Math at the Aquarium

aquarium

My husband and I recently visited the Georgia Aquarium, and I was struck by how much math is used in caring for and describing the characteristics of sea creatures. Below are a couple of examples. I’ve tried to word them as actual problems for different ages. I hope you enjoy working through them with your students! (The answers are below.)

  • How Big Is That Tank? (All ages)
    • Elementary Problem: Let’s say there’s a tank that is approximately the size of a football field (which the biggest one at the Georgia Aquarium is nearly such a size). Football fields are about 100 yd long by about 50 yd. Let’s say this tank is 30 ft, or 10 yd, deep. Using these estimates of the size of the tank, find the approximate volume in cubic yards if it is a gigantic rectangular prism. (The volume is found by multiplying the length times the width times the depth.)
    • Junior High Problem: Given the information in the elementary problem, about how many gallons does the tank hold? 1 yd equals 36 in, and 231 cubic inches equals 1 gallon.
    • Algebra Problem: We found out online that a tank at the Georgia Aquarium holds about 6,300,000 gallons of water. Given that the volume of a rectangular prism is V = Bh, where B is the area of the rectangular base and h is the height, and that a tank is a rectangular prism, use algebra to find the area of the rectangular base (B) of the tank if the depth of the tank is 10 yd. Give your answer in square feet. What percentage of the area of a football field is this if the area of a football field is 45,000 ft2? Hint: You will need to first convert all the measurements to cubic inches. Then solve for B. 1 yd equals 36 in, 1 ft equals 12 in, and 231 cubic inches equals 1 gallon.
  • How Much Do Those Sea Lions Eat? (Upper Elementary and Above) – In the show, we were told that each sea lion eats a certain percentage of its body weight each day that is close to 5%.
    • If a sea lion weighs 500 lb, how many lb of food does it need each day?
    • What about if it grows to 800 lb?
    • If you were in charge of ordering the sea lion fish to eat, how many pounds would you need to order per day if you needed food for a 400 lb and a 750 lb sea lion?

Now, there’s a lot more math involved at the aquarium. (Measuring the temperature of the tanks to make sure it is what the animals need, figuring out how many fish can be in one tank, etc.) But hopefully you enjoyed that little glimpse into aquarium math.

Remember, math is much more than a textbook exercise—it is a real-life “tool”…and one that works because of God’s faithfulness.

Reminder: An Algebra 2 curriculum is in process! We just submitted the first half to the publisher for layout. My husband and I would appreciate your prayers for us as we write the remainder. And in the meantime, be sure to check out our junior high program and other math materials.


Answers

How Big Is That Tank?

  • Elementary Problem: (100 yd)(50 yd)(10 yd) = 50,000 yd3
  • Junior High Problem: Converting cubic yards to cubic feet: 50,000 yd3(36 in/1 yd)(36 in/1 yd)(36 in/1 yd) = 2,332,800,000 in3
    Converting cubic inches to gallons: 2,332,800,000 in3(1 gal/231 in3) = 10,098,701.3 gal
    Note: The 50,000 yd3 came from the answer to the elementary problem.
  • Algebra Problem: Converting the volume to cubic inches: 6,300,000 gal(231 in3/1 gal)=1.4553 x 109 in3
    Converting the depth to inches: 10 yd(36 in/1 yd) = 360 in
    Solving the formula for B: V = Bh
    Diving both sides by h -> B=V/h
    Plug in the values: B = 1.4553 x 109  in3/360 in = 4.0425 x 106  in2
    Convert the final answer to square feet: = 4.0425 x 106  in2(1 ft/12 in)(1 ft/12 in) = 28,072.91667 ft2
    The percentage of the area of a foot field is P = 100 % (28,072.91667 ft2/45,000 ft2) = 62.38 %

How Much Do Those Sea Lions Eat?

