strategies for solving multiplication word problems

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10 Best Strategies for Solving Math Word Problems

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on. 

A Guide on Steps to Solving Word Problems: 10 Strategies 

One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

• Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
• Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

• Original number of students (24)
• Students joined (6)
• Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

• “Total,” “sum,” “combined” → Addition (+)
• “Difference,” “less than,” “remain” → Subtraction (−)
• “Times,” “product of” → Multiplication (×)
• “Divided by,” “quotient of” → Division (÷)
• “Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total,  5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is  x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

• Re-read the problem: Ensure the question was understood correctly.
• Compare with the original problem: Does the answer make sense given the scenario?
• Use estimation: Does the precise answer align with an earlier estimation?
• Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

2. Practice Regularly with Diverse Problems

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion 

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

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20 Multiplication Word Problems for 3rd to 5th Grades With Tips On Supporting Students’ Progress

Steven Eastes

Multiplication word problems are mathematical word problems that use real-life scenarios involving multiplication to find the solution. Multiplication word problems teach students to apply their knowledge of their times tables and build up skills in standard algorithm multiplication.

As children advance through elementary school, they will develop their times tables skills. Skills to tackle word problems involving multiplication develop alongside this from 3rd grade to 5th grade.

How to build mathematical skills to tackle multiplication word problems

As children develop their knowledge of multiplication, it is essential that they are exposed to visuals and concrete manipulatives to understand the concept of multiplication. These resources aim to aid children’s understanding of multiplication and allow them to make connections to real-world situations.

Multiplication Word Problems For 3rd - 5th Grade

Develop your 3rd - 5th grade students multiplication reasoning and problem solving skills with these 10 questions and answers per worksheet!

As children become more confident in their ability to multiply they will start to apply their skills to beyond one-step problems and begin to solve complex word problems, and multi-step problems that may involve more than one operation.

In two-step problems children may need to use their addition word problems , subtraction word problems , fraction word problems and division word problems skills to find the solution. These skills are built upon throughout lower and upper elementary. Furthermore, having a student who understands place value will also aid them in their problem solving skills.

It is important that children are exposed to arithmetic activities and fluency tasks together with regular word problems. To help, in this blog you will find multiplication word problems for all grades from 3rd grade up to 5th grade, complete with examples and solutions for you to use with your students.

Multiplication in 3rd Grade

In 3rd grade, children should be able to recall all products of two one-digit numbers and division facts for these tables. Additionally, they begin writing the multiplication, division and equals signs and show that multiplication of two numbers can be done in any order due to the commutative theory. 

They will also develop efficient mental methods using commutativity and associativity such as 5 x 8 = 40 and so 8 x 5 = 40 as well as deriving related facts such as , if 2 x 3 = 6 then 20 x 3 = 60. Students will also practice their written multiplication strategy starting with calculations of two-digit numbers by one-digit numbers via arrays and area models.

3rd graders use arrays, repeated addition, concrete materials and mental methods to solve word problems. By the end of 3rd grade, they also begin to successfully write and calculate multiplication statements and solve missing number problems. 

It is also important to develop our students’ vocabulary and to consider the different ways of saying we are multiplying. Multiplication word problems are fantastic at doing this by using phrases such as ‘the product of’, ‘equal groups’, ‘use multiplication tables’ and ‘arrays’. Concrete materials will obviously assist in this understanding too.

By the end of 3rd grade students will mentally know and use place value to understand about multiplying by 10 and 100, recognize and use factor pairs and be able to multiply three-digit numbers by one-digit numbers. 

When working on multiplication word problems, students will look at integer scaling problems and more complex correspondence problems such as ‘n objects are connected to m objects’. These two-step problems will be based on real-life scenarios around: measure, money and fractions.

Multiplication in 4th and 5th grade

In 4th grade, students continue to practice multiplying using the area model, multiplying 4-digit by one-digit numbers. In 5th grade, students are introduced to standard algorithm multiplication, where students will multiply 4-digit numbers by two-digit numbers. 

Children should use their knowledge of factors, multiples, and prime numbers to assist them in their problem solving. Being familiar with multi-step word problems and knowing how to apply their knowledge of multiplication in a quick, accurate manner is essential.

Why are multiplication word problems important for children’s understanding of multiplication

Word problems are a great opportunity to bring math to life. They enable children to see the link between the math they do in the classroom and how they can apply it in real-life scenarios and avoid the phrase ‘why do we need to learn this anyway?’

In lower elementary word problems allow for the chance to use concrete materials and manipulatives rather than a constant stream of multiplication word problem worksheets. 

Children get a hands-on opportunity to problem solve and visually see how to create arrays or use repeated addition. While this continues into upper elementary, learners will use concrete materials less and instead embark on the formal written methods of standard algorithm multiplication so that they become confident with mental and formal methods.

In addition, children develop key skills such as:

• building problem solving skills
• developing mathematical language skills
• develop an understanding between multiplication and division and how we can use, and may need to use both, to solve two-step problems. We may need to multiply before we use standard algorithm division for example.
• be able to apply mathematical concepts to real life situations.

Teaching how to solve multiplication word problems in elementary school

Once the concept of multiplication is embedded and children understand how to use concrete materials, for example how to visually create an array to represent the multiplication needed, the next step is to advance to multiplication word problems.

When providing children with multiplication word problem worksheets or multiplication word problems challenge cards, it is important that children are able to read the question carefully and understand the context before extracting the math from it. 

Students need to be able to interpret what they are being asked. What operation do they need to do? Or do they need to do two operations? Is it a one-step problem or a two-step problem? In the word problems below the focus will be multiplication, whether representing it visually, like in lower elementary, or moving up to formal written methods in upper elementary.

Example of a multiplication word problem

Amy is making the party bags for her birthday party. She has invited 10 friends and they will have three chocolates in their bag. How many chocolates will Amy need altogether?

How to solve this:

Firstly we need to know that Amy has invited 10 friends so there will be 10 party bags. She will put 3 chocolates in each bag. So we know:-

• There are 10 friends/party bags
• They will have 3 chocolates each
• We therefore need to multiply, or use repeated addition, to times 10 by 3 to solve the problem.
• So to solve this problem we could draw a number line starting at zero (0) and repeatedly add three (3) each time. We need to repeat this ten (10) times to attain the answer.
• We could mentally use our times table knowledge to do 10 x 3, or 3 x 10 or visually represent this as an array. We could even show this as a bar model.
• We could formally use multiplication to solve this problem.

How would we represent this visually?

Below are visual representations of the above problem to show how a child may represent this problem using any of the strategies above:

How we would represent this with repeated addition:

Or as an array:

Examples of multiplication word problems in the elementary setting

Below are examples of what can be expected at each grade level from grades 3 to 5. Through our tutoring program at Third Space Learning, our tutees will become familiar with word problems throughout their learning. They will encounter word problems on a regular basis with each lesson personalized to develop the learning our tutees need. 

