When something makes us uncomfortable, we make fun of it. I mean, why not, right? As a first-year teacher, I remember giving a geometry test, on which I asked students to define space. One student wrote: “The final frontier.” And I have to admit that I laughed.

So, whether or not I’ve convinced you that algebra is a useful, everyday skill, at least join me in a little laughter today. And be sure to come back next week, when we start celebrating National Math Awareness Month. (The excitement never ends, does it?)

These next two are great for math teachers, as they demonstrate very common errors that students make.

You have to be a Harry Potter geek to get the next one:

Happy weekend, everyone! Use some algebra and make the world a better place.

Got any math jokes? Feel free to share them in the comments section.

The post Finding the Funny in Algebra appeared first on Math for Grownups.

But there’s no denying one important thing: algebra is extremely useful in spreadsheets. And that’s because the power of a spreadsheet is in its ability to crunch numbers for you.

In fact, algebra teachers are using spreadsheets to help students better understand algebra and its real-world uses. Want to see how data is related? Use a spreadsheet to create a line of best fit. Want to find an average quickly? Spreadsheet. Want to know how many children and adults you’ve invited to your wedding? Open up Excel or Numbers or OpenOffice Spreadsheets.

(Yes, we’re back to the wedding. It’s consuming my life right now, so you get to play, too.)

When it came time for me to create the guest list for my wedding — undeniably the most painful part of this entire experience — I naturally reached for good-old Excel. Once I had everyone entered into a spreadsheet, I was able to create a variety of formulas that have helped me manage certain tasks. Here’s an example.

Our reception venue, which also provides the catering, offers a much lower rate for children. They’re getting chicken tenders, rather than the fancy-schmancy meal, so that’s only fair. But there are a lot of kids on our list, and I needed to get a rough estimate of what we would pay. This way, I could make really good decisions about who we could and could not invite. (Told you, this part was really painful.)

Each family, couple or person was listed in one row of the spreadsheet. In two of the columns for each row, I included the number of adults and kids who were invited.

So you can see that my sister, Melissa, has 4 children under 16 years old, while my mother and two brothers don’t have any. But each of their families has 2 adults. The column all the way to the right is the total people in their families who are invited. In fact, I used a very simple formula to find the last column: =SUM(B2:C2). This means, “Take the sum of the values in columns B2 through C2.” The formula allows me to make changes to the values in columns B2 through C2 and automatically update the last column.

But that’s not really where the algebra comes in. At the bottom of my spreadsheet, I use the SUM formula to total the number of kids and the number of adults. Then I use those values to find the cost of the reception food, using a formula I built. Here’s how that worked.

Let’s say I’ve invited 15 kids and 100 adults. I’ve let my spreadsheet automatically find those totals in cells B101 and C101. And let’s say that the cost per adult is $50 and the cost per child is $25. Algebra will help me create a formula based on the cells where this data is found.

=((B101*50)+(C101*25))

Looks ugly, right? Well, that’s because the spreadsheet needs some extra formatting to recognize the formula. But there’s a simpler way to show this:

y = 50a + 25k

In other words the total cost for the food (y) is equal to 50 times the number of adults (a) plus 25 times the number of kids (k). Algebra at work in the real world of wedding planning.

My job today is not to explain the algebra to you step by step. But I did want to demonstrate one really useful — and somewhat common — way that a regular person uses algebra in their regular life. (Okay, so maybe I’m not regular, but hopefully you get my drift.)

Do you use spreadsheets? What formulas have been useful to you in your spreadsheets? Did you think of that as algebra? Why or why not? Share your thoughts in the comments section.

The post Building Formulas: Spreadsheets, algebra and guest lists appeared first on Math for Grownups.

Weddings are magical events, filled with joy and love. They’re also damned expensive. Crazy costly. The average wedding in my neck of the woods costs about $25,000. Sure, couples can opt for a family BBQ or a quiet ceremony in a public park. But when you’ve waited as long as I have — I’m 45 years old — there’s no backyard large enough for everyone who wants to be there.

