Category: Math in Action

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Fireworks, Math, & the Creator

fireworks

As we celebrated our nation’s 250th birthday last week, many went out to see fireworks. Now’s a great time to stop and think about all the math that goes into planning a firework display, along with the wonder of how God governs creation consistently enough that fireworks are even possible (which math helps us see).

Let’s start with planning the display. Here are a few examples of some math involved!

  • Costs – Say a city has a $100,000 budget for a firework display. That cost might need to include paying a band, bringing in police officers, and other general costs in addition to the costs of the fireworks themselves. Basic math would help compare different options. For example, say they’re selecting different fireworks for a certain 30 seconds of the show.
    • How much would ten $50 fireworks cost (Answer: 10 x $50 = $500)?
    • How much more would it be to get 8 of $75 larger fireworks? (Answer: 8 x $75 = $600; $600 – $500 = $100)
  • Comparing – If one firework show shot off 100,000 fireworks altogether and another did 25,000, how much more did the one do than the other? (Answer: 100,000 – 25,000 = 75,000)
  • Buying Fireworks on Clearance – If you buy a $50 firework on a 40% off clearance, how much would you spend? (Answer: 40% of $50 is $20, or 0.40 x $50 = $20. Thus the final price is $50 – $20 = $30.)

Math is indeed a useful tool that helps with real-life tasks. Now let’s stop and think about the fireworks themselves, as fireworks not only require lots of math in their development and deployment, but our ability to put on firework displays points to our amazing Creator.

Fireworks contain carefully measured mixtures of chemicals. Different compounds containing metal produce different colors when heated, and manufacturers must mix them in just the right proportions (which we study in math!) to create bright, reliable colors. Manufacturers can only declare with confidence that a firework is red, blue, etc., because the same combinations of chemicals consistently produce the same reactions. And why do they do that? Because God created and sustains a consistent world!

Fireworks also include a fuse—a material that burns while the firework travels up so that the shell bursts safely high in the air and not near the ground. Manufacturers have to observe how quickly different materials they could use as a fuse burn up, and then select the right material and length to make the explosion at the desired point. Designing a fuse involves math, and again relies on materials burning in a consistent fashion.

Example: Suppose a fuse burns at 24 seconds per foot. How many feet of fuse are needed for it to burn for 6 seconds? (Answer: 24 sec/ 1ft = 6 sec/? ft24 sec. was divided by 4 to get 6 sec.; 1 ft. divided by 4 is 0.25 ft. Answer is 0.25 ft., or 3 in.)

How do we know what angle to launch a firework? Or how high it will travel before bursting? Again, we observe the consistencies God created and sustains in creation, such as gravity and the predictable path of a projectile. These consistencies can be described algebraically. Computers use lots of advanced math to calculate when to launch each firework and at what angle so the burst occurs at the desired place and exactly the right moment in the music. This is only possible because of the consistent way God governs creation! If He were not holding this world together in a consistent fashion, we’d have no reason to expect fireworks to go off in a consistent way.

fireworks

There’s much, much more we could talk about with fireworks, such as the lift charge needed to get the firework off the ground or the arrangement of stars in a shell, but hopefully that gives you a glimpse into how math helps us with fireworks…and how our ability to use math like this relies on God’s faithfulness in holding all things together. As you think back on the Fourth of July with your children, remember to praise the great Creator and Sustainer of all. And know that the math you learn applies outside of a textbook!

Looking for next year’s math curriculum? Check out our middle and high school courses that show students the purpose to math and how it points to the Creator at every turn! And don’t miss our supplemental resources that you can use with younger ones to bring math to life for them.

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Math and Weddings

weddings

In helping a friend plan her wedding, I was recently reminded of how math applies in planning an event. Here are a few ideas to share with your students.

A. Total cost given per-person cost: If the caterer charges $29.50 a guest, and you have 80 guests, how much will food cost? If you increase to 90 guests, how much will your catering cost go up?