  • 0.05(500 lb) = 25 lb
  • 0.05(800 lb) = 40 lb
  • 0.05(400 lb) + 0.05(750 lb) = 20 lb + 37.50 lb = 57.50 lb per day
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Hot Air Balloons, Algebra, & the Creator

hot air balloons

Hot air balloons have always fascinated me, and this last weekend I got a chance to see some up close. They’re huge—and it’s incredible to watch them float up and down by increasing or decreasing a flame of fire at the base.

But you know what’s even more amazing? The fact that day in and day out, the air in these balloons responds consistently to the heat from the flame used to control their movement. Let’s use math for a minute to look at some consistencies God both created and sustains in the atmosphere—consistencies that make hot air balloons possible.

Density & Temperature

For starters, there’s the Ideal Gas Law. This law is simply a way of describing the consistent relationship between the atmospheric pressure (P), the density of the air (ρ), the gas constant (R), and the temperature (T). Using letters to stand for each of these, we can describe the consistent relationship between them like this:*

P = ρRT

Now, using algebra (which is based on creation operating so consistently that we can multiply, divide, etc., by equal quantities on both sides of the equation, and know it will work even if we don’t know the actual values), we can rearrange this equation like this:

ρ=P/(RT)

Now we know that the density of air (ρ)—how tightly packed the molecules are—depends on the atmospheric pressure (P), the gas constant (R), and the temperature (T). Since the atmospheric pressure and gas constant are constant for a specific area on earth, we can view them as constant values and realize that as the temperature (T) changes, the density (ρ) will too!

In other words, if we change the temperature inside the hot air balloon, it will change the density of the air inside that balloon (increasing temperature decreases the density, and vice versa). Why do we care? Well, let’s look at another consistency…

Buoyancy, Density, & Volume

The buoyancy force (the force that makes the balloon float) changes as the density of the air inside the balloon changes…meaning that we can use temperature to change a balloon’s ability to float! The buoyancy force (FB) of a hot air balloon equals the difference between the density of the air outside of the balloon (ρa) and that inside (ρ), times the volume of the balloon (V), times the local acceleration due to gravity (g).

FB=(ρa – ρ)Vg

Look at that equation and think about what would get a higher buoyancy force. The lower the density inside the balloon (ρ), the greater the force will be, as when we subtract it from the outside density (where the air is not being heated but staying relatively the same temperature), we’ll get a greater number to multiply by the volume and the acceleration due to gravity. Thus getting a lower density (which we do by heating up the air inside the balloon) gives the balloon a greater buoyancy force (which helps it float).

Now, there’s another variable that affects the balloon’s ability to float.  Look back at the buoyancy equation and notice the V, which stands for volume.

FB=(ρa – ρ)Vg

The larger the volume (V), the greater the buoyancy force will be! So large balloons will float better than small ones (assuming you can evenly heat all the air inside to a temperature warmer than the outside air). And now you know why hot air balloons are so large!

(You might wonder how the g in the equation influences the buoyancy. The g in the equations depends on the consistent way God causes gravity to operate, so we can’t change it. It’s a fixed value—about 9 m/s^2 close to the surface of the earth.)

Getting the Balloon to Float

Besides the buoyancy force, the only other force acting on a balloon is the weight of the balloon, the basket, and anyone or anything in the basket. We can describe this force algebraically like this:

Fg=mg,
where m is the total mass of the balloon, basket, and everything in the basket and g is again the local gravitational constant.

Once the air in the balloon has reached a temperature such that the buoyancy force is greater than the gravitational force, or FB > Fg, the net force on the balloon will be upward and the balloon will start to rise. That’s why when we heat up the air in the balloon and it becomes less dense, making FB > F g, it rises in the air!

The Consistency of Creation & the Creator

Hot air balloons are one example of how men, using their God-given abilities to explore God’s creation—have utilized the consistencies God created and sustains around us to develop a useful device (in this case, a balloon that floats). But don’t miss the miracle of our ability to use hot air balloons. We can only get in a hot air balloon with confidence because atmospheric pressure and buoyancy operates in a consistent way, day after day, year after year. While individual balloons may have different volumes, densities, masses, and forces, the relationship between them stays the same no matter what the individual values. Without the consistencies of creation, we would be unable to use hot air balloons. It’s this consistency of creation that makes modern science (and hot air balloons)–as well as algebra–useful.

