Fractions - Christian Perspective

Posted on August 22, 2023October 14, 2023 by kate [loop] hannon

Math Moment: Math & the Human Body

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.

Posted on June 16, 2022June 16, 2022 by kate [loop] hannon — Leave a comment

Math, Fireflies, Light Bulbs, and the Creator’s Design

Many of us have been fascinated at one time or another by tiny lights dotting the backyard on summer nights. Fireflies, lightning bugs, or whatever you call them are fascinating to watch…and perhaps try to catch. What many don’t stop to think about, however, is how amazingly designed these creatures are.

Light Bulbs

To better understand the marvels of fireflies, let’s pause and take a look at light bulbs for a minute. If you’ve ever put your hand near a light bulb while it’s on, you know that in addition to light, light bulbs produce heat (most of which is infrared radiation). We can use math to measure what’s called the efficacy of the light bulb—that is, how much light they produce compared to how much power they use. The higher the efficacy, the less power is being wasted in heat.

To find the efficacy, divide the lumens produced (a lumen is a unit of measure for light) by the watts (a watt is a unit of measure for power). We could write that as a formula like this:

Or if we wanted to save our hands and use letters, we could write it like this:

We could even use a fraction to represent the division:

Note that we just used algebra! We’re simply using letters as symbols to stand for the efficacy, lumens, and watts of any light bulb. We can write formulas like this because God created and sustains a consistent universe.

If you run to your closet and pull out a package of light bulbs, you can measure the efficacy by inserting the lumens and watts listed on the bulb into the formula. For example, let’s consider a bulb I have in a lamp in my office. It says it is a 53 W (W is an abbreviation for watt) bulb that produces 850 lumens. Leaving units off for simplicity and inserting these numbers into the formula, we’d get this:

Fun assignment: Find the efficacy of the light bulbs listed in the table on step 6 of this page. Notice that some bulbs are more efficient than others! Then take a look at this chart showing the efficacy of different bulbs.

The higher the efficacy, the more the power is going into making light and less into making heat/non-visible radiation. Some bulbs produce more light with less power than others, but they all end up wasting a good deal of power. According to what I could find, an ideal green light that doesn’t waste power in heat would have an efficacy of about 683. That’s a much greater number than the 16.04 efficacy of the light bulb in my office!

What percent of the power is actually used to product light? To find that, we need to find the efficiency, which we’ll define “as the ratio of the total light power to the total power.”[i] The efficiency can be rather tricky to figure out, as light bulbs don’t come labeled with how much power goes towards light, but one way to approximate it is to divide the efficacy (in lumens per watt) of the bulb by 683 (the efficacy of ideal green light, which is the highest efficacy possible and thus can be used to approximate the total power while we use the efficacy to approximate the power used to produce the light).

Plugging in the efficacy we found for my office light bulb would give us the following:

If we express this as a percent by multiplying by 100 and adding a % sign, we’d get approximately 2.35%. That means only about 2.35% of the power this bulb uses goes towards making a light; in other words, the other 97.65% goes toward making heat/non-visible radiation. We would say this light bulb is about 2.35% efficient.

Fun assignment: Check out this table to view the efficiency of various lights…and calculate the efficiency of some lightbulbs in your closet by first finding the efficacy, then dividing that by 683, and finally expressing that result as a percent. Notice all the math you’re using!

Fireflies

Now, fireflies don’t plug into an electrical outlet or battery to produce light. Instead, a firefly produces light using chemicals. Yes, that’s right: God created these little bugs to have a mini chemical factory on board! These chemicals prove useful to man as well—one of the chemicals used has been useful in “biomedical research.”[ii]

The chemical reaction in the firefly produces energy…which is what powers their lights. When we talk about the efficiency of the lights fireflies produce, we’ll talk in terms of energy. Note, though, that power and energy are related–power is the rate of use of energy. We could say that efficient bulbs use less power and less energy.

Unlike man-made light bulbs, the firefly produces light without wasting much energy at all—sources indicate almost 100% of the energy turns into light[iii]—in other words, it’s almost 100% efficient. Compared to the 2.35% efficiency we found for the light bulb in my office, that’s amazing! Yet if the firefly didn’t produce light efficiently, they’d heat up and burn to death.[iv] Instead, God designed them to produce “the most efficient light in the world.”[v]

Conclusion

Next time you head outside and see the light from fireflies, ponder God’s magnificent design. Think about the wisdom and care God took with His creation, even giving us light displays at night made from tiny living chemical factories. And remember that math helps us explore, describe, and better appreciate His amazing world…as well as to improve inventions (like light bulbs). We’re able to explore and design because God made us in His image. That same God wants each of us to know Him and live in His presence forever.

