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Topics: Featured Math Concepts Conceptual Understanding Eureka Math Squared

From Read-Draw-Write (RDW) to Modeling–How Students Experience Problem Solving in Eureka Math²

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From Read-Draw-Write (RDW) to Modeling–How Students Experience Problem Solving in Eureka Math²

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Posted in: Aha! Blog > Eureka Math Blog > Math Concepts Conceptual Understanding Eureka Math Squared > From Read-Draw-Write (RDW) to Modeling–How Students Experience Problem Solving in Eureka Math²

Coherence is a key feature of the Eureka Math 2 ® curriculum. The problem-solving process employed in Grade Levels K–9 is a major part of that coherence. In Grade Levels K–5, students know it as the Read–Draw–Write (RDW) process. Starting in Grade Level 6 the process advances to Read, Represent, Solve, Summarize (RRSS) while maintaining the same foundational approach. Word problems become accessible as students cycle through reading and representing parts of a word problem to make sense of it. The process is simple, memorable, and powerful enough to support all students with language demands, sense-making, and algebraic thinking. This paper outlines the progression of problem-solving in Eureka Math 2 . We invite you to discover where your students fit into this progression, how you can support them with the work of prior grades, and build the foundation needed to problem-solve in subsequent grades.

Grade Levels K–2

The Read–Draw–Write process for solving word problems is introduced and intentionally taught step-by-step in Grade Levels K–2. You may not always recognize the developmental progression of this problem-solving process. After all, the first piece of the process is Read, a skill many of our youngest students have not learned yet. Let’s follow the journey our students take to problem-solving.

Kindergarten

One of the first experiences students have with problem-solving is counting. In the kindergarten Module 1, Topic G, Lesson 33, students use 10-frames and other problem-solving tools. Young students sometimes employ the Read-Draw-Write process without knowing it.

solve the word problem using rdw strategy

Are they counting a large set of objects or a small set?

Are the objects movable, or are they part of a picture?

Can they group the objects to count?

solve the word problem using rdw strategy

Even before students can technically read, they take in information and understand the task to get started.

The next step is Drawing. How can students organize the information they took in during the Read phase to solve the problem? For our young students, this may look like crossing out or drawing objects, it may be writing an equation or making tally marks, or it may be simply using their fingers to track their counting. Finally, students Write: they state or write the answer they have arrived at after contextualizing the problem. “There are 9 buttons!” or “I counted 25 erasers. I made 2 groups of ten and had five ones.”

solve the word problem using rdw strategy

Kindergarten students progress to more traditional problem-solving scenarios later in the year. In Grade Level Kindergarten Module 5 Topic A Lesson 2, students represent a math story by using pictures, number bonds, and number sentences.

There are some pigeons on our playground. Then, some more pigeons land on our playground. What could this math story look like?

solve the word problem using rdw strategy

The title Read–Draw–Write may be misleading. Understanding and recognizing the more subtle instances of this powerful problem-solving strategy when reading, drawing, and writing may not be applicable in the literal sense is important.

Grade Level 1

In Grade Level 1, RDW expands to include all addition and subtraction problem types. Most problems students were presented with in kindergarten were the dark-shaded problem types shown in the chart. Grade Level 1 signals the transition to working with all the problem types in the chart, including the more challenging types shown in white.

As students’ problem-solving development progresses, it is important to spend time crafting the problems. Problems should be varied in type, and the numbers in the problems need to be high enough so that RDW is necessary to find the answer. For example, in Grade Level 1, Module 2, Lesson 8, students see a Change Unknown problem.

Sample_Eureka Math

The numbers in this problem are large enough to make mental math more challenging, and the problem type lends itself to drawing to understand what the question is asking. If we ask students to use RDW with a problem that is too “easy,” for example:

Kit is coloring a rainbow.

She has 3 markers and she gets 4 more.

How many markers does she have?

Students won’t see the value in problem-solving with RDW because they could do mental math or count on their fingers, which we want them to do in circumstances like this. Teaching first-grade students to discern when to use RDW is important, and asking them to “show your work” may not always be appropriate.

solve the word problem using rdw strategy

Comparison problem types frequently provide the productive struggle that leads to students seeing the need to use RDW. In Module 4, the tape diagram is taught and explored in the context of measurement. It begins with concrete cube trains (read) and moves to a tape diagram, a pictorial recording (draw), and then an equation and a statement (write).

Grade Level 2

solve the word problem using rdw strategy

With these added problem-solving complexities, Grade Level 2 students will find the part between reading and drawing the most challenging. Drawing a model that shows what is being asked in the problem and what helps students solve the problem needs to be the focus in this teaching. For example, in Module 4 Lesson 3, this problem requires two-steps to solve it. First, a student must understand that they need to find the total number of cars and trucks. Second, they must understand that they are only solving for the number of trucks. The round numbers in this problem are intentional because we want students to attend to the set-up of the problem rather than worrying about the calculations.