Yet why is creation so consistent that we can describe how it will operate with letters and know that relationship will hold true, no matter the actual values we plug in?

The Bible gives us an answer: because of the biblical, consistent, faithful God. Jesus is faithfully upholding all things. We have a faithful Creator God.

He is the radiance of the glory of God and the exact imprint of his nature, and he upholds the universe by the word of his power. After making purification for sins, he sat down at the right hand of the Majesty on high,” Hebrews 1:3 (esv)

Transform Your How Your Students See Pre-Algebra and Algebra!

Want to teach algebra from this perspective? Check out our pre-algebra curriculum, and stay tuned for Algebra 2 next year! In fact, Algebra 2 students will get to explore hot air balloons in more depth as they explore God’s creation using math.


*Note: You may have seen this equation before written PV=nRT, where V is volume and n the number or mass of gas molecules. Since ρ = n/V, they’re actually the same equation.

Math, Man on the Moon, & the Creator

Photo Credit: NASAThis Saturday, July 20, 2019, marks the 50th anniversary of the Apollo 11 landing on the moon.

This achievement would never have been possible apart from the Creator’s faithful sustaining hand, and men using the ability He gave them to use math to explore His creation.

  • Day after day, God holds creation together in such a consistent way that we can use math to describe that consistency. For example, we can describe the force due to gravity as gravitywhere G is a constant value, the ms are 2 masses, and the r is the distance between those masses. There are many, many formulas used in exploration of space—each one is a way of describing a consistency God created and faithfully sustains.
  • By describing the consistencies around us mathematically, we can use math to figure out how to send a spacecraft into space. For example, using algebra we can calculate the acceleration due to gravity that the spacecraft has to overcome. Using more math, we can figure out how fast the spacecraft has to go to escape from the pull of gravity into space, which can be described like this:Escape Velocity(see “Gravitational Escape Velocity with Saturn V Rocket” for more information). Then we can use math to figure out how to design that spacecraft to do that!

Whole books could be spent describing the math behind getting man to the moon. The point here is that modern science (including the space program) rests entirely on there being consistencies in creation (which enable us to design a spacecraft so it can escape the earth’s pull—if creation weren’t consistent, we wouldn’t know ahead of time if the spacecraft would really make it). And those consistencies in turn exist because a faithful, consistent Creator is holding all things together.

Jeremiah 33:25-26a (esv) says, “Thus says the Lord: If I have not established my covenant with day and night and the fixed order of heaven and earth, then I will reject the offspring of Jacob and David my servant.” God has established His covenant with the “fixed order” of heaven and earth—with the consistencies all around us. Here He points to that very consistency as a reminder that He is a God who keeps His covenants. He will do all He’s said in His Word—saving all who believe upon Jesus, and punishing those who reject His gift of salvation.

As you remember the landing on the moon, lift your eyes higher to the Creator of it all. Truly, creation declares His praises and reminds us to take head to His Word.

“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.” Psalm 19:1–3 (kjv)

Note: Our upcoming Algebra 2 book will give students the opportunity to explore consistencies such as  and see more up closely how math helps us describe God’s creation, pointing us to the Creator. Be sure to check out the math curriculum we offer for other grades too!

Math Blog: Wedding Math

wedding

Since I’ve been working on planning my wedding, I thought it might be fun to share a glimpse at how math applies in event planning. It truly is a tool we can use in various situations God places us in!

