difficulties encountered in mathematical word problem solving of the grade six learners

Differentiated Teaching

Why do students struggle with math word problems? (And What to Try)

Word problems can be a real challenge for students of all ages. While some learners quickly grasp the concepts and transfer these skills to multi-step word problems, others struggle with even the most straightforward, basic word problems. As teachers, we must understand why this is so to help students succeed.

In this blog post, we'll explore common issues that cause difficulty when solving word problems and potential solutions that can assist learners in becoming more proficient problem-solvers. So, let's dive into what makes word problems so tricky and how you can help your students master them!

How to Help Learners Conquer Word Problems: Common Challenges & Solutions

Problem #1: students have difficulty reading & understanding the problems..

Word problems can be a daunting task for students of all ages. Solving math problems demands students to comprehend mathematical terms and have solid decoding abilities. If either of these skills is lacking, students may need help understanding the meaning behind certain words and phrases.

Considering that only a few sentences can determine the solution to a problem, it is essential to comprehend the language used in word problems. Yet, only  32% of 4th graders are proficient readers, according to the National Assessment of Educational Progress .

The challenge of comprehending the language in word problems is not only difficult for students who struggle with reading but can also be an obstacle for high-achieving math students. Often, these students know how to solve a problem but need help understanding what the problem is asking.

Word problems further complicate matters due to their use of language that's different from how we communicate.

For example, students may read a problem that says, “Sarah is baking a pie for her grandmother's birthday. She needs 7 apples for the recipe. At the store, apples are $2 a piece. If she has $11, will she have enough money to make the pie?”

Students must decode the words and phrases used to understand what the problem is asking them.

Solution: Provide word problems in audio formats & consider how you can incorporate explicit teaching into your math problem-solving routine.

One common strategy for addressing this is to read the problems aloud. Technology can help with this. Recording and storing problems where students can listen to them repeatedly can be helpful. However, you will need to teach your students to use this technology purposefully to help them better understand the word problems they are tackling. Without proper instruction, these recorded problems are no more helpful than reading the problems themselves.

However, this only addresses issues with decoding. It is essential to explain to students the meaning of words and math terms used in questions. A  Problem of the Day format  offers an excellent opportunity to deeply discuss a single problem with students without taking over your entire math lesson.

Explaining these concepts helps students build a stronger foundation for understanding word problems and increases their math comprehension.

Problem #2 :  Students have gaps in vocabulary that would help with math word problems.

Sometimes, story problems require students to have an understanding of math vocabulary. When students don't wholly understand math vocabulary, they struggle to understand what the problems are asking.

This is more than just decoding!

Even if they can read these words, they may need help understanding how to solve the problems. A strong foundation in math vocabulary is integral to any math classroom.

Solution: Explicitly teach and review math vocabulary regularly.

Ensure that students have a strong foundation in math vocabulary by explicitly teaching terms and concepts. This can be done through direct instruction, visual representations, and activities reinforcing the concepts.

Review these terms regularly throughout the year to ensure they stay fresh in students' minds.

Problem #3:  Students lack efficient & effective strategies.

Often, students are taught to use keywords early on. However, as problems become more complex, this quickly becomes an ineffective and inefficient strategy For addressing multi-step word problems.

Research has shown keywords often misdirect students' efforts and derail problem-solving with math word problems.

As a result, many state tests now purposefully include tricky problems designed to fool students who have been taught keywords as a problem-solving strategy.

Solution :  Teach a problem-solving strategy, like CUBES, that helps students break the problem down efficiently.

While keywords are ineffective, giving students a framework for breaking down word problems and identifying the information that CAN help them is a great way to support their problem-solving efforts.

The CUBES strategy (Circle, Underline, Box, Evaluate, Solve) can help older students with math word problems . This strategy helps them break down problems into manageable steps that make sense to them.

Problem #4:  Difficulty mapping out and visualizing the story behind each problem can lead to confusion in solving for an answer.

Another familiar struggle students face when solving word problems is difficulty mapping out and visualizing the story behind each problem. This can lead to confusion in solving for an answer because students may be unable to see how all the pieces fit together. In other words, they don't have a complete understanding of the context of the problem.

Solution:  Give students an active way to create a picture of what the problem is asking them.

Diagrams with labels, breaking the problem into simpler parts, and making a step-by-step plan with math word problems can help students understand the situation. Having them explain the story in their own words helps them clarify what they're trying to solve.

Encourage students who automatically add all the numbers to slow down and process the question with numberless word problems.