The word problems will increase their confidence, familiarity with vocabulary and mathematical understanding whether using our materials in tutoring sessions, in the classroom or in small intervention groups.

Multiplication word problems for 3rd grade

3rd grade is the first year that multiplication is formally introduced.  When solving word problems for 3rd grade, students will first use concrete materials to discover how to use repeated addition and arrays to solve word problems that have a context to them. They should be encouraged and aided in representing the word problem visually as well as developing their mental methods to solve such problems.

By the end of 3rd grade, students should be using their full knowledge and recall of times tables to 10 x 10 to help with multiplication of 2-digit and 3-digit numbers by a 1 digit number. Word problems may also involve multi step problems and there will be exchanges taking place too.

Mia is picking flowers. A flower has 5 petals on it. How many petals will be on 6 flowers?

Answer: 30 petals

How we can solve this using repeated addition:

How we can solve this using arrays:

How we can show this visually:

Sam is at the store and sees a bouncy ball is 10¢.

Sam wants to buy 8 balls. How much will it cost?

Answer: 80 ¢

Hansi has 4 packets of stickers with 5 stickers in each packet.

Robert has 3 packets of stickers with 10 stickers in each packet.

Who has the most stickers? Why?

Answer: Robert because Hansi has 20 stickers (4 x 5) but Robert has 30 stickers (3 x 10).

Daisy and Ollie are sharing some marbles. They have 5 boxes of marbles, and once they have shared them they have twenty marbles each. How many marbles are in each box?

Answer: 8 marbles.

If they have 20 marbles each then in total there are 40 marbles (20 x 2 = 40). If there are 5 boxes of marbles then there are 8 marbles in each box as 40 divided by 5 is 8. Some may also know the inverse here in that 5 x 8 = 40.

It is Christmas break and a family of 4 are going to the cinema! Each ticket costs $8. How much would it cost for the family to go to the cinema?

Answer: $32.

As 4 multiplied by 8 equals 32. We can solve this mentally and by knowing the times table fact 4 x 8 = 32 or 8 x 4 = 32.

We could also show this in bar model method:

Multiplication word problems for 4th grade

In 4th grade, students should be using their full knowledge and recall of times tables to 12 x 12 as children begin to multiply 4-digit numbers by 1-digit numbers and 2-digit numbers. Word problems may also involve multi-step problems and there will be exchanges taking place too.

Jack and Ella are practicing their area models and have both attempted the same question.

The question is: What is 1,235 x 7?

Jack says the answer is 7,259 but Ella says the answer is 8,645.

Who is correct and what mistake has one child made?

Answer: Ella is correct, the answer is 8,645 and the mistake made is that Jack forgot to add the two zeros when multiplying 7 x 200.

If a shop makes $2,782 in a day, how much will it make in one week?

Answer: $19,474

Note: For this question we must know that there are 7 days in one week as we then have to multiply 2,782 by 7.

A group of friends go for lunch at the local restaurant. 6 of them decide to buy chicken nuggets and fries which costs $7 each and the other 4 friends decide to buy pizza and salad for $8 each. What do friends spend more on, chicken nuggets or pizza?

Answer: Chicken nuggets

Chicken nuggets = 7 x 6 totals $42 whereas pizza = 8 x 4 totals $32. Therefore, they spend more on chicken nuggets.

A high school football team has a mean (average) attendance of 1,298 people each game. There are 9 games in a season, what is the total attendance for the whole season?

Answer: A total attendance of 11,682

Multiplication word problems for 5th grade

With the end of the elementary school journey in sight, word problems for 5th graders are expected to be able to use mental methods to solve the more simple multiplication word problems, such as multiplying by a multiple of 10. The standard algorithm is formally introduced in 5th grade. They will be able to multiply decimals as well as 4-digit numbers multiplied by 2-digit numbers. They will also be versed with two-step problems and using more than one operation in a question.

There are 67 candies in a bag. If the grocery store orders 8,657 bags, how many candies would there be altogether?

Answer: 580,019 candies 

Bobby chooses a number between 300 and 320.

She divides it by 6 then subtracts 17 from it.

She then divides that number by 4.

Her answer is 8.5.

What number did she start with?

Answer: 306

Here it is essential to work backwards from the answer 8.5 and do the inverse at each step. So we multiply instead of divide and we add instead of subtract.

Miss Dobson is making cakes to sell at the school fair.

Strawberries cost $5.60 per lb.

Eggs cost $1.70 per box.

Icing costs 89¢ per lb.

Cake cases are $3.25 for 10.

She uses 8 lbs of strawberries, 10 boxes of eggs, 11 lbs of icing and 40 cake cases to make 40 cakes.

Calculate the total cost for 40 cakes.

Answer: $84.59

The strawberries are: $5.60 x 8 = $44.80

The eggs are: $1.70 x 10 = $17.00

Icing costs are $0.89 x 11 = $9.79

Cake cases are $3.25 x 4 = $13.00

There are 26 white buttons in a pack and 13 blue buttons in a pack.

The school buys 1,460 packs of white buttons and 730 packs of blue buttons.

Is it true that the school would have four times as many white buttons as blue buttons? Show your working in your answer.

Answer: It is true because there are 37,960 white buttons and there are 9,490 blue buttons.

If we then multiply 9,490 by 4 we get 37,960. Or alternatively we could divide 37,960 by 4 and get 9,490.

More word problems resources

Third Space Learning offers a big collection of practice word problems covering a wide range of topics for all elementary grade levels. Take a look at our addition and subtraction word problems , time word problems , ratio word problems and percentage word problems .

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by former Deputy Headteacher Steven Eastes and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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• November 27, 2019

Multiplication and Division Word Problems

With these steps, you will never resent multiplication and division word problems again! Using these strategies for solving word problems will help your students master mixed word problems. Multiplication and Division Word Problems are so challenging for many students. It doesn’t matter whether they are in elementary school or high school. Word problems in general cause students to have to first read a problem and then comprehend what it is asking. Lastly, they have to actually choose the correct operation and get the arithmetic correct. As teachers, the first time we hand out multiplication and division word problems worksheets we immediately see how many students get them wrong. Don’t even get me started on mixed multiplication and division word problems. This is where the resentment begins!

Multiplication and Division Word Problems Grade 3

As teachers, we all know that this is a challenge! Whether you are a first-year teacher or even a veteran teacher, it is obvious that this math skill proves to be a very difficult one. 3rd grade word problems become very challenging because they are no longer basic addition and subtraction word problems like in kindergarten through second grade. Our students are now being exposed to mixed multiplication and division word problems.

When students were in the primary grades they had a 50 percent shot of getting the operation correct because they only had two options to choose from.  Also, many of the problems had a keyword like total, altogether, left or combine that helped them know what to do. But in 3rd grade, we introduce two step addition, subtraction, multiplication and division word problems. These include all the operations so their chances of guessing correctly have now gone from 50 percent down to 25 percent. Then when you add in the addition of two-step word problems that percent goes down to less than 7 percent.