  • Total Guest Count – One interesting aspect of event planning is figuring out how many people are coming…which involves addition in adding up all the friends and families being invited.
  • Budgets – Trying to plan an event on a budget involves adding up all the expenses and subtracting that from the total you have to spend to see how much you have left to spend (or how much over budget you’ve gone…which could be represented with negative numbers). For example, if you’ve spent $25 + $500 + $120, then you’ve spent a total of $645. If your budget is $1,000, you have $1,000 – $645, or $355 left to spend.
  • Total Cost of ItemsAddition and multiplication are used extensively in figuring out how much you’re really spending on a specific aspect of the wedding. Take table centerpieces for example. Suppose your centerpiece consists of a $2 vase, a $1 candle, and a $1 a flower . It costs $2 + $1 + 1 = $4. If you have 25 tables to put centerpieces on, it will cost a total of $4 x 25, or $100. If you pay 5% (notice the percent!) sales tax on all of that, then the total cost will be $100 x 1.05 = $105.

As you teach math this week, remember to show your students why they’re learning the concepts they’re learning. Math is about much more than passing a test or solving meaningless problems—we want students to understand how to use this tool in their own life so they’ll be equipped for the various tasks God’s given them…and to do so while praising the great Creator whose faithfulness in holding all things together makes math possible in the first place.

Reminder: If you need ideas or help making math come alive, check out our math resources and curriculum.

Waves, Math, and the Creator: Sound

Part 3 of 3

Note: This is the third and final post in a series of guest posts on Math, Waves, and the Creator by Dr. Adam F. Hannon. Get ready for a fascinating “listen” to sounds! – Katherine

Sound waves arise when a physical medium like a string on a guitar, a membrane on a drum, or even your own vocal cords in your throat vibrate.

When you pluck a guitar string, the string’s vibration causes the surrounding air molecules to vibrate with a similar wave pattern, and those waves move through the air as a compression wave until they reach our ears. There our eardrum receives the wave, vibrates as well, and sends that information to our brain for us to interpret the sound. There’s a lot going on in this whole process, but the neat thing is that we can use math to explore it!

Different Strings; Different Sounds

Have you ever wondered why different strings on a guitar produce different sounds? Well, there’s a mathematical relationship between the frequency (f) of the wave in the string, the wavelength (λ) of the wave in the string, the linear density (ρ) of the string (without getting technical, this is affected by what material the string is made out of—how dense it is), and the tension (T) on the string (that is, how tightly the string is held at its top and bottom). Because of the consistent way God governs this universe, we can describe the relationship mathematically, and then use it to design instruments!

Here’s the relationship[1]:

Since for a given string the tension and material the string are made of (and thus the linear density) are fixed, the frequency multiplied with the wavelength are a constant based on those values.

Harmony Between Notes

Have you also ever wondered why different notes sound better together than others? It has to do in part with the subtler tones that are also formed when the note is played.

When waves are bound (example: a guitar string is attached, or bound, at both sides), they produce not only a fundamental tone, but also what we call harmonics, or subtler tones that are mathematically related to that fundamental tone in a specific way. In the first harmonic, the wavelength is half the original wavelength (frequency is doubled). In the second harmonic, it is a third of the original wavelength (frequency is tripled). And so forth.

Figure 1. Harmonics on a string. Adapted from WikiMedia.

We can use—you guessed it—math to describe how these harmonics relate back to the wavelength of the fundamental tone.

Note: In the above equation, n = 1 in the fundamental tone, n = 2 in the first harmonic, n = 3 in the second harmonic, and so forth.[2]

Harmonics help us to understand why certain notes sound better together. Harmony actually means “agreement,” and notes that sound good together have “agreement” in the subtler sounds that make them up! For example, the second harmonic of the note C is the note G; not surprisingly, C and G sound good together.

When talking about harmonics, you’ll often hear people talk about frequencies instead of wavelengths. We looked at wavelengths here because they’re easier to picture, but as wavelengths change, so do frequencies. To see why, let’s use some simple algebra.

We can first divide both sides of the equation that relates the frequency and wavelength by the wavelength to solve for frequency directly. We can do this because of the consistent way God created the laws of math.


We can now substitute the equation we have for wavelength in terms of n and L. This leaves us with a way to determine the fundamental frequency and harmonic overtones from just the length of the string, tension, and density.
Looking at the equation, we can see that if we make a string tighter (increase the tension), we make the frequency higher and thus a higher pitch. Similarly, thicker strings (larger density) will have a lower frequency or pitch. Longer strings also will give a lower pitch and thus shorter strings a higher pitch (this is why when you hold down strings on a guitar going down the fret board you get higher pitches as you shorten the bound string length). Having different strings together, we can control their individual pitches with these parameters to have integer ratios of their frequencies that give different harmonies, and thus make the beautiful music we hear.