Further along in the Module, the numbers and the problem types increase in complexity. The focus remains on drawing or representing the problem, so students perform the correct operation with the correct numbers. Too often, students look at the numbers presented in a word problem and guess whether they should add or subtract them to get an answer. We hope to prevent that by teaching the RDW problem-solving process, as shown below.

solve the word problem using rdw strategy

Grade Levels 3–5

In Grade Levels 3–5, students use the RDW process to solve word problems involving all operations and to build multi-step problems. Lessons emphasize students developing strategies to address newer complexities of multiplication, division, and working with fractions in word problems.

Beginning in Grade Level 3, students are introduced to division through the context of word problems and encounter two types of division. In a partitive division problem, the number of groups and the total are known, but the number in each group is unknown. Partitive division asks, “How many are in each group?” In measurement division, the total and number in each group are known, but the number of groups is unknown. Measurement division asks the question, “How many groups are there?” Using the RDW process, students create a drawing that accurately represents the known and unknown number of groups and the number in each group to reveal the solution path.

Read-Draw-Write_EurekaMath2

In Grade Level 3, Module 1, Topic B, Lesson 9, students solve a partitive and measurement division problem using the RDW process. As they read and draw, they discern and represent what is known. Then, they identify the unknown and use division to solve it. In the problem shown here involving 24 desks, the number of groups is known. One approach is to begin by drawing 6 circles to represent the groups, then sharing the 24 desks between the groups. There is flexibility in the RDW process for students to draw and solve in a way that makes sense. In this case, a second student starts by drawing the 24 desks and knows they must form 6 equal groups. They can determine that forming six equal groups will result in 4 desks in each group.

Read-Draw-Write-Sample-3

How does thinking about what is known and unknown help you solve division word problems? Thinking about what is known helps me know if I should draw the number of groups or the number in each group. If the unknown is the number of groups, I can count the number of groups in my drawing to solve the problem. If the unknown is the number in each group, I can look at the number in each group in my drawing to solve the problem.

Later, in Lesson 18, students represent partitive and measurement division word problems with tape diagrams, rather than with equal groups. As a built-in feature of the RDW process, the teacher asks consistent questions: What is known? What is unknown? and How is it represented in the tape diagram? Students can consider those questions and rely on the familiar process of reading and representing the problem in chunks until identifying a path to solve it, even with the more abstract tape diagram. That process also reveals the difference between partitive and measurement division problems and deepens students’ understanding of problem-solving.

solve the word problem using rdw strategy

In Grade Level 4, word problem contexts expand to include multiplicative comparisons. There are multiple variations of the language in a problem that students encounter. Reading and drawing to represent the parts of the problem helps students distinguish between the known and unknown. In multiplicative comparison problems, the relationship between two quantities is often stated as “___ times as many as ___”, in other contexts, it is stated as “___ times as much as ___”, or even more specifically, “___times as heavy/long/tall as ___”. Both quantities may be given, and the total is unknown, or the total and one quantity are known, and the second quantity is unknown. Depending on the known and unknown quantities in the problems, students use multiplication or division to solve.

The RDW process supports students as they learn to interpret and evaluate multiplicative comparisons within word problems. For example, in the problem from Grade Level 4, Module 1, Topic A, Lesson 2 shown, students first Read and encounter comparison language in the phrase “4 times as many books.” Students typically represent the quantities with two separate tapes. The first tape shows 1 unit, the books that Ray reads. The second tape shows 4 units, or 4 times as many as Ray, the number of books Jayla reads. As part of the Draw step in the RDW process, students look at the tape diagram they’ve drawn and consider what it’s showing, what is known and unknown. This leads students to determine how to solve the problem. In this example, students recognize that they know the total of 4 units, so they can divide to find the unknown value of 1 unit.

How do you decide when to rename a product that Is a fraction greater than 1 as a mixed number? If it’s a word problem, thinking about what the product represents helps me decide when I should rename fractions greater than 1 as mixed numbers. If the answer doesn’t make sense as a fraction greater than 1, then I can rename it as a mixed number. Sometimes the question in the word problem helps me think about whether I should rename the fraction greater than 1 as a mixed number. When there isn’t a word problem or directions to write the answer as a mixed number, we can leave the product as a fraction greater than 1.