A numberless word problem is a story problem that does not include numbers . Instead, students are asked to analyze the problem without numbers before they are given the numbers to solve. This can help students notice patterns in the problem and determine what operations will be necessary for solving it. Adding these types of word problems to your instructional routine can be a great way to help students slow down and focus on understanding the scenario being presented in the problem. 

By providing students with different ways to visualize word problems, we can increase their chances of success and provide meaningful math instruction. Equipping them with the right tools and strategies gives them a better chance of tackling any difficult word problem they may encounter.

Problem #5:  Those with poor numeracy skills are disadvantaged when attempting to solve math word problems.

Computational fluency  is a common buzzword in math circles these days. We often discuss whether students know their math facts. However, math fact fluency becomes even more critical when students dive into more challenging word problems.

According to cognitive load theory, students focusing on rote processes such as basic facts have fewer mental resources left for higher-level thinking and processing.

In other words, the more mental energy it takes to work through the first step of a two-step problem, the less likely the student will have the resources to persist in accurately making it through the rest of the problem.

Solution: Build fact fluency practice into your routine in fun, engaging ways. 

Fact fluency practice doesn't have to be boring, but it is integral to being an effective mathematician. Therefore, finding ways to build it into your math class is essential.

Here are some of my favorite online games that students love:  30+ Awesome Online Games for Math Fact Practice .

Problem #6:  Students lack experience or are only provided with structured word problem practice.

Some curricula only include problems that follow a specific pattern or directly connect to the skill learned in a given lesson. However, formulaic word problems, where students follow a specific set of steps repeatedly, promote complacency.

Students begin to approach every word problem with the same steps. Soon they are grabbing numbers instead of taking the time to comprehend the problem and how best to address it.

Additionally, many word problems require students to apply knowledge from multiple different units to solve the problem. This can be challenging for students still working on mastering previously taught skills. It overwhelms those who have missed chunks of their instruction due to illness or being pulled from instruction.

As a result, these word problems often begin to feel impossible. 

Solution:  Incorporate variety into your problem-solving and allow for productive struggle.

Students need to be provided with an opportunity to approach a variety of different problems across time. They need to see problems that come in various formats. They need uniquely worded problems. This novelty prevents them from sticking with a rote set of strategies. The goal is to get them critically thinking about the problem at hand .

Offering variety builds confidence, competence, and the ability to address any problem they are given. Many students lack confidence in word problems. Varied experience reduces fears and helps students develop a bank of strategies to overcome barriers when complex problems arise.

To help foster independence, you can also support students through the gradual release process. Provide learners with a step-by-step guide to ensure they have completed the problem-solving process's critical steps when you aren't doing problems with them. This can help boost their confidence and reduce the risk of careless mistakes.

I've created a free mini-book for students with guiding questions and steps to help them independently complete word problems.

Get it here.

Building the math problem solver's toolbox

Word problems can be difficult for learners, but with the right strategies and resources, teachers can help their students learn to approach word problems confidently. By providing a variety of word problems that come in various formats and require different steps to solve, teachers can allow their students to develop problem-solving skills and build confidence when addressing any problem they are given.

Don't forget to grab the free problem solver's guide!

I hope you found this post helpful. Problem-solving is an essential skill for learners. Learn more about word problems or check out my Daily Problem Solving for engaging and meaningful word problem practice. 

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• 6th Grade Math
• Solving word problems

Grade 6 Math Word Problems: Tips, Tricks, and Answers

Do you want to stimulate your 6 th grader’s creative thinking skills? Then, enjoy this brilliant math article. In this comprehensive guide, we will provide you with a treasure trove of fun solving strategies, tips, tricks, and answers to tackle those tricky grade 6 math word problems that have been confusing your students for some time now.

In this page, you will discover why math word problems are important for 6th-graders and simple methods of breaking down complex word problems into manageable steps.

Nevertheless, we will introduce you to Mathskills4kids.com , an outstanding website with thousands of common types of grade 6 math word problems and a step-by-step approach to solving them. Interestingly, we will illustrate how to use diagrams and models to solve math word problems efficiently.

Learn to love Grade 6 Math word problems with these worksheets and answers

Hello and welcome to Grade 6 Math word problems worksheets and answers , where your 6 th Grade students will learn to love and solve math problems and activities at all times.

We understand that word problems can often frustrate students, as they require a solid understanding of mathematical concepts and the ability to interpret and apply them to real-life situations. That's why we have compiled a collection of proven strategies and techniques to empower your students to approach word problems confidently and accurately.