And that’s the variable that matters in wedding planning — the number of guests. The smaller the guest list, the smaller the budget. When the guest list grows, you can expect to shell out a lot more. That’s because the biggest cost of a wedding is the reception — unless you’ve got your heart set on the latest gown to walk the runway in Paris.

If you’re like me, there’s some flexibility in this list. Children or no children? Cousins or just immediate family? What about college friends you haven’t seen in years or office mates? All of these decisions have a direct affect on your bottom line. And this is where the algebra comes in.

Many reception venues follow a simple formula: a flat rental fee, plus a per-person rate. If the number of guests is the variable, you can easily set up an equation to help you settle on the number of people you can afford to attend the reception. Here’s an example.

Let’s say that the venue you’re considering has a flat rental fee of $3,000. In addition, there’s a $75 per person rate to cover food and drinks. (Of course, this rate depends on the menu chosen, plus other add ons, like upgraded linens, top-shelf liquors, etc.) Basically, you need to multiply the per-person rate by the number of people invited and then add the flat fee. In other words:

In this equation, y is the total cost of the reception venue, and x is the number of guests. Break it down, if you’re confused: The total cost of the reception venue is $75 times the number of guests, plus $3,000.

But why take the time to write an equation? Well, this allows you to play with the number of guests or your total budget. For example, if you know you want to invite between 150 and 200 people, you can come up with a range for your budget:

In this scenario, you can expect to pay between $14,250 and $18,000, depending on your final number.

More likely, you know your budget and want to find out the maximum number of people who can attend the wedding. For example, if your budget for the reception venue is $15,000, how many people can you invite?

With a budget of $15,000, you’ve got a guest list of 160 people.

The beauty of creating an equation to help in this problem is that you can play around with the numbers. Once you have the equation, you can try different things, without thinking too hard. And if you’re comparing the costs of several venues or several packages at one venue, you can create several — very similar — equations, one for each option.

I get it. Most brides and grooms aren’t going to take this step. Who wants to do math when planning one of the most magical days of their lives? But this is a clear example of how algebra can reduce the stress of planning a wedding — and possibly save you some cash.

So what do you think? Have I convinced you that algebra can be useful? Share your thoughts in the comments section. And how have you saved money in planning your wedding? Did math help at all? Dig deep and be honest!

The post Say “I Do” to Algebra: Using math to plan a wedding appeared first on Math for Grownups.

Here’s an example: Let’s say you need to build a fence around your tomato plants. If you know that the bed is 4 feet by 2 feet, how much fencing do you need? (Yes, I’m ready for spring and summer and fresh veggies. Will this cold weather ever end??)

This is a perimeter problem. Some of you might write down the formula for perimeter of a rectangle: P = 2l + 2w. But I’d be willing to bet that most of us simply add: 4 + 2 + 4 + 2 = 12 feet. No formula needed, right?

But what if we turn the problem on its head? Let say you have 12 feet of fencing, and you’re building a tomato plant bed that must be no longer than 4 feet. How wide can the bed be?

Again, there are tons and tons of ways to approach this problem. One is with literal equations. What do you know about the information you have? The perimeter and the length. What are you solving for? The width.

P = 2l + 2w

The object of the game is to solve the formula for w, in terms of P and l. (Stay with me here. I promise this is easier than that previous sentence made it sound.) To do that, you need to get w by itself on one side of the equation. This is where the algebra comes in.

The most important rule about solving algebraic equations is this: Whatever you do to one side of the equation, you must do to the other. Period. End of Sentence. Amen. Shalom. To do that, you need to undo the operations. It’s like taking something apart. Here’s how it works:

Don’t panic! This is not as messy as it looks. All you need to do now is substitute what you already know, use the order of operations to simplify, and you’ll have w.

So the width of the tomato bed must be 2 feet. My point is not that you must always solve a problem like this one in this way. Nuh-uh. My point is that there’s algebra behind this problem – no matter how you solve it. And whether you like it or not.

How would you have solved this perimeter problem? See if you can spot the algebra in your approach. And share in the comments section.