In Grade Level 4, Module 4, Lesson 33, students solve the problem: A kitten weighs 4 ⁄ 5 kilograms. A puppy is 6 times as heavy as the kitten. How many kilograms does the puppy weigh? Again, students can read the problem in chunks and draw a tape diagram to represent the weights of the kitten and puppy. The same process of reading and representing the problem supports problem-solving, even when one of the values is a fraction. However, with a fractional value, students consider whether to state their answer as a fraction greater than one or a mixed number. In the Write step, students return to the word problem to write an accurate solution statement and use the problem’s context to decide which number type makes sense to answer the question posed. As students engage in that decision-making process, they are reasoning abstractly and quantitatively and engaging in Standard for Mathematical Practice 2 (MP2). The Debrief discussion shown here emphasizes the role of the RDW process in deciding how to record an answer.

As the repertoire of problem types continues to expand along with number types, RDW continues to be a supportive process students use to read and understand a problem, create a drawing that clarifies the known, unknown, and solution path, and to state the answer in a way that makes sense.

In Grade Level 5, the complexity of word problems advances to multi-step (3+ steps) word problems. Students reiterate the RDW steps of reading a chunk and representing the information in a drawing multiple times. Students practice refining this process to create an accurate drawing and to use the RDW process efficiently in Module 3, Lessons 20 and 21.

Read-Draw-Write_Sample2_EurekaMath2

In Lesson 20, through the RDW process, students explore multiple ways fractional amounts can be represented in tape diagrams. In reading and understanding the language of the problem, students determine whether it is a comparison problem, which helps them decide how many tapes to draw. Students also represent fractional amounts such as “ 2 ⁄ 5 of his money” and “ 1 ⁄ 3 of the remaining money.” When students draw step by step as they read, they first partition the tape diagram into 5 parts and label 2 parts to represent 2 ⁄ 5 . This leaves 3 parts unlabeled and 1 ⁄ 3 is simpler to identify.

Does the Read-Draw-Write process help us solve multI-step word problems Involving fractions? How? Yes. We read, draw, and write in chunks.When we learn new information, we pause to draw and then go back to reading and draw when we learn something new. We can write expressions or equations as we realize which operations we can use to find unknown information. Yes. The model I draw helps me decide which operation to use to find an unknown value. Each time we find new information by evaluating an expression, we can compare it to our model and ask, Does that make sense based on what I see in the model?

In Lesson 21, students encounter additional multi-step word problems with fractional amounts and take on more responsibility in determining how to represent and solve. When students use a self-selected method to solve a comparison word problem involving fractions, they model with mathematics and practice Standard for Mathematical Practice 4 (MP4). The key question of the lesson: Does the Read–Draw–Write process help us solve multi-step word problems? How? has them reflecting on the process throughout the lesson and finally in the Debrief, as shown. The flexibility of the process supports students as they read and return to modify their drawings multiple times. RDW also continues to aid students in identifying the known and unknown information and a solution path.

Representing comparisons and fractional amounts in Grade Levels 4 and 5 prepares students to visually represent ratios in Grade Levels 6 and beyond. The number choices and problem types continue to grow in complexity over the years. However, the RDW process remains a foundational tool for solving word problems.

Grade Levels 6–Algebra I

Much of the progression of mathematics in the middle school years includes algebraic understanding and representation, and the RDW routine progresses similarly. Instead of using drawing as the main problem-solving strategy, Eureka Math 2 Story of Ratios uses algebraic thinking as the main strategy. RDW progresses to RRSS: Read, Represent, Solve, Summarize. The representation can still be a drawing, but it could also be an equation with variables representing the unknown.

solve the word problem using rdw strategy

The Read portion of the routine is used to find the same information as in RDW, to identify what the problem is asking us to find and what we know. In the Represent portion of the routine, students choose the representation that makes the most sense to them, such as tape diagrams, a double number line, a table, or a graph, and then they share their representations with one another. Pairs then use their representation to solve the problem. After completing the problem, the teacher directs students to summarize their findings by asking questions such as, “Does my answer make sense?” and “Does my result answer the question?”

Have groups work to solve problem 3. Circulate as students work, and observe the strategies groups use as they read, represent, solve, and summarize. Encourage students to return to problems 1 and 2 if necessary, and ask the following questions to advance their thinking:

  • What is the problem asking you to find? What do you know that is given in the problem? What do you know based on your chosen method of travel?
  • What tool can you use to represent the problem?
  • Does your model show what is known and whot is unknown? How can you improve your model?
  • What units do you need to consider in the problem?
  • Does your answer make sense?
  • Does your result answer the question?

To continue practicing the routine, students choose from a list of transportation methods and determine how long it will take for that method to transport them to the moon. The teacher is given a list of possible questions to advance students’ use of the RRSS routine. Beyond the Read portion of the routine, questions such as “What tool can you use to represent the problem?” and “Does your model show what is known and what is unknown?” gently guide students through the Represent portion of the routine.