From understanding problem-solving strategies to breaking down complex questions into manageable steps, this guide will equip you with the knowledge and resources to make math word problems a breeze. So, let's dive in and unlock the secrets to conquering grade 6 math word problems together!

BROWSE THE WEBSITE

Download free worksheets, grade 6 math topics.

• Whole numbers

Multiplication

• Exponents and square roots
• Number theory
• Add & subtract decimals
• Multiply & divide decimals
• Fractions & mixed numbers
• Add & subtract fractions
• Multiply fractions
• Divide fractions
• Operations with integers
• Mixed operations
• Rational numbers
• Problems solving
• Ratio & proportions
• Percentages
• Measuring units
• Consumer math
• Telling time
• Coordinate graph
• Algebraic expressions
• One step equations
• Solve & graph inequalities
• Two-step equations
• 2D Geometry
• Symmetry & transformation
• Geometry measurement
• Data and Graphs
• Probability

Start practice on Sixth Grade here

Why are math word problems important for 6th-graders.

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6 th graders because they help them to:

• Learn how to use different math concepts and skills in various contexts
• Develop their logical thinking and reasoning abilities
• Enhance their communication and literacy skills
• Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

Strategies for solving Grade 6 math word problems

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

• Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
• They should rewrite the problem in their own words or summarize it in a sentence.
• Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
• They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
• Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

Breaking down complex word problems into manageable steps

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

Words like "difference," "subtract," "take away," or "minus" indicate s ubtraction .

Words like "product," "multiply," "times," or "of" indicate multiplication .

Words like "quotient," "divide," "per," or "out of" indicate division .

Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals .

Words like "equal," "same as," or "is" indicate equations .

Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities .

Words like "average," "mean," or "median" indicate statistics .

Words like "area," "perimeter," "volume," or "surface area" indicate geometry , etc.

• Use parentheses, brackets, or other symbols to group the parts of the problem that belong together . For example, if the problem says:

You can rewrite it as:

• (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

• Solve each part of the problem separately and write down the intermediate results . For example, using the previous problem:
• (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
• 12 + 8 = 20
• (total number of apples) / (4 people) = (number of apples per person)

This way, you can keep track of your work and avoid making mistakes.

• Combine the intermediate results to get the final answer. For example, using the previous problem :

This way, you can answer the question and check your answer.

Common types of grade 6 math word problems

There are many types of word problems that you may encounter in grade 6 math . Some of the most common ones found on Mathskills4kids.com are:

• Ratio and proportion problems : These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
• Percent problems : These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
• Fraction problems : These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
• Decimal problems : These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
• Measurement problems : These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
• Algebra problems : These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

A step-by-step approach to solving different types of word problems

No matter what type of word problem your 6 th graders are faced with, they can use the following steps to solve it:

• They should read the problem carefully and identify the given information and the question.
• They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
• They can now solve the equation or expression and find the variable's value.
• They can check their answer by plugging it back into the equation or expression to see if it makes sense.
• They can now write their answer in complete sentences and include the appropriate units.

Using diagrams and models to solve math word problems

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

• Tape diagrams : These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
• Number lines : These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
• Tables : These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
• Charts : These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
• Drawings : These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

Providing answers and explanations to sample Mathskills4kids’ Grade 6 math word problems

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com :

Answer : 6 cups of flour

Explanation : This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

Answer : $15

Explanation : This is a percent problem. We can use a formula to find the sale price of the shirt.

Sale price = Original price - Discount

Discount = Percent off x Original price

We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

Discount = 40% x $25

Discount = 0.4 x $25

Discount = $10

Sale price = $25 - $10

Sale price = $15

Tips for improving problem-solving skills in Grade 6 math

Here are some tips that can help students improve their problem-solving skills in grade 6 math :

• Please encourage them to practice regularly and try different types of word problems.
• They should review the concepts and skills they have learned and apply them to new situations.
• They can use different strategies and methods to solve word problems and compare their results.
• Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
• They should learn from their mistakes and try to avoid them in the future.