The Harmony of the Universe

Harmonics—which are produced from bound waves—are not constrained to music and sound alone. We just can’t “hear” all of the other kinds of harmonics God put in place in the other kinds of waves He created.

For example, in light waves, if a special sets of mirrors are used to only allow light of certain wavelengths to remain in a confined space, only waves of appropriate harmonics are confined. (Side note: This can be used in conjunction with special materials to make lasers.) In the waves of electrons in an atom, the atomic orbitals the electrons can occupy are harmonic in nature, as the electrons are bound in the position they can occupy in space.

Since the Bible makes it clear Jesus is the one who created and sustains all things (Colossians 1:16–17), He is the One who has put the incredible order and boundaries we see all throughout His Creation…and math puts a magnifying glass on what He has created, giving us a glimpse into His handiwork we’d otherwise miss.

We can only imagine how remarkable it would be if we could “hear” all the harmony of the universe caused by all the waves around us. Looking at the incredible order in waves—which math helps us see—should cause us, like Job, to bow before our Maker, humbled in His presence.

“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 42:5-6 (KJV)


[1] Equations adapted from Romine, Gregory S. Standing Waves on a String: P28, Lab 6. Stanford Physics Department, 2004, https://web.stanford.edu/dept/astro/dorris/StandingWaves.pdf

[2] Ibid.

Additional Sources Consulted/for Additional Reading:
Sound & Frequencies Explained (video)
Overtone Wiki Page
How Do Harmonics Work
Fundamental Frequency and Harmonics (Physics Classroom)

Math, Waves, and the Creator: Light Waves

Part 2 of 3

Note: This is a continuation of a series of guest posts on Math, Waves, and the Creator by Dr. Adam F. Hannon. This particular one would be great to have middle school and high school students read in order to give them a glimpse into how math helps us shine light on God’s creation, pointing to the Creator. I hope you enjoy! – Katherine

 “And God said, Let there be light: and there was light.” Genesis 1:3 (KJV)

God spoke, and light came into being. We feel its warmth (very much so in the summer months!) and enjoy its illumination, yet math gives us a fresh glimpse into just how amazing all the light around us is.

As discussed in the previous “Wave, Math, and the Creator” blog post, light is a wave—or more specifically, two coupled waves (an electric and a magnetic wave) in one. We saw in the previous blog how we can use algebra and trigonometry to describe waves, including light waves.

Let’s continue exploring light with math—only this time, we’ll use basic math, along with just a touch of algebra (the part a pre-algebra student could still follow).

As we do so, we’ll discover amazing order God placed in the very light all around us.

Measuring the Properties of Light Waves

There are a lot of different aspects of light waves we could look at. For example, we could look at how fast a wave is traveling in a certain direction—or its velocity.

We can use a number to describe this velocity.

Velocity of Light Wave

Figure 1.1 The velocity of a wave is how fast the wave is traveling in a certain direction. For example, if the  wave above took 1 second to travel 1 centimeter toward the right, we would say its velocity was 1 centimeter per second, or 1 cm/sec.

Or we could look at how frequently one part of the wave repeats in a given amount of time, called the frequency.

Again, we can use a number to describe the frequency.

Figure 1.2: In the video, the two waves have the same wavelength but different frequencies. During the time it takes the top green wave to pass one full period through the dashed line, the bottom purple wave passes through twice, thus it has twice the frequency.

We can also look at the wavelength—at how long each of the repeated wave structures are.

Again, we can use a number to describe the wavelength!

Figure 1.3 The marked distance between the peak of each wave is the wavelength. Notice that the top wave has a greater wavelength than the bottom one.