This lesson that specifies the use of the RRSS routine is rare. Generally, the routine is not called out in the problem prompts or lesson structures. Instead, the tool is part of the students’ toolkit, and students reach for it when they deem it appropriate. Because of this, teachers will likely need to post the steps to the routine, say the steps during think-alouds, and remind students during problem-solving activities. Consider using the advancing questions from Lesson 21 in other problem-solving situations.

Teacher-Note-Sample

The first instance of the routine in Grade Level 7 is in Module 1, Lesson 11, when students are further encouraged to represent the problem “…by using a tape diagram, an equation, a graph, a table, or any other model.” Advancing students’ thinking toward an algebraic representation, students use a double number line, then a graph, and finally an equation for the distance formula,  d=rt , in subsequent problems in the lesson. The RRSS routine is mentioned in Launch and in a Teacher Note but not called out further in the lesson guidance. Encouraging students to use RRSS as a tool in their kit will again be important for Grade Level 7 teachers.

There are many instances in Grade Level 8 when using the RRSS routine would aid students in problem-solving. However, the routine is not called out by name until Module 4, Lesson 10. In this Grade Level 8 lesson, students use linear equations to solve real-world problems. Students begin working with the routine as a class. Then, they use the routine with a partner and eventually work with it independently. While other representations may help students write the linear equation, representation of the problem with a linear equation is a specific task requirement. Students analyze the number of solutions to the equation in the context of the situation as they summarize the solution in the last step of the routine. Students recognize that the solution to the equation does not always answer the question from the problem, an additional complexity to problem-solving at this level.

The work with Read–Draw–Write and Read–Represent–Solve–Summarize engages students in many of the mathematical practices, but ultimately leads to the final goal, success with the modeling cycle (MP4) for problem-solving in high school mathematics. Math Practice 4 begins with, “Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.” 1 There are many ways to model the process of mathematical problem-solving. Most start with a real-world problem, iterate, formulating a solution strategy, performing some computations, interpreting the results, ensuring those results are accurate, and then reporting final results if they are validated.

The Algebra I Eureka Math 2 curriculum takes the modeling cycle to its fruition, giving students multiple experiences with real-world problems. The first instance is in Module 1, Lesson 7 titled Printing Presses. Students work in groups to find an entry point for solving a problem about printing presses. Students analyze a variety of solution paths, building connections between quantitative reasoning and the process of writing and solving an equation in one variable. Connections are made to the RDW and RRSS routines when the teacher asks, “What assumptions can be made? What information do we know remains constant?” and “What are the important quantities? How are these quantities related?” The answers to all of these questions result in ways to read and represent the information from the problem.

In Module 2, students watch a video showing a “regular” showerhead and a low-flow showerhead. To further develop the modeling cycle, instead of giving students the problem, students explore questions related to the problem before narrowing their focus to one question. Information is withheld to allow students to independently determine what is required to answer the question. Additional information is provided only after students decide what assumptions need to be made during the formulation and computation stages of the modeling cycle. Students eventually connect different solution paths to a system of linear equations and explore the effects of changing the assumptions within the context as groups interpret and verify their results.

In other lessons, Algebra I students analyze falling objects and projectile motion, maximize area, and determine how a search and rescue helicopter relates quadratic functions to the real world. Connecting linear and exponential functions to the real world involves lessons in which students work with world populations, temperatures of objects cooling over time, and invasive species populations. The final Module of Algebra I brings all the years’ learning together as students use the modeling cycle to analyze paint splatters, reflect on the role of a city planner, consider a financial deal proposed by a business owner, plan a three-dimensional model of the solar system, and plan a fundraiser that maximizes profit.

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Two-Step Word Problems - Fractions

Related Topics: Lesson Plans and Worksheets for Grade 5 Lesson Plans and Worksheets for all Grades More Lessons for Grade 5 Common Core For Grade 5

Videos, examples, and solutions with examples and solutions to help Grade 5 students learn how to solve two-step word problems. Common Core Standards: 5.NF.1, 5.NF.2

New York State Common Core Math Module 3, Grade 5, Lesson 7

Download Worksheets for Grade 5, Module 3, Lesson 7 (Pdf)

Lesson 7 Concept Development Problem 1 George weeded 1/5 of the garden, and Summer weeded some, too. When they were finished, 2/3 of the garden still needed to be weeded. What fraction of the garden did Summer weed? Problem 2 Jing spent 1/3 of her money on a pack of pens, 1/2 of her money on a pack of markers, and 1/8 of her money on a pack of pencils. What fraction of her money is left? Problem 3 Shelby bought a 2 ounce tube of blue paint. She used 2/3 ounce to paint the water, 3/5 ounce to paint the sky, and some to paint a flag. After that she has 2/15 ounce left. How much paint did Shelby use to paint her flag? Problem 4 Jim sold 3/4 gallon of lemonade. Dwight sold some lemonade too. Together, they sold 1 5/12 gallons. Who sold more lemonade, Jim or Dwight? How much more? Problem 5 Leonard spent 1/4 of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had 3/8 of his money left. What fraction of his money did he spend on the comic books?