Bonus: additional resources to reinforce Grade 6 math problem skills

If you want to enhance your student's Grade 6 math word problem skills , or if you need some extra help, here are some additional and useful web links that you can check out:

• Math Playground : This website has a lot of fun and interactive games that let 6 th graders practice different types of math word problems, such as fractions, decimals, ratios, proportions, and more. They can also watch videos explaining how to solve some problems. https://www.mathplayground.com/wordproblems.html .
• Khan Academy : This website has many videos and exercises covering various topics in Grade 6 math, including word problems. Students can learn at their own pace and track their progress. https://www.khanacademy.org/math/cc-sixth-grade-math .
• IXL : This website has many practice questions aligned with the Common Core standards for Grade 6 math. Students can choose from different categories of word problems, such as expressions and equations, geometry, statistics, and more. They can also get instant feedback and explanations for their answers. https://www.ixl.com/math/grade-6 .
• Math Goodies : This website has a lot of worksheets and lessons that teach 6 th graders how to solve different types of word problems, such as percent, ratio, proportion, and more. They can also find tips and tricks for solving word problems faster and easier. https://www.mathgoodies.com/math-mammoth/worksheets/pdf/grade_6_word_problems.pdf .

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

Math word problems can be challenging for many 6th-graders, but they are also important for developing their mathematical thinking and reasoning skills.

Using the strategies and steps we discussed in this article, your student's ability to solve different types of word problems in Grade 6 math can be improved.

You can also use the diagrams and models we have shown you to help your students visualize the problem and find the solution. Encourage them to practice as much as possible, and they must not be afraid to ask for help if needed.

You can also use the web links that we have provided to reinforce your student’s learning and have fun with math. We hope this article has helped your 6th-grade students feel more confident and prepared for tackling Grade 6 math word problems.

Happy problem-solving!

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Word problems in mathematics education: a survey

• Survey Paper
• Published: 13 January 2020
• Volume 52 , pages 1–16, ( 2020 )

Cite this article

• Lieven Verschaffel   ORCID: orcid.org/0000-0002-5283-6470 1 ,
• Stanislaw Schukajlow 2 ,
• Jon Star 3 &
• Wim Van Dooren 1  

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Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and debates that have dominated the field. After a short introduction, we begin with research that has conceived word problems primarily as problems of comprehension, and we describe the various ways in which this complex comprehension process has been conceived theoretically as well as the empirical evidence supporting different theoretical models. Next we review research that has focused on strategies for actually solving the word problem. Strengths and weaknesses of informal and formal solution strategies—at various levels of learners’ mathematical development (i.e., arithmetic, algebra)—are discussed. Fourth, we address research that thinks of word problems as exercises in complex problem solving, requiring the use of cognitive strategies (heuristics) as well as metacognitive (or self-regulatory) strategies. The fifth section concerns the role of graphical representations in word problem solving. The complex and sometimes surprising results of research on representations—both self-made and externally provided ones—are summarized and discussed. As in many other domains of mathematics learning, word problem solving performance has been shown to be significantly associated with a number of general cognitive resources such as working memory capacity and inhibitory skills. Research focusing on the role of these general cognitive resources is reviewed afterwards. The seventh section discusses research that analyzes the complex relationship between (traditional) word problems and (genuine) mathematical modeling tasks. Generally, this research points to the gap between the artificial word problems learners encounter in their mathematics lessons, on the one hand, and the authentic mathematical modeling situations with which they are confronted in real life, on the other hand. Finally, we review research on the impact of three important elements of the teaching/learning environment on the development of learners’ word problem solving competence: textbooks, software, and teachers. It is shown how each of these three environmental elements may support or hinder the development of learners’ word problem solving competence. With this general overview of international research on the various perspectives on this complex and fascinating kind of mathematical problem, we set the scene for the empirical contributions on word problems that appear in this special issue.

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Verschaffel, L., Schukajlow, S., Star, J. et al. Word problems in mathematics education: a survey. ZDM Mathematics Education 52 , 1–16 (2020). https://doi.org/10.1007/s11858-020-01130-4

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Status of Grade Six Pupils' Skills in Solving Mathematics Word Problems in San Cristobal Elementary School

• Aileen A. de Villa
• Harold A. Beladas
• Jean P. Beladas

INTRODUCTION

Mathematics plays a very important role in our daily living. It is a subject that deals with problems that involve a process of analysis, computation, and other mental skills. Historically, learning mathematics and teaching it has been motivated by the belief that a study of mathematics helps individuals to learn, to reason, and to apply such reasoning to everyday problems. Mathematics develops the mind to think critically and analytically. It is more than counting, measuring, and computing. It is an eye-opener to all sciences. As far as mathematics instruction is concerned, the major goal is the involvement of the students in the process of discovering mathematical ideas and formulating a process. One of the interesting concerns about learning mathematics is the fact that it develops the mind to solve problems that need higher order thinking skills.

