Math at a Concert

math-at-a-concertMusic—it’s probably not the first thing you think of when you think of math. Yet God has hidden order in every sound wave, and math helps us express, utilize, and enjoy that order.

A recent trip to a chamber ensemble left me in awe—not only at the heart-stirring music, but also at how much math applied in an orchestra hall. Here are a few ways math applies:

  • The Music Itself – Harmonics, the arrangement of notes, the arrangement of sections within a piece, the rhythm—math helps us describe and work with the order God placed within sounds.
  • The Instruments – Instruments come in all sorts of shapes and sizes…and math helps us understand the relationship between the shape, size, and sounds produced.
  • The Room – The acoustics in the room make a big difference in how the audience hears the sound. And how can the builders figure out how to build a room with good acoustics? By using math!
  • Recording – Modern technology allows us to record music and enjoy it over and over again. How? By mathematically describing and reproducing sounds, of course.
  • The Business Side – Ticket prices, facility maintenance costs, artists’ schedules—math helps out in multiple ways behind the scenes of a concert.

The list could go on, but hopefully you get the idea. Math helps us both describe the order God placed within sounds and proves useful in making music and sharing it with others! Next time you find yourself staring at a math problem, remember that those apparently meaningless numbers in the textbook really represent real-life quantities and consistencies—such as aspects of music.

P.S. (Added 05/13/15) – I spent the morning researching more details about the harmonics and math in music itself and now really can’t wait to guide students through exploring some aspects of it in Book 2 of Principles of Mathematics: Biblical Worldview Curriculum. (Book 2 is scheduled to come out later this year/early next; Book 1 should ship by the end of the month.) The order God has placed in the very sounds around us is simply amazing!

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Silos, Snow, & Math Curriculum Sale

You know you might be writing a math curriculum when the sight of silos out the window causes you to think to yourself, “Calculating the volume of a silo would be a great application problem!”

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Credit: http://www.goodfreephotos.com

Or when digging out your car from a snowstorm causes you to wonder at the thousands upon thousands of tiny hexagons—each a marvel of God’s creative engineering—that you’re tossing carelessly aside. (See my previous blog post about snowflake math.)

Or when a long drive has you pondering the amazingly consistent way God holds all things together that allows us to algebraically describe the relationships between speed, velocity, acceleration, distance, time, etc.

Or when you spend a snowed-in day researching trigonometry and functions and end up excited to no end at how they help us describe the order God has hidden in sounds!

I continue to be amazed at how math applies literally everywhere, pointing us to God’s faithfulness, creativity, power, care, and wisdom—and helping us with the tasks He’s given us to do. And I’m getting super excited about sharing some of those glimpses with you in my new math curriculum. The curriculum includes lots of these sorts of real-life examples so students can begin seeing math in connection with God’s creation.

While we’re still in the final editing stages, we’re close enough to completion that the curriculum is now available for pre-order (orders will ship later this spring). As a pre-order special, we’re offering the complete curriculum for $42.96 (an $12.02 savings!).

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I’d love it if you’d take a look…and tell your friends!

Any questions about the curriculum? Please leave them below.

Snowflake Math

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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!

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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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Biblical Math Curriculum Coming Soon

Principles of Mathematics: Biblical Worldview Curriculum

For those of you who’ve been wondering where I’ve been…I’m still here! I’ve just been under tight deadlines to finish up a junior high math curriculum in order to have it available this spring. Master Books will be publishing the curriculum. I’d appreciate your prayers for the project, and I will try to post more details soon :).

If you haven’t already, be sure to sign up for our biblical math blog updates to keep posted.

Edit: I just posted a few more details about this biblical worldview curriculum if you’d like to take a look.

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.

Teaching Problem-Solving Skills Through Summer Projects

A great way to help your students learn problem-solving skills is to give them opportunities to use math outside a textbook, guiding them through figuring out what information they know, what they need to know, and what steps they can take to get from one to the other. And summertime is a great time of year to work on problem solving.

