write and solve a story problem to add 12 and 18

Story Problems

Once you know your basic operations ( addition , subtraction , multiplication , division ), you will encounter story problems, also known as word problems, which require you to read a problem and decide which operation to perform in order to get the answer. There are key words here that often indicate which operation you will use. We will give you a list of them, but remember that for many problems, there may not be a key word, and you’ll have to use your best judgment in order to figure out what to do!

Here are the key words:

For addition:

In addition to, sum, total, more than, altogether, in all, combined, extra, raise, plus, both, additional

For subtraction:

How many more, difference, how many less, fewer, left (sometimes, left over), change, lost, decreased (by), less, remain, take away

For multiplication:

How many times, times, multiplied by, of, every, product, by, twice as much, three times as much (and so on), rate, at this rate, doubled, tripled (and so on), in all

For division:

How much/many will each receive?, divided among, split up between, per, ratio, percent, each, divide (or split) evenly, cut, average, share, quotient, equally (split, divided, etc)

For telling that something equals another amount:

is/are, yields

In order to solve a story (word) problem successfully:

• Read the entire problem thoroughly
• Make a list of the numerical (number) information you’ll need. If the numbers have units attached (for example, 12 inches), make sure you attach units in your list so you don’t get confused.
• Write out the number equation you’ll need to solve.
• Complete the solving process carefully.
• When you get your answer, reread the problem and ask yourself, “Does this answer make sense?”
• Remember to label your answer with the correct units, if needed.

Example Story Problems

In this section, we’ll give you several examples of story (word) problems, starting with simple problems and working up towards more complex problems.

Nick had 8 toy trucks in his toy box. His friend Nathan brought over 3 more toy trucks. How many toy trucks did the boys have altogether?

What is the key word in this problem?

If you look back at the list of key words at the top of the page, you’ll find that altogether listed as a key word.

Altogether is our key word. Now, what operation will we have to perform to get the answer to this problem?

We know we’ll have to do addition, because altogether is a key word that means adding.

Now, what will our problem look like?

We know we’ll be adding together 8 + 3, because those were the two numbers mentioned in the problem.

What is 8 + 3?

Therefore, our answer is 11 toy trucks altogether.

Now, let’s try another one.

John had 15 books on his bookshelf. John’s dog, Buster, came in and slobbered all over four of them. How many books did John have left that were not slobbered on?

If you look back at the list of key words at the top of the page, you’ll find that left is listed as a key word.

Left is our key word. Now, what operation will we have to perform to get the answer to this problem?

We know we’ll have to do subtraction, because left is a key word that means subtract.

This problem is a subtraction problem. Now, let’s get it set up. How will this problem look?

We know we’ll be subtracting 15 – 4, because those were the two numbers mentioned in the problem.

Now, perform the subtraction. What is 15 – 4?

Our final answer is 11 books.

Now, let’s try a couple harder problems.

Dan is getting ready to go to a concert. He wants to figure out how many people will be there. He knows that there are 250 rows of seats, and each row has 40 seats in it. How many seats are there in the concert hall in all?

If you look back at the list of key words at the top of the page, you’ll find that in all is listed as a key word.

In all is our key word. Now, what operation will we have to perform to get the answer to this problem?

We choose multiplication because we see the keyword in all, but also because it makes sense. Essentially this may be seen as an addition problem, which is why the keyword is also in the addition section, but since the adding of the rows would all be the same, we can multiply to make the process faster.

This problem is a multiplication problem. Now, let’s get it set up. How will this problem look?

We would use 250 x 40 because we decided that this is a multiplication problem. Since we want to figure out a total number of seats in the hall, we’re going to multiply the two given numbers together, as if we were calculating area.

Now, perform the multiplication. What is 250 x 40?

Our final answer is that there are 10,000 seats at the concert Dan is attending.

Let’s look at one more example. Three friends go out to dinner. Near the end, they get the bill and they owe the restaurant $27.89. They want to split the bill evenly between the three of them. How much will each person pay?

If you look back at the list of key words at the top of the page, you’ll find that split evenly is listed as a key word.

Evenly is our key word. Now, what operation will we have to perform to get the answer to this problem?

We choose division because we see the keywords “split” and “evenly.” Also, division makes sense because they want to divide the bill between three people. Because they’re splitting it up, we would choose division.

This problem is a division problem. Now, let’s get it set up. What would our equation be?

We choose $27.89 / 3 because we know we have to split up the amount of money, $27.89, between the three friends, so we know we have to divide by three.

Now, perform the division. What is $27.89 / 3? (Round to the nearest cent)

When we divide, we get an answer of 9.2966666, with a repeating 6 at the end. We want to round it to the nearest cent, which is the hundredths place after the decimal. We see that that number is already a 9, and a 6 after it means round up. However, we can’t make one place value a ten, so we increase the tenths digit by one, turning the 2 into a 3. If this doesn’t make sense, please read rounding numbers . Thus, your final answer is $9.30 after rounding.