Wow! Have you ever even thought about that? This why as teachers we start to notice that students are struggling with word problems. Because in lower grades they have a better chance of just guessing and getting the problems correct. As they get in the upper elementary grades they start getting more word problems wrong which makes that red flag go up that these students do not really understand word problems. This is why many teachers resent 3rd grade multiplication and division word problems.

Numberless Word Problems

Starting in first grade, or maybe even kindergarten, our students should be exposed to word problems without numbers. This will help them start developing an understanding of the word problem scenarios and not just guessing the operation. If you have not already checked out numberless word problems then you need to do that now. These have been in a game-changer in my classroom at getting students to understand the scenarios rather than just guessing the operation, that’s why I created FREE videos and a step by step guide to start using them in your classroom. In addition to everything I am telling you in the paragraph below, I use numberless word problems a couple of times a week as my number talks. When using numberless word problems, I am sure to go over one and two step multiplication and division word problems as well.

It’s more than just Multiplication and Division Word Problems Worksheets

So what strategies do I use to teach multiplication and division word problems? Well, to be honest, there are many. Word problems are not one of those skills that you will be able to teach in one day. Heck, you won’t even be able to have them master this skill in one week. They are a skill that you will need to practice for months before your students will ever have the chance to fully master this skill. Teaching word problems involves using many different strategies and interventions, not just one.

The first strategy I always use is taking out the numbers. I have them look at the scenario of the multiplication and division word problems. As they are looking at the scenarios, I have them act out what is happening in the problems. This means that I split my students into groups and give each group a word problem without any numbers. Then I give them time as a group to come up with a skit to show what is happening in their problem. After a few minutes, I then will display that group’s word problem on the board. They will read the problem to the class and then act out the skit. We do this strategy one day every couple of weeks, just to get in that repetition.

Finding keywords for multiplication and division word problems helps, but should not be the only way.

The next strategy I use is to CUBE the multiplication and division word problem. If you do not know what CUBES is then here is a short version. It is an acronym where each letter stands for a different thing to do in the word problem.

C-circle the numbers.

U-underline the question.

B-Box the keywords or math action words.

E-eliminate extra information or silly answer choices.

S-show your work to solve the problem.

This strategy is only beneficial if the students are doing it while actually thinking about what is happening in the problem. For instance, when I first taught this strategy as a first-year teacher I kept thinking this doesn’t work. Well, that was because the students were just going through the motions doing the steps,  rather than actually thinking about the word problem.

Oh and also a quick tip is to have your students identify the keywords. Do not just make a list of keywords and put them on the wall. It is more helpful for them to identify them on their own throughout the year and you just add to the chart each time!

The key ingredient for teaching word problems

Lastly, I provide many opportunities to practice with word problems as a class, with partners, and independently. You can do this through games, task cards, small group work, or even exit tickets. I have heard many many teachers looking for ways to get their students to become successful at word problems, but I have found that consistency is the key ingredient. You have to consistently practice word problems with and without numbers in order to help your student master this skill.

You can find many many multiplication and division word problems practice worksheets on Teachers Pay Teachers. This resource not only included multiplication and division worksheets, but it also includes multiplication and division games as well. I have an entire Multiplication and Division Bundle that covers everything from 1 step two-step problems, as well as strip diagrams, input-output tables, and equations.

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Help your students learn how to solve word problems

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Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
• Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

Most Popular Math Word Problems this Week

Arithmetic Word Problems

• Addition Word Problems One-Step Addition Word Problems Using Single-Digit Numbers One-Step Addition Word Problems Using Two-Digit Numbers
• Subtraction Word Problems Subtraction Facts Word Problems With Differences from 5 to 12
• Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
• Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
• Multi-Step Word Problems Easy Multi-Step Word Problems

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Word Problems and Multiplication

In our Word Problems and Multiplication lesson plan, students learn strategies for solving word problems that contain multiplication. They will practice writing word problems that require multiplication and will solve problems using multiplication.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to have students solve problems as a class using each of the strategies

Description

Additional information, what our word problems and multiplication lesson plan includes.

Lesson Objectives and Overview: Word Problems and Multiplication lesson plan lists several strategies for solving word problems using multiplication. Some of the strategies include making a diagram, eliminating possibilities, and looking for patterns. Several clue words are listed to help students know when multiplication is necessary to solve a word problem. At the end of the lesson, students will be able to solve word problems using multiplication. This lesson is for students in 3rd grade and 4th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. If you’d like to add to the activity worksheet, you can have students draw cards with pictures on them to determine what their multiplication problems should be about. For an additional activity, you can have students solve problems as a class using each of the strategies. Finally, you can also have students work together to create a poster that shows their strategy for solving a word problem.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.

WORD PROBLEMS AND MULTIPLICATION LESSON PLAN CONTENT PAGES

The Word Problems and Multiplication lesson plan includes two content pages. The lesson begins by reminding students that they complete math problems every day without thinking about it. There are many real-world situations that require you to use different math operations, like multiplication. You can use different strategies to solve multiplication word problems.

The first thing you should do when solving a multiplication word problem is to explore! You should figure out what you already know, what information the problem gave to you, what you need to find out, and what question is being asked.

The second step is to plan. You need to decide what strategy you’re going to use to solve the problem. The lesson lists some problem solving strategies that you can think about using, including guess and check, look for a pattern, make an organized list, and draw a diagram.

The third step is to solve by using your chosen problem solving strategy. During this step, you’ll do all of the actual math. It’s important to have already identifies the key words in the word problem, because these will tell you which operation you will need to use (this lesson only uses multiplication, but other word problems will require the use of addition, subtraction, and division). Some words and phrases that indicate that you need to use multiplication are times, rate, each , and product of . The lesson also lists a few more.

The fourth step is to examine. You should re-read the question to make sure your answer makes sense, and check your work. If your answer doesn’t make sense for the problem, try solving using a different strategy.

The lesson then delves into two different example problems and shows how to solve them step-by-step using the four steps described above.

WORD PROBLEMS AND MULTIPLICATION LESSON PLAN WORKSHEETS

The Word Problems and Multiplication lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

CREATE YOUR OWN ACTIVITY WORKSHEET

For the activity worksheet, students will write their own multiplication problems using the pictures shown on the worksheet and numbers 100 or less.

SOLVING WORD PROBLEMS PRACTICE WORKSHEET

The practice worksheet asks students to solve four word problems.

WORD PROBLEMS AND MULTIPLICATION HOMEWORK ASSIGNMENT

For the homework assignment, students will write their own multiplication word problems (like the activity worksheet). They should be creative, use numbers 100 or less, and attach a picture if they want.

