As students hurriedly attempt to finish their assignments or exams, students can make some crucial mistakes due to misinterpretations. For example, students may have calculated the volume of a beach ball instead of its surface area or used multiplication instead of division. This can happen to students of all ages! However, I would like to take this moment to provide tips for 5th and 6th graders who struggle with math word problems. Taking some extra seconds to make sure we know exactly what these problems are asking could go a long way. For example, let’s take a look at this imaginary word problem:
“My teacher wants the class to read an entire 240-page book in 30 days. I usually read about 10 pages a day. Would I be able to finish this book at my current pace? Use your math skills to justify your answer.”
Please keep in mind that many word problems, such as the one above, can be solved in multiple ways. For the sake of simplicity, I will be going through a step-by-step approach that could help students solve word problems for any subject matter.
Let’s go through the following steps:
1) Where are the objective and background information?
First, make sure to identify the word problem’s objective, or goal. In this case, our objective is to figure out if I could finish my assigned book on time by reading 10 pages a day. To perform the necessary calculations, we need to note any background information, such as the amount of time given to finish the book and how many pages the book has. If there is any information within the problem that could be useful, feel free to box, highlight, or draw a squiggly line underneath the text! As an example, I have bolded the key background information for this word problem below:
“My teacher wants the class to read an entire 240-page book in 30 days. I usually read about 10 pages a day. Would I be able to finish this book at my current pace? Use your math skills to justify your answer.”
2) Do you need any formulas? If so, jot them down and assign variables.
Does your word problem require the Pythagorean Theorem or the Quadratic Formula? If the question is related to science, maybe students will need to know formulas for calculating density, speed, or air pressure. Since rate is mentioned in the problem, the formula to consider is rate=amount of pages/time. We can assign p to the number of pages in the assigned book and d to the number of days given to finish the book: rate=p/d.
3) Make note of any unknowns you need to solve for.
What we do not know in this problem is the ideal rate at which I need to read this book. In other words, how many pages a day should I be reading and how does that compare to my usual rate? Let us set x to my ideal reading rate for this particular book.
4) Solve!
To solve for x, we would simply use the rate = amount of pages/time formula. In other words, divide the total number of pages (p) by the number of days given to finish the book (d). Then, we can compare this result to my usual reading pace. 240 pages divided by 30 days would give me an ideal reading rate of eight pages a day: rate=240/30.
Since this result is lower than my current reading pace at ten pages per day, I am now confident that I will be able to finish the book on time. Whew!
Now that I have introduced these four steps to carefully tackle word problems, let us put our brains together to work on this next one:
“I have several toy blocks that are shaped like cubes that each have a volume of 8 cubic centimeters. Let’s say I want to store these blocks in a rectangular toy box that is 10 centimeters long, 6 centimeters wide, and 6 centimeters deep. What is the highest number of blocks that I can fit inside this box?”
To find out, I will once again walk through the four-step process for solving this problem.
1) Where are the objective and background information?
Our current objective is to find how many of my toy blocks I could store inside the toy box. In order to solve this problem, I will use the information I already know. For instance, I already know that the cubic toy blocks each have a volume of 8 cubic centimeters. The dimensions of the toy box were also given. All of this information should be noted somewhere so that we can easily reference it during this process.
“I have several toy blocks that are shaped like cubes that each have a volume of 8 cubic centimeters. Let’s say I want to store these blocks in a rectangular toy box that is 10 centimeters long, 6 centimeters wide, and 6 centimeters deep. What is the highest number of blocks that I can fit inside this box?”
2) What formula(s) and variables can we use in this situation?
In order to solve this problem, we should first calculate the box’s volume to see how much space we are limited to. Since the box is shaped like a rectangular prism, we can use the volume formula: . Then, we divide the box’s volume by the volume of each block. (We will call the volume of each block “b”.) This division would give us the highest number of blocks it takes to fill up the entire box.
3) What are we solving for?
What we do not know in this problem is the maximum number of blocks that I can store in my toy box. Like with the previous problem, I will use x equal to my unknown.
4) Solve!
First, let’s calculate the toy box’s volume using our formula! Multiply the length (10 centimeters) by the width (6 centimeters) and the depth (6 centimeters).
10 x 6 x 6 = 360
With this formula, we find that the toy box’s volume is 360 cubic centimeters. The last step would be to divide this number by the volume of each block (b). 360 cubic centimeters divided by 8 cubic centimeters would give me a total of 45 toy blocks that I can store in this box – that is a lot!
360/8=45
There are several ways in which a student can solve the above examples, but I hope that this guide provides some insight on a useful method for preventing simple mistakes on 5th and 6th grade word problems. Take a deep breath, read carefully, and those word problems will be properly solved in no time. If you would like additional help, My Private Professor in Orange County offers 5th and 6th grade tutoring in a variety of subjects, including math!
Amy Hua is a tutor at My Private Professor, which provides individualized online & in-person tutoring to students in all subjects, including K-12 math, science, language arts, history, foreign language, AP exams, test prep, essays, & college counseling, by top tutors from top universities.
