Math and the Presidential Primaries

Math and the Presidential PrimariesOne of the things I stress a lot in my math resources is that math isn’t confined to a textbook. As I’ve been following the presidential elections this year, it occurred to me that it provides a great opportunity to show students math in action. Math is used quite a bit behind the scenes in determining each party’s candidate. Consider these applications:

  • Probably the most obvious math concept the elections show in action is percents. What percent of the vote went for each candidate? What percent of a specific area went to each candidate? What percent of the total delegates to a convention does each candidate have pledged to them? How many votes would a candidate have to receive in order to earn a specific percent if 40% of a specific population end up voting?
  • More percents and other math concepts are used in determining how many delegates are actually assigned to each candidate after an election. This article by the Washington Times gives an overview.
  • Addition (along with more percents, as well as formulas) are used behind the scenes in deciding how many delegates each state gets to send to the national conventions in the first place. See The Green Papers: Republican Detailed Delegate Allocation – 2016 for more details about the republican side; and The Green Papers: Democratic Detailed Delegate Allocation – 2016 for the democrat side.
  • Statistics show up extensively throughout the election process. Polls are based on surveying a random sample of the population and trying to determine the views of the whole off of it. It’s a great time to look at how statistics work (and how easily they can be twisted). See Chapter 11 in Principles of Mathematics for an overview and example.

As you follow the elections, consider looking into your particular state’s primary or caucus system and examining the math behind it. Point out the use of percents, addition, etc. Look at the statistics behind a couple of presidential polls and at what they truly tell us.

Then sit back and remember that math only proves useful because this universe is consistent, and because God gave man the ability to subdue the earth. We’re made uniquely in God’s image, created to worship Him. Remind your students that math is far from meaningless bookwork—it’s a real-life tool that helps us in the tasks God has given us to do.

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Math and Chocolate

Math and chocolate–since those are two of my favorite words, imagine my joy when I came across the news that a University College London (UCL) student had been exploring the math behind chocolate fountains.chocolate-fountain

Notice how the chocolate in a chocolate fountain doesn’t flow straight down–it curves slightly inward at each tier. The research–which involved lots of math!–concluded that this is due to surface tension.

“Chocolate fountains are just cool, aren’t they!” said Adam Townsend (UCL Mathematics), lead author of the paper based on his MSci project. “But it’s also nice that they’re models of some very important aspects of fluid dynamics. We’ve used some serious maths to solve a fun problem- why the chocolate ‘curtain’ on a chocolate fountain always falls inwards.” – See more at: https://www.ucl.ac.uk/news/news-articles/1115/251115-chocolate-fountain-physics#sthash.LVBoAQGl.dpuf

Want to learn more? Here’s the UCL article: “Exploring the Physics of Chocolate Fountains”

I would add that chocolate fountains are yet another example of how math helps us understand and describe the orderly way God created and sustains this universe. Until next time, have fun using math to explore God’s creation.

Improbability of Evolution Math Lesson Plan

I was pleased to learn about this middle school math lesson plan that uses math to show the improbability of evolution. (The main math concept is probability, along with large numbers and scientific notation, although others are also used.) While designed specifically for a public school setting, it could be easily adapted for Christian or homeschool. (Thank you, Mr. Karl Priest, for putting it together and letting me know about it!)

I especially loved the suggestion given to have students try to write tally marks to help drive home how much a million is. Coupled with quotes like the one below, it brings home the point that, even from a human reasoning perspective, evolution doesn’t make sense:

“Imagine 10^50 blind persons each with a scrambled Rubik cube, and try to conceive of the chance of them all simultaneously arriving at the solved form. You then have the chance of arriving by random shuffling of just one of the many biopolymers on which life depends. The notion that not only biopolymers but the operating programme of a living cell could be arrived at by chance in a primordial soup here on the Earth is evidently nonsense of a high order.” Fred Hoyle, “The Big Bang in Astronomy”, New Scientist, Vol. 92, No. 1280 (1981): p.527

evo-mathI would just add that evolution and creation can’t be proved—they occurred in the past. The issue ultimately comes down to faith, and that faith shouldn’t rest in our human reasoning of probability, but in the Word of the God who was there and has told us what happened. However, math does show us how even from a human reasoning perspective, evolution doesn’t make sense…and this lesson plan does a wonderful job showing that.

As the cartoon at the end of the lesson plan (and shown here) reminds us, you can’t reason someone into the kingdom of heaven. God has to do a work to change a heart. Let’s make sure we’re sharing the gospel with people as we remind them that creation clearly proclaims a Creator.

Note: If you’re stuck on how to begin sharing the gospel, check out the free resources at LivingWaters.com. He has a lot of helpful training materials to help.

Math at a Concert

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

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

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

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

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

Battleship, Probability, and More

As I sat playing Battleship the other day, I got to thinking about how many concepts of math I was using as I played. (For those not familiar with the game, Battleship involves trying to guess where your opponent’s ships are located on a grid.)

To begin with, I used numbers to identify the columns on the grid, combined with letters to identify the rows.