Now, let’s go through some harder story (word) problems. All of the story problems we’ve done have had only one step, and we’ve been able to easily decide if they are addition, subtraction, multiplication, or division. However, some story problems have more than one step, involving more than one key word and/or operation. We’ll show you a few of these now.

Carly is making a dress. She needs 1 yard of yellow fabric, 1.5 yards of purple fabric, and .5 yards of green fabric. Yellow fabric costs $5.95 per yard, purple fabric costs $3.95 per yard, and green fabric is on sale for $7.00 per yard. How much will she spend in all if she buys just enough fabric to make her dress? (Ignore tax in your calculations). Click Next Step for the first part of the solution.

First, we have to figure out how much Carly is spending on each amount of fabric; then, we can use the key word “in all” which tells us that we need to add the amounts together for a final total. In order to figure out how much each piece of fabric costs, we need to multiply the price by the amount she needs to get a total.

First, let’s calculate the yellow fabric cost. She needs one yard, and it costs $5.95 per yard, so she’ll be spending $5.95.

Now, let’s calculate the purple fabric cost. She needs 1.5 yards, and it costs $3.95 per yard; therefore we have to multiply 1.5 times $3.95, which comes out to be $5.93 (we round to the nearest cent).

Finally, let’s calculate the green fabric cost. The green fabric is on sale for $7.00 per yard, and she needs .5 yards of it, so we multiply $7.00 times .5 and get $3.50.

Now, we have three money amounts (one for each color fabric) that we can now add together to get a total amount that Carly will spend. We know that we have to add these amounts together, like this:

$5.95 + $5.93 + $3.50 = $15.38

Thus, our final answer is that Carly will spend $15.38 on fabric for her dress.

Now, we’ll give you one to practice on. John is planning to carpet three rooms in his house. One room is 15 by 12 feet, one room is 17 by 14 feet, and the last room is 10 by 12 feet. John has 130 square feet of carpeting already. How much more carpeting does he need in order to carpet all three rooms?

First, you have to figure out how many square feet he has to carpet overall. That means we need to figure out the area of each room, and add those together. We multiply the dimensions together as follows: 15 x 12 = 180 ft 2 17 x 14 = 238 ft 2 10 x 12 = 120 ft 2

Now, we have the area of each floor he has to carpet, so we can add these all together to find out the total amount of carpeting he needs.

180 + 238 + 120 = 538 ft 2 . This is the total amount John will need. However, the problem said that he already has 130 ft 2 of carpet, so we need to figure out how much more he needs. Therefore, we need to subtract 130 from 538, and we get 408 ft 2 leftover. This is how much more carpeting John will need to finish off his three rooms.

Final answer: 408 ft 2 .

The Smith family is going to take a vacation to Florida. They live in Illinois, and have figured out that the trip is 1,150 miles from their house to the hotel in Florida. They get 28 miles per gallon of gas, and plan on travelling at an average rate of 60 miles per hour. Gas costs about $2.89 per gallon.

a) How long will it take them to get to Florida? (in hours)

For this part, you divide the total miles (1,150) by the speed they’re travelling (60 mph) and you would get 19.16666 (repeating). You would round the answer to 19.2 hours.

Final answer: 19.2 hours.

b) How much money should they leave for gasoline (going one way)?

First, you would divide the total number of miles (1,150) by the amount of miles they get per gallon of gas (28); this gives you 41 gallons—the total amount needed for the trip. Then, you would multiply the number of gallons (41) by the cost per gallon of gas ($2.89) and round to the nearest cent, which gives you $118.49. This is the amount they should save for gas going one way.

Final answer: $118.49

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Addition Story Problems

  We have been adding with pictures and completing addition story problems {Freebie} .   This week we are also going to use {these} simple addition story problems.  With these story problems the students will be able to read, comprehend, and complete the entire problem on their own. 

Up to now I have been displaying the word problem on the Smartboard and we have been completing it as a group before dismissing for independent practice.  I think they are really going to enjoy completing these simple to read story problems on their own- so exciting!!!

10 Comments

This is totally awesome, although I'm Kindergarten this year, I've taught 1st grade the last 3 years, and this would have made me happy to see Kindergarten doing this!

Angela The Daily Alphabet

Angela, I'm SO excited to see what my students this year will be able to accomplish in 1st, 2nd, 3rd grade & up!

Those are great! Jennifer

First Grade Blue SKies

Love these! What program did you use to make these?

Courney- I use microsoft word!

I used these last year with my kinders for class and then homework. Parents had to help but the kids truly enjoyed these fun problems. I would use more if you had a pack to purchase! thank you! Great blog!

Hi there… I loved your freebie but once I tried to download it nothing appeared on the download…Do you know why???

