Word problems in math impose a significant challenge on students. Most math students consider word problems hard for two reasons: either they do not understand word problems, or they do not know how to express their answers in words. Advanced-level word problems have more complexity of the statements. Research has shown that metacognitive strategies influence students’ success in solving math word problems. On the contrary, if a good math teacher does not teach students word problems correctly, they approach word problems with confusion.
What Are Word Problems in Math?
Word problems in math are hypothetical or real-life scenarios that need to be solved by a way of a mathematical calculation.
Why Are Word Problems Important in Math?
Math education is not just about asking students simple questions like 2+2 or 4-3. Regular practice of complex word problems makes students understand how math works in real life. It also helps them develop critical thinking skills and become problem solvers of tomorrow.
Solving Math Word Problems Using the GRASS Method (Step by Step Method)
An excellent way to solve math word problems is by using “GRASS”. GRASS is an acronym for Given, Required, Analysis, Solution, and Statement. You can use the GRASS method to break down a word problem and make it easier to solve. Here is a breakdown of the steps you should follow to solve word problems in math.
1. GIVEN: Read the question carefully. Figure out what values are given.
First of all, read the question carefully and understand what the writer is asking. Then underline the values given in the question.
2. REQUIRED: Figure out what is required.
Underline or highlight what the question is asking for. Let’s say you have to solve this word problem: Sara had four apples, and she had given three to her brother. In this problem, you need to underline four, given, and three to get the idea of the most critical parts of the question.
3. ANALYSIS: Analyze the question and use appropriate math operations.
The next step is to analyze the question and determine the operation to be used. To analyze the question, you can draw a picture of the problem to understand the problem quickly. For example, you can illustrate people or objects given in the question to visualize the problem more efficiently.
To determine the operation, identifying some common keywords could be helpful. Below we have shared a table of keywords with you to help you determine the correct mathematical operation.
4. SOLUTION: Solve the question.
Once you have determined the correct mathematical operators for the problem, you can easily perform a mathematical operation to solve the problem. This is where your knowledge of the underlying concept comes into play.
5. STATEMENT: State your answer in simple words.
Congratulations! You have done the hard work in the previous steps. The last step is to state your answer in the simplest words possible. Your answer must be short, clear, and precise.
Some Common Keywords Used in Word Problems
Here is a table showing a list of different keywords used in elementary-level word problems. Note that this is not a comprehensive and definite list. You should practice critical thinking to master word problems rather than memorizing these keywords.
Word Problems in Math – Some Examples
In this section, we have demonstrated how to apply the GRASS method to solve word problems on addition, subtraction, multiplication, and division.
Addition Word Problems
Addition word problems involve situations where there is an increase of something as due to combining one or more quantities.
Example: A truck was driven 932 km in January and 227 km in February. Over how much distance was the truck driven in the two months?
Given:
Distance covered in January = 932 km
Distance covered in February = 227 km
Required:
The distance covered in January and February
Analysis:
Write down how you are going to solve this problem:
Distance covered in 2 months = Distance covered in January + Distance covered in February
Solution:
Distance covered in 2 months = Distance covered in January + Distance covered in February
= 932 km + 227 km
Statement:
The total distance covered by the truck in January and February is 1159 km.
Subtraction Word Problems
Subtraction word problems involve situations where there is a loss of quantity or numbers because of removing a smaller part from a bigger object or a group of objects.
Example: Mathew had $9,800 in his bank account in January 2021. He spent on buying a TV set for $460 in April 2021 and a dishwasher for $340 in October 2021. What was Mathew’s bank balance in August 2021?
Given:
There are three values given in this problem:
Mathew’s bank balance in January 2021: $9,800
Amount spent in April 2021: $460
Amount spent in October 2021: $340
Required:
Mathew’s bank balance in August 2021
Analysis:
In this problem, we are given three quantities, and we need to find out Mathew’s bank balance in August. To better visualize the problem, we can draw a timeline for the events that took place.
Note that we don’t need to consider the amount spent in October 2021 in our calculations because we need to figure out the bank balance in August. Therefore, we need to consider the values for the months of January, April, and August only.
Bank Balance in August 2021 = Bank Balance in January 2021 – Total Spending up to August 2021
Solution:
Bank Balance in August 2021 = Bank Balance in January 2021 – Total Spending up to August 2021
= $9800 – $460
Statement:
Mathew’s bank balance in August 2021 was $9,340.
Multiplication Word Problems
Multiplication word problems involve situations where we have to combine groups of equal sizes repeatedly.
Example: A jacket was priced at $300. Each month for three months, the price was increased by $15. How much was the jacket increased in price?
Given:
Price of jacket: $300
Increase in the price each month: $15 (let’s represent this with the letter K)
Required:
The increase in the price for over three months (let’s represent this with the letter L)
Analysis:
One way to represent this problem is by using a tape diagram.
Since this problem involves repeated addition of the same quantity (that is K in this case), we can multiply the value of K by the number of times it is repeated (that is 3 in this case).
Solution:
Let’s multiply the value of K by 3 to get the value of L.
L = K X 3
Putting the value of K in the equation, we get
L = $15 X 3
Statement:
The total increase in the price of the jacket for three months is $45.
Division Word Problems
Division word problems involve situations where we divide or distribute something into equal parts. The resultant number is a fraction or a whole number.
Example: Olivia prepared food boxes to give away 300 donuts to charity. She put 8 donuts into each box. How many boxes of donuts were there? How many donuts were left over?
Given:
Total number of donuts = 300
The number of donuts in each box = 8
Required:
The number of boxes =?
The number of leftover donuts =?
Analysis:
Let’s visualize this problem using a tape diagram.
To find the number of leftover donuts, we need to find out the number of donuts packed in the boxes first. The problem states that Olivia put 8 donuts in each box, which implies that she distributed the donuts equally. Therefore, to get the total number of boxes, we can divide the total number of donuts by the number of donuts put in each box.
The quotient will indicate the number of boxes.
The remainder will indicate the number of leftover donuts.
If we get zero as the remainder, we can say that no donuts were left over. Otherwise, we can simply state the number of leftover donuts.
Solution:
Statement:
37 boxes of donuts remained with 4 donuts left over.
Can Online Word Problem Solver Help Math Students?
Many students rely heavily on online problem-solvers these days. While an online word problem solver can help students finish a math assignment faster, it may cease their ability to give reasons and think critically about math problems.
In the absence of an effective math tutor, students take longer than usual to master math word problems. MathProject is an award-winning after-school math program that focuses on increasing the math knowledge of students and developing their confidence to solve any kind of word problem without any difficulty. Call now at 1-844-628-4243 to book a free assessment.
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Citations
Language and the Performance of English-Language Learners in Math Word Problems — https://meridian.allenpress.com
The impact of metacognitive strategies and self-regulating processes of solving math word problems — https://iejee.com
Division (mathematics) — https://en.wikipedia.org