B. Total with tip: If your total caterer bill is $2,500, and you add a 20% gratuity off the $2,500, how much would the total with tip be?

C. Here is what you’ve spent on center table decorations: $41.23, $32.12, $20.15, and $50.60. If all that decorates 5 tables, what is the cost per table?

D. The baker charges $356 for a cake that feeds 50. What is the cost per person?

Always remember, math is a useful tool that helps us with real-life tasks!

Solutions: A. $29.50 x 80 =$2,360.00; if increase to 90, total is $29.50 x 90=$2,655.00; difference is $2,655.00-$2,360.00=$295.00.
B. 1.20 x $2,500 = $3,000 (Multiplied by 1.20 to include the 20% tip, as 100% + 20% = 120% = 1.20; could also have found 20% and added that to $2,500).
C. $41.23+$32.12+$20.15+$50.60=$144.10; $144.10/5=$28.82
D. $356/50=$7.12

Algebra 2 eCourseNeed a curriculum that shows students every concept as a useful tool? Check out Kate’s Middle School and High School curriculum, along with elementary supplements that can enrich whatever curriculum you use. Enjoy 30% off most materials through the end of April!

 

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Why High School Math? (Plus AI, Logic, & the Creator)

Does algebra even matter?

As I released my new Consumer Math course, I kept hearing how excited moms were for a high school math that was actually practical. While Consumer Math certainly is that, other high school math should be too!

In all of my math courses, I’ve striven to show students why they’re learning what they’re learning. Granted, algebra might not be something students incorporate into their daily life. However, they use technology based on it daily. For example, how fast will a metal pan heat up? We can use an algebra equation to figure that out.

formulawhere

formula

We can write formulas like the one above because of the consistent way heat transfers into pans based on their heat capacity. And why is creation so consistent? Because a faithful God governs creation in a predictable way! Algebra should be something students finish up with a deeper wow at our amazing Creator.

Now, high school math problems can get challenging and involved. Some multi-step problems can make your head spin. These problems not only prepare students for real-life math problems, but they also teach them to look at a situation where they don’t know what to do and think of different ways they could potentially approach it. That’s a skill we need with real-life non-mathematical problems too!

And then there’s logical thinking skills. If a > b and b > c, we can conclude that a must also be greater than c…but we couldn’t conclude that it’s greater than h, for instance. Why do we care? Learning how to draw logical conclusions helps us think through real-life scenarios.

I’ve put below a video Answers in Genesis recently released that shows an AI, when prompted to answer “according to strict math, logic, and mathematical probability” agreed a biblical Creator makes sense and evolution is foolish. Logic matters…and algebra and geometry help students develop it.

Looking to Help Your Students See Math’s Purpose This Year?
Check out these high school and junior high school programs, complete with optional eCourses that will walk students through the lessons. Also check out the Big Book of Math timeline, usable to add in math’s application and purpose to any curriculum. It is possible for students to see God in math while developing skills that will last a lifetime.

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Math and Taking Care of a Baby

baby

Have a young person who loves children but who doesn’t see the point of math? Try walking them through some ways you use it when taking care of a baby!

  • How Many Supplies to Get: How many diapers do you need a week if baby uses 5 a day (5 x 7 = 35)? How many jars of baby food if baby uses 2 a day (2 x 7 = 14)? Multiplication comes in handy when figuring out your shopping list.
  • Costs: How much per diaper is diapers in bulk versus those in a smaller package (divide package cost by diapers in package)? If a baby dose is 2 mL, how many doses are in a 10 mL bottle (10 divided by 2 = 5)? Division aids in analyzing costs, as does comparing numbers (you’ll need to compare your results to see which is truly less expensive).
  • Timing: When does baby need his next bottle if he eats every 3 hours and last had one at 9 am? How long of a nap did he get if he went down at 1:30 and woke at 2:45? Mommies and daddies have to do lots of mental time calculations as they care for baby.
  • What Eaten: How many ounces of food is baby getting? Add up each amount they’ve had to find the total.