When hunting for my opponent’s aircraft carrier, I knew the carrier takes up 5 spaces…which meant my opponent’s carrier couldn’t be hiding anywhere with less than 5 spaces. I also knew that when I hit the carrier, I needed to continue guessing the spaces around my hit until I’d located all 5 spaces upon which the carrier sat. I was doing a lot of counting as I played.

Since the aircraft carrier takes up 5 spaces and the battleship takes up 2, I knew the carrier should be easier to find. But why is this? Well, on the very first guess, there’s a 5/100 (which reduces to 1/20) probability of hitting the carrier (there are 100 spaces total, 5 of which have the carrier on them), and a 2/100 (which reduces to 1/50) of hitting the battleship.

While we don’t often think of the math used in games, it’s there none-the-less. Even games can turn into teaching opportunities. Math isn’t a mere textbook exercise, but rather a way of describing real-life consistencies God created and sustains. It’s a practical tool we use all the time…even when playing a game.

Teaching Problem-Solving Skills Through Summer Projects

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

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

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

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

Review: Make It Real Volume 2 – And a 25%-Off Coupon Code at Make It Real Learning

Some time ago, I reviewed Make It Real Activity Library, Volume 1. Recently, they released a volume 2. Volume 2 is very similar to volume 1; once again, I appreciated how the series, designed as a curriculum supplement, provides numerous, stand-alone, real-world application problems for students. The series does not claim to be Christian, so Christian parents/teachers will want to discuss some of the lessons with their students, examining how we interpret the results or topic in a biblical worldview. Again, please see my previous review for more thoughts, as well as for a 25%-off coupon code good on all of the publisher’s products through the end of 2012.

Note: I received a free copy of this product to review. See my review policy disclosure.

Math Behind Fireworks, GPS Units, and More

This week, I thought it might be helpful to take just a moment to reflect on teaching math OUTSIDE of the textbook. Since math describes the consistencies God placed and sustains all around us, we find it useful in all sorts of situations–including ones that don’t instantly make us think of math.

For example, this past July 4, our family went to see the fireworks. As I was watching the fireworks, I wondered how they timed the fireworks so perfectly. It hit me: they must use math! Sure enough, a quick Internet search later confirmed my suspicions. (If you’d like to learn more, see www.ohiorc.org/pm/math/richproblemmath.aspx?pmrid=16 for a somewhat technical description.)

On the way home from the firework display, we plugged in the GPS unit. How did the unit know where we were? Once again, it was using math! Here are two easy-to-understand resources I found that offer an overview of the math behind GPS units.

http://electronics.howstuffworks.com/gadgets/travel/gps1.htm

http://www.youtube.com/watch?v=3zRlbboMvb0

My point is simply that if we take the time to explore how something works (the mechanics behind a device), we’ll likely find yet another example of math in action. Being inquisitive about everyday life will turn up lots of wonderful opportunities to show your children that math is a tool to describe consistencies in God’s creation.

Math and Gardening

Gardening

Spring has arrived! The azaleas are in full bloom, reminding me it’s time to head outside and do some planting.

While working in the garden, you have a wonderful opportunity to have your child apply those math concepts he’s been learning! Graphing, multiplication, addition, measurement, area, perimeter–these and other concepts prove helpful in the garden. Why? Because math is a way of describing God’s creation! We can use math in real life because God created man with the ability to “subdue the earth,” and because He faithfully holds all things together in a consistent fashion.

Kidsgardening.org offers an entire section filled with ideas for teaching math while gardening. While written for school teachers, most of the ideas can easily be adapted to a home setting. Be sure to take a look at page 2, which offers a variety of simple ideas on how different concepts apply (you may want to print this page to consult throughout the summer). The other pages offer more detailed ideas.

The suggestions offered, as well as others you might think of, could be used or adapted for a wide variety of ages–a young child can help you count the number of earthworms in a section of soil (or the number of seed packets you need/the number of seeds to plant in each hole, etc.), while an older one can start a plant business or calculate the surface area of leaves.

Don’t let the ideas limit you. Even if you aren’t planning on growing a vegetable garden, you can still have your child grow some plants indoors or on the patio and measure their growth–or design a pretend garden on paper.

Speaking of designing on paper, you may want to use graph paper, letting each square represent a foot. The graph paper should aid in visually seeing how much area each plant needs.

Lastly, here’s a page with handy math formulas. It explains how to find the area of your yard, the amount of mulch and fertilizer you’ll need to cover it, and more.

Hope you have fun using math in the garden! Please let me know how your gardening applications go.

Math While Traveling

Traveling…and math? Most of us don’t couple the two in our minds, yet a lot of math goes into getting from one place to another. Here are just a few examples, along with some links to resources you can use with your children.

Math is used to help design airplanes, to find a plane’s capacity, to schedule flights, and more. See www.planemath.com for some engaging, interactive activities illustrating some of math’s aeronautical uses. NASA also has some more activities and lessons on aerospace topics, many of which show some of the math involved.

Whether your travels involve air or auto travel, this page titled “Mathematics on the Go” offers some simple ideas of how you can illustrate math’s usefulness while traveling. Some of the ideas would make great family games on your next car trip!

Math’s applications in traveling is just one example of how math serves as a real-life tool–a tool we can use because of God’s faithfulness in consistently holding all things together.