[i] Debbie Hadley, “How Do Fireflies Light Up?” ThoughtCo., https://www.thoughtco.com/how-do-fireflies-light-1968122 (accessed June 13, 2022).

[ii] Yong Xu, Plant Factory Using Artificial Light, 2019, 2.1.6.1, https://www.sciencedirect.com/topics/engineering/luminous-efficacy

[iii]National Pest Management Association, “The Science Behind Fireflies: 6 Things You Didn’t Know About Lightning Bugs,” https://www.pestworld.org/news-hub/pest-articles/the-science-behind-fireflies/ (accessed June 13, 2022) and Debbie Hadley, “10 Fascinating Facts About Fireflies,” ThoughtCo., https://www.thoughtco.com/fascinating-facts-about-fireflies-1968117 (accessed June 13, 2022).

[iv] Debbie Hadley, “10 Fascinating Facts About Fireflies,” ThoughtCo., https://www.thoughtco.com/fascinating-facts-about-fireflies-1968117 (accessed June 13, 2022).

[v] National Pest Management Association, “The Science Behind Fireflies: 6 Things You Didn’t Know About Lightning Bugs,” https://www.pestworld.org/news-hub/pest-articles/the-science-behind-fireflies/ (accessed June 13, 2022).

Posted on June 18, 2019 by kate [loop] hannon — 1 Comment

Algebra, Giraffes, and God’s Handiwork

The following is adapted from the new Algebra 2 program we’re writing; check out our store for other math curriculum that will help math come alive for your students.

Ready for a glimpse of God’s handiwork as we apply algebra out of a textbook? Well, here we go! We’re going to look at how blood pressure relates to the distance from the heart.

First off, here’s a basic definition of blood pressure from Blood Pressure UK: “When your heart beats, it pumps blood round your body to give it the energy and oxygen it needs. As the blood moves, it pushes against the sides of the blood vessels. The strength of this pushing is your blood pressure.”[1]

Have you ever noticed that when a nurse takes your blood pressure, they always do it on the top part of your arm? That’s because “[m]edical personnel are trained to measure blood pressure at heart level.”[2]The top of your arm is at the same level as your heart. This is important, as, because of gravity, the pressure changes throughout the body.

If a person’s blood pressure equaled a specific amount at heart level (which we’ll call P₀), then the pressure at another part of the body (which we’ll represent with a P) could be approximately found by this formula, where h is the distance from the heart:

Blood pressure at another part of the body = Blood pressure at the heart + (density of the blood)(acceleration on the blood due to gravity)(height or distance from the heart)

To better understand this, know that if you were to take your blood pressure on your feet while standing, it would be higher than if you were to take the pressure on your arm. That makes sense, as gravity is pulling blood downwards, creating more pressure on your feet.

This also means that if you were to elevate your feet and take your blood pressure there, there’d be less pressure. BUT your heart would have to work harder to overcome gravity to get blood to your feet.

Stop and bend over for a second. You get a head rush, don’t you? That’s because of the extra blood pressure as your head gets lower.

Now think of a giraffe. Its head is waaaay above its heart. Does its heart have to pump extra to get blood there? And when it bends down to drink, how much pressure does its head have to be able to handle?

While there’s more to blood pressure than just the distance from the heart, we can temporarily ignore those other factors and just look at the change in pressure between what it would be at the heart and what it is at a different location. In the formula above, we used P₀ to stand for the blood pressure at the heart. Let’s remove that and just look at the change in the pressure from the blood pressure at the heart.

We’ll also assume that the acceleration due to gravity and density stay the same: 9.807 m/s² (which is the approximate gravity on earth), and an approximate density of blood (ρ) of 1,060 kg/m³. If we substitute these values in for ρ and g, we get this:

Depending on what value we plug in for our height (h), we’ll get a different value. The product will show us the change in pressure from the heart due to the change in height.

