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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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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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Multiplication Word Problem Worksheets 3rd Grade

Welcome to our Multiplication Word Problem Worksheets for 3rd 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.

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Multiplication Word Problems up to 10x10 Online Quiz

Multiplication word problem worksheets, 3rd 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 3rd 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.

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3rd Grade Multiplication Word Problem Worksheets

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• PDF version Series 3.2 (6 sheets)
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• PDF version Series 3.4 (6 sheets)

Looking for some easier Multiplication Problems?

In our 2nd Grade Multiplication word problem area, you will find a range of multiplication word problems aimed at 2nd graders.

The following areas are covered:

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• Multiplication Word Problems 2nd Grade

Looking for some harder Multiplication Problems?

In our 4th Grade Multiplication word problem area, you will find a range of multiplication word problems aimed at 4th graders.

• multiplication related facts to 10x10 e.g. 6 x 70;
• problems needing written multiplication methods to solve (e.g. HTU x U; TU x TU)
• Multiplication Word Problems 4th Grade

More Recommended Math Worksheets

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Looking for more 3rd Grade Word Problems?

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Using the sheets will help your child to:

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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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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.

Related Worksheets

» Addition Word Problems

» Subtraction Word Problems

» Division Word Problems

» Word Problems

» Multiplication

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Using multiplication to solve word problems, lesson plan.

• Printer Friendly Version
• Grade Levels 4th Grade
• Related Academic Standards CC.2.1.4.B.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. CC.2.2.4.A.1 Represent and solve problems involving the four operations.
• Assessment Anchors M04.A-T.2 Use place-value understanding and properties of operations to perform multi-digit arithmetic. M04.B-O.1 Use the four operations with whole numbers to solve problems.
• Eligible Content M04.A-T.2.1.2 Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers. M04.A-T.2.1.4 Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits × 1 digit, excluding powers of 10). M04.B-O.1.1.1 Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 × 8 or 24 = 8 × 3. M04.B-O.1.1.2 Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 × 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects.
• Competencies

Students learn different strategies to solve multiplication word problems. They will:

• create word problems that require the use of multiplication.
• create or match a number sentence to a word problem involving multiplication.
• identify different strategies and methods that can be used to solve multiplication word problems.

Essential Questions

• How are relationships represented mathematically?
• What makes a tool and/or strategy appropriate for a given task?
• Equivalence: The relationship between expressions which have an equal value.
• Multiple: The product of a given number and a whole number.

60–90 minutes

Prerequisite Skills

• Word Problem Template ( M-4-2-1_Word Problem Template.docx )
• Observation Checklist ( M-4-2-1_Observation Checklist.docx )
• Multiplication Practice worksheet and Multiplication Practice KEY ( M-4-2-1_Multiplication Practice.docx   and M-4-2-1_Multiplication Practice KEY.docx )
• base-ten blocks
• chart paper
• dry-erase boards

Related Unit and Lesson Plans

• Using Models and Algorithms to Solve Multiplication Problems
• Multiplication Using Arrays
• Partial Products

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

• Rags-to-Riches game http://www.quia.com/rr/10206.html

Formative Assessment

• Observe initial group work to see if students have a general understanding of problems that require multiplication to solve.
• Use the dry-erase board activities to help determine if students understand the two types of multiplication problems: sharing and grouping.
• Gauge whether students need additional instruction using the think-pair-share activity from the Routine section of the Extension.
• Use the Observation Checklist to measure individual student comprehension of the material.
• Teacher observation may be used to help guide the level of difficulty of instruction at any time during the lesson.

Suggested Instructional Supports

Instructional procedures.

“In today’s lesson, we are going to use multiplication to solve word problems. First, let’s make a list of key words or phrases that are related to the concept of multiplication. These will be like clues, helping us to know when to use multiplication. Now, can anyone think of some words or phrases that might be telling us to multiply?”

Allow students to brainstorm and call out key words or phrases as you write their suggestions on the board or overhead. (Some examples include times , per , each , every , product .)

“We are going to look at a few examples of word problems that require multiplication. Remember, when we see words from the list we created in a problem, it might be a clue telling us to use multiplication!”

Present the following word problem.

• At the amusement park, Kelly bought three strips of tickets. Each strip had four tickets. How many tickets did Kelly have?