Below are a few summertime math project ideas to illustrate the point. While the specifics will vary based on your project, a few potential questions are listed under each heading to illustrate the different types of things you could have your child use math to find.

  • Home Improvement ProjectsHow much paint do we need for a room? How much fertilizer do we need for the lawn? Which is the cheaper way to buy the paint/fertilizer? How wide should we make a shelf to leave 12 inches on either side?
  • CanningHow much fruit do we have? If 1 pound of peaches produces a certain number of cups of canned peaches, how many cups of canned peaches will we be able to make if you buy 10 pounds of peaches? How about if we buy 20 pounds? How much will all that cost? How much change will we get back if you pay $40 cash? How many jars will we need to hold the canned peaches? If we have to double a recipe, how much of each ingredient do we need now? If it takes 20 minutes to do the actual canning, 40 minutes to prep the fruit, and 5 hours to cool, what time do we need to start to finish by 6 pm?
  • Road TripsHow much should we expect the trip to cost us [add up admission prices, fuel costs (let the student figure out that he needs to find this by figuring out the number of miles you plan on traveling and the car’s average miles per gallon), food, souvenirs, etc.)]? What time do we need to leave if it takes 8 hours and we need 45 minutes for rest stops, 1 ½ hours for lunch, and 1 hour for traffic…and need to arrive by 5 pm?
  • HobbiesHow much fabric do we need to make this shirt? Is there enough fabric on the two spools combined? How many yards of ribbon will we need? How many feet of wood? How would we enlarge this birdhouse pattern?

Did any other summer projects that use math come to mind? Please leave a comment and share!

When Math Feels Daunting – Plus Summer Reading Coupon

Math—especially upper-level math—can feel daunting. Teaching it can seem insurmountable.

How do we do it? Step by step. Whether a course, concept, or problem, it becomes doable when we break it down into steps.

In our next post, we’ll take a look at some ways to help to teach your child problem-solving skills. For now, I just want to point out that the same principle of breaking problems down to steps applies to teaching. While it may be tempting to look at your child’s whole future math courses and wonder how you’ll get through it, just take each day step-by-step. Trust that God will provide solutions at each stage. He gives us our daily bread, not grace for the rest of our lives. Run to the One who knows math inside out and seek His grace and wisdom. As you do, you just might find math class teaching you (and your students) more than just math.

Side note: Summertime is a great time of year to explore supplemental math resourcesBiblical Math Resources you might not have time for during the school year. To help, we’re offering 10% off the math resources in our store through June 30, 2014. Just use code SUMMER10.

Whether you have your older students work through something like Revealing Arithmetic (just have them read the first section of each chapter to gain a biblical view of arithmetic) or Mathematics: Is God Silent?, or have fun Exploring the World of Mathematics together or doing some of the hands-on suggestions in Revealing Arithmetic, we hope you enjoy!

Remember, too, that your library may have some hands-on math books with great summertime ideas, and feel free to explore our blog for some other resources we’ve mentioned over the years.

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.

Math: A Gift

Have you ever thought about how our very ability to use math is an amazing gift? To start with, you’re able to read the numbers! Your eyes take in an image. Your brain turns that image right-side up, connecting it with what you’ve learned about the language of mathematics, and gives an interpretation. And all that happens automatically…and much faster than it takes us to describe it.

We don’t often think of the gift of being able to assimilate math, but it’s been on my mind a lot lately due to lingering post-concussion syndrome that’s made my brain not function as usual. I’m realizing in a fresh way how utterly reliant we are on God for even the brainpower to be able to learn and use math. We truly cannot do anything without His enabling.

Whether it’s grasping multiplication facts or algebra, your ability to learn (or teach) math is nothing short of an incredible gift. We are indeed fearfully and wonderfully made.

“I will praise thee; for I am fearfully and wonderfully made: marvellous are thy works; and that my soul knoweth right well.” Psalm 139:14 (KJV)

New ICR Fibonacci Numbers/Math Video

This 1:26 video from Institute for Creation Research touches on Fibonacci numbers…and ends with a reminder to “praise God for all He has created”…which includes math!

Enjoy 🙂