This lesson includes a quiz to test students’ understanding of the lesson material. For the quix, students will solve a multiplication word problem.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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Strategies for Solving Word Problems – Math

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

• Circle any numbers you’ll use.
• Lightly cross out any information you don’t need.
• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. 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!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

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 (no, really).

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.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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How to Solve Multi-Step Word Problems

Multi-step word problems may initially seem daunting, but with a structured approach, they become manageable and less intimidating. Here, we provide a step-by-step guide to help you navigate these complex problems with ease.

A Step-by-step Guide to Solving Multi-Step Word Problems

Step 1: understand the problem.

The first step in solving multi-step word problems is to read the problem carefully. Look for keywords and phrases that suggest what arithmetic operation(s) you will need to apply. Words like ‘in total’, ‘altogether’ or ‘sum’ suggest an addition, ‘less than’ or ‘remain’ hint towards subtraction, ‘product’ or ‘times’ indicate multiplication, and ‘quotient’ or ‘divided by’ point to division.

Step 2: Identify the Steps Needed

After understanding the problem, list out the necessary steps to reach the solution. Each word problem is a unique puzzle with its sequence of operations. Some problems may require you to perform multiplication before addition, while others may need subtraction followed by division.

Step 3: Assign Variables

For problems with unknown quantities, assign a variable (for example, \(X\) or \(Y\)) to each unknown. This strategy makes it easier to organize information and apply arithmetic operations.

Step 4: Write Equations

Formulate equations based on the identified steps and assigned variables. Keep in mind the order of operations (BIDMAS/BODMAS) – Brackets, Indices/Orders, Division and Multiplication (from left to right), Addition, and Subtraction (from left to right).

Step 5: Solve the Equations

Solving the equations might require simple substitution or more advanced techniques like elimination or matrix method in the case of multiple variables. Don’t forget to check your solutions to make sure they satisfy the original equations.

Step 6: Answer the Question

Finally, ensure that your answer responds to the question asked in the problem. For example, if the problem is asking for the total number of apples, your answer should be a number and mention ‘apples’.

Practical Example

Let’s apply these steps to a sample problem: “Sarah bought \(2\) books. Each book cost twice as much as a pen. She bought \(4\) pens. If each pen cost \($5\), how much did she spend in total?”

Step 1: The problem involves multiplication (each book cost twice as much as a pen) and addition (total amount spent).

Step 2: First, find the cost of a book and then calculate the total cost.

Step 3: Let’s say \(X\) is the cost of a book.

Step 4: The equations will be \(X = 2 \times the\:cost\:of\:a\:pen\) and Total cost = cost of books + cost of pens.

Step 5: Substituting the given cost of a pen (\($5\)), we find \(X = $10\). The total cost is then calculated as \((2 \times $10) + (4 \times $5) = $40\).

Step 6: The total amount Sarah spent is \($40\).

In conclusion, with a systematic approach, you can effectively solve any multi-step word problem. Remember, practice is the key. The more problems you solve, the better you will become at identifying the necessary steps and solving them accurately.

by: Effortless Math Team about 11 months ago (category: Articles )

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Exploring the Power of the CUBES Math Strategy for Word Problems

Math problem-solving is one of the most challenging things we teach. The CUBES strategy is all about helping students tackle those tricky word problems with ease. Whether you’re dealing with pesky volume or area questions, or trying to figure out how many more apples Sally has than Timmy, the CUBES math strategy can be a great way to help those learners who struggle with word problems develop a systematic method to approach these problems. By breaking down the problem into smaller, more manageable chunks, you can quickly solve even the most complicated math problems.

So if you’ve ever found yourself scratching your head in frustration over your struggling learners’ battle with story problems, fear not! The CUBES math strategy is here to make your life a whole lot easier. Stick around to learn more about how this awesome strategy can help you help your struggling students become math problem-solving pros!

What is the CUBES Math Strategy?

The CUBES math strategy is a tool designed to help give students a systematic approach to breaking down and solving math word problems. The acronym C.U.B.E.S stands for:

• C ircle key numbers & units
• U nderline the question
• B ox math action words
• E valuate the problem
• S olve the problem & check your work

By breaking down the problem into these steps, students can better understand the context of the problem and effectively solve it.

Benefits of using the CUBES strategy in math word problems

While CUBES is not the ideal method for all math problem solving, especially as word problems become more complex, you can use the strategy as a starting point to guide struggling students in being more attentive and systematic when tackling word problems.

Many struggling learners struggle with executive functioning and need a clear-cut plan for tackling this next-level math skill, and incorporating a strategy like CUBES into your teaching can give them steps to approach word problems rather than leaving them overwhelmed and unsure where to begin. This can help students build confidence in their ability to successfully solve math story problems and prepare them to solve multi-step problems, ultimately enhancing their problem-solving skills.

Step-by-Step Guide to Using the CUBES Strategy

Implementing the CUBES strategy means teaching students the key steps and working through a gradual release process until they can effectively do this themselves. This systematic approach helps students understand the problem and empowers them to tackle word problems with confidence. Here’s a little more about each step your students will need to achieve:

C- Circle the numbers & units

C stands for “circle the key information.” This includes the numbers, units, and core information needed to solve the problem. This includes identifying math vocabulary that represents a number, such as “several,” “half,” or “a dozen.” Some questions may not involve numbers at all, in which case you would circle each instance of the word “none.” It is also important to identify units (such as feet, miles, or kilograms) and whether there is a decimal point.

While we don’t want students solely relying on keywords when faced with a word problem, it can be helpful for them to recognize which words are references to mathematical symbols. For example, “+” means addition, and “-” means subtraction.

U- Underline the question

After students read the problem and circle numbers/units, they must underline the question. While this may seem silly, if students aren’t attending to what is being asked, they won’t get the right answer. Helping students stay on target is a key component of the CUBES strategy for solving math problems.

Once your student has underlined the question and knows exactly what he or she needs to solve, it’s time to move on to step B: boxes and bullets.

B- Box math action words

Notice this doesn’t say keywords…Again, we don’t want students focused solely on using keywords for math problem solving. Research has shown time and time again this is an ineffective strategy once problems become more complex.

That said, students need to look at word problems through the lens of critical readers. What in the problem gives them a clue as to what they need to do to solve it?

Just like the author of a story gives us details to help us infer and get to the story’s resolution, the author of a word problem helps us find the path to the solution. We need to be critical readers to get there. This is where boxing key information can be helpful. Here are some common examples that are often viewed as keywords but are critical for students to attend to to solve problems accurately:

• Addition: add, added, both, sum, total
• Subtraction: difference between, less than
• Multiplication: times twice as many/much as of every
• Division: split equally among/between each share out of

E- Evaluate or Equation

At this stage, it’s time to implement your strategy to solve. For some students, this will be writing and solving the equation. Others may need to evaluate by drawing a picture or using manipulatives to model the problem.

Either way, by this stage your learners should have broken down the problem to the point that they feel confident implementing a method that will lead them to the final step – solving.

