Wednesday, June 19, 2024

How To Solve Math Word Problems

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Practice Word Problems Often

Using Algebra To Solve Word Problems

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary .

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

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Fun And Original Ways To Teach Math Word Problems

by Sara Ipatenco

  • copied!

Solving word problems is a key life skill. Someday your students will need to know how to buy enough food for a party, figure out how much tile is necessary for a bathroom, double a recipe, determine the price of an item on sale, or calculate how many miles are left on a road trip. Word problems can be tricky, however, making it essential to teach your students multiple ways to solve these types of math equations. Once you have introduced the many ways to reach an answer, your students can choose the one that works best for them.

Here are ten fun ways to get your students excited about word problems!

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Your Child Might Struggle With Word Problems Because

They experiencetrouble with reading: Proficient reading skills go a long way in deciphering the problem. If the student isnt the best reader, they might have difficulties understanding and absorbing the information.

They have difficulty picking up on clues and concepts: Clues in word problems are phrases that help kids figure out what they need to do to solve the problem. Even the strongest readers could struggle to find the clues and translating them into a number sentence.

Theyre not interested or unfocused: Lets face it, word problems arent the most exciting thing to do in class. Students may get bored and lose their focus on the problem or rush through it, resulting in the wrong answer by missing essential details.

Solving Math Word Problems With Pictures

Algebra 1 Help: Solving Money Word Problems 1/2

After your child identifies keywords within problems, the next step is to plan. There are many different types of strategies that your child can use. Creating illustrations, graphs, and diagrams are the most popular.

This is because many students are visual learners and benefit from using illustrations to help solve word problems. In fact, visual learners make up65% of the students in a classroom.

Some math problems come with pictures or images for your child to refer to. For example:

This helps students learn and understand ways that they can organize their thinking to solve word problems.

Students also work with many word problems that do not come with any visuals or diagrams. This is why its a great idea to encourage your child to create their own images to help!

Heres an example of how to use illustration to plan and solve a word problem:

There are 12 hens in a coop. Each hen lays 4 eggs a week. At the end of the week, Simon equally distributes and packs the eggs into 6 boxes. How many eggs are there in each box?

To solve this problem, your child will need to first calculate how many total eggs there are. Once they calculate 48 eggs , they need to take this amount and divide it among 6 boxes. Your child can draw six boxes, then draw eggs into the boxes to visually represent how many eggs there are in each box.

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Where Can You Find More Algebra Word Problems To Practice

Word problems are the most difficult type of problem to solve in math. So, where can you find quality word problems WITH a detailed solution?

The Algebra Class E-course provides a lot of practice with solving word problems for every unit! The best part is…. if you have trouble with these types of problems, you can always find a step-by-step solution to guide you through the process!

for more information.

The next example shows how to identify a constant within a word problem.

Writing Equations For Word Problems

  • First, you want to identify the unknown, which is your variable. What are you trying to solve for?Identify the variable: Use the statement, Let x = _____. You can replace the x with whatever variable you are using.
  • Look for key words that will help you write the equation. Highlight the key words and write anequation to match the problem.
  • The following key words will help you write equations for Algebra word problems:


Let’s look at an example of an algebra word problem.

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Effective Ways To Help Your Students Conquer Math Word Problems

If a train leaving Minneapolis is traveling at 87 miles an hour

Word problems can be tricky for a lot of students, but theyre incredibly important to master. After all, in the real world, most math is in the form of word problems. If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?This sweater costs $135, but its on sale for 35% off. So how much is that? Here are the best teacher-tested ideas for helping kids get a handle on these problems.

Differentiate Word Problems To Build Skills

How to Solve Math Word Problems

Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.

Learn more:Differentiating Math

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Iv Work The Problem One Step At A Time

  • Rewrite the given facts in a more organized manner.
  • Given diagrams or charts should show all of the given information.
  • Express the unknown in terms of a variable.
  • Write out each step.
  • An important problem solving skill is the ability to distinguish between facts that you know from those you dont know. Write down the required equations and formulas. Break down complex ideas into smaller parts.

    Draw A Simple Picture And Label It

    Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

    For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

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    Math Word Problems To Challenge Students Grades 1 To 8


    • Teaching Tools

    You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

    A jolt of creativity would help. But it doesnt come.

    Whether youre a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

    This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

    There are 120 examples in total. Helping you sort through them to find questions for your students, the resource is categorized by the following skills with some inter-topic overlap:

    The list of examples is supplemented by tips to create engaging and challenging math word problems.

    The Goal Of Math Instruction

    Solving Multiplication Word Problems

    I think this begs the question, Why are we doing this anyway?? Does it really matter if kids can solve word problems? Why cant we just teach the facts?

    Well, I believe that ultimately our goal is not to produce quick and efficient machines , but rather to raise up strong problem solvers.

    To help develop critical thinkers, and kids who apply logical reasoning and think outside the box.

    I love this quote from S.Y. Gillan from the book, Problems Without Figures:

    Every problem in arithmetic calls for two distinct and widely different kinds of work: first, the solution, which involves a comprehension of the conditions of the problem and their relation to one another second, the operation. First, we decide what to do this requires reasoning. Then we do the work this is merely a mechanical processAdding, subtracting, multiplying and dividing do not train the power to reason, but deciding in a given set of conditions which of these operations to use and why, is the feature of arithmetic which requires reasoning.

    Do you hear what hes saying? Were not just teaching kids to do the work: the actual process of adding 2 numbers together. Were teaching kids to reason and then apply their reasoning to solve problems.

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    How Do You Solve Word Problems In Math

    Ask yourself this, what do you think is the #1 phrase a student says as soon as they see a word problem?

    You guessed it, my teacher friend, I dont know how to do this! I think the most common question I get when Im teaching my math classes, is how do I solve this?