Here is an updated link 🙂 http://www.teacherspayteachers.com/Product/Addition-Story-Problems-aligned-to-Common-Core-Freebie

These type of addition are really nice and great for all the young generations and the uniuq and talented people. In this proces they can becmoe successful writing college essays and can become a star in the world.

all the technical KINGDOM777 solutions and staff we need for 에볼루션 카지노 operators who provide world

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Making Sense of Story Problems

by Deborah Peart, Grade 2 Lead

Many people have an aversion to word problems. They cringe at the mention of them. In elementary classrooms, teachers often report that this is what their students struggle with most. When word problems show up in math class, even students who enjoy reading will release a sigh and let their shoulders droop. “Do words even belong in math class?” they wonder. The answer is yes, they do! But students need guidance in how to make sense of story problems because in many classrooms they are taught to compartmentalize their learning in math class. While students are often encouraged to integrate social studies and language arts, mathematics is more frequently taught in isolation. In order for students to see math in the world around them, we must consider all the ways in which we can bring mathematics to life through stories.

For the first 20 years of my teaching career, my expertise was in literacy: phonics, word study, and reading comprehension. Literacy was my favorite block of the day and the focus of my graduate work. Ironically, it was the elective I took in elementary mathematics at the end of my grad program that lit a spark in me. That professor answered my questions, and helped me connect mathematics to the world in ways no one else had in the past. I was inspired. As a result, I shifted my studies and professional pursuits towards mathematics. 

For the past decade, I have immersed myself in the study of elementary mathematics. In my work on the IM K–5 Math curriculum writing team I have re-engaged my literacy background to think deeply about how our youngest learners engage with mathematics as emergent, novice, and decoding readers. When word problems show up in the early grades, how can we assure that all students have access to the content?

How can we support “sense-making” of stories in math class?

The mission of Illustrative Mathematics is to create a world where learners know, use, and enjoy mathematics. By using stories to help students see math in the world around them and recognize the ways in which using math is a part of their daily lives, word problems can become an enjoyable part of math learning. This starts with calling word problems “story problems” in the early grades. From there, other supports embedded in the curriculum include: 

• providing relevant contexts and images with which students can engage
• supporting reading comprehension with routines and instructional practices, like Act it Out and Three Reads
• encouraging students to use visual representations to support sense-making
• inviting students to write their own math stories and ask questions that can be answered by them

Provide Relevant Contexts

During the process of writing this curriculum, the K–5 team had many conversations inspired by articles and books that we had read on the topic of culturally relevant pedagogy and practices. From these conversations we had time for reflection and made decisions about prioritizing contexts that were inviting to all students. Sometimes the context is an introduction to another culture or experience, while at other times the context is relevant to the students for other reasons. Launching an activity by establishing the context with pictures, and students sharing their own experiences, is an important part of this process. With unfamiliar contexts, it is important for students to have an introduction to them, notice and wonder about them, and ask questions that will help them gain access to the math content. Having a shared understanding of the context is the first criteria for supporting sense-making of math stories.

Support Comprehension with Routines

In the early grades, independent reading skills vary greatly. In order to support comprehension of story problems, we offer several instructional routines and supports.

Act it Out (K–2)

In this routine, students are presented with a story and a picture to help establish the setting. Once the story has been read aloud, the students notice and wonder about the picture and share with their partners what they believe the story is about. After the story is read a second time, students have the opportunity to act it out. By the end of the routine, after students have shared their interpretations of the story with a partner or group, there is a class representation made of the story including expressions. With this routine, students connect language to mathematical representations and approach problems from a place of understanding. 

Three Reads (K–5)

Before students begin solving problems, it is critical that they know what they are being asked to do. Math Language Routine 6: Three Reads supports reading comprehension, sense-making, and meta awareness of mathematical language. In this routine, students are supported in reading a math story 3 times, as the title suggests. Each time there is a particular focus. The first read is done without a question presented to allow students to consider what is happening in the story. This relieves the pressure of rushing to find the solution and creates space for a conversation about the situation. The second read focuses on mathematizing the story by posing a question about the things that can be counted or measured in the story. It is not until the third read that the question or prompt is revealed, and students discuss possible methods for finding a solution.

Students need to understand what the story is about and what they are being asked to find a solution for in order to avoid “number plucking.” If students are given the support they need with comprehension, they can approach problem solving from a position of understanding and confidence. If students relate to the context and understand the actions of the story, they can connect mathematical ideas and representations. When students have positive experiences with story problems, they will soon be inspired to write their own, and consider the mathematical questions they can pose.

Encourage Visual Representations

Starting in kindergarten, students use math tools to model the mathematics in story problems. Using 10-frames and connecting cubes, students represent addition and subtraction long before writing expressions or equations. 

By grade 1, in addition to using concrete models like connecting cubes, students begin to include discrete mathematical drawings to represent people or objects and actions in story problems. These representations set the foundation for the introduction of the tape diagram in second grade. 

