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.)

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Math and the Presidential Primaries

Math and the Presidential PrimariesOne of the things I stress a lot in my math resources is that math isn’t confined to a textbook. As I’ve been following the presidential elections this year, it occurred to me that it provides a great opportunity to show students math in action. Math is used quite a bit behind the scenes in determining each party’s candidate. Consider these applications:

  • Probably the most obvious math concept the elections show in action is percents. What percent of the vote went for each candidate? What percent of a specific area went to each candidate? What percent of the total delegates to a convention does each candidate have pledged to them? How many votes would a candidate have to receive in order to earn a specific percent if 40% of a specific population end up voting?
  • More percents and other math concepts are used in determining how many delegates are actually assigned to each candidate after an election. This article by the Washington Times gives an overview.
  • Addition (along with more percents, as well as formulas) are used behind the scenes in deciding how many delegates each state gets to send to the national conventions in the first place. See The Green Papers: Republican Detailed Delegate Allocation – 2016 for more details about the republican side; and The Green Papers: Democratic Detailed Delegate Allocation – 2016 for the democrat side.
  • Statistics show up extensively throughout the election process. Polls are based on surveying a random sample of the population and trying to determine the views of the whole off of it. It’s a great time to look at how statistics work (and how easily they can be twisted). See Chapter 11 in Principles of Mathematics for an overview and example.

As you follow the elections, consider looking into your particular state’s primary or caucus system and examining the math behind it. Point out the use of percents, addition, etc. Look at the statistics behind a couple of presidential polls and at what they truly tell us.

Then sit back and remember that math only proves useful because this universe is consistent, and because God gave man the ability to subdue the earth. We’re made uniquely in God’s image, created to worship Him. Remind your students that math is far from meaningless bookwork—it’s a real-life tool that helps us in the tasks God has given us to do.

Improbability of Evolution Math Lesson Plan

I was pleased to learn about this middle school math lesson plan that uses math to show the improbability of evolution. (The main math concept is probability, along with large numbers and scientific notation, although others are also used.) While designed specifically for a public school setting, it could be easily adapted for Christian or homeschool. (Thank you, Mr. Karl Priest, for putting it together and letting me know about it!)

I especially loved the suggestion given to have students try to write tally marks to help drive home how much a million is. Coupled with quotes like the one below, it brings home the point that, even from a human reasoning perspective, evolution doesn’t make sense:

“Imagine 10^50 blind persons each with a scrambled Rubik cube, and try to conceive of the chance of them all simultaneously arriving at the solved form. You then have the chance of arriving by random shuffling of just one of the many biopolymers on which life depends. The notion that not only biopolymers but the operating programme of a living cell could be arrived at by chance in a primordial soup here on the Earth is evidently nonsense of a high order.” Fred Hoyle, “The Big Bang in Astronomy”, New Scientist, Vol. 92, No. 1280 (1981): p.527

evo-mathI would just add that evolution and creation can’t be proved—they occurred in the past. The issue ultimately comes down to faith, and that faith shouldn’t rest in our human reasoning of probability, but in the Word of the God who was there and has told us what happened. However, math does show us how even from a human reasoning perspective, evolution doesn’t make sense…and this lesson plan does a wonderful job showing that.

As the cartoon at the end of the lesson plan (and shown here) reminds us, you can’t reason someone into the kingdom of heaven. God has to do a work to change a heart. Let’s make sure we’re sharing the gospel with people as we remind them that creation clearly proclaims a Creator.

Note: If you’re stuck on how to begin sharing the gospel, check out the free resources at LivingWaters.com. He has a lot of helpful training materials to help.

Snowflake Math

snowflake1

Math might not be the first thing you think of when you see snow, but believe it or not, math helps us describe God’s handiwork in each tiny snowflake.

To start with, we can observe that the general shape of each flake is approximately the same. Snowflakes can be described by the six-sided shape we refer to as a hexagon.

Looking at the structure of water molecules and the angles (more math) there gives us a glimpse into why hexagons are formed.