I am so pleased to be Meagan Francis‘s guest this month on The Kitchen Hour, her 45-minute podcast for parents on the go. We talk about math anxiety, math education and how to encourage our kids to embrace math — while overcoming our own fears. Listen and/or download the podcast at The Kitchen Hour.

The post It’s Not Tomato Season Yet, But You Still Need Algebra appeared first on Math for Grownups.

I had never seen the word applied to mathematics until recently. No kidding! That’s when I learned about literal equations. I mean, I already knew about them; I just didn’t know what they were called. And yes, you know about them too. They’re one of the ways that we use algebra in our everyday lives – without even knowing it.

Literal equations are equations with more than one variable. Ta-da! See, you knew about them, too. Here are some examples, in case you’re not convinced:

Look at all of those variables. Each equation has more than one, which means that each of the above is a literal equation. That’s it. Easy.

Now, the algebra of literal equations is much, much easier than most mathematics, especially if the equation is simple, like the distance formula. (Don’t panic. This is not one of those train-leaving-Pasadena questions.) The algebra is in identifying the variables, substituting into the equation and then solving.

Let’s say that you’re an avid cyclist. In fact, you’ve got all the cool accouterments, like a gel-padded seat, clip-on pedals and a speedometer. You average about 16 miles per hour on flat roads, and you love trying out new routes, just riding where your bike takes you. But it’s critical that you know the half-way mark for most of your routes – otherwise, you won’t have enough steam to get back home.

That’s where the distance formula can come in.  If you know your speed (or rate, r) and the time you’ve been out, you can find the distance. This way, you know when to turn around and head back to enjoy those endorphins.

One gorgeous Saturday morning in March, you head out on an unfamiliar route, cruising at about 16 miles per hour. Checking your watch, you find that you’ve been on your bike for half an hour. How far have you traveled? You can actually do this math in your head – just multiply 16 by 0.5. How do I know this? With the literal equation d = rt.

See? You just used a literal equation. And you did it on your bike. As Chris Traeger would say, “You are literally the most impressive cyclist I know.”

How have you used literal equations recently? Want to share in the comments section? Feel free. Also, feel free to challenge my thesis that algebra is an important part of a solid middle and high school education. I can take it. Really.

The post Using Algebra – Literally appeared first on Math for Grownups.

While I often argue with this point, there is some truth to it. Just like grammar, chemistry and baking, math is a pretty precise subject matter. Sure, there are many different ways to add 24 and 37 in your head, but fact is, you can’t just decided that the answer is –19, right?

Rules make math work. And algebra helps us write down these rules. Now, we don’t necessarily need to think of math rules in this way, but believe me, when teaching and writing about math, it sure does help. And there are some real-world situations when an equation can  really help make math easier.

Let’s consider the process for multiplying fractions. Do you remember what it is? Take a look at this problem, and see if you can figure it out:

Of course there are several ways to describe what is happening above, right? You can do it in plain English:

To multiply two fractions, multiply the numerators and multiply the denominators.

Or, you can write this using algebra. This is not as hard as you might think! First, assign a variable to each of the unique numbers on the left side of the equation:

a = first numerator

b = first denominator

c = second numerator

d = second denominator

Then substitute those variables for the numbers themselves:

Now, perform the rule that was described in plain English above: multiply the numerators and multiply the denominators.

How about that! Lickity split, we made like mathematicians and created a rule described algebraically. How hard was that really? 

Now you can use this rule to multiply any fractions of any kind. I don’t care if they’re elementary fractions made up of just numbers or if they’re fancy-schmancy algebraic functions that have — gasp! — variables in them. You don’t even have to think of the a, b, c or d. Instead, think of those variables as place holders. (Hint: this is where your mind can be really flexible, even though the rule is not.)

Because you know this rule, you can solve this problem (even with the x and the y). Just multiply the numerators and then multiply the denominators.

Because of the rule for multiplying fractions — which includes the variables a, b, c and d — you can see how to multiply any fractions. That’s where the algebra comes in handy.

Now, I know exactly what you’re thinking. When will I ever need to solve a problem like the one above. And here’s my honest answer: for most of you, never. Really and truly. I won’t lie.

