Category: Biblical Math Blog

Math from a Biblical Worldview

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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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Math for Kids Who Don’t Get It

Visual Math

Over the years, I’ve heard from many parents who have children struggling with math. It’s a subject synonymous with frustration for many.

Often, the frustration tones down when students are really shown math’s purpose. When students understand why they’re learning something and are given opportunities to apply it outside of a textbook, there becomes a purpose to learning that’s sadly lacking in many math presentations. As Christians, we should want to show our students math as a way of describing God’s creation, which involves actually letting them see math in action.

For some students, though, that’s not enough. God has wired them in a way where they need additional help memorizing facts and mathematical processes.

My son is one of those. I tried everything I could think of to help him learn his math facts, but it felt like they’d never stick. Reading, too, seemed an impossibility until I found out he likely has dyslexia and began teaching him differently. Watching his progress in reading with a change in approach led to exploring how to change his approach in math too.

While there are a lot of different ways to help struggling math learners, I want to share just one in this post: visuals. Some people’s brains (including my son’s) remember pictures rather than words. This is often referred to as “right-brained” learning; although we all have two sides to our brain, some learners tend to remember better if taught pictorially.

Switching to a more visual-based curriculum helped my son tremendously, but I learned I still had to modify when we hit various stick points, such as with multiplication facts. When I used a program with visual aids for his multiplication facts [Right-Brained Multiplication and Division], he went from hating multiplication to loving it and wanting to learn more in a day. (At least that one day—all kids have their good and bad days.) I began researching ways to make math more visual, both for him and other students wired visually.

Here are a couple of examples of using visual cues (combined with patterns when possible) to help aid memory:

  • When multiplied, 1 is like a running back who runs away, leaving the other number behind.
  • The negative sign is ornery. It always wants the opposite. negative sign
    When two are together, they get hurt and make a medical sign (the + sign).
  • Manipulatives can also be a great visual. Try to be consistent with them. Visually-orietented students are memorizing the picture of the manipulative, not the fact or the rules, so they need to see it built the same way over and over again repetitively. Manipulatives that help students think in terms of what makes 10 seem to work best.
    7 + 4 = 117 + 4 = 11
    In the picture, 7 and 3 make 10. The extra 1 makes 11.

Manipulatives can also help make prealgebra more visual. A circle or household object can be used as a placeholder for the unknown.

As they get older, math can be made more visual by such things as using color (such as a different color for the top and bottom of a fraction, different units of measure, different unknowns, or congruent sides or angles) and taking notes (in which they can use color and draw their own visual aids as needed).

There’s a lot more that could be said about helping struggling math learners, but hopefully that give you a few ideas. If your child is struggling with a math concept, I’d love if you dropped a comment and shared about it. I will either respond there with some ideas to try or address it in a future post! Be sure to also check out the resources below for help in making math more visual.

Pictorial Resources
– New visual aids – I’ve put a bunch of pictorial ideas in Visual Aids that are now available as part of my Principle of Mathematics eCourses. The eCourses themselves also show concepts more visually than a textbook can.

– The Big Book of Math is an awesome tool to show visual learners math’s purpose.

 

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Math Blog: Consumer Math Interview

Podcast

Earlier this fall, I had the privilege of doing an interview with the Homeschool Minnesota podcast about Consumer Math. Check out the recording to learn…

  • why teaching students consumer math is so important.
  • how the biblical worldview affects how we view money.
  • more about my Consumer Math course, including where it fits into a high school schedule.
  • some things that can be done to start preparing students to be wise stewards even before high school.
  • and more!

I hope the podcast will encourage you.

Prefer Audio Only? Listen to the podcast version or look for the Homeschool Minnesota podcast wherever you normally listen to podcasts.

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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 & Curriculum Planning

books

It’s that time of year again: time to start planning for next homeschool year. As you plan, consider showing your students how you’re using math to help you!

