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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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.

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.

Why, Oh, Why Must I Learn Math?

I recently asked some folks this question:

What are you/your children’s biggest struggles in math?

The responses varied (stay tuned for others in future blogs), but several voiced the same struggle: why.

Knowing why you need to learn something certainly doesn’t seem like too much to expect. It’s actually a very reasonable question. As Alfred North Whitehead said, “There can be nothing more destructive of true education than to spend long hours in the acquirement of ideas and methods that lead nowhere.”

So why math? Well, math is a way of describing the consistent manner in which God holds His creation together. Thus it helps us work with the world around us—from everyday tasks to sending men to the moon. It helps us complete various tasks that God gives us to do here on earth.

For example, fractions give us a handy way of describing division, helping us work with real-life relationships. Oh, and don’t forget that music notes, sewing, and cooking all use fractions! (There’s more on the why of fractions in my previous post “Why Learn Fractions?”)

One mother shared that her child wondered why finding the area of triangles matters. While triangles might not at first appear to be the most practical shape, they can actually help us measure such real-life distances as the height of a building and the distance across a stream. (In fact, that’s exactly what students learn to do in Principles of Mathematics while studying triangles.) As for finding their area, triangles also help us measure other shapes. For example, if we want to find the area of a hexagon (which is what bees make their honeycombs out of), we would use triangles to do it. Triangles—along with the rest of geometry—are incredibly practical!

For those of you wondering the “why” of high school math, I recently had an article published in The Old Schoolhouse magazine on that exact topic. You can read “What’s the Purpose of High School Math?” online (note: it may take a minute to load)…and I’d love if you’d then leave a comment here and let me know what you think.

And for those wondering how to teach math in such a way that your students will understand why they’re learning each skill they study, check out the math resources I wrote specifically to help students understand math’s true purpose…and to praise the Creator of all as they study. After all, math applies because Jesus is upholding all things by the power of His Word (Hebrews 1:3) in such a predictable way that we can describe it mathematically! Math, when properly taught, should encourage us to trust Him more and more.

Have a specific math topic you’d like to know the “why” of? Leave it as 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.
    Transforming Math
  • 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.

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.