Now, in real life, it’s not easy to measure the frequency of a light wave—it corresponds to a really short amount of time. But it is easier to measure the wavelength. And then—you guessed it!—we can use math to help us find the frequency. Let’s take a look at how.

Using Math to Find the Frequency

Because of the consistent way God governs all things, there is a consistent relationship between the velocity, frequency, and wavelength of a wave:

velocity = frequencywavelength

Since in math we tend to use letters instead of writing out the whole words (it saves time and makes it a lot easier to work with the equation!), we’ll use symbols to represent this same relationship (the v represents the velocity, the f the frequency, and the λ the wavelength):

v = f λ

Now that we know the relationship between the velocity, frequency, and wavelength [1], we can use math to help us figure out the frequency. In a light wave, the velocity is the speed of light, which, because of the consistent way God governs all things, is always constant 670,616,629 miles per hour (or roughly 3.00 x 1017nm/sec). Note: The “sec” stands for “second,” and the nm stands for nanometers or 1 billionth the length of a meter—it’s very small! Thus, we can write that amount for the velocity (which we represented with a v) in the equation, giving us this:

3.00 x 1017 nm/sec = f λ

And now if we know the wavelength, we can easily find the frequency!

Example: If the wavelength (λ) of a light wave is 650 nm, what is its frequency?

We know this relationship: 3.00 x 1017 nm/sec = f λ

Substituting in 650 nm for the wavelength (λ) gives us this: 3.00 x 1017 nm/sec = f(650 nm)

If we now divide both sides by 650 nm, we’ll find the frequency.

frequency equation

Note: Notice that we divided both sides by the same amount to simplify the answer—we’re able to do that because of the consistent way God governs creation.

The THz stands for Terahertz. Tera means a trillion. We just saw that a 650 nm light wave has a frequency of 462 Terahertz; in other words, it is repeating the wave-like pattern 462 trillion times per second! Can you imagine something happening a trillion times over and over again in a single second!?

Discovering the Colors of Light—and Invisible Light

One of the neat things we discover as we use math to explore light is that different wavelengths result in different colors.

While we are used to white light, we also encounter colored lights, such as the red light in a small laser pointer. Notice how the color varies as the wavelength varies.

 

Figure 1.4: Approximate wavelengths of different colored lights.[2]

Some light, though, is invisible. It turns out that there are more to light waves than just what we think of as “light”! There are kinds of light waves with smaller and larger wavelengths that we can consider as invisible light. These different invisible light waves along with visible light are all called electromagnetic waves and make up a whole spectrum as shown in the figure below.

Electromagnetic Spectrum

Figure 1.5: Schematic of the electromagnetic spectrum. Going from left to right goes from longer wavelengths to shorter wavelengths.

Just think of the fact we can also only see a small portion of the electromagnetic spectrum—what beauty must exist to God who can see in the entire spectrum!

We are literally “in the dark” to most of the light waves around us—we only know much about them because we can use tools and equipment to detect them.

Applying What We Learn About Light

Not only does math help us appreciate the amazing beauty God put in light, but math helps us apply what we learn to build technology.

For example, take CDs, DVDs, and “Blue-Ray” discs. Did you know that the CD/DVD/Blue-Ray player reads the data off these disks using light, and that each of them use light with different wavelengths (and thus different colors)[3]?

  • CDs – 780 nm wavelength (infrared)
  • DVDs – 650 nm wavelength (red)
  • Blue-ray – 405 nm wavelength (indigo…somebody named that wrong!)

Every time you use a CD/DVD/Blue-ray disc, you’re reaping the benefits of math in action.

Let There Be Light

That’s just a glimpse into how math reveals design and beauty in the very light around us—the light God created by the simple command, “Let there be light” (Genesis 1:3 KJV).

As you enjoy the bright summer light today, pause and reflect on the Creator’s power and might Who simply spoke light into existence.

He is the same Creator who shone into the darkness of our sin with the Light—Jesus Christ.

“In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not…. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:” John 1:3-4, 12 (KJV)

Note: Stay tuned for the final blog in the Waves, Math, and the Creator series. In it, we’ll explore sound waves.