However, there are times when creating a rule for a specific real-word problem is very useful. That’s when we might create an equation. Stay tuned, when we’ll talk wedding receptions, guest lists, the price per person and rental fees.

So what do you think of algebra and math rules? Did this example help you understand how algebra is important in developing and stating these rules? Do you disagree with me about why this is important? I can take it — so please do share your thoughts in the comments section.

The post Coloring Inside the Lines: How algebra helps appeared first on Math for Grownups.

Algebra is a branch of mathematics that uses letters and other symbols to represent numbers and quantities in formulas and equations. This system is based on a given set of axioms.

What does this mean? Well, it’s basically the step beyond arithmetic, where we only deal with numbers. Algebra allows us the flexibility of an unknown — the variable — so that we can make broader statements about situations.

Look at it this way: 8 + 3 is always 11. Always. But 8 + x depends on the value of x. This means we can pretty much substitute whatever we want for x. See? Flexibility. (Of course 8 + x has no meaning without some kind of context. But we’ll get to that later in the month.)

Algebra allows us to discover and create rules. These rules might be formulas or equations that describe a particular situation. Because of algebra, we know that the circumference of a circle is 2πr, where π is the number 3.14… and r is the radius of that circle.

Now, let’s take this definition one step further. What is the circumference of a circle with radius 1?

C = 2πr = 2π(1) = 2π

But what about the circumference of a circle with radius 2?

C = 2πr = 2π(2) = 4π

If you look closely at this, you can draw a conclusion: The larger the radius of a circle, the larger its circumference. When the radius is 1, the circumference is 2π; when the radius is twice as long, the circumference is twice as big.

This points to a critical aspect of algebra: relationships.

Algebra is a branch of mathematics that deals with general statements about the relationships between values, using numbers and variables to describe them.

The formula for the circumference of a circle is a description of the relationship between the circumference and the radius of any circle. When the radius changes, so does the circumference. When the circumference changes, so does the radius. (π is a constant, even though it is technically a Greek letter. Whenever you see π, you know you’re dealing with the number 3.14…)

So that’s it. Algebra is nothing more than a way to describe the relationships between values (numbers, measurements, etc.). In the example of circumference, we’re dealing with two branches of math. The geometry describes why the circumference is twice π times the radius. The algebra is how we describe that relationship in the form of a formula.

Without algebra, we really don’t have ways to describe many things about our lives — from geometry formulas to finding compound interest on a loan. We can fumble around and come to a conclusion, but in the end, algebra can make this process much simpler.

What do you think about these definitions of algebra? Does thinking about algebra in these ways make it a little less threatening? If so, how? Share your ideas in the comments section!

The post Numbers and Letters Together: What is algebra? appeared first on Math for Grownups.

But of course when there are calls to remove algebra from high school math curriculum, things get pretty serious. If you had driven past me at lunch time one fall day last year, you might have seen me (literally) shaking my fist and shouting at my radio. My local public radio station was airing a talk show featuring some doofus (I think he was a philosophy professor?) who was advocating that we actually stop teaching algebra. Seems it upsets students too much and, heck, we don’t need it anyway.

Want to make me mad? All you have to do is suggest this in a serious way.

So, prompted by all of the online ribbing that I get from people, I’ve decided to take on a challenge. This month, I’ll be writing about exactly how algebra is useful. My goal is to convince anyone who thinks differently that they’re wrong. But I know this is a tough sell. So I’ll settle for a couple of small concessions.

My thought is that I’ll focus on everyday uses for algebra (from spreadsheets to formulas), algebraic thinking (how we can think critically, thanks to algebra) and why I believe algebra is a cornerstone subject for middle and high school students.

Want to challenge my thinking? Go right ahead! Want to offer your own experience? Please do! I’d love to promote a real conversation on this topic. I can always learn something new about how real, live people use the math devoted to finding x.

In the meantime, share your algebra story in the comments section. I’d love to hear from everyone — whether algebra was the first time math clicked for you or you were one of those folks who said forget it, once letters were introduced to your math.

The post Algebra: What good is it anyway? appeared first on Math for Grownups.