Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.
A Math Problem
We begin with a problem. I have a friend, James, who has a part-time job where he earns $12.50 per hour. On Saturdays, he works 5 hours and on Fridays he works 3 hours. James wants to know how much money he has to spend at the end of one week.
Putting on Math Labels
The first step in correctly setting up our math word problem is to label the important parts of the problem. By important, I mean the parts of the problem that we need to use to solve the problem. How do we know what these are? We begin by looking for the kind of answer the problem wants. In our problem, the problem is asking about the total amount earned at the end of a week. I go ahead and highlight the phrase that says that: how much money he has to spend at the end of one week. Next, I think of what I need to calculate that answer. Well, I need to know how much he worked and how much he makes. The problem tells me that he makes $12.50 per hour. I can highlight this part. The problem also tells me that he works 5 hours on Saturday and 3 hours on Fridays. I go ahead and highlight this information also. Do I need anything else to solve? No, so I can ignore the other words in the problem.
Now, I can label these parts of the problem. I am going to label what I am looking for, my answer, with an x. I write this x next to the highlighted part of the problem that tells me what to solve for. I can abbreviate to 'S' for Saturday's earnings and 'F' for Friday's earnings.
Writing the Math Expression
I am now done with labeling and now need to write my math expression that will allow me to solve the problem easily. This part requires a bit of thinking, but it's worth it!
I begin writing my math expression by putting down x = since I know that my answer equals something. I put down x for my answer part that I've labeled, and I put the equals sign down to let me know that I need to solve something to find my answer. What goes after the equals sign? Well, the problem wants to know how much James earns in a week. If James only works on Fridays and Saturdays, then the total amount of earnings for the week will be his Friday earnings plus his Saturday earnings. I've labeled those parts of the problem already, so I am going to write those labels down. I can either write 'Friday earnings' or 'F,' and I can write 'Saturday earnings' or 'S'. I put a plus sign in between these two parts to let me know that I need to add them together. So, now my math expression looks like x = F + S. But what is F and S? If James gets paid $12.50 per hour, then the amount he earns each day depends on how many hours he works. I need to multiply his earnings by the number of hours he works. For Friday it would be $12.50*3, and for Saturday it would be $12.50*5. So, I can replace the 'F' with $12.50*3 and the 'S' with $12.50*5. I now have the math problem x = $12.50*3 + $12.50*5.
Solving the Problem
This problem looks easy to solve, doesn't it? All I have to do is do the multiplications and add the results. That's not bad at all. Let me go ahead and do that to see what kind of answer I get. Multiplying the $12.50 times 3 gives me $37.50, while multiplying the $12.50 times 5 gives me $62.50. I now need to add these together to get $100.00. And guess what? I am done solving my problem. James makes $100 at the end of a week, and that is how much money he has to spend at the end of one week.
You can see how correctly setting up your math word problem makes it very easy to solve for the answer at the end. The hardest part is writing the math expression, but with a bit of thought, it can be done. Once it's done, the rest is easy!
What we've learned is that the correct way of setting up your math word problem is to follow certain steps.
1. Label your important parts. You first need to figure out what the problem is asking for, and then you need to think about the information you need to find that answer. You highlight these parts of the problem. Then you put labels on them so you can keep them organized and not let them confuse you. Use either descriptive phrases or letters. I usually label the answer as x to keep it separate from all the other labels.
2. Write the math expression to solve. Once you've labeled everything, now it's time to write the math expression. You begin with x = and then write down the other labels using the correct math operation to find your answer. This part requires a bit of thought to know how to arrange your labels and what math operation to put. Think in terms of your basic addition, subtraction, multiplication, and division. You know what these operations do, so don't over-think the problem. For your labels, write down the important numbers for them as we did with our problem.
3. Solve the math expression. Once you're done writing the math expression, your next and final step is to solve it. Follow your order of operations to solve and get your answer.
You should be able to do the following after viewing this video lesson:
- Label the various parts of a math word problem
- Solve math word problems by following a series of steps
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