write and solve a story problem that goes with 6÷6

Write and solve a story problem that goes with 6 divided by 6

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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More Division Stories

Videos and solutions to help Grade 6 students demonstrate further understanding of division of fractions by creating their own word problems.

Related Topics: Lesson Plans and Worksheets for Grade 6 Lesson Plans and Worksheets for all Grades More Lessons for Grade 6 Common Core For Grade 6

New York State Common Core Math Grade 6, Module 2, Lesson 6

Worksheets for Grade 6

Lesson 6 Student Outcomes

• Students demonstrate further understanding of division of fractions when they create their own word problems.
• Students choose a partitive division problem, draw a model, find the answer, choose a unit, and then set up a situation. Further, they practice trying several situations and units before finding which are realistic with given numbers.

Lesson 6 Summary

The method of creating division stories has five steps, to be followed in order: Step 1: Decide on an interpretation (measurement or partitive). Today we used only measurement division. Step 2: Draw a model. Step 3: Find the answer. Step 4: Choose a unit. Step 5: Set up a situation. This means writing a story problem that is interesting, realistic, short, and clear and that has all the information necessary to solve it. It may take you several attempts before you find a story that works well with the given dividend and divisor.

Classwork Opening Discussion Partitive division is another interpretation of division problems. What do you recall about partitive division?

• We know that when we divide a whole number by a fraction, the quotient will be greater than the whole number we began with (the dividend). This is true regardless of whether we use a partitive approach or a measurement approach.
• In other cases, we know what the whole is and how many groups we are making and must figure out what size the groups are.

Example 1 Partitive Division. Divide 50 ÷ 2/3

Exercise 1 Using the same dividend and divisor, work with a partner to create your own story problem. You may use the same unit, dollars, but your situation must be unique. You could try another unit, such as miles, if you prefer. Possible story problems:

• Ronaldo has ridden 50 miles during his bicycle race and is 2/3 of the way to the finish line. How long is the race?
• Samantha used 50 tickets (2/3 of her total) to trade for a kewpie doll at the fair. How many tickets did she start with?

Example 2 Divide 45 ÷ 3/8

Exercise 2 Using the same dividend and divisor, work with a partner to create your own story problem. Try a different unit. Remember spending money gives a “before and after” word problem. If you use dollars, you are looking for a situation where 3/8 of some greater dollar amount is $45.

Opening Example 1 Partitive Division. Divide 50 ÷ 2/3

Lesson 6 Problem Set Solve.

• 15/16 is 1 sixteenth groups of what size?
• 7/8 teaspoons is 1/4 groups of what size?
• A 4-cup container of food is 2/3 groups of what size?
• Write a partitive division story problem for 6 ÷ 3/4.
• Write a partitive division story problem for 5/12 ÷ 1/6.
• Fill in the blank to complete the equation. Then, find the quotient, and draw a model to support your solution. 1/4 ÷ 7 = 1/□ of 1/4 5/6 ÷ 4 = 1/□ of 5/6
• There is 3/5 of a pie left. If 4 friends wanted to share the pie equally, how much would each friend receive?
• In two hours, Holden completed 3/4 of his race. How long will it take Holden to complete the entire race?
• Sam cleaned 1/3 of his house in 50 minutes. How many hours will it take him to clean his entire house?
• It took Mario 10 months to beat 5/8 of the levels on his new video game. How many years will it take for Mario to beat all the levels?
• A recipe calls for 1 1/2 cups of sugar. Marley only has measuring cups that measure 1/4 cup. How many times will Marley have to fill the measuring cup?

Lesson 6 Problem Set Sample Solution

• Write a partitive division story problem for 45 ÷ 3/5
• Write a partitive division story problem for 100 ÷ 2/5

Lesson 7 Student Outcomes

Students formally connect models of fractions to multiplication through the use of multiplicative inverses as they are represented in models. The reciprocal , or inverse, of a fraction is the fraction made by interchanging the numerator and denominator. Two numbers whose product is 1 are multiplicative inverses . Example 1: 3/4 ÷ 2/5

Lesson 8 Student Outcomes Students divide fractions by mixed numbers by first converting the mixed numbers into a fraction with a value larger than one. Students use equations to find quotients.

