, and decimals to e-books on more advanced topics such as geometry, algebra, linear functions, and quadratic functions. The majority of the e-books deal with upper-level concepts. The website offers a general mapping of lessons to grades for volume 2, although homeschool parents should be aware that most homeschoolers are not required to follow these standards* (many homeschool curriculums vary from them) and thus will want to look at the lessons to see if their student knows the needed skills.

Each real-world scenario stands on its own and can be printed and handed straight to the student. Duplicate worksheets containing answers (and often detailed solutions) are included. The formatting is professional and clean. The scenarios could be used as periodic assignments to both provide a refreshing break from everyday math lessons and to teach students to use math practically. The e-books do not typically present any of the math itself (so you will want to make sure your child knows the information needed to complete the scenario); they are designed for the student to apply what he has learned or is learning to real-life scenarios.

The scenarios themselves vary greatly. Some of them rank among the most excellent, well-thought-out activities I have encountered. For example, students will get to find the cost of keeping a pet (using real petsmart.com data), make cell phone comparisons and investment decisions, examine different pool designs, and understand the math behind various pieces of data all around us we take for granted. On the flip side, the books also include scenarios mentioning topics I found unnecessary, such as AIDS and teen pregnancy. I would plan on finding some great scenarios, but know that you also might find some you would not want to use or would want to discuss. Many of the topics, such as those on health or population issues, warrant discussions and explorations of a biblical worldview of that topic. Others, such as those that examine aspects of God’s creation (such as the phases of the moon or the order in sound waves) just need a reminder that God is the One who put this incredible universe together. Since the material comes as an e-book, you have the ability to select just the scenarios that will work for your family by screening them on the computer and printing only those you want when you want them.

The thing I loved about many of the scenarios is that, unlike a typical word problem, they really take the student into the scenario and let them experience the decision in a way few math books even approach. When used selectively, I can see them being wonderful ways to present math as a practical tool, especially in the high school years where textbooks focus more and more on abstract math.

25%-Off Coupon Code

The publishers have offered a 25% discount (good through the end of 2012) for readers of this blog; this is not an affiliate code, and I do not get any commission on it. I am just passing it along in case any of you wanted to use it. To use the discount, enter christianperspective25 as the code during checkout at www.makeitreallearning.com.

Disclosure: I requested and received a free copy of this product to review. See my review policy here.

* For information on homeschool laws by state, see www.HSLDA.org. This is not meant to be legal advice. Requirements vary state by state.

Free Videos: For All Practical Purposes

For All Practical Purposes

For All Practical PurposesFirst of all, thank you to everyone who provided feedback on the cover! It was VERY helpful. The graphic designer was able to make a few changes based on the concerns raised, making what I believe will be both a catchy and meaningful cover (I love the final design). Now it’s time to make some updates to the inside material and get it off to the printer : )

Secondly, I’d like to let you all know about a free video series that’s available on Google Videos: For All Practical Purposes. This series of 26 half-hour episodes does an excellent job presenting math’s practical uses in a fun and meaningful way. I was blessed by watching them several years ago when I was first beginning my  research, but I didn’t realize they were still available online until a website reader e-mailed me this past week with the news. (Thank you, Angela!)

A far cry from a boring classroom presentation, these videos make math both interesting and exciting through real-life examples and footage. I loved how the series made complex concepts simple, enabling the viewer to learn without even realizing it. One or two of the videos have very brief sections that discuss evolution from a non-biblical perspective, but on the whole the videos stayed clear of the topic of origins and focused on math’s practical uses. Since these videos were produced in the 1980s, a few videos feature rather archaic computers; however, the principles the videos present about math in action have not really changed.

This series is great for high-school students (or younger with assistance). One idea would be to watch a video a week as a supplement to your middle school or high school math course as a way of showing math’s usefulness in real-life situations–a usefulness that’s only possible because our consistent, faithful God holds all things together! The company that made this series has also produced a full sized high-school/college textbook by the same title. I was able to purchase one through AbeBooks (http://www.abebooks.com) for $3.99, including shipping.

Free Geometry Resource

Cornerstone Curriculum, publishers of the Making Math Meaningful curriculum series, is offering a rough draft of the first several hundred pages of their geometry course for free online. Based on a quick look at the course, it seemed to present geometry as a useful tool. I have looked at some of the author’s other resources and know he strives to help students really understand the concepts he presents and not merely memorize formulas.

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.

Bridge-Building Resources (All Grades)

In my previous post on shapes, we briefly talked about how learning shapes doesn’t have to be confined to a textbook–how shapes help us understand and appreciate the shapes God placed around us.

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.

Thoughts on Pi

Someone recently wrote and asked me if I had any information on pi from a Christian perspective I could share. So here are some thoughts on this mind-boggling–and incredibly useful–number.

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. 2018 Update: NASA has put together a Pi Day Challenge that shows just how useful pi is! Note that NASA does not come from a biblical worldview, so please use discernment (while most problems looked great, one at least hinted at finding life on other planets).

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.

Additional Thoughts (added March 2017)

Be careful when exploring pi to stand in awe of the Creator and not the creation itself. Throughout the years, men have been in awe of the number pi…yet that awe has often turned into an “almost cultlike following”[6] to the number instead of into awe of the Creator. To help put things in perspective, here’s a brief excerpt from Principles of Mathematics that explores pi, how it points us to the Creator, and how it’s been sadly twisted. http://www.christianperspective.net/wp-content/uploads/pi.pdf

 


[1] The American Heritage Dictionary of the English Language, New College Edition, 1980, s.v. “pi.”

[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.

[6] “There is almost a cult like following that has arisen over the concept of π.” Ibid., p. 13.

Thoughts on Shapes

Throughout history, men have used their knowledge of shapes to help them design buildings. Because of the consistent way God holds things together, we can predict how different shapes will hold up under pressure. One shape that supports weight well is the arch. You can easily see this by holding a piece of paper flat between your hands and having someone push down gently in the center of the paper. You should notice the paper bends easily under the pressure. But if you bend the paper to form an arch, you’ll notice the paper does not bend as easily. An arch shape holds up better under pressure than a flat shape does. [1]

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.


[1] This experiment is based on one given in The Art of Construction. The book offers numerous experiments and information related to building. Mario Salvadori, The Art of Construction: Projects and Principles for Beginning Engineers and Architects, 3rd ed. (Chicago: Chicago Review Press, 1990). Originally published as Building: The Fight Against Gravity.