S- Solve & Check

Once the strategy has been chosen, guide your students through the process of solving the problem. This may involve writing out the equation, solving for the unknown variable, and checking their work to ensure they have found the correct solution.

Encourage your students to show their work and explain their reasoning as they solve the problem. This will not only help them understand the process better but also allow you to provide feedback and support if needed.

It’s important to emphasize the importance of checking their work to ensure they have found the correct solution. This may involve plugging the solution back into the original problem to verify it or checking their work for errors in calculations.

Once your students have successfully solved the problem, congratulate them on their hard work and encourage them to reflect on the process. Ask them questions such as what strategies worked well for them, what challenges they encountered, and how they can apply what they have learned to similar problems in the future.

By guiding your students through the process of problem-solving and encouraging them to reflect on their work, you are helping them develop essential critical thinking skills that will serve them well in all areas of their education and beyond. 

Tips for Implementing the CUBES Math Word Problem Strategy

Whenever you’re preparing to implement a strategy with your struggling learners, it can be helpful to get some tips from teachers who have been there. In asking for advice from colleagues, here’s what they had to say.

To teach the cubes strategy, you should:

• Teach the strategy as a whole. Because this is such a visual strategy, it’s useful to provide multiple examples of how to solve problems with CUBES on a poster or anchor chart. You can use the chart below as an example of what to include.
• Use a standard problem as an example. Before having students practice on their own, have them watch and listen as you model how to use the CUBES strategy on the board using a Problem of the Day or by writing in student journals. Visual learners will appreciate watching you write out each step and manipulate your complex number sentence cube.
• Use anchor charts you make together in class. Then transfer that knowledge into modeling one or two more examples with students using cubes they create out of construction paper, or if necessary, manipulatives like buttons or dry beans.
• Don’t fall into the trap that the standard algorithm is the only way to solve once the strategy has been used. Let students draw pictures, use manipulatives, make number lines, or whatever other strategies you’ve taught. The CUBES math strategy is to help them break up the problem. It isn’t the guiding principle of the math calculations.
• Students can use CUBES to filter out irrelevant details and focus on the essential details needed to solve the problem. By guiding students to evaluate the problem systematically, you can help students make informed decisions and tackle complex math challenges. It is great for learners who might get bogged down in all the details.

How to Successfully and Easily Teach Word Problems in Multiplication and Division

Eastern Shore Math Teacher

Are you looking for some practical ideas for teaching word problems in multiplication and division?  Word problems put multiplication and division equations into context and help students understand what is happening with the numbers.  Students need to start with acting out and then draw pictures and write equations for the word problems.  There are several different standards involving multiplication and division word problems for elementary students.  

Providing opportunities to do math puzzles daily is one way to help students be more successful with word problems.  If students know their facts, they can focus on understanding the problem and not on the computation. So get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. 

Students who feel successful in math class are happier and more engaged in learning.  Check out  The Bonus Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys for students to use in your classroom to cultivate a positive classroom community in mathematics.    You can also sign up for other freebies from me Here at Easternshoremathteacher.com .

I like to use literature and real-world situations to teach word problems using multiplication and division.   For example, students can see 4 plates with 3 cookies on each plate and then connect the repeated addition and multiplication equation to the word problems.   Students always connect with problems involving food! After reading a book or describing a situation, students can model the problem using equal groups or arrays and then write the equation.

Word Problems Using Multiplication 

Starting in 3rd-grade students learn about the concept of multiplication and begin to solve problems using multiplication with concrete materials. 

3.OA.A.1 Interpret products of whole numbers, e.g. interpret 5 X 7 as the total number of objects in 5 groups of 7 objects each.  For example, describe a context in which a total number of objects can be expressed as 5 X 7.

Students develop an initial understanding of the multiplication of whole numbers by modeling situations and understanding the meaning of the numbers (factors), and total (product).

The symbol X means groups of (or times).  

Teachers should provide students with a variety of multiplication situations to model using concrete materials. Ask students to identify the number of groups, the number of items in each group, and the total number of items.   Next, introduce students to numerical representations by writing equations that represent their models.  

Check out this Repeated Addition to Multiplication Resource .  

Word Problems Using Division

Once students have been introduced to multiplication, they can begin to learn the concept of division by using concrete materials. 

3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g. interpret 56➗8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.   For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ➗8.

Division can be understood by thinking in terms of finding a missing factor (either the number of groups or the number of items in a group). There are two meanings of division fair share and repeated subtraction.  

In fair share, you know the total number of items (product), and the number of groups (factor) and you are looking for the number of items to put in each bag (missing factor).  

In repeated subtraction, you know the total number of items (product) and the number of items for each group (factor) and you are looking for the number of groups that can be made.  

Teachers should provide a variety of division situations for students to model using concrete materials.  Opportunities to identify the information in the problem and the missing information should be provided.  Next, the information should be connected to symbolic representation and expressions.  

Word Problems Division and Multiplication

As students learn about the concept of multiplication and division, they can be introduced to word problems to act out.

3. OA. A. 3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.  

It is important for students to have many opportunities to use concrete materials to model the situations and identify the number of groups and the number of items in a group. Then, once students have an understanding, they can begin to draw pictures.  

In 4th grade, students continue to solve multiplication and division word problems.  In addition, they are introduced to comparison word problems.  

4.OA.A.2 Multiply or divide to solve word problems involving comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.  

Teachers should provide a variety of multiplicative comparisons for students to model, describe, and solve. In addition, students should make connections between models (such as bar models) and written equations.    Here are some examples of Multiplicative Comparison Problems .

In addition, in 4th-grade, students will multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers using the area model.  Check out this resource to help with using the area model with students.  

Don’t forget to incorporate all the different Multiplication and Divison Problem Situations

Word Problems with Two Step Equations

After students have had opportunities to solve multiplication and division word problems, they begin to solve two-step word problems that include more than one operation.  

3.OA.D.8  Solve two-step word problems using the four operations. First, represent these problems using equations with a letter standing for the unknown quantity. Then, assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

This continues into 4th grade with problems where students need to interpret remainders.  

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

Read more… What’s the Best Proven Way to Teach Word Problems with Two Step Equations?

Problem Solving Teaching Methods

Teaching students these 4 steps for solving problems allows them to have a process for unpacking complex problems.  

As you teach, model the process of using these 4 steps to solve problems.   Then, encourage students to use these steps as they solve problems.   Click here for Posters, Bookmarks, and Labels to use in your classroom to promote the use of the problem solving steps in math.  

Understand the Problem

 Read & Think

• Circle the needed information and underline the question. 
• Write an answer STEM sentence.  There are_____ pages left to read. 

Plan Out How to Solve the Problem

Make a Plan

• Use a strategy.  (Draw a Picture, Work Backwards, Look for a Pattern, Create a Table, Bar Model)
• Use math tools.