Example 1: Introduction to Calculating the Quotient of a Mixed Number and a Fraction

Carli has 4 1/2 walls left to paint in order for all the bedrooms in her house to have the same color paint. However, she has used almost all of her paint and only has 5/6 of a gallon left. How much paint can she use on each wall in order to have enough to paint the remaining walls?

Calculate the quotient. 2/5 ÷ 3/4

Lesson 1 to Lesson 8 Review

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Education Standards

Michigan integrated technology competencies for students.

Learning Domain: Creative Communicator

Standard: Students communicate clearly and express themselves creatively for a variety of purposes using the platforms, tools, styles, formats and digital media appropriate to their goals.

Standard: Students create digital artifacts to communicate ideas visually and graphically.

Learning Domain: Empowered Learner

Standard: Students explore age-appropriate technologies and begin to transfer their learning to different tools or learning environments.

Learning Domain: Global Collaborator

Standard: Students perform a variety of roles within a team using age-appropriate technology to complete a project or solve a problem.

Michigan State ELA Standards

Learning Domain: Language

Standard: Recognize and observe differences between the conventions of spoken and written standard English.

Standard: Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful).

Learning Domain: Speaking and Listening

Standard: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others’ ideas and expressing their own clearly.

Standard: Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).

Standard: Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others.

Standard: Explain their own ideas and understanding in light of the discussion.

Standard: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

Standard: Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.

Standard: Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 on page 26 for specific expectations.)

Learning Domain: Writing

Standard: With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others.

Michigan State Math Standards

Learning Domain: Operations and Algebraic Thinking

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

Standard: 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.

Standard: Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Animated Division Stories Viewing Party Invitation

Animated division story example, animated division story student example 1, animated division story student example 2, animated division story student example 3, animated division story student example 4, animated division story student example 5, animated division story student example 6 (spanish), blank division storyboard, division storyboard student examples, learnzillion video, animated division stories (problem-based interactive learning).

Students will work with a partner to write, solve, check, and animate a division story problem based on a division expression using a sharing model.

Introduce (or Review) Solving Division Word Problems

Watch the excellent instructional video created by Isabel Pimental on Learnzillion.com to help introduce or review solving division word problems.

Practice solving division word problems as a class. Draw pictures to help students visualize equal groups.

• There are 28 kids at a party.  There are 7 tables.  How many kids will be able to sit at each table?
• A box of muffin mix makes 30 muffins. Sarah can bake 6 muffins on a tray at a time.  How many batches of muffins will Sarah need to make?
• Charles has 48 stickers in his collection. He buys a sticker book with 8 pages. He wants to put an equal amount of stickers on each page.  How many stickers should be put on each page.

Write a Division Story Together

Use the attached storyboard to write a division story together.

Students who have difficulty understanding how to divide their objects into equal groups may benefit by having a list of possible groups or "containers" that hold items.

You can divide items into groups such as:

View Past Student Storyboards and Animated Division Projects

View and discuss example student storyboards together.

Let students know that they will be writing their own division stories and animating them.

Show students what the finished product will look like by viewing projects created by previous students.

Create Division Stories

Partner students and have them write division stories using the attached storyboard.

*It is helpful to preview and make a list of the available templates, characters, backgrounds, and props in your chosen animation program so that students' stories do not include items which may be unavailable.

Each frame on the storyboard represents a new scene.

With your partner:

Decide on a dvision fact.

Decide on what objects you will divide and how you will divide them.

Decide who will be character 1 and who will be character 2.

Write your dialogue in conversational writing (Write how you usually speak).

Speak your dialogue aloud to make sure it makes sense.

Don't forget to have character 1 check the division problem by using multiplication.

Make your story entertaining!

Animate Division Stories

Choose an animated video maker.

Here are some possible choices:

• Lego Movie Maker
• Renderforest

*Animation Apps and Programs can be pricey.  You may want to request that parents (who are financially able to) donate $1 towards your one month subscription to the animation maker of your choosing.