In grade 2, students are introduced to the tape diagram as a representation designed to help them make sense of story problems. While students are not required to use tape diagrams, they use them to make connections to the mathematical ideas being presented. By analyzing the structure of the tape diagram, considering what the question mark represents or how the labels reflect the details of the story, students can visualize the actions and make decisions about their strategies for solving the problem.

Students learn to use tape diagrams in part-part-whole situations, as well as compare situations and determine which best represents the story. The use of this visual representation also allows students the space to deepen their understanding of the relationship between addition and subtraction, as they use their knowledge of number relationships to choose methods that make sense to them for solving. To emphasize that these diagrams are for making sense of stories and not for finding the solutions, several activities in the curriculum involve matching diagrams to stories without the cognitive load of solving a problem.

Tape diagrams are a powerful tool because they can be used to represent all four operations, additive and multiplicative comparisons, fractions, decimals, and percents. It is a representation with longevity, as it is used not only in the elementary grades, but throughout middle school.

Let’s invite students to enjoy math stories. In reading class, students engage with stories and relish in the fact that there is a problem to be solved. In these stories, the reader takes comfort in knowing that the problem will be solved if they just keep reading. Once students feel connected to and understand the actions of a math story, they will have the courage and confidence to solve problems on their own. 

Math stories are often presented as words on a page with some unrelatable problem to solve and unanswered questions. It’s no wonder some students are intimidated. If we want students to transfer the reading strategies and skills they acquire during the literacy block, here are a few recommendations:

• Provide relevant contexts and images with which students can engage. 
• Support reading comprehension with routines and instructional practices. 
• Encourage students to use visual representations to support sense-making.
• Invite students to write their own math stories and ask questions that can be answered by them.

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Addition and Subtraction, Part 1: Story Problems

In this resource, we discuss the teaching and learning of addition and subtraction. Often, students’ understanding of this topic is heavily grounded in rote computation of numbers, separated from any real-life context. Unfortunately, this can leave gaps in their understanding of the concepts that underlie those computations. This resource shows how the use of context—story problems—can help students develop a real grasp of addition and subtraction.

Key Concepts

A story problem introduces addition and subtraction not as a mathematical procedure, but as a hypothetical real-life problem in context. The student then must take the conceptual leap of turning the real-life problem into a mathematical problem—providing some of their earliest experiences with the important mathematical practice of “modeling.”

Story Situations

There are several different kinds of mathematical relationships that students must infer from story problems. These are known as “situation types.” The Common Core State Standards (CCSS) expects K-1 students to understand four situation types:

• Put-together/take-apart

Teachers who understand the situation types (and what is new and challenging about each one) are better able to select and sequence problems that help students build their conceptual understanding of addition and subtraction.

Building Conceptual Understanding of Addition and Subtraction

The ability to add and subtract are widely recognized to be fundamental mathematical skills. However, we do not always recognize the other important conceptual understandings that students gain through solving story problems, beyond the computational skills gained by practicing addition and subtraction facts without context.

In this problem, we start with the problem in context: we see that there are 5 fish in a tank, and a child is adding 3 more. Next, students must represent this situation mathematically. This can be done with manipulatives (as is shown with the yellow blocks below) and by using the number sentence, 5 + 3 = ?. Students who are newer to solving story problems will rely on the more concrete representation of manipulatives.

As students build fluency of composing and decomposing numbers (and familiarity with story problems), they can jump to representing the problem with a number sentence.

Once students solve the mathematical problem to discover the answer is 8, students must return to the context of the problem and interpret the results. In this case, 8 refers to the total number of fish in the tank.

As we mentioned previously, students develop their understanding of the addition and subtraction operations as they use them to solve story problems. There are several categories of story problems, known as situation types , that describe the relationship among quantities in story problems. The four situation types that the Common Core State Standards (CCSS) require students to learn in grades K-1 are:

Teachers who understand the situation types (and what is new and challenging about them) are better able to support their students in developing a strong conceptual understanding of addition and subtraction. For this reason, we want to spend the rest of this resource familiarizing you with the four addition and subtraction story situations.

The Addition and Subtraction Story Situations

To get a better idea of what we mean by “situation type,” let’s return to our example addition problem, which represents an add-to situation . In this problem, one quantity (3 fish) is added to an existing quantity (5 fish), resulting in a new quantity (what we discover to be 8 fish). The details of the problem can change (for example, it could involve cookies instead of fish) as can the unknown quantity (for example, perhaps we knew how many fish we had in the end, but not how many we started with), but the relationship among quantities is the same for all add-to problems.

Below, we represent the add-to situation as a diagram, and label each quantity as the CCSS refers to them ( start is increased by change to become result ). We don’t recommend introducing the diagram as a model to students, but it be may be helpful as teachers to see the situation type represented visually.

Another important thing to understand is that the situation type itself isn’t how we know whether to use addition or subtraction . Rather, we determine the needed operation based on which quantity is unknown. In our example above, 3 fish are being added to an aquarium of 5 fish, and the unknown is the total number of fish (5 + 3 = ?)—so this requires addition. But if we added 3 fish to a tank that now has 8 fish, this is still an “add-to” situation: ? + 3 = 8), but we would use subtraction to find the unknown (8 – 3 = ?).