Do the Problem

Solve the Problem

• Show your work to solve the problem.  This could include an equation. 

Check Your Work on the Problem

Answer & Check

• Write the answer into the answer stem.
• Does your answer make sense?
• Check your work using a different strategy.

Check out these Printables for Problem Solving Steps in Math .

Ideas to Teach Word Problems of Multiplication and Division

Using literature.

There are so many great books to use to teach multiplication and division.  Books help students understand what is happening with numbers and connect it to the real world.  Two great books to use are:

• Amanda Bean’s Amazing Dream by Cindy Neuschwander is another fun book that will help kids see the importance of multiplication.   Amanda Bean loves to count but isn’t sure why she needs to learn multiplication. Until she has a crazy dream full of sheep on bicycles, knitting grannies, and more, and she can’t count them fast enough.  The focus of this book is on repeated addition (and why multiplication is a “faster way to count”). The pictures also include lots of examples of arrays. 
• The Doorbell Rang by Pat Hutchins is an excellent book for introducing division as sharing equally. Sam and Victoria are just about to sit down and enjoy fresh cookies when two friends arrive, and the four children divide up the cookies four ways. Soon, the doorbell rings again, and then again, and each time the number of cookies per person dwindles.

Click here for a list of books to use when teaching multiplication and division.

Acting it Out or Modeling

Using concrete materials to act our or model problems is essential. For example, after reading a book or giving students a situation, give them materials to act out the problem.    For example, after reading The Doorbell Rang, you could provide students with plates and cookies to act out the situation.  

Eventually, students can begin to draw pictures and write equations to represent the problems.  

Using 4 Steps to Solve Problems

Providing students with a method for unpacking word problems is essential.   Model using the 4 steps for solving word problems and support students in using the steps for solving word problems.    Click here for Posters, Bookmarks, and Labels to use in your classroom to promote the use of the problem solving steps in math.  

Read more… 4 Best Steps To Problem Solving in Math That Lead to Results .

Teaching Resources for Multiplication and Division Word Problems

• Division and Multiplication Word Problems- Digital and Print
• Repeated Addition to Multiplication Resource .  
• Multiplicative Comparison Problems
• Problem Solving Steps in Math
• Multiplication Area Model

Additional Resources

• How Do You Successfully Teach Word Problems in Addition and Subtraction?
• What’s the Best Proven Way to Teach Word Problems with Two Step Equations?
• 4 Best Steps To Problem Solving in Math That Lead to Results
• How to Solve Multiplication and Divison Word Problems Video

Word Problems with Multiplication and Division 

Start with a good book, and have students act out the problem, and you are on your way to building a conceptual understanding of multiplication and division word problems.  By using the 4 steps to problem solving with students, you are helping them unpack the problem and make a plan for solving the problem.  

Providing opportunities to do math puzzles daily is one way to help students be more successful with word problems.  If students know their facts, they can focus on understanding the problem and not on the computation. So get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students.  You can also sign up to receive other freebies from me Here at Easternshoremathteacher.com . 

Check out  The Free Ultimate Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys to use in your classroom. 

Students need to act out and visualize what is happening in word problems to be successful.  Using these ideas will help students build their understanding and lay the foundation for more complex problems.  What ideas do you have for teaching word problems in multiplication and division?

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Multiplication Word Problem Worksheets

This page hosts a vast collection of multiplication word problems for 3rd grade, 4th grade, and 5th grade kids, based on real-life scenarios, practical applications, interesting facts, and vibrant themes. Featured here are various word problems ranging from basic single-digit multiplication to two-digit and three-digit multiplication. Another set of printable worksheets hone children's multiplication skill by multiplying large numbers. Free worksheets are included.

Single-digit Multiplication Word Problems

The printable PDF worksheets presented here involve single-digit multiplication word problems. Each worksheet carries five word problems based on day-to-day scenarios.

• Download the set

Multiplication Word Problems: Two-digit times Single-digit

The word problems featured here require a grade 3 learner to find the product by multiplying a two-digit number by a single-digit multiplier.

Multiplication Word Problems: Two-digit times Two-digit

The worksheets presented here involve multiplication of two-digit numbers. Read the word problems and find the product. Apply long multiplication (also known as column multiplication) method for easy calculation.

Theme Based Word Problems

Our engaging theme-based pdf worksheets help young minds understand the fundamentals of multiplication. Answer the word problems based on three fascinating themes - Winter Season, Ice rink and Library.

Multiplication Word Problems: Three-digit times Two-digit

Read the word problems featured in these printable worksheets for grade 4 and find the product of three-digit and two-digit numbers. Write down your answers and use the answer key below to check if they are right.

Three-digit Multiplication Word Problems

Solve these well-researched word problems that involve three-digit multiplication. Perform multiplication operation and carry over numbers carefully to find the product.

Multiplication: Three or Four-digit times Single-digit

The word problems featured here are based on practical applications and fact-based situations. Multiply a three or four-digit number by a single-digit multiplier to find the correct product.

Multi-digit Word Problems: Multiplying Large Numbers

Sharpen your skills by solving these engaging multi-digit word problems for grade 5. Apply long multiplication method to solve the problems. Use the answer key to check your answers.

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Fifth Grade

Multiplication

" class="arrow-title-img"> Multiplication Word Problems

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Easy-to-remember strategies for easy solving grade 5 multiplication word problems.

Get more contents on multiplication word problems..., all practices skills about multiplication word problems.

• Multiplying by one digit numbers word problems
• Multiply numbers ending in zeros word problems
• Multiplying by two digit word problems
• Multiplying three or more numbers word problems
• Multiplying decimals by whole numbers word problems
• Multiplying two fractions word problems
• Multiplying mixed numbers word problems
• Multiply by 1 digit numbers
• Multiplication patterns over increasing place values
• Multiply numbers ending with zeros
• Properties of multiplication
• Choose numbers with a particular product
• Estimate products
• Box multiplication
• Lattice multiplication
• Multiply by 2 digit numbers complete the missing steps
• Multiply 2 digit numbers by 2 digit numbers
• Multiply 2 digit numbers by 3 digit numbers
• Multiply 2 digit numbers by larger numbers
• Multiply three or more numbers up to 2 digits each
• Multiply by 3 digits numbers
• Multiply three numbers up to 3 digits each
• Inequalities with multiplication
• Multiplication input output tables
• Multiplication input output tables find the rule
• Multiply a decimal by a power of ten
• Multiply by a power of ten with decimals, find the missing number
• Multiply by a one digit whole number using blocks
• Multiply a decimal by a 1 digit whole number using the distributive property
• Multiply a decimal by one digit whole number
• Multiply a decimal by two digit whole number
• Multiply three or more numbers one of which is a decimal
• Multiply decimals using grids
• Multiply 2 decimals products up to hundredth and thousandths
• Inequalities with decimal multiplication products up to thousandths

In a bid to attract your kid’s attention to engage in this great resource, we have developed easy-to-remember strategies for easy solving grade 5 multiplication word problems.