    Students see word problems and immediately enter freak-out mode! Lets take solving word problems in the classroom and make it easier for students to SOLVE the problem!

    What Is A Word Problem

    A word problem in maths is a maths question written as one sentence or more that requires children to apply their maths knowledge to a real-life scenario.

    This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.

    For example:

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    How To Solve Word Problems

    As your child advances in school, they will come to a few stumbling blocks. There are some problems that prove difficult to a lot of students to understand. The most common issue is with word problems. Students struggle with seeing the math behind the words.

    A proven step-by-step method for solving word problems is actually quite simple.

    • Read the problem out loud to yourself
    • Draw a Picture
    • Think What do I need to find?
    • List what is given
    • Check your work

    Lets put these steps into practice. Consider the word problem below.

    Example: Kevin loves to read. He likes many different types of books. He has 3 large bookcases that each have 9 shelves on it all filled with his books. If each shelf can hold 16 books, how many books does Kevin have?

    Read the Problem Out Loud

    Kids have a tendency to rush through every problem. This is due to time limits on classwork and tests. If your child does not know what the problem is asking, then they cannot solve the problem. When your child reads the problem aloud, they are saying and hearing the problem. They can form a clearer picture in their head of the problem and they are more prepared to solve it.

    Draw a Picture

    Ask What Do I Need to Find?

    List What is Given

    • Kevin has 3 book cases
    • Each book case has 9 shelves
    • Each shelve holds 16 books

    Find the Key Words


    equal parts split between separated, percent

    *this can be a key word for addition and multiplication


    Check your answer

    Solving Math Word Problems With Distractors

    Math Help : Solving Math Word Problems

    For students that try to sprint through solving word problems, distractors are often the reason they trip.

    Which, quite honestly, is one of the reasons distractors are often thrown into word problems! They are meant to keep students on their toes and to ensure they are carefully reading what the problem is asking.

    Distractors are words and information that are included in a problem, but really have nothing to do with it. Its unnecessary information that students are expected to navigate around.

    Thinkster Math CEO Raj Valli shares more on having students think on their feet with word problems that include distractors:

    One tip that Thinkster tutors share with parents is to work on characterizing information and variables.

    In the above video example, the problem requires students to determine how many fruits are in a basket. Characterizing all items in the basket and distinguishing between fruits and vegetables will ensure your child isnt carelessly adding carrots into the final answer.

    Heres another example of a problem with a distractor that requires characterization:

    A used car dealership has 91 cars and 29 trucks on the lot. Each day the dealership sells 13 cars. How many days would it take for all the cars to be sold?

    A student that is rushing through the problem may add 91 and 29, then divide that amount by 13.

    A student that takes the time to carefully dissect the problem will identify that there is a distractor.

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    Five Proven Steps On How To Solve Math Word Problems Quickly

    One of the most common complaints of students during Mathematics examinations is that they often run out of time in that case, advice on how to solve math problems more quickly will help them finish timed exams. Math is a complicated discipline, and while some problems are routine and straightforward, some problems require zigzag mazes and long expositions of solutions before an answer can be found. Many teachers, while willing to give plenty of help to their students so that they can be faster in Math, do not have the time to do so. In that case, it is up to the student to figure out techniques on how to solve math problems more quickly than they did before. Here are five effective means to do so:

    Set up easily solvable equations. After reading the question you should be able to translate all the given data into mathematical equations. Also, keep in mind to select proper notation for your equations. Refrain from using the same letter to represent different unknowns to avoid confusion and to proceed more quickly. There is also an art in choosing notation for instance, in adding seven consecutive integers, it is easier to have

    x – 3, x – 2, x – 1, x, x + 1, x + 2, and x + 3 as the unknowns,

    instead of x, x + 1, x + 2, x + 3, x + 4, x + 5, and x + 6.

    Try adding both sets. Which one is easier to add?

    Solve Word Problems Regularly

    This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so theyll get comfortable with the process.

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    Ratios And Percentages Word Problems

    Best for: 4th grade, 5th grade, 6th grade

    82. Finding a Missing Number: The ratio of Jennys trophies to Merediths trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

    83. Finding Missing Numbers: The ratio of Jennys trophies to Merediths trophies is 7:4. The difference between the numbers is 12. What are the numbers?

    84. Comparing Ratios: The schools junior band has 10 saxophone players and 20 trumpet players. The schools senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

    85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

    86. Determining Percent of Change:A decade ago, Oakvilles population was 67,624 people. Now, it is 190% larger. What is Oakvilles current population?

    87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

    88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

    Solving Math Word Problems With Patterns

    How to Solve Math Word Problems â Solving Math Word Problems

    Another type of word problem that students encounter are problems with patterns.

    For some students, these types of problems may seem difficult at first, especially if they are not taking the time to organize their thinking. But those that do take the time to use charts and visuals will find that there really is nothing to fear with pattern word problems!

    Lets try the following problem:

    A bakery sells a different number of cakes each month. In March they sell 3 cakes, in April they sell 9 cakes, and in May they sell 27 cakes. If this pattern continues, how many cakes will they sell in July?

    Its not easy to try and figure out the answer mentally! This is why creating a chart helps students organize their thinking to reach the correct answer.

    Once this information is displayed carefully, your child should be able to spot that they actually need to do two calculations. The word problem requires them to determine the number of cakes sold in July, but they cant reach the answer without first determining how many cakes are sold in June.

    Taking the time to carefully organize the data ensures that they do not miss this important step!

    Here is another pattern word problem that you can have your child try to solve:

    As your child solves the problem, make sure they underline keywords and important details, then organize their thinking with a chart! This is a great way to make sure they slow down when approaching the problem to minimize the risk of careless mistakes.

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