  • Math can help you compare the cost of different curriculum…or of buying the same curriculum from different vendors. Have a coupon? Shipping? You’ll need to use math to calculate the total costs to compare.
  • Math can help you track what you’re spending so you can make sure it doesn’t exceed the money you’ve budgeted in your overall budget for curriculum…or if it does, you can adjust somewhere else.
  • Math can help you figure out how to pace yourself through the books. Dividing the total pages or lessons by the days you plan to school (or what to use that particular material) gives you a rough starting point.

Math is a tool that helps us with the work God’s given us to do–including with homeschool planning! Your students are going to need to use basic math throughout their lives…and now’s a great time to give them an illustration by showing them how you’re using math.

Be sure to also check out my new Consumer Math course that’s designed to really equip high school students with both the knowledge and biblical perspective they need to navigate life’s little (and big) financial decisions.

Consumer Math
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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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Valentine’s Day Math & the “Heart” of Budgeting

Valentine's Day Math

Math is a useful tool we can use to help us in everyday situations…including around Valentine’s Day! Here are some math-in-action Valentine ideas:

  • Make cards, having the child measure dimensions. Practice simple arithmetic by asking questions such as how much would be on each side if you stuck a 3 in. heart in the middle.
  • If eating chocolates, have the student count the total chocolates. Have them figure out how many would be left if they ate 1, 2, etc.
  • Find the price per rose if you get a dozen for $24 (or $20 if the student knows decimals).
  • Find how much 12 roses would cost if bought individually for $2.50.
  • Point out that they can use facts they’ve memorized or step-by-step processes they’ve learned to solve the situations above because God is faithfully holding all things together. Thus $24 divided by 2 always equals $12, 5 chocolates minus 3 will equal 2, etc.
  • Discuss the need to keep a budget in mind when deciding how to celebrate things like Valentine’s Day (see below).

The “Heart” of Budgeting

We often don’t think about the cost of ordinary purchases, yet they can add up. According to the NRF, $27.5 billion dollars is expected to be spent on Valentine’s Day this year. That’s a lot of money!

We make choices every holiday about how much we’ll spend. Those choices affect other choices–like how much money we have to give away or to save.

It’s easy to spend a lot on holidays, and retailers make it even easier. A pricey card, fancy restaurant dinner, ornate flowers, and decadent chocolates–the bill could easily reach the averages I saw of around $200. But holidays can also be meaningful with a low price tag, using a homemade card, meal cooked with love, origami flowers, and a homemade dessert. The point is that living expenses like these can vary drastically–and students need taught how to navigate these decisions in different seasons to live within what God gives them and be faithful to other goals (like giving).

If we want to raise students who see their money as God’s and remain free from the love of money we’re warned about in 1 Timothy 6:10, then we need to teach them to look at what God’s entrusted to them and have an overall plan that can then guide these decisions. If they learn to set aside money to give and save and for their bills, it can help them know what is left for things like Valentine’s Day, thereby guarding them against spending more than they meant to due to a marketing pull. The heart of budgeting is to be free to manage resources God gives us with a big (and eternal) picture in mind.

I’m excited about my new Consumer Math course, as it will disciple students on both the mechanics of making a budget and on thinking through both big and little decisions in light of biblical principles. It will help them grasp the heart as well as the how of budgeting. Check out the details I’ve posted about it. I would also greatly appreciate your prayers for everyone working on it as the final editing is completed. I can’t wait to share a preview and more information in the upcoming weeks!

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Math Blog: Christmas Budgets

Christmas gifts

Christmas is a great time of year to talk about budgeting with your students. And budgeting itself is a great way to show basic math in action and to discuss biblical stewardship.

You could give your student a real or hypothetical Christmas budget to manage—or even a budget for one person’s Christmas gift. (If you don’t do presents, you could always do a budget for an event or for end-of-year giving.) Then walk with them through all the decisions they’d have to make to live within that budget, pointing out both the math they’d have to use and discussing some biblical truths on wise stewardship.