In the table below, we provide an example problem for each type of story situation and a diagram that represents each situation’s relationship among quantities.

Discussion Questions

After reading this resource, it may be helpful to discuss the following questions as a team.

• What ideas about the teaching-learning of addition and subtraction discussed in this resource strike you as important in your setting?
• How does your curriculum handle addition and subtraction story problems? Which situations does it introduce first? What about it do you like and/or notice that has opportunity for improvement?
• What experiences have your students had that currently inform their understandings of addition and subtraction?
• How do your students represent story problems?
• What do you want to learn more about and what steps can you take to do so?

In our resources linked below, we take a closer look at the situations, and discuss what situations (and which unknown quantities within situations) are challenging for students and how to support them to overcome the difficulties.

First, we take a close look at the situation types that students typically first experience: add-to , take-from , and put-together/take-apart .

Second, we discuss the compare situation.

Finally, we return to add-to and take-from situations to cover how students solve for unknown start or change values .

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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.

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A Sample Student Lesson Plan for Writing Story Problems

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This lesson gives students practice with story problems by teaching them how to write their own and solve the problems of their classmates. The plan is designed for third-grade students . It requires 45 minutes and additional class periods .

Students will use addition , subtraction, multiplication , and division to write and solve story problems.

Common Core Standard Met

This lesson plan satisfies the following Common Core standard in the Operations and Algebraic Thinking category and the Representing and Solving Problems Involving Multiplication and Division subcategory.

This lesson meets standard 3.OA.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.

• White paper
• Coloring pencils or crayons
• Story problems
• Subtraction
• Multiplication

Lesson Introduction

If your class uses a textbook, choose a story problem from a recent chapter and invite students to come up and solve it. Mention to them that with their imaginations, they could write much better problems, and will do so in today's lesson.

Instruction

• Tell students that the learning target for this lesson is to be able to write interesting and challenging story problems for their classmates to solve.
• Model one problem for them, using their input. Begin by asking for two student names to use in the problem. "Desiree" and "Sam" will be our examples.
• What are Desiree and Sam doing? Going to the pool? Getting lunch at a restaurant? Going grocery shopping? Have the students set the scene as you record the information.
• Bring the math in when they decide what is going on in the story. If Desiree and Sam are getting lunch in a restaurant, maybe they want four pieces of pizza, and each piece is $3.00. If they are grocery shopping, maybe they want six apples at $1.00 each, or two boxes of crackers at $3.50 each.
• Once the students have discussed their scenarios, model how to write a question as an  equation . In the above example, if you want to find the total cost of the food, you may write 4 pieces of pizza X $3.00 = X, where X represents the total cost of the food.
• Give students time to experiment with these problems. It's very common for them to create an excellent scenario, but then make mistakes in the equation. Continue working on these until they are able to create their own and solve the problems that their classmates create.

For homework, ask students to write their own story problem. For extra credit, or just for fun, ask students to involve family members and get everyone at home to write a problem, too. Share as a class the next day—it's fun when the parents get involved.

The evaluation for this lesson can and should be ongoing. Keep these story problems bound in a three-ring binder in a learning center. Continue adding to it as students write more and more complex problems. Make copies of the story problems every so often, and collect these documents in a student portfolio. The problems are sure to show the students' growth over time.

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Math Story Word Problems

The Math Story Word Problem Generator is a versatile MagicSchool AI powered tool designed to simplify the creation of custom math word problems. Educators can use this resource to craft math word problems that are tailored to specific mathematical concepts and story topics, making learning more engaging and relatable for students.

Key Features

Customization: The Math Story Word Problem Generator offers a high degree of customization. It enables educators to design math word problems that align with the mathematical concept they are teaching and incorporate story topics that resonate with their students.

• The Math Story Word Problems Generator is one of the Best AI tools for Math Teachers
• Concept Reinforcement: Utilize this tool to create math word problems that reinforce and assess students' understanding of specific mathematical concepts. Customized problems can make abstract concepts more tangible and relatable.
• Engagement: By incorporating story topics, educators can make math learning more engaging and relatable to students' interests and everyday experiences. Story-based problems encourage active problem-solving and critical thinking. ‍
• Differentiated Learning: Tailor math word problems to meet the diverse learning needs of your students. This tool allows you to provide varying levels of complexity and support, catering to different skill levels and abilities.

In summary, the Math Story Word Problem Generator is a valuable resource for educators seeking to create custom math word problems that align with specific mathematical concepts and story topics. By offering customization, engagement, and support for differentiated learning, this tool enhances the effectiveness of math instruction and makes learning more enjoyable and relatable for students. It is an essential companion for educators committed to promoting mathematical proficiency in their classrooms.