“First of all, what are the ‘clues’ in the problem that indicate we need to multiply?” ( the word “each” )

“Work with your neighbor to generate two different ways of solving this problem.”

Give students a few minutes to develop two different solution methods. When they are finished, ask for volunteers to share their methods and record them on chart paper. Methods can include repeated addition (4 + 4 + 4 = 12); skip counting by 4s (4, 8, 12); writing a multiplication equation (3 × 4 = 12); and modeling using a manipulative (counters, chips) and then counting up the total.

“These are all good methods, and it is important to understand them all, but right now we are going to focus on writing multiplication equations.”

Give each student a dry-erase board. Present the following problems to students. For each problem, ask them to write a multiplication number sentence for the word problem on their dry-erase boards and hold the boards up. Remind students that when writing a number sentence for a multiplication problem, they need to use a multiplication symbol and an equal sign.

• The man selling cotton candy had five pink-colored bags. There were four times as many green-colored bags as pink. How many green-colored bags of cotton candy did the man have to sell?
• The man selling cotton candy had 15 bags of cotton candy to sell. Each bag cost $3 and he sold all the bags. How much money did he receive?
• There were five roller coasters at the amusement park. There were six times as many children’s rides as roller coasters. How many children’s rides were there?

“Can someone summarize how you know when to use multiplication to solve a word problem? What clues help you?” ( the key words)

“Now, see if you can create your own multiplication word problem. If we stick with the topic of an amusement park, can you create a word problem that would require multiplication? Think about the people, rides, games, food, tickets, and souvenir shops you might see at an amusement park. Take a few moments with the people around you and see if you can write a word problem that would require multiplication. Then record your problem on chart paper.”

Ask volunteers to share their problems. As a class, discuss if each example is indeed a word problem that requires multiplication. If so, ask students to write the corresponding multiplication number sentence necessary for solving. These problems, if authentic, can be used throughout the unit as review.

“A moment ago, we practiced solving multiplication word problems by writing multiplication equations. Now, we are going to talk about some different strategies using base-ten blocks. Let’s do an example together.”

Present the following problem.

• An amusement park ride has 12 cars. Each car can carry three people. How many people can the ride carry?

Provide the students with base-ten blocks. Encourage students to use the blocks (in more than one way) to solve the problem. Then have students record the process they used, along with number sentences for the solutions. Ask students to share their solutions. Two possible strategies might include making groups of three cubes and then counting up by threes 12 times or making a list of 12 threes to add (repeated addition). Other students might think (6 × 3) + (6 × 3). Students break apart products into the sum of simpler products using multiplication facts they know. Students may not know 12 × 3, but they know they can break 12 into two groups of 6. Another approach might be to break apart, or decompose, 12 to (10 + 2) and think (10 × 3) + (2 × 3).

As students discuss their strategies, point out how in each solution there are 10 groups of 3, with 2 extra groups of 3 that need to be added on. Record the following number sentence for students to see: (10 × 3) + (2 × 3) = 36.

“Is the equation true or false? (10 × 3) + (2 × 3) = 12 × 3. Why?” ( True. Both sides of the equation equal 36.) “What is another number sentence that is the same as 12 × 3?” Guide students to realize that any way of breaking up the 12 into a sum of two addends and multiplying each addend by 3 would work. ( Some examples include (9 × 3) + (3 × 3), (8 × 3) + (4 × 3), etc.)

Provide additional problems based on the amusement park context.

• An amusement park ride has seats arranged in long rows. There are 12 seats in each row. There are four rows. How many children can ride?
• Tickets for the rides are bought in books of 15 tickets per book. There are five children who want to ride the rides. An adult bought five books so each child could have one book. How many tickets did the adult buy in total?
• Karl took three rides before lunch and five times as many rides after lunch. How many rides did Karl take in total?
• One game at the amusement park cost $0.25. Karl wanted to play the game three times. How much would it cost to play three times?

“For each word problem, identify the key words that indicate multiplication and then write three equal multiplication equations that could be used.” Monitor performance and explanations. Post some of the strategies that students use on chart paper and have students discuss the similarities between the strategies. Encourage students to try decomposing numbers to solve the multiplication problems. For example, use the above problems: 12  4 = (10 × 4) + (2 × 4) and 15 × 5 = (10 × 5) + (5 × 5), etc.