This study used experimental research design in determining the status among grade 6 pupils with ninety (90) respondents. A questionnaire was prepared, validated, distributed, tallied, and interpreted to identify difficulties encountered by the pupils and used frequency and percentage to interpret the data.

The Performance Level of Grade Six pupils in solving word problems was low with a percentage of 68%. Most of them were specifically poor in solving word problems. Only eight (8) of the pupils fell under excellent level, ten (10) pupils fell under good level, 16 pupils fell under the average level, and 56 were low. The difficulties of the Grade Six (6) pupils in solving word problems reveals that most of the respondents marked the difficulties given to the highest extent, which means they are incompetent in acquiring many mathematics skills and lacking in cognitive abilities of learning. Only a few of them found it easy to solve word problems, at a percentage of 2%.

DISCUSSIONS

The performance level of Grade Six Pupils in San Cristobal Elementary School was low. The reading and understanding the language used within a word problem has the greatest number of respondents. This is the greatest number of difficulties encountered by Grade Six Pupils. The researchers came up with the proposed activities: a. Big Brother/Peer Teaching Approach, b. Trial and Error Approach, c. Use of Instructional Materials, d. Create a table or a graph, and e. Problem of the Day. The students should establish good study habits and a healthy studying environment. They should attend makeup classes and seek the assistance of the parents to cope up with less mastered skills in mathematics.

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Analysis of Sixth Graders' Difficulties in Solving Mathematics Word Problems on Whole Numbers, Fractions, and Decimals

U I Kusuma 1 and H Retnawati 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1320 , The 2nd International Seminar on Innovation in Mathematics and Mathemathics Education (ISIMMED 2018) 20–24 November 2018, Yogyakarta, Indonesia Citation U I Kusuma and H Retnawati 2019 J. Phys.: Conf. Ser. 1320 012008 DOI 10.1088/1742-6596/1320/1/012008

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1 Graduate Program of Mathematics Education, Universitas Negeri Yogyakarta Indonesia, Jl. Colombo No. 1 Depok, Catur tunggal, Sleman, 55281, Yogyakarta, Indonesia

2 Departement of Mathematics Education, Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta, Indonesia, Jl. Colombo No. 1 Depok, Catur tunggal, Sleman, 55281, Yogyakarta, Indonesia

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Operation which involve whole numbers, fractions, and decimals are important concepts that must be possessed by students. It is a part of mathematics that is very close to everyday life. In fact, many students who have difficulty in understanding the fractions, especially in the word problems. This study aims to describe sixth graders' difficulties in solving mathematics word problems on the operation which involve whole numbers, fractions, and decimals. This research is descriptive with students of grade six as the subjects. Data were collected by tests and in-depth interviews. Tests were used to analyze students difficulties in solving mathematics word problems on the operation which involve whole numbers, fractions, and decimals. Interviews were conducted to know the difficulties experienced by the students in depth. The unstructured interviews were conducted with students' error. The results showed that students' difficulties in solving mathematics word problems on the operation which involve whole numbers, fractions, and decimals are caused by: 1) Students' difficulties in the word problem, 2) Students' difficulties in understanding the concept of fractional operations, 3) Students have less numeracy skills, and 4) Inaccuracy.

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LITERACY AND NUMERACY SKILLS ON WORD PROBLEM IN MATHEMATICS OF SENIOR HIGH SCHOOL STUDENTS

2021, IOER International Multidisciplinary Research Journal

In Mathematics, problem solving is the basis of learning. The students must be skilful in solving a word problem. However, only some of the students can solve problems and others are experiencing difficulties. Hence, this qualitative-descriptive study is conducted to examine students' errors and learning attitudes when solving Mathematical word problems. The sample consists of thirty-three (33) Grade 11 students of FAITH Fidelis Senior High, Tanauan City, Batangas. Making use of Newman's Error Analysis consisting of decoding, comprehension, transformation, process skill, and encoding stages, the researcher was able to determine the stages where students usually commit errors. It is also the objective of the researcher to examine the students' learning attitude in solving word problems as to three components, namely, affective, behavioural, and cognitive. It also determined the different strategies used by teachers in correcting the errors of students in solving word problems. The results showed that students only have a developing level of proficiency in the transformation (78.79%), process (79.80%), and encoding (80.81%) stages of solving word problems. In the decoding stage, students are on the advanced level of proficiency (13.13%) and on the proficient level (23.23%) on the comprehension stage of solving word problems. This study also revealed that students possess a positive attitude in the affective and cognitive component but acquire a negative attitude in the behavioural component of learning in solving word problems. Lastly, the study proposed a Mathematical learning strategy derived from the different strategies used by teacher in correcting error in solving word problems in Mathematics. These strategies can help students with the proper way of conceptualizing word problems.