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Algebraic properties | Lesson
• Algebraic properties | Worked example
• Solution procedures | Lesson
• Solution procedures | Worked example
• Equivalent expressions | Lesson
• Equivalent expressions | Worked example
• Creating expressions and equations | Lesson
• Creating expressions and equations | Worked example

Algebraic word problems | Lesson

• Algebraic word problems | Worked example
• Linear equations | Lesson
• Linear equations | Worked example
• Quadratic equations | Lesson
• Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

• Translating sentences to equations
• Solving linear equations with one variable
• Evaluating algebraic expressions
• Solving problems using Venn diagrams

How do we solve algebraic word problems?

• Define a variable.
• Write an equation using the variable.
• Solve the equation.
• If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

• 7 + 10 − 13 = 4 ‍   brought both food and drinks.
• 7 − 4 = 3 ‍   brought only food.
• 10 − 4 = 6 ‍   brought only drinks.
• 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 ‍  
• (Choice A)   $ 4 ‍   A $ 4 ‍  
• (Choice B)   $ 5 ‍   B $ 5 ‍  
• (Choice C)   $ 9 ‍   C $ 9 ‍  
• (Choice D)   $ 14 ‍   D $ 14 ‍  
• (Choice E)   $ 20 ‍   E $ 20 ‍  
• (Choice A)   10 ‍   A 10 ‍  
• (Choice B)   12 ‍   B 12 ‍  
• (Choice C)   24 ‍   C 24 ‍  
• (Choice D)   30 ‍   D 30 ‍  
• (Choice E)   32 ‍   E 32 ‍  
• (Choice A)   4 ‍   A 4 ‍  
• (Choice B)   10 ‍   B 10 ‍  
• (Choice C)   14 ‍   C 14 ‍  
• (Choice D)   18 ‍   D 18 ‍  
• (Choice E)   22 ‍   E 22 ‍  

Number Line

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

word-problems-calculator

• High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential...

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14 Types of Math Story Problems Your Child Should Know

Are you familiar with the different types of math story problems?

In Teaching Math With Story Problems, Not Word Problems , we talked about how powerful math story problems can be to help children learn and understand math and how it relates to the real world.

As you use math story problems into your math lessons, you will want to make sure that you are using different types of math story problems.  This will allow you to vary the wording of the problems.  Then, your children will be able to fully develop their skills and understand any kind of problem that comes their way.

Cognitively Guided Instruction, which is a student-centered approach to teaching math, groups different word problems into types.  The different types for elementary aged children are described below.  There is also a FREE set of templates for each type of word problem you can download at the end.  These templates will allow you to create custom word problems for your child based on their personality and what they are learning in math.

(Note: This post contains affiliate links for your convenience. Click here to read our full disclosure .)

Math Story Problems That Join

There are three different types of math story problems that join .  Notice, we are not saying addition here as we want children to understand the story as a whole and then solve it in a way that makes sense to them rather than thinking of the problem as an addition problem.

When children start thinking of problems as addition or subtraction, then they may just start grabbing numbers and doing that operation to them without really understanding the problem as a whole.

Within the joining problems, there are three types: Results Unknown, Change Unknown and Start Unknown.  Here are some examples:

Join: Results Unknown: There were 37 cans of beans on the shelf.  Then, the man put 54 more cans of beans on the shelf.  How many cans of beans are on the shelf now?

Join: Change Unknown: Anthony had 16 colored pencils.  He bought some more colored pencils.  Then, he had 50 colored pencils.  How many markers did Anthony buy?

Join: Start Unknown: Some children were playing in the sand.  3 more children joined them.  Then, there were 10 children playing in the sand altogether.  How many children were there to start with?

You can see for each of these types of problems there are two numbers being combined and then a total amount.  The only difference between the problem types is which piece of information is missing in each problem.

Remember when presenting the problems to be as hands off as possible in your guidance as described in our Teaching Math With Story Problems post.

Math Story Problems That Separate

There are three different types of math story problems that separate .  Notice again, we are not saying subtraction here as we want children to understand the story as a whole and then solve it in a way that makes sense to them rather than thinking of the problem as a subtraction problem.

Here are some examples:

Separate: Results Unknown: Lucas has 14 football cards.  He gave 4 football cards to his friend.  How many football cards does Lucas have left?

Separate: Change Unknown: The family found 32 seashells.  Then, they lost some.  They had 18 seashells left.  How many seashells did they lose?

Separate: Start Unknown: Jason had some grapes.  He ate 18 grapes.  Then, he had 12 grapes left.  How many grapes did Jason have before he ate any?

For each of these types of problems we have a starting amount and then some of that amount goes away.  The only difference with each problem is which pieces of information we are given for the problem.

Part-Part-Whole Math Story Problems

Understanding which information in a story problem are parts and which is the whole is important to understanding the problem.  Putting the information into Part-Part-Whole Circles is a great way to visualize this.