Station Rotation

Set up three work stations for students. Station 1 will provide word problems that focus on equation writing. Station 2 will offer students an opportunity to practice writing word problems. Station 3 will focus on writing numbers in expanded notation (distributive property over addition).While students are working at each station, monitor student progress. Provide necessary interventions and support as needed. Keep track of student understanding on the Observation Checklist ( M-4-2-1_Observation Checklist.docx ).

Station 1: Writing Equations

Provide the following word problems for Station 1. Ask students to use different strategies to solve the problems and create as many varied equations as they can to solve the problems. Use the first word problem below to model that equations have equal signs.

• 3 × 15 = 15 + 15 + 15 = ____.
• On the classroom bookshelf, students counted eight mysteries. There were three times as many realistic fiction books as mysteries. How many realistic fiction books were on the classroom bookshelf?
• A farmer planted 16 rows of tomatoes. The farmer planted five tomato plants in each row. How many tomato plants did the farmer plant?

Station 2: Writing Multiplication Word Problems

For Station 2, students will use the Word Problem Template ( M-4-2-1_Word Problem Template.docx ) to create two different word problems that require multiplication to solve. Ask them to show at least two strategies they could use to solve each problem.

Station 3: Writing Numbers in Expanded Notation (Distributive Property over Addition)

For Station 3, provide the following number sentences and ask students to explain if the sentences are true or false and how they know.

• (10 × 4) + (3 × 4) = 13 × 4
• 24 × 4 = (20 × 2) + (4 × 2)
• 18 × 6 = (10 × 6) + (8 × 6)

Use base-ten blocks to model a multiplication problem. Ask students to write the number sentence that matches the model on a dry-erase board and hold it up. Repeat by modeling two or three other examples for students. Then have students explain to a partner how they would solve a problem like 14 × 5. Observe and listen to students to monitor for understanding. Correct any misunderstandings.

Ask students to solve 18 ×7 as a journal response. Then have students explain what they did and why they did each step. Finally ask students to explain why they used the strategy they did to solve the problem.

• Routine: Write a two-digit by one-digit multiplication problem on the board. Have students individually think about, then write down, two different ways to represent the problem. Pair students up and have the partners share representations. Discuss the results. This think-pair-share activity can be used as a warm-up at the beginning of another class session or as an exit ticket for this lesson.
• Expansion: Have students make a poster showing different ways of solving one-digit by two-digit multiplication problems. They can put each strategy into its own column and title it. Or have students who have mastered the concepts explain strategies to students who need assistance.

Students can also use the technique of writing in expanded notation to solve a multiplication problem: 18 × 6 = (10 × 6) + (10 × 6) − (2 × 6). Ask students if they can explain why this works. Breaking apart 18 into 10s can help in solving this problem. One group of 10 is not enough; 2 groups of 10 are too much. Students should see that instead of using 18 groups of 6 as the original problem states, estimation is used. Since the number of groups is overestimated by 2, the two extra groups of 6 have to be subtracted. Once students are able to explain why this method works, have them try to create other multiplication problems where this method can be used. Students can then exchange multiplication problems with a partner and try to solve the problems using expanded notation.

• Small Group: Use the Multiplication Practice worksheet ( M-4-2-1_Multiplication Practice.docx ). This worksheet has been created specifically for small-groups of students.
• Technology Connection: Have students practice two-digit multiplication with the Rags-to-Riches game. In this game, the focus is on tens and on place value. Students practice their multiplication skills and get results immediately. See Rags-to-Riches at http://www.quia.com/rr/10206.html .

Related Instructional Videos

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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Multiplication Word Problems — Examples & Practice - Expii

Multiplication word problems — examples & practice, explanations (3).

Words to Math: Multiplication

In this section, we will learn to translate phrases into a mathematical expression by identifying key words that indicate multiplication .

When talking about multiplication, you will most likely see the terms " times ", " multiplied by ", " product of ", and " by a factor of ".

Let’s take a look at an example.

Sarah went to the grocery store to buy oranges. She realized that each bag of oranges contained 4 oranges.

Image source: By Clker-Free-Vector-Images CC0 , via pixabay.com

She bought 5 bags of oranges. How many oranges did she buy in total?

We know that the term " of " often refers to multiplication, so the operator ‘×’ is required.

The term " total " refers to equality, so the operator ‘=‘ can be used.

Since Sarah bought 5 bags of oranges and each bag contains 4 oranges, we can rewrite this into a mathematical expression.