Yet despite being the same shape, you’re not likely to find two identical snowflakes. What a wondrous variety God’s hid within snow!

snowflake math

We could also talk about the symmetry and patterns in snowflakes (more math concepts). And if we wanted to expand beyond the flakes themselves, we could talk about the temperature at which water freezes (which we describe using a number), at the altitudes of different types of clouds (which we use numbers to describe), etc.

Snowflakes are an example of how we use math to describe God’s creation…and in the process see His incredible design!

“Hast thou entered into the treasures of the snow? or hast thou seen the treasures of the hail, Which I have reserved against the time of trouble, against the day of battle and war?” Job 38:22-23

“Then Job answered the Lord, and said, I know that thou canst do every thing, and that no thought can be withholden from thee. Who is he that hideth counsel without knowledge? therefore have I uttered that I understood not; things too wonderful for me, which I knew not. Hear, I beseech thee, and I will speak: I will demand of thee, and declare thou unto me. I have heard of thee by the hearing of the ear: but now mine eye seeth thee. Wherefore I abhor myself, and repent in dust and ashes.” Job 42:1-6

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Battleship, Probability, and More

As I sat playing Battleship the other day, I got to thinking about how many concepts of math I was using as I played. (For those not familiar with the game, Battleship involves trying to guess where your opponent’s ships are located on a grid.)

To begin with, I used numbers to identify the columns on the grid, combined with letters to identify the rows.

When hunting for my opponent’s aircraft carrier, I knew the carrier takes up 5 spaces…which meant my opponent’s carrier couldn’t be hiding anywhere with less than 5 spaces. I also knew that when I hit the carrier, I needed to continue guessing the spaces around my hit until I’d located all 5 spaces upon which the carrier sat. I was doing a lot of counting as I played.

Since the aircraft carrier takes up 5 spaces and the battleship takes up 2, I knew the carrier should be easier to find. But why is this? Well, on the very first guess, there’s a 5/100 (which reduces to 1/20) probability of hitting the carrier (there are 100 spaces total, 5 of which have the carrier on them), and a 2/100 (which reduces to 1/50) of hitting the battleship.

While we don’t often think of the math used in games, it’s there none-the-less. Even games can turn into teaching opportunities. Math isn’t a mere textbook exercise, but rather a way of describing real-life consistencies God created and sustains. It’s a practical tool we use all the time…even when playing a game.

Why Learn Fractions?

Have you ever wondered why we need to know how to add, subtract, multiply, and divide fractions? After all, don’t we use decimal notation for most real-life problems?

Division, Algebra, and Fractions

One main use of fractions is found in algebra. While most curricula present fractions as a way of describing partial quantities, it is also a way of describing division. 3/4 represents three quarters of a whole and what we would get if we divided three by four (3 ÷ 4 = 3/4).

Because it represents division, the fraction line basically replaces the division sign in algebra. It thus gives us a very helpful way of describing and working with consistencies in God’s creation, such as the Law of Gravity, which can be represented algebraically like this:  Notice the fraction line!

For a more simple example of algebra and fractions in action, consider this formula for finding the width of a rectangle if we know the length and the area:

w = width of a rectangle
l = length of a rectangle
A = area of a rectangle

Again, notice the fraction line!

The skills learned with fractions later help students use algebra to explore God’s creation and solve real-life problems.

More Fractions in Real Life

Fractions also apply in various non-algebraic real-life problems too. Below are some examples.

Measurement – If there’s 1/2 a yard of fabric on one bolt and 1/4 on another, how much yardage is there?
Music – A quarter note represents a quarter of a whole note.
Cooking – We might need to use a 1/4 cup three times to measure 3/4 cup, since the 3/4 cup measuring cup is in the dishwasher.
Produce sold by the pound – A quarter pound of apples at $1.99 a pound is how much?
Unit conversion – We use a ratio worth one (written as a fraction) when converting units (such as miles to kilometers–or dollars to a foreign currency).

The Bottom Line

Each aspect of math is a tool to help us describe God’s creation and serve Him. Fractions are no exception!