The way these story problems are worded in the next two types make them great for working on this concept of part-part-whole.

Part-Part-Whole: Whole Unknown: Samuel had 8 pairs of jeans.  He also had 5 pairs exercise pants.  How many pairs of pants does he have altogether?

Part-Part-Whole: Part Unknown: Sully has 8 building sets.  Four of the building sets are to create vehicles.  How many of the building sets do not create vehicles?

While usually I suggest not providing your children with much guidance on how to solve math story problems, for these two types it can be helpful to have a printed part-part-whole circle set they can draw on or place manipulatives on.  You could also draw one on the whiteboard before you present the problem.

If your child wants to use another way to solve the problem, let them.  But, then afterward, you can help them fill in the part-part-whole circle set correctly.

Compare Story Problems

These story problems have the child compare the pieces of information to determine the missing piece. They are definitely more challenging than the eight problem types already discussed.

Compare: Difference Unknown: Fifteen ducks are sitting on the shore.  Nine ducks are swimming in the water.  How many more ducks are sitting on rocks than swimming in the water?

Compare: Larger Quantity Unknown: There are 5 people shopping in the produce section of the grocery store.  There are 8 more people in line at the grocery store than there are in the produce section.  How many people are in in line at the grocery store?

Compare: Smaller Quantity Unknown: Benji walked for 20 minutes. Pedro walked for 10 minutes less than Benji.  How long did Pedro walk for?

Multiplying and Dividing Story Problems

Finally, we have three types of math problems working with multiplication and division. These are the first level of multiplication and division problems where the groups are of equal amounts.  However, they can be use for children to review their basic facts or to target multi-digit multiplication and division.

Multiplying with Equal Groups: Product Unknown: There were 8 children drawing pictures.  Each child drew 4 pictures.  How many pictures did they draw altogether?

Dividing with Equal Groups: Group Size Unknown: Mrs. Johnson goes to the store and buys 512 small bags of chips for a large youth group.  She buys 32 boxes of chips.  If each box is the same size, how many bags of chips are in each box?

Dividing with Equal Groups: Number of Groups Unknown: The man gave 2 samples to each shopper.  He gave out 128 samples.  How many shoppers received samples?

Download the Templates

So now that you know the different types of math story problems your children should practice with, download the templates below and start creating some!

Just pick which type of problem you want to practice and then fill in the blanks in one of the templates for that type.  You can make them easy with single digit numbers or more challenging if your child is working at a higher level.  And your child will love having the problems customized to his personality and interests!

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Story Problems and Equations

Let’s solve story problems and write equations to match.

Math Mights was adapted from IM K-5 Math™ ©2021 by Illustrative Mathematics®, released under the Creative Commons Attribution 4.0 International License (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/.

Additions and adaptations are ©2021 by Strategic Intervention Solutions, LLC

Lesson Standards

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Teacher Resources

Visit the lesson page on MathMights.org for additional resources.

Download Full Packet

Download the full year's Math Mights extension activities.

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You Write the Story: Student-Generated Math Word Problems

If I asked you to name a math skill that students have trouble mastering, odds are that solving math word problems might enter the conversation. We often think that just by solving more and more word problems, students will somehow get better at it. But how about if we take a different approach and choose quality over quantity?

Part of the problem is that over the years very well-intentioned teachers have tried to turn the process of solving word problems into an algorithm—if you follow these steps, then you can solve math word problems. As a result, we see widespread use of “strategies” like CUBES. Unfortunately, CUBES only works with the simplest of problems. Consider this problem:

Not a terribly complicated problem, right? It’s a fairly straightforward multiplication problem with a little extra information thrown in. So let’s apply the CUBES strategy. To start with, nowhere in the CUBES strategy does it actually tell students to read the problem! And if you’ve ever watched students use CUBES to try to solve a problem, you’ll quickly see that they don’t. They scan the text, circling the numbers as they go. We’ve basically given them permission not to read. Next, notice that keywords don’t help at all in this problem. The only keyword is increase, which indicates addition. Finally, since students don’t really understand what the numbers in the problem represent, they can’t identify that the $8 increase is extra information. Hence, they end up adding the three numbers, not even realizing they are adding together money and memberships. For an alternate method that actually helps students solve math word problems based on understanding , check out this post on the Three Reads Protocol.

So how can we actually help students become more accomplished in solving word problems? Well, we emphasize quality over quantity. Instead of solving pages of word problems, we let students write their own! If students can write word problems, trust me, they can solve them. One of my favorite activities is called  You Write the Story.  It’s super effective and super low-prep—an awesome combination! Students are given an expression, and their task is to write a story problem, draw a model showing the problem, and then solve it. You can see from the index cards below how easy it is to differentiate the task.

Of course, writing word problems is a skill we need to teach. Don’t rush this! Do plenty of guided writing before you assign it as an independent task. Here’s a process I find to work well. First, I’m going to ask students what they notice about the expression. This helps them focus on the magnitude of the numbers and the operation (addition). Next, model what it sounds like to develop the idea for a story problem. It’s a story, so we need to think about the characters, the setting, and the action taking place.