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Isaac Taley

Due to the importance of word problems in mathematics, curriculum planners for high school mathematics in Ghana have recommended the inclusion of word problems in mathematics textbooks, teaching, and tests. Nevertheless, examination reports, research findings, and teachers' discourse show that high school students shy away from answering word problem tasks. Using a phenomenology enquiry, this study explored the teaching and learning experiences of teachers and students regarding the inclusion of word problems in the high school mathematics curriculum. Twenty-eight participants consisting of 12 mathematics teachers and 16 students were purposively sampled from four senior high schools in the Ashanti Region of Ghana. Semi-structured interviews were used to gather the views of the participants while thematic analysis and percentages were used to analyse the data. The study showed that both teachers and students appreciated the importance of word problems. Nonetheless, more students than teachers used word problems to bridge the wedge between mathematics concepts and real-life applications. Besides, more teachers than students used word problems to help students internalise mathematics concepts. Additionally, the study also showed that instructional-related and student-related factors caused about a third of senior high school students to dislike worded problems. Based on the findings in this study, it was recommended that teachers should consciously teach mathematics vocabulary, reword and translate worded tasks where necessary. Consequently, students' dislike for word problem-solving may reduce.

This paper aims to show how the Familiarization rewording, Conceptual rewording and their combination influence on facilitating the process of solving word problems. In this study, eighty students studying at fourth grade were randomly assigned to one of the mentioned conditions plus a control group. All the participants answered to a pretest (Standard test). Then all of them, except for the control group which received Standard test answered one of the three tests (FR, CR, and FR+CR). The results indicated that types of rewordings facilitated students&#39; performance in solving the given word problems. Further, the findings revealed that rewordings had influenced students ability in solving three types of word problems (Compare, Change and Combine) similarly.

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Math word Problems With Answers for Grade 6

Grade 6 maths word problems with answers are presented. Some of these problems are challenging and need more time to solve. Also detailed solutions and full explanations are included.

• Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
• If the area of a circle is 81pi square feet, find its circumference.
• Find the greatest common factor of 24, 40 and 60.
• In a given school, there are 240 boys and 260 girls. a) What is the ratio of the number of girls to the number of boys? b) What is the ratio of the number of boys to the total number of pupils in the school?
• If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
• Find k if 64 ÷ k = 4.
• Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
• What is x if x + 2y = 10 and y = 3?
• A telephone company charges initially $0.50 and then $0.11 for every minute. Write an expression that gives the cost of a call that lasts N minutes.
• A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
• A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
• A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
• A small square of side 2x is cut from the corner of a rectangle with a width of 10 centimeters and length of 20 centimeters. Write an expression in terms of x for the area of the remaining shape.
• A rectangle A with length 10 centimeters and width 5 centimeters is similar to another rectangle B whose length is 30 centimeters. Find the area of rectangle B.
• A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 5 classes were half full, 3 classes were 3/4 full and 2 classes were 1/8 empty. A total of 70 students were absent. How many students are in this school when no students are absent?
• The perimeter of square A is 3 times the perimeter of square B. What is the ratio of the area of square A to the area of square B.
• John gave half of his stamps to Jim. Jim gave gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Thomas and kept the remaining 12. How many stamps did John start with?
• Two balls A and B rotate along a circular track. Ball A makes 4 full rotations in 120 seconds. Ball B makes 3 full rotation in 60 seconds. If they start rotating now from the same point, when will they be at the same starting point again?
• A segment is 3 units long. It is divided into 9 parts. What fraction of a unit are 2 parts of the segment?
• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
• Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them.
• Linda spent 3/4 of her savings on furniture. She then spent 1/2 of her remaining savings on a fridge. If the fridge cost her $150, what were her original savings?
• The distance bewteen Harry and Kate is 2500 meters. Kate and Harry start walking toward one another and Kate' dog start running back and forth between Harry and Kate at a speed of 120 meters per minute. Harry walks at the speed of 40 meters per minute while Kate walks at the speed of 60 meters per minute. What distance will the dog have travelled when Harry and Kate meet each other?

Answers to the Above Questions

• a) 13:12 b)12:25
• 0.50 + N * 0.11
• 4.5 gallons
• 450 centimeters squared
• 108 cubic centimeters
• 1250 meters/minute
• Carla:5 years, Jim: 6 years, Peter: 19 years.
• 3000 meters