Lesson 7 Homework Solve the word problem using the RDW strategy. Show all your work.

  • Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it, and gave the left overs to his friends. What fraction of the pie did he give to his friends?
  • Liang went to the bookstore. He spent 1/3 of his money on a pen and 4/7 of it on books. What fraction of his money did he have left?
  • Tiffany bought 2/5 kg of cherries. Linda bought 1/10 kg of cherries less than Tiffany. How many kg of cherries did they buy altogether?
  • Mr. Rivas bought a can of paint. He used 3/8 of it to paint a book shelf. He used 1/4 of it to paint a wagon. He used some of it to paint a bird house, and have 1/8 of paint left. How much paint did he use for the bird house?
  • Ribbon A is 1/3 m long. It is 2/5 m shorter than ribbon B. What’s the total length of two ribbons?

Lesson 7 Homework This video shows how to solve word problems using diagrams and an area model. Solve the word problem using the RDW strategy. Show all your work. 4. Mr. Rivas bought a can of paint. He used 3/8 of it to paint a book shelf. He used 1/4 of it to paint a wagon. He used some of it to paint a bird house, and have 1/8 of paint left. How much paint did he use for the bird house?

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Eureka Math Grade 5 Module 3 Lesson 15 Answer Key

Engage ny eureka math 5th grade module 3 lesson 15 answer key, eureka math grade 5 module 3 lesson 15 sprint answer key.

Engage NY Math 5th Grade Module 3 Lesson 15 Sprint Answer Key 1

Eureka Math Grade 5 Module 3 Lesson 15 Problem Set Answer Key

Solve the word problems using the RDW strategy. Show all of your work. Question 1. In a race, the-second place finisher crossed the finish line 1\(\frac{1}{3}\) minutes after the winner. The third-place finisher was 1\(\frac{3}{4}\) minutes behind the second-place finisher. The third-place finisher took 34\(\frac{2}{3}\) minutes. How long did the winner take? Answer: Fraction of time of Second place finisher crossed the line after = 1\(\frac{1}{3}\) minutes = \(\frac{4}{3}\) Fraction of time of Third place finisher is behind the second place  = 1\(\frac{3}{4}\) minutes  = \(\frac{7}{4}\) Fraction of time the third place finisher took = 34\(\frac{2}{3}\) = \(\frac{105}{3}\) Fraction of time the second place runner took = \(\frac{105}{3}\) – \(\frac{7}{4}\) = \(\frac{420}{12}\) – \(\frac{21}{12}\) = \(\frac{399}{12}\) = \(\frac{133}{4}\) Fraction of time the First place runner took = \(\frac{133}{4}\) – \(\frac{4}{3}\) = \(\frac{399}{12}\) – \(\frac{16}{12}\) = \(\frac{383}{12}\) = 31 \(\frac{11}{12}\) . Therefore the First Runner took = 31 \(\frac{11}{12}\) .minutes.

Question 2. John used 1\(\frac{3}{4}\) kg of salt to melt the ice on his sidewalk. He then used another 3\(\frac{4}{5}\) kg on the driveway. If he originally bought 10 kg of salt, how much does he have left? Answer: Fraction of Salt used by John =1\(\frac{3}{4}\) kg = \(\frac{7}{4}\) kg Fraction of Salt used again =3\(\frac{4}{5}\) kg = \(\frac{24}{5}\) kg Fraction of salt used = \(\frac{7}{4}\)  + \(\frac{24}{5}\) = \(\frac{35}{20}\)  + \(\frac{96}{20}\) = \(\frac{131}{20}\)  = 6 \(\frac{11}{20}\) . Total Salt = 10 kg. Fraction of salt left = 10 – \(\frac{131}{20}\)  = \(\frac{200}{20}\)  – \(\frac{131}{20}\)  = \(\frac{69}{20}\)  = 3\(\frac{9}{20}\)  . Therefore Fraction of salt left = 3\(\frac{9}{20}\)  .