Be sure to watch tutorials with students and remind them that they must follow their storyboards.

Follow your storyboards to animate your division stories.

Each frame on your storyboard represents a new scene.

Animated Division Stories Viewing Party

Upload student animations to Youtube.com and showcase them with a viewing party!

Students will gain an even deeper understanding of division by watching each other's division animation stories.

Project students' animated division stories onto a screeen and invite administrators, teachers, parents, and other students to attend the event.

Students will beam with pride as they share their achievements.

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How to Write a Division Story Problem

How to Calculate Win-Loss-Tie Percentages

After students learn basic math skills such as addition, subtraction, multiplication and division, the next step is learning how to apply these skills to real-life situations. Word problems present situations in which students must use the information to determine the formula for finding a solution. Help students learn how to use division skills by writing division story problems. With practice, students will learn how to identify and solve division story problems.

Create division problems by performing the opposite operations of multiplication problems. For example, instead of creating a problem that asks how many times a factor increases, ask how many times one number divides into another number.

Use keywords for division story problems. Keywords that indicate a division story problem include the words “per” and “out of.”

Write a division story problem such as, “Glenda makes $2,000 per month working 22 days each month. How much money does Glenda make each day?” Another division story problem could be, “If a tray of crackers contains 225 crackers and you want to divide the crackers evenly among 15 students, how many crackers will each student get?” A third problem might be, “A baseball pitcher won 95 percent of all the games he started. The pitcher started 20 games, so how many games did he win?” This story problem can require both multiplication and division to solve, especially for young learners.

Solve the problem yourself to make sure you know the correct answer. For problem 1, divide 2,000 by 22 to get 90.9; Glenda earned $90.90 each day. For problem 2, divide 225 by 15 to get 15; each student gets 15 crackers. For problem 3, multiply 95 by 20 to get 1,900. Then divide 1,900 by 100 to get 19; the pitcher won 19 out of 20 games.

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About the Author

Kathryn Hatter is a veteran home-school educator, as well as an accomplished gardener, quilter, crocheter, cook, decorator and digital graphics creator. As a regular contributor to Natural News, many of Hatter's Internet publications focus on natural health and parenting. Hatter has also had publication on home improvement websites such as Redbeacon.

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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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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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Teaching Math Word Problems with Pictures

Help your students visualize their answers.

If you google word problem jokes, this one will pop up a lot:

“If you have 4 pencils and I have 7 apples, how many pancakes will fit on the roof?

Purple, because aliens don’t wear hats.”

It’s hilarious because it’s true! Many of our students see nonsense in word problems. They not only have to figure out what the word problem is asking them to do, but then they have to actually solve it. It’s a process. However, if we want them to internalize the concept, not just the numbers, pictures can help! Visuals can help students comprehend meaning when the words aren’t making sense to them. Don’t underestimate the power of teaching word problems with pictures. Here are a few easy ways to incorporate visuals into everyday math:

The power of “acting it out”

Before you go from manipulatives to drawing, try having students act out problems. If the problems involve eating, bring in food and have a student actually act like they are in the story problem. If the problem involves a specific number of boys and girls, have that many students get up and show the class what is going on in the problem. Taking this step will help students visualize the problem and think about the actions rather than just guessing if they should add, subtract, multiply, or divide.

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Getting ready to draw

When you’re ready to start solving word problems with pictures, follow Jan Rowe’s steps :

• Read the entire problem: Get all the facts and underline keywords.
• Answer the question: What am I looking for?
• Draw a picture or diagram: Visualize as a real-world situation.
• Solve the problem: Set up the equation and solve.
• Check your solution: Is this answer reasonable?

Drawing as a step of the process

Visual representations are a good starting point for word problems because it is an intermediate step between language-as-text and the symbolic language of math . Drawing lowers the affective filter because it can be less stressful. We aren’t stepping straight into that equation; we are just drawing to figure out what the question is actually asking us. Remind students that we are not in art class. It is perfectly OK for your math pictures to be just scribbles as long as you know what they represent. Another great perk of the “Draw a Picture” strategy is that you, as a teacher, can really step inside the student’s brain to see how their mathematical brain works. Encourage labeling so that you can catch misconceptions right away. These drawings can lead to great math talk conversations, which build that academic language that we all want to hear.