[1] Equation from David J. Griffiths, Introduction to Electrodynamics, 3rd ed. (USA: Upper Saddle River, NJ: Prentice Hall, 1999), p. 368.
[2] The exact colors given for different lights varies by source, as the there are a range of hues within red, orange, etc., and the borders are hard to concretely define since what may be orange to one person might still be red to another (see this Live Physics page for one list of approximate ranges). The point is that different colors of light do have different wavelengths. These values came from those given in Griffiths, p. 377. The figure was adapted with those numbers from one by Gringer.
[3] Values from Kumar, T. Ravi, and R. V. Krishnaiah. “Optical Disk with Blu-Ray Technologoy.” International Journal of Computer Engineering & Applications III, no. II/III (July-September 2013), p. 160. https://arxiv.org/ftp/arxiv/papers/1310/1310.1551.pdf.

Math and Music – Short Video

Music & Math

This short video offers a brief peek at the mathematical relationship between different musical notes. In it, you’ll see just a glimpse at how math (including algebra and pi) can help us describe the order God has placed in the sounds around us.

After you watch it, stop and think for a moment about math and music. Although we don’t always think about it, there’s a structure even to something like a song…and it’s math that helps us describe this order. God is the One who both created and sustains sound waves and who gave us the ability to appreciate and compose songs. Let’s praise His name.

Math Tax Worksheet for Students

Math & Taxes

Math & TaxesWith Federal income taxes nearly due, I thought it might be fun to put together a worksheet you can use with students to let them apply math to filing taxes.

Download Math Tax Worksheet

The worksheet is an extremely simplified version of the 1040, with instructions and pretend numbers for students to use. To use it, students need to know multi-digit addition and subtraction, along with rounding (although you could round the numbers for them if needed).

Please let me know if you find the worksheet helpful. A few of you have suggested that I send out ready-to-go worksheets, so I thought I would give it a try.

Remember, one of the goals in teaching math is to equip students to use math in their own lives to complete various tasks. God created man to work, and math is a tool that can help us in that. We can use math because He gave us the ability; thus we, unlike animals, can even file income taxes. And since income taxes are due each year, it’s an example of how math helps us with real-life tasks.

Math Curriculum & Facebook Q&A

We’ve got math curriculum for elementary to algebra and geometry to help you teach math in a way that connects it with God’s creation and real-life tasks.

Have questions about any of it? Let me know–I’d love to answer them. I’m planning to do a Facebook Live Q&A sometime this week (follow our Facebook page for exact timing and to watch the recording afterwards) and will be addressing lots of common questions there too. Hope you can join in!

Super Bowl, Super Football Math

Football Math

Football MathHere are a few examples of how you can use the Super Bowl to show your students that math really does apply outside of a textbook.

We learn math, not just to pass a test, but to be equipped to use it to help us in tasks God’s given us here on earth (and to behold His glory and faithfulness in holding all things together—see God and Math?).

Believe it or not, the Super Bowl was replete with examples of math in action.