Question 3. Sinister Stan stole 3\(\frac{3}{4}\) oz of slime from Messy Molly, but his evil plans require 6\(\frac{3}{8}\) oz of slime. He stole another 2\(\frac{3}{5}\) oz of slime from Rude Ralph. How much more slime does Sinister Stan need for his evil plan? Answer: Fraction of slime stolen from Messy Molly = 3\(\frac{3}{4}\) = \(\frac{15}{4}\) oz Fraction of slime stolen from Messy Molly again = 2\(\frac{3}{5}\) = \(\frac{13}{5}\) oz Total Fraction Stolen = \(\frac{15}{4}\)  + \(\frac{13}{5}\) = \(\frac{75}{20}\) + \(\frac{52}{20}\) = \(\frac{127}{20}\) = 6\(\frac{7}{20}\) . Fraction of more slime required = 6\(\frac{3}{8}\) – \(\frac{127}{20}\) = \(\frac{51}{8}\) – \(\frac{127}{20}\) = \(\frac{255}{40}\) – \(\frac{254}{40}\) = \(\frac{1}{40}\) . Therefore, Fraction of more slime required = \(\frac{1}{40}\) oz.

Question 4. Gavin had 20 minutes to do a three-problem quiz. He spent 9\(\frac{3}{4}\) minutes on Problem 1 and 3\(\frac{4}{5}\) minutes on Problem 2. How much time did he have left for Problem 3? Write the answer in minutes and seconds. Answer: Time given for 3 problems = 20 minutes Fraction of time Spent on Problem 1 = 9\(\frac{3}{4}\) minutes = \(\frac{39}{4}\) . Fraction of Time spent on Problem 2 = 3\(\frac{4}{5}\) = \(\frac{19}{5}\) . Fraction of Time spent on Problem 3 = x 20 = \(\frac{39}{4}\) + \(\frac{19}{5}\) + x x = 20 – \(\frac{39}{4}\) – \(\frac{19}{5}\) x = \(\frac{400}{20}\) – \(\frac{195}{20}\) – \(\frac{76}{20}\) x = \(\frac{129}{20}\) = 6\(\frac{9}{20}\) . Therefore, Fraction of Time spent on Problem 3 = 6\(\frac{9}{20}\) .

Question 5. Matt wants to shave 2\(\frac{1}{2}\) minutes off his 5K race time. After a month of hard training, he managed to lower his overall time from 21\(\frac{1}{5}\) minutes to 19\(\frac{1}{4}\) minutes. By how many more minutes does Matt need to lower his race time? Answer: Fraction of Time lowered = 21\(\frac{1}{5}\) minutes to 19\(\frac{1}{4}\) minutes. = \(\frac{106}{5}\) – \(\frac{77}{4}\) = \(\frac{424}{20}\) – \(\frac{385}{20}\) = \(\frac{39}{20}\) =1\(\frac{19}{20}\) . Fraction of Time shaved = 2\(\frac{1}{2}\) =\(\frac{5}{2}\) . Fraction of More Time Matt need to lower his race time = \(\frac{5}{2}\) – \(\frac{39}{20}\) = \(\frac{50}{20}\) – \(\frac{39}{20}\) = \(\frac{11}{20}\) = \(\frac{33}{60}\) = 33 minutes .

Eureka Math Grade 5 Module 3 Lesson 15 Exit Ticket Answer Key

Solve the word problem using the RDW strategy. Show all of your work. Cheryl bought a sandwich for 5\(\frac{1}{2}\) dollars and a drink for $2.60. If she paid for her meal with a $10 bill, how much money did she have left? Write your answer as a fraction and in dollars and cents. Answer: Fraction of Cost of sandwich = 5\(\frac{1}{2}\) = \(\frac{11}{2}\) dollar = 5.5 dollar Fraction of Cost of Drink = $2.60. Total Cost = 5.5 +2.60 = 8.1 $. Amount paid = 10$. Money left = 10 – 8.1 = 1.9 $ .

Eureka Math Grade 5 Module 3 Lesson 15 Homework Answer Key

Solve the word problems using the RDW strategy. Show all of your work. Question 1. A baker buys a 5 lb bag of sugar. She uses 1\(\frac{2}{3}\) lb to make some muffins and 2\(\frac{3}{4}\) lb to make a cake. How much sugar does she have left? Answer: Total Quantity of Sugar = 5 lb Fraction of Quantity of Suagr used for muffins = 1\(\frac{2}{3}\) lb = \(\frac{5}{3}\) Fraction of Quantity of Suagr used cake = 2\(\frac{3}{4}\) lb = \(\frac{11}{4}\) Fraction of Quantity of Sugar used = \(\frac{5}{3}\) + \(\frac{11}{4}\) = \(\frac{20}{12}\) + \(\frac{33}{12}\) = \(\frac{53}{12}\) Fraction of Quantity of Sugar left = 5 – \(\frac{53}{12}\) = \(\frac{60}{12}\) – \(\frac{53}{12}\) =\(\frac{7}{12}\) . Therefore, Fraction of Quantity of sugar left = \(\frac{7}{12}\) .