If you sit back and think hard enough, you might be surprised how much math you use in a day–even when carrying for little ones. Math applies outside of a textbook like this because God governs creation in a consistent fashion, and He gave us the ability to have dominion over it (Genesis 1:28). Whether that be in a science lab or changing diapers, math helps us with the tasks He’s given us to do.

I’m super excited about my new high school Consumer Math course, as it will help students see how they can use basic math in tons of different settings they’ll encounter as adults–and how to do so with the heart of one stewarding God’s resources, not pursuing money itself. We’re making the finishing touches on it now, so keep an eye for its release soon! (And keep the whole team in prayer as we complete it.)

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Math Moment: Math & Astronomy

astronomy

Did you know that math helps us explore outer space, learning more about the vastness of God’s creation–and how perfectly designed earth is for life?

Have you ever tried to count the stars? We can’t possibly count them all, but we can use math to estimate the number of stars. While there are different ways to do this, one way is to estimate the total mass of a galaxy (which in itself takes a lot of math) and then divide that total mass by the average mass of a star (which again takes math to estimate). So how many stars are there? Well, there’s an estimated 100 to 400 billion stars in our galaxy alone, which would then need multiplied by the number of galaxies (currently estimated to be in the trillions). That’s a lot of stars! Notice we just used math to approximate the stars in our galaxy, but we can’t fully count them all!

Yet God calls each star by name–and it’s because of His power that they continue.

He determines the number of the stars; he gives to all of them their names. Psalm 147:4
Lift up your eyes on high and see: who created these? He who brings out their host by number, calling them all by name; by the greatness of his might and because he is strong in power, not one is missing. Isaiah 40:26

Think about how much greater God is than we are! We can’t even count the stars, and He calls them by name and keeps them in their places. He is greater than we can even imagine.

Have you ever wondered how we know how far it is to the moon, sun, and stars? We can’t just stretch a tape measurer across these distances! Instead, we make the measurements that we can from earth and then use geometry to figure out the distances. When we do, we see that the earth is just the right distance from the sun. If it were closer to the sun, we’d burn up…if further away, we’d freeze.

Now, the earth and the other planets don’t just sit in space; they orbit around the sun in elliptical orbits. How do we know that? Again, men used math! Johannes Kepler used data that had been recorded about Mars to figure out what orbit around the sun would result in those readings. He discovered that planets orbit in ellipses, and that no matter where they are on the ellipse, if you were to go back the same amount of time and look at the resulting area formed between those two locations and the sun, it’d always be the same. So that means God governs creation so consistently that we can mathematically describe how a planet will orbit.

When Kepler shared some of his findings, he paused to praise the Creator.

"Crying out with the royal Psalmist: Great is our Lord and great His virtue and of His wisdom there is no number…To Him be praise, honour, and glory, wourld without end. Amen." [Stephen Hawking, ed. On the Shoulders of Giants: The Great Works of Physics and Astronomy. Philadelphia: Running Press Book Publishers, 2002, pg. 1157.]

Well, I hope that gives you a little glimpse into how math helps us explore outer space and how as we do, we see that truly, the Heavens declare God’s praises.

math history

Discover more about how we use math to explore the heavens–along with lots of other historical and present-day applications of math in Kate’s new Math History Timeline!

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Math Moment: Math & the Human Body

cells

VIDEO TRANSCRIPT: Our bodies are remarkable. We can eat, see, move, smell, and so much more. We’re clearly incredibly designed! But when we use math to see how our bodies work, we get a deeper appreciation for how amazingly God knit us together.

Notice that a child’s head is bigger in comparison to the rest of its body than the adult’s head. A big head helps protect a child when they fall. However, if we kept growing with that same ratio between our head and body, we wouldn’t be able to walk as adults! God gave us just the body proportions we needed for each stage of life.

While we’re talking about our heads, let’s zoom in on our ears. It takes advanced math, including trigonometry, to record sounds digitally so hat we can listen to them. But our bodies constantly collect and interpret sounds for us…all without us thinking about it!

