Math is an important subject in the academic curriculum because of its real-life application. From addition and subtraction to algebra and trigonometry, maths includes everything. Most curriculums are designed in such a way that students understand the topics from the very beginning. However, some math topics can be hard to understand if a student doesn’t follow certain steps.
One such topic is algebra. Algebra is the branch of mathematics that deals with symbols and uses them to find an answer. Generally, these symbols are assigned a numerical value. Algebra forms the foundation of advanced mathematics as almost all major maths topics, like trigonometry, calculus, etc.
When your kid is starting to study algebra, he will be introduced to word problems. These problems are math problems written as a scenario, story, or situation. For example:
Sam has 40 oranges. If he gave away three oranges to Nick and borrowed five oranges from Julie, how many oranges Sam was left with?
Note: We will use the above example problem in our article and solve it step by step.
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Word problems of this type require a step-by-step procedure to arrive at the solution. You should first try to explain the steps to your kid before actually solving the problem. Another point to remember is to solve basic problems first and then move to the challenging ones. With that said, here are the steps on how to solve word problems in algebra.
Understanding the problem
The very first step in solving a word problem is to analyze the problem. Most of the time, students skip understanding the problem and try to solve it just by looking at the numbers. As a parent, you must ensure that your child spends some time analyzing the problem.
Here are the sub-steps to understanding the problem:
Read the word problem carefully.
The most common mistake that your kid might make is to assume what the question is asking before reading the problem. This can waste time as you won’t get the correct answer. Thus, it is important to read the problem completely to figure out the information given.
Determine what is to be found.
After reading the problem, the next step is to find out what exactly the question demands. For example, does it ask you to find out the quantity, weight, numbers, etc.? Write down what you need to find or underline. Either you will find a certain value or an expression representing variables.
- In our case, it is the number of oranges Sam is left with.
Point out what you know and what you will find out.
Word problems in algebra provide some information in the statement itself. You need to write what you already know and make a list of it. Or, you can underline it in the question itself.
- For instance, we know the number of oranges he had initially and the amount that he gave away and borrowed in our problem.
Assign variables to unknown quantities
Assigning a variable to the unknown value makes the problem easier. If you are asked to find a value, there will be only one unknown quantity. But if you are asked to find an equation, there will be multiple variables.
- E.g. Let x be the number of oranges that Sam is left with.
Look for keywords
Keywords are the specific words that indirectly tell you what operation needs to be done. You should always highlight such words in the question. If your child points out and understands the meaning of each keyword, the problem will become easier to solve.
- For instance, Addition keywords include some, more, and borrowed. Subtraction keywords include difference, fewer, and gave away.
Finding the solution
Now your kid is ready to actually solve the word problem. The next step is to use the collected information and manipulate it to find the answers. The exact sub-steps to follow while finding the solution are as follows:
Write an equation
An equation is a mathematical expression that includes variables and operations. After finding out the information given in the problem, the next step is to write down a logical equation. This equation helps to understand the problem in terms of symbols.
- For instance: We know Sam had 40 oranges initially. He gave away (keyword for subtraction) three oranges and borrowed (addition) five oranges. And he is left with x number of oranges. Thus, the equation becomes: 40+5-3=X
Solve the equation and find an unknown variable
After writing down the equation, we have to simplify it and find the answer. If there is only one variable in your equation, you can separate it and determine what number is equal to it. Use the general rules of algebra to separate variables. Remember that the equation must be balanced i.e. whatever you do on the LHS, you must do the same operation on RHS.
- For instance, our equation is: 40+5=x+3
Subtract 3 from both sides: 40 + 5 – 3 = x +3 -3
40 + 2 = x
42 = x.
Solve the equation to find many unknown variables
Not all word problems in algebra are the same. Some may involve a single variable, while some may include multiple variables. However, the basic approach of separating and evaluating the variables remains the same. You must remember to combine the like terms on one side and unlike terms on the other.
- For example: While combining two terms, remember that only terms with the same exponent and variable can be combined e.g., 5x and 19x can be combined, 4XY and 6XY can be combined.
Interpret your final answers
After doing the calculation of the equation, now is the time to interpret the final answers. Look back at the list of known and unknown information. Also, look at what you were asked to find. It will serve as a reminder to tell what you actually needed to solve. So, write down a statement indicating the meaning of your final answer.
- For example, You assumed x to be the number of oranges Sam was left with. And you have found out that x = 42. Hence, the number of oranges left with Sam are 42 (= x).
Checking the answers
As a final step, you need to re-assess all your work. This means that you will cross-check numbers, information, and units. Now that you have arrived at an answer, you need to think if it makes sense.
- Did the question ask for the speed, but you have found out the acceleration?
- Did the question ask to find out all the unknowns, but you have found only one?
- Did the question ask to find out the unknown quantity in a different unit than what you have found?
The catch here is to guide your kid to ask these questions before making the answer final. Also, a lot of times it happens that the answer got wrong because of a silly mistake. This means that you may have done addition instead of subtraction or multiplication instead of division.
Further, you should also tell your child to cross-check the units of the answer. It is an effective way to find out if your answer is wrong. Units help define what type of quantities you are dealing with.
- For example, The unit of length is meters (m)
The unit of time is seconds, minutes, or hours.
The unit of weight is kg or g (kilograms or grams).
The unit of speed is m/s (meter/second)
The unit of acceleration is m/s2 (meter/ second*second)
In a nutshell
Here you have, a detailed guide on how to solve word problems in algebra. All these steps may seem complicated and time-consuming but after practice, things will become more comfortable and faster. You need to ensure that you instruct your kid to start solving the problems by himself. Start by giving him/her fundamental problems and then advance to tougher ones.
Also, remember that the focus should be on accuracy and not on the time consumed to solve the problem in the beginning. As the student is grasping the topic from the very basic, it may take some time to become familiar. With that said, rigorous practice can help your kid to achieve the best results.
Cuemath- Helping your kid develop problem-solving skills
As maths is all about practice, your kid must get familiar with a wide range of word problems. Every word problem will bring new challenges and keywords. If your kid gets experienced in different types of problems, he will solve problems in exams much faster. Algebra is not tough if you Understand Algebra the Cuemath way. Cuemath believes in breaking down every step required to solve the problem. Also, it aims to help students learn algebra with visual diagrams. With this type of methodology, your kid will understand algebra and maths in much greater detail.
(Disclaimer: The article is sponsored, and hence promotes some commercial links.)