In this lesson, our instructor Vincent Selhorst-Jones goes over Word Problems answering the questions: What is a word problem and why are they so hard? By the end of this lesson you will be able to effectively solve word problems and understand the Math-specific method. You will also learn tips to make solving word problems easy and have practice examples at the end of the lesson.
Word problems form the bedrock foundation of why we should care about math. While arithmetic and algebra are useful tools that we must learn to do well in math, we connect math to the real world through word problems. It is through word problems
that we find value in math.
Learning how to solve word problems teaches us crucial skills such as logic, thoughtfulness, and problem-solving. Even if you have no interest in doing math later in life, these skills are important for virtually anything you might be interested in doing
later on. Studying word problems isn't just about doing well in math: it's about preparing yourself for dealing with puzzling situations for the rest of your life.
There is no one way to solve all word problems because they can take so many shapes. However, there are some general guidelines that will help us work on them. We will use a four step process for approaching word problems. By following this method, you'll
have clear, concrete tasks to accomplish at every step. While creativity and thought are still necessary, these guidelines can be used on virtually any problem.
#1 Understand the Problem. Figure out what the problem is asking about. You don't have to solve anything right now, or even figure out exactly what you're looking for: you just want to have some idea of what's going on. This might seem obvious,
but remember, you can't solve something before you know what's going on.
#2 What Are You Looking For? Once you understand what's going on, you need to figure out what you are trying to find. In math (especially for the next few years), this will often take the form of setting up variables. Define any variable
the problem asks for, along with any others you will need to solve it. Make sure to write down a reminder about what each variable means so you don't forget later.
#3 Set Up Relationships. Use what you know to set up relationships between your unknowns and whatever information the problem gives you. In math (especially for the next few years), this will usually take the the form of making equations.
You will set up equations involving your unknown variable(s) and whatever else you know. Sometimes you'll realize you have more unknowns than you originally thought. That's okay: just make some new variables, then figure out equations that will involve
these new variables as well.
#4 Solve it! Once you've done the above three steps, you're ready to solve it! Often this is the easiest part. After all, it's like doing any other exercise now: you have some equations to solve. Just roll up your sleeves and work on it like
a normal (non-word) problem. [As a rule of thumb, to solve a problem you need as many relationships as you have unknowns. For example, if you need to figure out three variables, you must have three equations relating them to each other.]
This general method of problem-solving is great: it will work in pretty much any situation, no matter what you're working on. But let's simplify it a little and consider the specific approach you'll need in math for the next couple years:
Understand what the problem is talking about,
Set up and name any variables you need to know,
Set up equations connecting those variables to the information in the problem statement,
Use the equations to solve for the answer.
While a few word problems ( ∼ 5-10%: mostly concept questions and proofs) won't use that exact formula, you can always fall back on the more general method.
Here are some extra tips for working on word problems:
Tip-Draw Pictures: While it may not be possible for every problem, it can help massively when you can. Basically, if a problem talks about geometry, shapes, or something that is physically happening, you want a picture to look at. If the
problem doesn't give you one, draw it yourself! When you're not sure how something works or what to do, sometimes a quick sketch can clear things up.
Tip-Sum of Parts = Whole; Whole = Sum of Parts: You will often have problems where you can't directly solve for something, but the thing is part of a larger whole or built out of smaller pieces that you can solve for. In that case,
figure out how it relates to those other things and solve for those instead, then use that information to get what you want.
Tip-Try Out Hypothetical Numbers: Sometimes it can be hard to figure out what's going on because we aren't working with numbers. Try plugging in hypothetical numbers to help you understand what is going on. This is a great way to test the
equations you set up. It's easy to make a mistake while setting up equations, so check them afterwards with values you understand.
Tip-Student Logic: The hardest part is often figuring out the relationships the problem gives you. Luckily, you've got a secret weapon: you're a student. This means you can use student logic. You can pretty much be certain the problem
is based on whatever you're currently learning. For example, if you're studying logarithms, you know the problem can almost certainly be solved with logarithms.
Tip-Jump in! Working on word problems can sometimes be paralyzing. You're not sure where to start, you don't know exactly what you're looking for, you don't see how to solve it. It's okay! That happens to everyone sometimes. The important
thing is to not freeze up. Instead, just try something. Even if you can't set up the equation right the first time, or you pick the wrong variable, you'll wind up learning from your mistakes. As long as you pay attention to what you're doing and
think about what makes sense, you will see where you went wrong. By seeing where you went wrong, you can realize what you have to do for the problem. The fastest way to learn can be by making a mistake!
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.