Say your child’s hypothetical (or real) budget has $100 in it. They could then list the different things they want to buy or give and how much each will cost and total up the costs. Is it more than $100? They’ll have to either readjust what they buy or give or change the $100 budget (which, in real life, would require taking that money from somewhere else in an overall budget). As they work through this exercise, they’ll use a lot of basic math skills, such as addition and subtraction. Want to see what percent they’re spending on what? That will bring in percentages. Want to see how much they’re spending on a particular person? That might require addition…or even division, if they bought a package with multiple items in it and need a per-item price. Need to find a total with tax? That uses percentages.

Not only does this exercise help show students how math applies (which can help students understand why they’re learning it in the first place), but you can also use it to help them think about wise stewardship. At any point in time God’s entrusted us with a certain amount of money. We need to seek Him for what we’re to do with it…and follow the wisdom He’s set forth in His Word.

Did you know there’s more than 2,000 Bible verses on money? There’s no lack of things to explore—a biblical view of debt (especially since many go into debt over Christmas), giving, avoiding the love of money (i.e., escaping materialism), and saving, to name a few. I’ve been amazed as I’ve written my new Consumer Math course (coming out in 2025) just how much God has to say about personal finances…and how much I need to remind myself of those principles regularly. A good place to start is 1 Timothy 6:10.

For the love of money is a root of all kinds of evils. It is through this craving that some have wandered away from the faith and pierced themselves with many pangs. 1 Timothy 6:10 (ESV)

Discuss with your student that this doesn’t make money evil—just loving it. Talk about what that looks like—and what it might look like for them to steward the Christmas budget out of a love for God instead.

You might also discuss debt, and how the Bible warns about how debt ends up making us a slave in a way (Proverbs 22:7). After all, a recent survey indicated that around 46% of Americans are still paying off last year’s Christmas debt. That means that all year long, rather than having money earning interest, they’ve been paying interest on purchases from the prior year. With teen students, you could explore the concept of interest and how much these people have spent extra for what they bought.

There’s much more that could be explored, but hopefully that gives you a few ideas of how math and budgeting can help navigate Christmas gifting decisions—and of how you can use the time of year to have biblical stewardship conversations with your students. Remember too that children learn by watching, so consider letting them watch you think through some of the financial decisions you’re making.

(Look for more details about Consumer Math in the upcoming months–a full-scale high school curriculum that will help your students explore math in their everyday money decisions from a biblical worldview. We’re in the final editing stages, and I look forward to sharing more soon.)

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Short Story: Changing Shells

Crab with Shell

Dedicated to Alice Faye Hannon, my mother-in-law, who has recently entered into God’s presence and her new “shell.”

Jeremy was very sad. His Grammy, whom he loved very much, had just died. Her body was now still; where was she now?

“Let me tell you a story,” his mom said.

Shelly the hermit crab lived in Temporal Aquarium with many other hermit crabs. She was loved by many of the other crabs.

One day, though, the crabs couldn’t find Shelly. Her shell was still there, but she wasn’t inside of it! They all felt sad. What had happened to Shelly?

The aquarium owner had given Shelly a new shell to live in—a beautiful shell that wasn’t tight and didn’t pinch her like her old shell did. He’d moved her into a new home—a great big lake where she wouldn’t feel cramped anymore.

Shelly’s shell was empty because Shelly had a new shell.

“So you see,” Jeremy’s mom explained, “Grammy had to change shells too. When we die, we don’t stop living—we just change shells like that hermit crab. We either live in a new perfect shell with God in Heaven, or we live on in a miserable place away from all that’s good. Grammy put her faith in Jesus; because of that, we know she’s in Heaven enjoying her new shell.

“You see, our sin separates us from God and His perfect place called Heaven. But Jesus died to pay the price for our sin so that we could enter Heaven. You know how when you make bad choices there’s a consequence? Well, Jesus took our consequence. But we have to trust Him and ask Him to make us God’s child. When we do, then our lives change now and forever—and a beautiful new shell in God’s perfect world awaits us when we have to leave this one behind.”

For this perishable body must put on the imperishable, and this mortal body must put on immortality. 2 Corinthians 15:53 (ESV)

Yes, we are of good courage, and we would rather be away from the body and at home with the Lord. 2 Corinthians 5:8 (ESV)