In fact, apart from our very interesting, captivating and simple problems, your kids will be guided with fun multiplication rules for multiplying by 1, 2, 3 to 12.

Moreover, when it comes to calculating problems with two and more digit numbers, it will be very easy to solve, as your kids has been provided with simple solutions for multiplying 2-digits, and larger digit numbers efficiently.

All these Multiplication methods worksheets pdf- how to multiply big numbers fast are given to make multiplication word problems grade 5 simple and enjoyable.

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A Math Word Problem Framework That Fosters Conceptual Thinking

This strategy for selecting and teaching word problems guides students to develop their understanding of math concepts.

Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts. Many students, however, struggle with word problems because of the various cognitive demands. As districtwide STEAM professional development specialists, we’ve spent a lot of time focusing on supporting our colleagues and students to ensure their success with word problems. We found that selecting the right word problems, as well as focusing on conceptual understanding rather than procedural knowledge, provides our students with real growth.

As our thinking evolved, we began to instill a routine that supports teaching students to solve with grit by putting them in the driver’s seat of the thinking. Below you’ll find the routine that we’ve found successful in helping students overcome the challenges of solving word problems.

Not all word problems are created equal

Prior to any instruction, we always consider the quality of the task for teaching and learning. In our process, we use word problems as the path to mathematics instruction. When selecting the mathematical tasks for students, we always consider the following questions:

• Does the task align with the learning goals and standards?
• Will the task engage and challenge students at an appropriate level, providing both a sense of accomplishment and further opportunities for growth?
• Is the task open or closed? Open tasks provide multiple pathways to foster a deeper understanding of mathematical concepts and skills. Closed tasks can still provide a deep understanding of mathematical concepts and skills if the task requires a high level of cognitive demand. 
• Does the task encourage critical thinking and problem-solving skills?
• Will the task allow students to see the relevance of mathematics to real-world situations?
• Does the task promote creativity and encourage students to make connections between mathematical concepts and other areas of their lives?

If we can answer yes to as many of these questions as possible, we can be assured that our tasks are rich. There are further insights for rich math tasks on NRICH and sample tasks on Illustrative Mathematics and K-5 Math Teaching Resources .

Developing conceptual understanding

Once we’ve selected the rich math tasks, developing conceptual understanding becomes our instructional focus. We present students with Numberless Word Problems and simultaneously use a word problem framework to focus on analysis of the text and to build conceptual understanding, rather than just memorization of formulas and procedures. 

• First we remove all of the numbers and have students read the problem focusing on who or what the problem is about; they visualize and connect the scenario to their lives and experiences. 
• Next we have our students rewrite the question as a statement to ensure that they understand the questions.
• Then we have our students read the problem again and have them think analytically. They ask themselves these questions: Are there parts? Is there a whole? Are things joining or separating? Is there a comparison? 
• Once that’s completed, we reveal the numbers in the problem. We have the students read the problem again to determine if they have enough information to develop a model and translate it into an equation that can be solved.
• After they’ve solved their equation, we have students compare it against their model to check their answer.  

Collaboration and workspace are key to building the thinking

To build the thinking necessary in the math classroom , we have students work in visibly random collaborative groups (random groups of three for grades 3 through 12, random groups of two for grades 1 and 2). With random groupings, we’ve found that students don’t enter their groups with predetermined roles, and all students contribute to the thinking.

For reluctant learners, we make sure these students serve as the scribe within the group documenting each member’s contribution. We also make sure to use nonpermanent vertical workspaces (whiteboards, windows [using dry-erase markers], large adhesive-backed chart paper, etc.). The vertical workspace provides accessibility for our diverse learners and promotes problem-solving because our students break down complex problems into smaller, manageable steps. The vertical workspaces also provide a visually appealing and organized way for our students to show their work.  We’ve witnessed how these workspaces help hold their attention and improve their focus on the task at hand.

Facilitate and provide feedback to move the thinking along

As students grapple with the task, the teacher floats among the collaborative groups, facilitates conversations, and gives the students feedback. Students are encouraged to look at the work of other groups or to provide a second strategy or model to support their thinking. Students take ownership and make sense of the problem, attempt solutions, and try to support their thinking with models, equations, charts, graphs, words, etc. They work through the problem collaboratively, justifying their work in their small group. In essence, they’re constructing their knowledge and preparing to share their work with the rest of the class. 

Word problems are a powerful tool for teaching math concepts to students. They offer a practical and relatable approach to problem-solving, enabling students to understand the relevance of math in real-life situations. Through word problems, students learn to apply mathematical principles and logical reasoning to solve complex problems. 

Moreover, word problems also enhance critical thinking, analytical skills, and decision-making abilities. Incorporating word problems into math lessons is an effective way to make math engaging, meaningful, and applicable to everyday life.

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Multiplication Word Problems 4th Grade

Welcome to our Multiplication Word Problems for 4th Grade. Here you will find our range of printable multiplication problems which will help your child apply and practice their multiplication and times tables skills to solve a range of 'real life' problems at a 4th grade level.

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• 4th Grade Multiplication Problems Worksheets
• Easier & Harder Multiplication Worksheets
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Multiplication Word Problems 4th Grade Online Quiz

Multiplication word problems, 4th grade multiplication problems.

Here you will find a range of problem solving worksheets involving multiplication.

Each sheet involves solving a range of written multiplication problems.

There are 3 levels of difficulty for each worksheet below: A,B and C.

Worksheet A is the easiest level, suitable for children at the beginning of their grade.

Worksheet B is a medium level worksheets for children who are working at the expected level in their grade.

Worksheet C is set at a harder level, suitable for children who are more able mathematicians.

The problems in each worksheet are similar in wording, but the numbers involved become trickier as the level gets harder.

To encourage careful checking and thinking skills, each sheet includes one 'trick' question which is not a multiplication problem. Children need to spot this word problem, and work out which operation they need to solve it.

Using these sheets will help your child to:

• apply their multiplication and times tables skills at a 4th grade level;
• apply their times table knowledge to work out related facts;
• recognise multiplication problems, and try to spot 'trick' problems;
• solve a range of 'real life' problems.

Some of the sheets have a UK version with spelling and currency symbols set for the UK.

4th Grade Multiplication Word Problem Sheets

Series 4 sheet 1 set.

• Series 4 Sheet 1A (easier)
• Series 4 Sheet 1B (medium)
• Series 4 Sheet 1C (hard)

• PDF Series 4.1 (6 sheets)
• PDF Series 4.1 UK version (6 sheets)

Series 4 Sheet 2 Set

• Series 4 Sheet 2A (easier)
• Series 4 Sheet 2B (medium)
• Series 4 Sheet 2C (hard)
• PDF Series 4.2 (6 sheets)
• PDF Series 4.2 UK version (6 sheets)

Series 4 Sheet 3 Set

• Series 4 Sheet 3A (easier)
• Series 4 Sheet 3B (medium)
• Series 4 Sheet 3C (hard)
• PDF version Series 4.3 (6 sheets)
• PDF version Series 4.3 UK version (6 sheets)

Multiplication Word Problems Walkthrough Video

This short video walkthrough shows several problems from our Multiplication Problems Worksheet 4.3A being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

Looking for some easier Multiplication Problems?