  • The Super Bowl Name – Notice the Roman numeral in Super Bowl LII. The Super Bowl name (along with the first quarter, second quarter, first down, second down, etc.) is an example of ordinal numbers.
  • The Team Jerseys – Perhaps the most obvious numbers on the field are those on the team jerseys. There’s an example of how we can use numbers like names—in this case, to identify different players.
  • The Field – Yep, there are numbers on the field itself (50-yard line, etc.), and distance is constantly measured throughout the game. How far of a field goal needs kicked? How much distance left to go to get to the next first down? In a more background way, laying out the football field itself required measurements. And how much grass is needed? Or paint? Again, measuring (think geometry) in action!
  • Confetti (and Other Costs and Profits) – So how much confetti was needed to fire off at the end of the game? And how much would it cost? How much did everything at the Super Bowl cost altogether? How much was brought in through ticket sales? Math can help us answer these behind-the-scenes questions.
  • The Ads – A lot of math goes on behind the scenes when it comes to ads. Below are a few examples.
    • How much money did NBC receive in advertising? If you knew the price of the ads sold, that could be calculated using addition. (In 2017, one source said it was around 385 million.)
    • When deciding if they should buy an ad, companies use math to help them compare different options. One useful measurement often used to compare options and develop an overall advertising plan is Gross Rating Points (GRPs), which is found by multiplying two different measurements together.[1] One can also look at how much the ad costs per thousand people it reaches, which is found by dividing the cost of the ad by the total people reached (in thousands).[2]
    • How much does an ad cost altogether? That would take adding up the cost of making the ad, the actual cost of buying the ad space, etc.
    • Is the ad a good ad to run? There’s no perfect way to tell this, but there are a lot of ways to try…and math can help. For example, one could test the ad before paying millions to air it in the Super Bowl. One testing method called the MSW* ARS shows ads (inside programs) to a sample group of people. Ads are given a score based on subtracting the percent that was for the target brand after the ad with the percent that was for the target brand before the ad (in other words, seeing the difference the ad made).[3]
    • Was the ad effective? Again, there’s no perfect way to measure this, but there are a lot of ways to try. Marketers use numerous formulas when evaluating sales and advertising to try to make sure that their advertising is really making a difference in sales.
  • The Graphics – Numerous graphics were introduced throughout the game. While we don’t often think of math and graphic design in the same sentence, graphic design often does use math. Not only does the computer program(s) used in designing use a lot of math behind the scenes, but graphic designers often use math to help position items, scale them, determine proportions, etc. Oh, and colors are specified using—you guessed it—numbers.
  • Statistics – What was the average cost of a 30-second Super Bowl ad? What is the football player’s percent complete? How many yards has the quarterback thrown so far (this would require adding)? And a host of other stats that use numbers (and addition to find those numbers)!
  • The Special Effects – Think of all the work that went in behind the scenes into coordinating various special effects. Math likely had a part in a lot of it: the angles of the lights, the levels of the various microphones (yes, math helps us measure audio levels too!), etc.

A lot goes in to an event like the Super Bowl—including a lot of math. The list above is by no means exhaustive, but hopefully it will get you (and your students) thinking.

Math’s much more than a textbook exercise—it’s a real-life tool we can use while praising the Creator.

Reminder: We’ve got a lot of math resources (and even curriculum) to help you teach math from this perspective.


[1] J. Craig Andrews and Terence A. Shimp, Advertising, Promotion, and Other Aspects of Integrated Marketing Communications, 10th ed. (Boston, MA: Cengage Learning, 2018), p. 348.[2] Ibid., p. 356.

[3] Ibid., p. 386-388.

Weather Prediction & Math
– Plus God’s Handiwork in Snowflakes

With a lot of the U.S. facing cold temperatures and snow recently, I thought it might be a good time to write about how math helps us explore the weather.

  • Basic Math & the Weather – Have you ever noticed how many times numbers appear in news reports on the weather? Consider this recent ABC News article on the storm currently plowing through the East Coast. The number of flights canceled, the amount of snow collected, a comparison with previous snow records, wind measurements, temperatures—reporting on all of these things uses basic math and numbers.
  • Algebra, Calculus, & Predicting the Weather – One question a lot of parents and teachers get when it comes to math—especially algebra and upper math—is why it’s needed. Well, to help us predict the weather is one answer! We use lots of algebra and upper math in exploring the weather. For a simple explanation of the use of super computers and equations in weather prediction, see NOAA’s “Weather Prediction: It’s Math!” For more details, see EDN’s “The Math of Meteorology.”

The weather is just one example of how math isn’t a dry textbook exercise—it’s a way to describe God’s creation and help us with real-life tasks.

Biblical Math ResourcesP.S. Math can be a lot more fun (and make a lot more sense) when students understand why they’re learning what they’re learning and see it in context with real life and science. We offer curriculum and supplemental resources to help you transform math this year.

Bonus: God’s Handiwork in Snowflakes
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. Check out our previous blog post on “Snowflake Math.