Let’s start by looking at a human. The top of my head is about 0.508 meters above my heart (about 20 inches). What would the approximate blood pressure be due to the distance from my heart when I bend down and touch my head to the floor? To find that, I’ll replace the h in the formula with 0.508 meters.

We wrote the answer in both metric units and mmHg, which is the same units you’ve probably heard your blood pressure given at the doctor’s office when you go for a checkup. Normal blood pressure runs between 80 to 120 mmHg, so it makes sense that the change in pressure would be around 39.610 mmHg which is on the same order of magnitude with normal blood pressures but still less than the average.

In comparison, what would a giraffe’s blood pressure be at the top of its head due to the distance from the heart when it bends down for a drink if it’s head was 6 ft (1.829 m) above[3] its heart? We’ll plug 1.829 m into the same formula.

Notice that the change in pressure due to the distance from the heart is 142.611 mmHg versus only 39.610 mmHg for a human. That is more than 3.5 times as much!

When they bend, giraffes have a much higher blood pressure rushing to their heads due to their larger size! If God had not specially designed the giraffe to handle this pressure, giraffes would have died out from all the blood rushing to their head went they bend down. In a 2017 article published on the Answers in Genesis website[4], Karin Viet explains what a testimony to God’s design giraffe’s are:

Evolutionists also encounter a design dilemma for the evolution of a long neck. That six-foot neck requires an intricate blood vessel system to maintain proper blood pressure between the heart and brain. A giraffe bending its neck down to drink water is a marvelous display of design. The 25-pound heart that pumps blood way up that neck against gravity suddenly pumps down with gravity, which should cause the delicate brain to explode. But the blood vessels are uniquely designed with reinforced walls, bypass valves, a cushioning web, and sensor signals to moderate the pressure when the giraffe bends its neck down.
The reverse of this intricate system happens when the giraffe raises its head so that the pressure is regained and the giraffe doesn’t pass out. In addition, the tight skin on giraffe legs has been compared to an astronaut’s G-suit, because it prevents high blood pressure from pressing blood out of the capillaries.

Giraffes were given just what they need—G-suit and all—to be able to handle the higher pressure caused by their long necks. And it’s math (including algebra!) that helps us understand how giraffes are a marvel of God’s grand design![5]

Don’t let your students miss out on seeing how math helps us explore God’s handiwork. Stay tuned for our Algebra 2 curriculum…and in the meantime, check out our other math resources and curriculum.

[1] “What is blood pressure?” Blood Pressure UK, (England, 2008), http://www.bloodpressureuk.org/BloodPressureandyou/Thebasics/Bloodpressure, s.v., “Blood Pressure.”

[2] Based on physics.wm.edu/~labs/107_manual/ch11.pdf

[3] Based on a neck of 6 ft, as shared by the San Diego Zoo https://animals.sandiegozoo.org/animals/giraffe and the fact that its heart is located in the giraffe’s chest.

[4] https://answersingenesis.org/mammals/giraffes-towering-testimonies-to-gods-design/

Posted on August 10, 2016August 10, 2016 by kate [loop] hannon — Leave a comment

Back-to-School Math Encouragement and Free Resources

$Transforming Math$

It’s the time of year again where many of you may be heading back to school after a summer break.

Here are some free resources to help encourage/equip you to teach math from a biblical worldview as you go.

Free Transforming Math Video – Watch this 18-minute video to get a glimpse into how biblical principles really can transform math, making it an exciting exploration of God’s creation. When you sign up for the video, you’ll also get a free read-aloud story that illustrates how often we really do use numbers, and a series of emails with other information and reminders to help you teach from a biblical worldview.
Math, Lightning, & Thunder – I recently blogged over on The Creation Club about how we can use math to help us approximate the distance to a lightning strike. Even a summer thunderstorm gives us an opportunity to explore God’s creation and marvel at God’s greatness (after all, He’s the one who makes the lightening and brings forth the wind – see Jeremiah 51:16).
Upcoming Articles – I have articles coming out this fall/winter in both the Old Schoolhouse Magazine and Homeschool Enrichment. If you get either of those magazines, be sure to take a look.
Sample Lessons – Watch a free preview of a lesson on place value, one on fractions, and one on lines and angles.

Note: If you’ve found these resources helpful, please share with a friend.

Posted on April 3, 2014February 23, 2017 by kate [loop] hannon — Leave a comment

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.

Category: Fractions