Here’s what it might sound like:

For some reason, I’m thinking about milking cows! Silly, right? So, the story is about Farmer Jon and his son. The story takes place in Farmer Jon’s barn. What’s happening is that Farmer Jon and his son are milking cows. And the numbers in the story represent the cows that Farmer Jon and his son milked. Now I’m ready to put it together and write my story.

Farmer Jon and his son were milking cows in the barn. Farmer Jon milked 34 cows and his son milked 18 cows. How many cows did Farmer Jon and his son milk?

We also want to model the process for drawing a representation. A simple part/whole diagram is perfect for helping students visualize what the numbers in a problem stand for and what number they are looking for. Remember, it’s important for students to label their diagrams so they can make a connection to the meaning of the numbers in the problem and their relationships.

You Write the Story can easily be adapted. Students need to be able to solve problems with the unknown in any position. So how about a card that looks like this?

And, you can even provide students with a model and ask them to write a story, provide the equation, and solve the problem. Here are a couple of examples.

So, there you have it! Are you ready to give You Write the Story a try? If you do, I’d love for you to drop a comment and share your experience.

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Addition word problems

 Addition word problems arise in any situations where there is a gain or an increase of something as a result of combining one or more numbers. Think of addition as combining parts to form a whole.

Consider the following situations. Problem #1: John has 800 dollars in his checking account. He received from his job a check for 1,200 dollars and deposit the amount in his checking account. How much money does he have in his checking after the deposit? Solution The fact of receiving money from his job is a gain. Therefore, we need to perform addition.

Total amount in checking account = 800 + 1200 = 2000 dollars Problem #2: Peter sells ice cream for a living. On Monday his revenue was 150 dollars. On Tuesday, his revenue was 100 dollars. Finally, on Wednesday, his revenue was 50 dollars. How much is Peter's revenue so far? Solution Peter is experiencing a gain in revenue. Therefore, we use addition.

Peter's revenue = 150 + 50 + 100 = 300 dollars Problem #3: Eiffel Tower is about 1063 feet high. The Statue of Liberty along with its foundation and pedestal is about 305 feet. If you could put the Statue of Liberty on top of the Eiffel Tower, how high up in heaven will the two monuments reach? Solution The situation above is a combination of parts to form a whole. Therefore, we use addition.

Problem #4:

Ana found a 15 dollar bill on the floor on Saturday.

Then on Sunday her parents gave her 155 dollars. How much does Ana have all together?

CLUE: Saturday~15 dollars Sunday~155 dollars

Solution: 15+155 = 170 dollars all together

Subtraction word problems

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Addition Word Problems (1-step word problems)

These lessons look at some examples and solutions of addition word problems that can be solved in one step. We will illustrate how block diagrams (used in Singapore Math) can be used to help you to visualize the addition word problems in terms of the information given and the data that needs to be found.

Related Pages Addition & Subtraction Word 2-Step Word Problems and Bar Models More Word Problems More Singapore Math Lessons

Example: There are 1030 books in the library. We bought 67 more books for the library. How many books are there in the library now?

1030 + 67 = 1097

There are 1097 books in the library now.

Example: 1085 girls and 531 boys took part in an art competition. How many students took part in the competition altogether?

1085 + 531 = 1616 1616 students took part in the competition altogether.

Example: After giving $1085 to his wife, Simon had $746 left. How money had he at first?

1085 + 746 = 1831

Simon had $1831 at first.

Example: Margret sold 1392 meatballs on Friday. She sold 1940 more meatballs on Saturday than on Friday. How many meatballs did she sell on Saturday?

Solution: 1392 + 1940 = 3332 She sold 3332 meatballs on Saturday.

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model. Because the whole is missing, this is an addition problem.

Example: Mr. Gray sold 64 drinks in the morning. Mr. Frank sold 25 drinks at night. How many drinks did they sell altogether?

How to solve addition problem using part-whole model?

Example: Maya had some stamps. She gave 7 stamps to her younger brothers. Maya then had 14 stamps. How many stamps did Maya have at first?

Examples of 4th Grade word problems and bar models

Example: Dad bought two hammers. One cost $18 and the other costs $28 more. What was his total bill?

Model Drawing - addition word problems

Example: A girl jumps 42cm for her first jump in a high jump competition. Her second jump is 46cm. How high did she jump in total?

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Lesson Plan

Making story problems, view aligned standards.

Students will be able to represent and solve addition word problems using objects.

Students will be able to explain how to solve an addition word problem by acting with objects.

Introduction

• Gather the students together for the start of the lesson.
• Using objects, tell a story problem about the classroom. For example, "I have three pencils, and you have two pencils, how many pencils do we have in all?"
• Say, "In math we call this a story problem. Today we are going to practice solving lots of story problems!"