Note: For more thoughts on fractions, as well as other arithmetic concepts, and ideas on how to teach them from a biblical worldview (including lots of practical ideas you can use), see Revealing Arithmetic.

The Life of Leonhard Euler (1707-1783)

Leonhard Euler
Artist Jakob Emanuel Handmann’s rendition of Leonhard Euler. Found on Wikipedia.

I’ve started the algebra section in the math curriculum I’m writing–which meant the time had finally come to cover Euler’s life. Leonard Euler has to be one of my favorite mathematicians. This short extract from the curriculum highlights some important lessons his life teaches. – Katherine

It’s fitting that we end our first week looking at algebra by exploring the life of a man God gifted with an amazing mathematical mind. Leonhard Euler (pronounced “oiler”) has been called “the leading mathematician and theoretical physicist of the eighteenth century.”[1] He left his mark on nearly every branch of math. He wrote an enormous amount of mathematical papers—one resource I read estimated that, while working, he wrote around 800 pages a year,[2] and another called him “the most prolific mathematician in history.” [3] In addition to numerous other works, Euler wrote math textbooks, and his presentations of many concepts are still those we use today. We can think of Euler as the man who went back and “polished” the various branches of mathematics, making them easier to use and understand.

Beyond being a brilliant mathematician, however, Euler’s life provides a beautiful illustration of a famous mathematician who truly viewed math as a testimony to God’s faithfulness and served the Lord despite tremendous challenges.

Euler’s father had been a preacher, and Euler himself, wanting to please his father, had studied to become a minister as well. Fortunately, his father eventually realized that God had clearly designed his son to be a mathematician instead of a preacher. I think the lesson Euler’s father had to learn was critical for us all: God made us all different, and that’s a good thing!

After Euler was allowed to pursue mathematics instead of his seminary studies, the Lord opened up a position for Euler in Russia. Although originally hired to conduct medical research for the government-sponsored academy, Euler was quickly able to switch his focus to mathematics.

During his first stay in Russia, the country underwent a period of turmoil. Euler feared speaking much in public for fear of the spies who literally were everywhere. So, unable to do much else, Euler applied himself with all the more diligence to his mathematical pursuits. God used the upheaval to help Euler complete the tasks before him.

Euler’s life had its fair share of trials. While still fairly young (probably his early 30s),[4] Euler lost sight in one eye. Later, he lost sight in his other eye too. But Euler didn’t waste time in self-pity. God had blessed Euler with an amazing capacity to calculate mentally and remember things, so he kept on solving math problems despite not having good eyesight. As one biographer comments,

He was able to do difficult calculations mentally, some of these requiring him to retain in his head up to 50 places of accuracy![5]

Euler was definitely a man with a remarkable intellect. Yet unlike many of the French philosophers of his time, Euler recognized that his intellect needed submitted to God’s authority. One time, a French philosopher named Diderot came to Russia and began spreading his skepticism about God’s existence. The queen asked Euler to combat him.

“Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it before all the Court, if he [Diderot] desired to hear it. Diderot gladly consented…Euler advanced toward Diderot, and said gravely, and in a tone of perfect conviction: ‘Sir, a+bn/n = x, hence God exists; reply!’”[6]

Diderot was embarrassed and immediately went back to France. Euler’s simple faith, which recognized that math’s very ability to work depends on a faithful, consistent Creator, had baffled the French philosopher.

May we, like Euler, view math’s very ability to work as a testimony to God’s faithfulness and existence and use our intellects for His glory.


[1] Stuart Hollingdale, Makers of Mathematics (New York: Penguin Books, 1994), 275.

[2] Ibid.

[3] E..T. Bell, Men of Mathematics (New York: Simon and Schuster, 1965), 139.

[5] William DunHam, Journey Through Genius: The Great Theorems of Mathematics (New York: John Wiley and Sons, 1990), 210.

[6] E.T. Bell, Men of Mathematics (New York: Simon and Schuster, 1965), 147.

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.

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.