Now take a look at these cells from a human body. Notice that the cells are approximately spheres. Using math, we can explore the surface area and volume of cells as they grow. Here are the formulas for the surface area and volume of a sphere. The ratio between them would be the division of one over the other, which we can show using a fraction line and which simplifies to 3/r, where r is standing for the radius of the sphere. The radius, or r, is going to get bigger as the cell gets bigger. What happens to the surface area? Well, let’s say this cell has a radius of 1 and this one of 3.

Notice that if we plug those values into 3/r, the ratio gets smaller as the radius gets bigger. That means that in comparison to the volume, there’s less surface area. This would be problematic if our cells just kept growing, as the cell absorbs nutrients through its surface area. If the cell gets too big, it will die, as it won’t be able to get enough nutrients. But don’t worry–our great Creator designed cells to divide into smaller cells before they get too big. Once again, math helps us see His design.

Next, let’s talk about the viscosity of our blood. I know viscosity is a big word, but it basically describes the thickness of a liquid. Water has a lower viscosity than the orange liquid shown here.

Here’s the formula for viscosity. God put special proteins in your blood that makes these values just right for your blood to flow around your body…and to change when you get a cut so the blood becomes thicker and we don’t bleed to death. God sure thought of everything, didn’t He?

Now there’s a lot more we could say about our bodies, but hopefully that gives you a glimpse into how incredibly designed you are. God knit you together in your mother’s womb. He knew all that would take place in your life before you took your first breath. You can trust Him and cast your cares on Him, because He cares for you.

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Math Moment: Math and Technology

airplane

VIDEO TRANSCRIPT: We live in a society permitted with technology. From the time we wake up in the morning to the time we go to bed, we’re surrounded by technology…we’re using technology…we’re using products that were manufactured using technology…and most of the time we’re using it without even thinking about it. Yet it’s very existence is shouting out at us God’s faithfulness. To see how, let’s think through the process of developing technology.

Obviously, an airplane doesn’t just assemble itself, and this technology didn’t just appear. Men, including Wilbur and Orville Write, experimented over and over again to understand different aspects of God’s creation and figure out how to design a plane that would actually fly. Math is used a lot in airplane design–trying different wing lengths, building models, and so much more.

None of this would be possible, though, if creation weren’t consistent. Lift, gravity, and drag operate the same way day after day, year after year. In fact, we can use math to describe these consistencies of creation and to figure out how to design planes that will actually fly.

But imagine if gravity or lift changed every day. An airplane would fly one day and not the next!

Technology relies on a consistent creation. But why is creation consistent? Well, the Bible tells us that Jesus “upholds the universe by the word of his power” (Hebrews 1:3b). Jesus is the One upholding creation so consistently and so reliably that we can rely on gravity to work consistently and then design airplanes based on that. Technology is truly shouting out at us that God is faithful and we can trust Him.

A consistent creation by itself, though, doesn’t lead to airplanes. After all, airplanes don’t just assemble themselves; man has to have the ability to explore the consistency of creation and design planes. And we do! And the Bible gives us an answer as to why we do. It tells us that we’re made in God’s image. God gave us the ability to explore His handiwork and the task of subduing the earth and exercising dominion (Genesis 1:27-28). We use math in this process! You can’t get a degree in any field of science without a lot of math. Math helps us describe the consistencies of God’s creation.

From exploring the relationship between the power, voltage, and current flowing through an outlet, to the relationship between centripetal acceleration, velocity, and the radius being traveled, to that between the force, mass, and acceleration of a baseball, we use math to describe the consistencies all around us–consistencies that remind us that a faithful, never-changing Creator is upholding all things.

So next time you use technology, remember that God hasn’t changed. He doesn’t have good days and bad days like we do. We can always trust Him and everything He’s said in His Word, the Bible.

Reminder: Check out our math materials for curriculum and resources to help you teach math as a part of God’s creation.