Total Number of Oranges = 5 Bags × 4 Oranges = 20 Oranges

When talking about equality, you will most likely see the terms " equal to ", " is ", " the same as ", and " amounts to ".

Here are some phrases about multiplication translated into a mathematical expression .

• 4 times 5 equals 20→4⋅5=20
• The product of 11 and 3 amounts to 33→11⋅3=33
• 7 multiplied by a number →7⋅x
• 8 by 9 plank of wood →8⋅9

We are now going to take a look at some of the types of problems you might encounter about multiplication word problems.

Example 1 Translate the following into a mathematical expression:

8 times 7 is 56.

Related Lessons

(video) solving multiplication and division word problems.

by Ruth Erquiaga

Ruth Erquiaga has a very good explanation and strategy on how to identify and approach word problems. Specifically, the video focuses on multiplication and division .

The key word that designates multiplication or division is " each ". " Each " means that the groups being combined or split up need to be equal in size, which is true of multiplication and division, but not necessarily true of addition and subtraction .

Other words like " total ", " area ", " in all ", and " altogether " can designate multiplication or division as long as the context of the problem allows you to work with equal sized groups.

The video covers a general strategy for translating word problems.

• Read the problem entirely
• Find if the total is given. A given total means that the problem will be division or subtraction. No given total means the problem will be addition or multiplication.
• Find if the groups are equal. Equal groups will mean multiplication or division. Unequal groups will mean addition or subtraction.

From steps 2 and 3, you can conclude which operation you need to do!

Word Problems with Multiplication

The key to solving word problems is to translate them into mathematical expressions. This is made easier if you can pick out key phrases that tell you what type of operation the problem is asking for. We'll call these signal words .

Image source: By K Whiteford CC0 via publicdomainpictures.net

Which signal word tells us that we need to use multiplication for this problem?

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Example problems

1.  Write a multiplication sentence to each problem and solve.  You can draw pictures to help you.

Word problems with two operations

In the following week, he ate three times on Monday, Tuesday, and Friday, and four times on the rest of the days.  How many meals did he eat during the week?

Now we have the one kind of situation three times, and the other kind of situation four times.  We calculate those separately, and then add.

1.  Fill in the numbers to the number sentences for each problem, and solve.  For the last problems, write the number sentence yourself.  You can write words above the numbers to describe the numbers.  You can also draw pictures to help you!

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Course: 3rd grade   >   Unit 7

• Multiplication word problem: soda party
• Division word problem: blueberries

Multiplication and division word problems (within 100)

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

• Grades 6-12
• School Leaders

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14 Effective Ways to Help Your Students Conquer Math Word Problems

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

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

1. Solve word problems regularly

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

Learn more: Teaching With Jennifer Findlay

2. Teach problem-solving routines

There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.

Learn more: Word Problems Made Easy

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3. Visualize or model the problem

Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.

Learn more: Math Geek Mama

4. Make sure they identify the actual question

Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed. 

Learn more: Robert Kaplinsky

5. Remove the numbers

It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking. 

Learn more: Where the Magic Happens Teaching

6. Try the CUBES method

This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.

Learn more: Teaching With a Mountain View

7. Show word problems the LOVE

Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use. 

8. Consider teaching word problem key words

This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.

Learn more: Book Units Teacher

9. Determine the operation for the situation

Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.

Learn more: Solving Word Problems With Jennifer Findlay

10. Differentiate word problems to build skills

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

Learn more: Differentiating Math 

11. Ensure they can justify their answers

One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.

Learn more: Madly Learning

12. Write the answer in a sentence

When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.

Learn more: Multi-Step Word Problems

13. Add rigor to your word problems

A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.

Learn more: The Routty Math Teacher and Alyssa Teaches

14. Use a problem-solving rounds activity.

Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.

Learn more: Teacher Trap

Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .

Plus, 60+ Awesome Websites For Teaching and Learning Math .

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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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• 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.

Teachers would you like a strategy that will help your students finally understand how to solve word problems rather than guessing?

Sign up now and receive tips and freebies and access this amazing strategy.

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Rachel Griffith

I help teachers and student grow academically. I am from a small town in Texas and enjoy helping others be successful. You will pretty much always find me sitting on the computer working unless I am chasing around my two little ones. 

Help your students learn how to solve word problems

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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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