Question 2. A boxer needs to lose 3\(\frac{1}{2}\) kg in a month to be able to compete as a flyweight. In three weeks, he lowers his weight from 55.5 kg to 53.8 kg. How many kilograms must the boxer lose in the final week to be able to compete as a flyweight? Answer: Fraction of weight need to lose in month = 3\(\frac{1}{2}\) = \(\frac{7}{2}\) = 3.5 kg Weight lost in 3 weeks = 55.5 –  53.8 = 1.7 kg Weight need to lose in final week = 3.5 – 1.7 = 1.8 kg.

Question 3. A construction company builds a new rail line from Town A to Town B. They complete 1\(\frac{1}{4}\) miles in their first week of work and 1\(\frac{2}{3}\) miles in the second week. If they still have 25\(\frac{3}{4}\) miles left to build, what is the distance from Town A to Town B? Answer: Fraction of work completed in first week = 1\(\frac{1}{4}\) miles = \(\frac{5}{4}\) Fraction of work completed in second week = 1\(\frac{2}{3}\) miles = \(\frac{5}{3}\) Fraction of work left to built = 25\(\frac{3}{4}\) miles = \(\frac{103}{4}\) Fraction of Distance from Town A to Town B = \(\frac{103}{4}\) + \(\frac{5}{4}\)  + \(\frac{5}{3}\) = \(\frac{108}{4}\) + \(\frac{5}{3}\) = \(\frac{324}{12}\) + \(\frac{20}{12}\) = \(\frac{344}{12}\)= 28\(\frac{2}{3}\) . Therefore, Fraction of Distance from Town A to Town B = 28\(\frac{2}{3}\) miles.

Question 4. A catering company needs 8.75 lb of shrimp for a small party. They buy 3\(\frac{2}{3}\) lb of jumbo shrimp, 2\(\frac{5}{8}\) lb of medium-sized shrimp, and some mini-shrimp. How many pounds of mini-shrimp do they buy? Answer: Quantity of shrimp needed = 8.75 lb =8\(\frac{3}{4}\) = \(\frac{27}{4}\) Quantity of jumbo shrimp = 3\(\frac{2}{3}\) lb = \(\frac{11}{3}\) Quantity of  medium – sized shrimp = 2\(\frac{5}{8}\) lb = \(\frac{21}{8}\) Quantity of mini shrimp = x \(\frac{35}{4}\)  = \(\frac{11}{3}\) + \(\frac{21}{8}\) + x x = \(\frac{210}{24}\)  – \(\frac{88}{24}\) – \(\frac{63}{24}\) x =  \(\frac{59}{24}\) = 2 \(\frac{11}{24}\) Therefore, Quantity of mini shrimp = x = 2 \(\frac{11}{24}\) lb .

Question 5. Mark breaks up a 9-hour drive into 3 segments. He drives 2\(\frac{1}{2}\) hours before stopping for lunch. After driving some more, he stops for gas. If the second segment of his drive was 1\(\frac{2}{3}\) hours longer than the first segment, how long did he drive after stopping for gas? Answer: Total time of the drive = 9 hours . Fraction of Time drived for first segment = 2\(\frac{1}{2}\) hours  = \(\frac{5}{2}\) Fraction of Time of second segment = 1\(\frac{2}{3}\) hours longer than the first segment = \(\frac{5}{3}\) + \(\frac{5}{2}\) = \(\frac{10}{6}\) + \(\frac{15}{6}\) = \(\frac{25}{6}\) =4 \(\frac{1}{6}\) Fraction of Time of first and second segment= \(\frac{5}{2}\) + \(\frac{25}{6}\) = \(\frac{15}{6}\) + \(\frac{25}{6}\) = \(\frac{40}{6}\) = 6\(\frac{4}{6}\) Fraction of Time he drive after stopping gas = 9 – \(\frac{40}{6}\) = \(\frac{54}{6}\) –  \(\frac{40}{6}\) = \(\frac{14}{6}\) = 2\(\frac{2}{6}\) . Therefore, Fraction of Time he drive after stopping gas = third segment = 2\(\frac{2}{6}\) hours .

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Teaching with Jennifer Findley

Upper Elementary Teaching Blog

December 5, 2018 | 1 Comment | Filed Under: Decimals , Fractions , Geometry & Measurement , Math , Math Centers , Multiplication & Division , Word Problems

Word Problem Strategies : Analyzing Word Problems with Free Organizers/Mats

Word problems used to be the bane of my existence as a new teacher. Thankfully, I learned new strategies and resources to help me implement and teach word problem strategies all year. To be honest, teaching word problems all year was the ONE thing that I did that had the greatest impact (if you are interested in more information about word problems and how I teach them, see the links at the bottom of this article). On this post, I will share one of those word problem strategies that involves helping students think through and analyze word problems using graphic organizers or word problem mats.

One of my go-to word problem strategies to help my students comprehend and solve word problems involves using graphic organizers or mats. Read more and grab free versions of different organizers on this post.