Jayden had two boxes of books with twelve books in each box. He gave four books to his sister. How many books did Jayden keep for himself?

Draw a picture:

Try photography instead of drawing

Story problems are grounded in reading. Photograph Math is an activity that can help visual learners grasp the math skill first, then add in the language. All you’ll need is a camera (or phone) to take pictures. Here’s how it works:

• Students brainstorm the ways in which, and the places where, they use math.
• They stage a photograph representing one of these ideas.
• Students write their own real-life word problems to go with their posed photograph(s).
• Students take a photograph of the menu inside the cafeteria. They write problems that help them figure out how much money they need to get specific lunches, snacks, or drinks. Extension: Think about how much you would need to get a snack every day, for a week, etc.
• Someone might take a photo of a number on a library book. Then try to figure out what value that number would have based on the number of digits and round the number to the nearest whole, tenths, or hundredth.
• Students take a photo of your stash of whiteboards markers. They could write problems about the amount of each color you have. They may choose to think about what happens if another teacher borrows a certain number of markers, etc.

Photograph math can help students to start thinking like a mathematician in all aspects of life. If students begin to see the math around them, then they can truly begin to comprehend the story problems that we present to them in class.

Read a math picture book

Remember when I said story problems are grounded in reading? Why not use actual stories? Children’s picture books can provide a rich context from which to begin mathematical investigations . As students see math concepts play out in stories and illustrations, they are engaged and better able to construct meaning. Seeing the problem-solving process in action through a book can serve as a model for students when they go off on their own to solve problems. Here is a list of 16 picture books about math .

Assign math as picture prompts

Consider starting each week with a relevant picture prompt. Sometimes, the picture is of a mathematical error we came across in real life. The challenge to students is to figure out the mistake. Other times, we simply provide an image and challenge students to come up with a story problem to accompany it. Giving students ownership of these problems can strengthen and extend their comprehension of story problems.

• Put up a sign of a price mistake in a store. Then write on the board: “Ms. Caudill saw this sign at Walmart this weekend and laughed. Why? How might you fix it?”
• Show students the following prompt: Write a story problem using the photo and the following word bank: apples, tomatoes, sweet potatoes, pound, gallon, farmer’s market.

The truth is, story problems are challenging for all students. We have to find ways to make the story problems relative to students’ lives if we want them to succeed.

How do you teach word problems with pictures? Share in the comments below.

Want even more strategies for teaching word problems check out 14 effective ways to help your students conquer math word problems ., want more articles like this make sure to sign up for my weekly newsletter for third grade teachers .

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story problem for 36 divided by 6

To solve the story problem, "36 divided by 6," we need to find out how many times 6 can be divided into 36 evenly. Here's how you can solve it step by step:

Step 1: Start with the given dividend, which is 36 (the number being divided). Step 2: Divide 36 by the divisor, which is 6. Step 3: Count how many times 6 can be subtracted from 36 without resulting in a negative number. Step 4: Continue subtracting 6 from 36 until you reach a number less than 6. Step 5: Count the number of times you were able to subtract 6 from 36. Step 6: The number of times you subtracted 6 is the quotient or the answer. Applying these steps, let's solve the story problem: Step 1: Start with the number being divided, which is 36. Step 2: Divide 36 by 6: 36 ÷ 6. Step 3: Subtract 6 from 36: 36 - 6 = 30. Step 4: Subtract 6 from 30: 30 - 6 = 24. Step 5: Subtract 6 from 24: 24 - 6 = 18. Step 6: Subtract 6 from 18: 18 - 6 = 12. Step 7: Subtract 6 from 12: 12 - 6 = 6. Step 8: Subtract 6 from 6: 6 - 6 = 0. Since we were able to subtract 6 a total of 6 times before reaching 0, the quotient or the answer to the story problem "36 divided by 6" is 6. Therefore, the answer to the story problem is that 36 divided by 6 is equal to 6.