In our 3rd Grade Multiplication word problem area, you will find a range of multiplication problems aimed at 3rd graders.

The following areas are covered:

• basic multiplication fact sheets;
• multiplication facts to 10x10;
• 2 digits x 1 digit
• Multiplication Word Problem Worksheets 3rd Grade

Looking for some harder Multiplication Problems?

In our 5th Grade Multiplication word problem area, you will find a range of multiplication problems aimed at 5th graders.

• multiplication fact sheets;
• multiplication related facts to 10x10 e.g. 6 x 70, 8 x 0.6, etc;
• problems needing written multiplication methods to solve e.g. 2 digits x 2 digits, decimal multiplication
• Multiplication Problems Printable 5th Grade

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Looking for more 4th Grade Word Problems?

Here is our set of 4th grade math problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

• apply their addition, subtraction and problem solving skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

• 4th Grade Math Word Problems

Multiplication Times Table Charts

Here you will find a selection of Multiplication Times Table Charts to 10x10 or 12x12 to support your child in learning their multiplication facts.

There is a wide selection of multiplication charts including both color and black and white, smaller charts, filled charts and blank charts.

Using these charts will help your child to:

• Learn their multiplication facts to 10x10 or 12x12;
• Practice their multiplication table.

All the free printable Math charts in this section are informed by the Elementary Math Benchmarks.

• Large Multiplication Chart
• Large Multiplication Charts Times Tables
• Multiplication Times Tables Chart to 10x10
• Times Table Grid to 12x12
• Blank Multiplication Charts to 10x10
• Blank Printable Charts to 12x12
• Multiplication Math Games

Here you will find a range of Free Printable Multiplication Games.

The following games develop the Math skill of multiplying in a fun and motivating way.

• learn their multiplication facts;
• practice and improve their multiplication table recall;
• develop their strategic thinking skills.

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at solving multiplication word problems by tens and hundreds.

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Fun teaching resources & tips to help you teach math with confidence

How to Tackle Math Word Problems & Make Sense of Operations

Do your students struggle to make sense of math word problems? They’re not alone! Using meaningful word problem strategies can help kids make sense of operations & have confidence solving word problems.

As students learn the four math operations, it’s imperative that they learn to apply the operations to show higher level thinking.  Students should be able to determine which one to use and apply it to real-life situations , especially considering that our end goal is to create productive thinkers who can change the world.

One way we do this is by providing students with word problems that highlight the math operation and include problems that may happen in the real world .  Let’s explore some common reasons why students struggle with math word problems and learn two word problem strategies to help them overcome these challenges.

*This is a guest post from Jessica at Math with Purpose .

Common Reasons Students Struggle with Word Problems:

1. they’re developing reading comprehension skills.

It’s no surprise that word problems can be a challenge for many students.  After all, many of these students are developing their own reading skills and then being asked to read and interpret informational text in a word problem.

Many word problems include multiple steps which require students to infer what to do first.  In fact, the National Foundation for Educational Research found that poor inferring skills lead to poor comprehension.

It is a skill that students must be explicitly taught and is usually one of the later skills due to its complexity. That means our students are expected to do a higher level of reading comprehension every time they read that short word problem in math class !

2. They’re Relying Only On Keywords (Rather than the Meaning of Operations)

Students can encounter difficulty when translating words into mathematical symbols or equations. They may struggle to identify which mathematical operations are needed to solve the problem and how to represent the problem in a mathematical format.  Many teachers teach students to circle key words and memorize them to determine which operation to use.

Students may learn that addition means to “add to” or “make a total” while subtraction is an action of “taking away”.  Students look for keywords that they can circle to determine whether adding or subtracting.   But what happens when the action is there, but students actually need to solve using a different math operation? Here’s an example:

Gabbi had some stickers.  She earned 12 more stickers for completing her homework.  Now she has 56 stickers.  How many stickers did she have at first?

In this problem, it’s clearly an “add to” situation.  Gabbi is adding to her collection.  However, to solve the problem, a student would need to subtract from the total to find the missing part .

While keywords can help with some problems, they don’t actually work for the variety of word problems students will encounter .

In fact, according to the University of Arizona, students will solve 15 different addition and subtraction problem types by the end of Grade 2 and 9 different multiplication and division problem types by the end of Grade 4.

Read more about the problems with relying on key words in word problems here .

Word Problem Strategies to Help Students Comprehend Operations Before Solving

In order to help students comprehend and solve complicated word problems, math educators have to think like a reading teacher and acknowledge there is a whole set of skills required for students to do the mathematics.

Instead of using basic strategies such as circling key words and plugging in numbers that may work some of the time, teachers can push for greater depth and understanding using two easy word problem strategies .

1. Make connections to prior knowledge and experiences:

One of the first reading strategies students learn is to make a movie of the text in their head and make real-world connections to the story.  The most meaningful connections are text to self connections where students relate the text to their own lives.

Students can do the same thing with a word problem!  They can read the story and make a picture of what’s happening – maybe even act it out with real life objects .

Teachers can also change the nouns in the word problem to be more relatable for each class including student names in the problems and objects that they enjoy doing each day.  This one simple change will help students engage with the text and want to find out more.

2. Visualize the problem by drawing a picture:

Once students are connected to the story of the word problem, it’s time to connect it to mathematics .

Instead of relying on keywords, students can draw visuals of the part-whole, comparison or equal groups models to show what operation will be needed to solve the problem.

Through drawing bar models , students will identify the variable and lay the strong foundation for algebra even beginning in Grade 2.

These visuals aren’t complicated and can be taught easily while students are comprehending the word problem.  You can find out more about these visual models for word problems in this blog post and even snag free posters for each representation for your classroom.

Solving math word problems is a valuable skill that empowers students to apply mathematical knowledge in real-life situations , but it also requires students to use a variety of skills to accomplish.  By thinking like a reading teacher, math educators can employ the skills they use during reading to truly help students master word problems by making connections and visualizing the problem .

If you are looking for more support to help students walk through the variety of word problems they will encounter, consider The Problem Solving Handbook .

It includes 3 video lessons for each problem type, plus practice and challenge problems for students to truly master word problems.

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Join 165,000+ parents and teachers who learn new tips and strategies, as well as receive engaging resources to make math fun. Plus, receive my guide, "5 Games You Can Play Today to Make Math Fun," as my free gift to get you started!

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Multiplication word problems for grade 3

Simple multiplication.

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