Teaching Word Problem Strategies with Word Problem Organizers

These word problem graphic organizers/mats help walk students through the thinking and analyzing process that is automatic for us. Through this analysis, the students have a better chance of comprehending the word problem, choosing the correct operation to solve it, and determining if their answers make sense.

In the same manner that we teach students to comprehend texts, we should also teach them how to breakdown and analyze a word problem. Using graphic organizers/mats helps break the process down into manageable steps for the students.

The free download (available a few sections down) has several different versions to allow you to choose which works best for your students and their needs. Having the different versions will also allow you to differentiate the organizers.

Practice solving word problems with these free word problem organizers.

My go to version to begin with has the students following these steps:

  • What operation are you planning to use? Write or underline the evidence from the problem that supports that operation.
  • Solve the problem and show your math work.
  • Write the answer in a complete sentence.

And here is an example from one of the more advanced organizers with more steps:

  • Retell the problem in your own words.
  • What operation are you thinking will solve this problem? Why?
  • Write the answer to the problem in a complete sentence.
  • Prove your answer is correct.

Using the Word Problem Organizers

You have a ton of variety in how you choose to use these organizers, however I definitely recommend following this sequence:

  • Introduce the organizer/mat by going over the steps and how they help the student comprehend the word problem and/or organize their work. Understanding the purpose behind the organizer is huge with students because you don’t want them to view it as busy work.
  • Model how to complete the organizer/mat whole group with at least one word problem (and more if the students need it and depending on the complexity of the organizer you choose).
  • Allow the students to work in pairs or triads to complete the organizer as a form of guided practice before they are required to do so independently.

The graphic organizers/mats can also be used as a guide for students when discussing the word problem with partners. They don’t always have to fill in each part of it, but instead they can discuss some of the parts. This will give the same benefits in less time.

Also, placing the word problem organizers/mats in page protectors and letting the students use expo markers instantly makes it more engaging.

Here are some ways you can use these word problem mats to help your students practice analyzing word problems:

  • Math centers
  • Small group teaching
  • Independent work
  • Homework – send home a page protector and expo marker and let the students use the mats at home or they can use the mats as a guide as they work through word problems. These organizers will also help parents support students if they struggle with a word problem.

Analyze word problems with these free word problem mats.

About the Digital Word Problem Organizers

There are digital versions of each of the word problem organizers included in the download below. The digital access link can be found on page 6. Each slide has text boxes for students to type into and interactive ways to complete some of the tasks.

The digital organizers are available in two versions, one with a designated spot to write a word problem and one without the space.

Download these digital word problem organizers for your upper elementary math students!

Should the students use the mat with every word problem they solve?

They certainly can (especially if you use dry erase markers and/or have them discuss some of the parts instead of recording it all) but they don’t have to. Using the organizers will help them work through complex problems but will take more time. When I use these in math centers, I only require one word problem to be worked on fully on the more advanced organizers. However this depends on the mat you choose. Some of them are more simple and don’t require any extra work- the mat simply organizes the work they would already do.

Download the Word Problem Strategies Mats

Click here or on the image to download the Word Problem Mats. Remember there are several versions so you can choose the ones that work best for your grade level and your students’ needs.

One of my go-to word problem strategies to help my students comprehend and solve word problems involves using graphic organizers or mats. Read more and grab free versions of different organizers on this post.

Need More Word Problem Strategies and Resources?

Check out these helpful resources, blog posts, and freebies for even more help teaching word problems.

Teaching Word Problems without Key Words (And What to Teach Instead)

Word Problem of the Day: FREE Starter Packs

8 Ways to Help Students Be Successful with Word Problems

Show the LOVE with Word Problems: Helping Students Answer Word Problems Effectively

Teaching Students How To Justify Answers in Math

Close Reading in Math Strategies and Freebies

10 Ways to Get Students Writing in Math

Solving Multi-Part Word Problems

4th Grade Word Problem of the Day TpT Resource

5th Grade Word Problem of the Day TpT Resource

The task card word problems shown in the images are part of my task card collections for 3rd-5th grade math. Click on the links below if you wish to see these resources in your grade level.

3rd Grade Common Core Math Task Card Collection

4th Grade Common Core Math Task Card Collection

5th Grade Common Core Math Task Card Collection

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solve the word problem using rdw strategy

Welcome friends! I’m Jennifer Findley: a teacher, mother, and avid reader. I believe that with the right resources, mindset, and strategies, all students can achieve at high levels and learn to love learning. My goal is to provide resources and strategies to inspire you and help make this belief a reality for your students. Learn more about me.

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Solve the word problems using the RDW strategy. Show all of your work. Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave the leftovers to his friends. What fraction of the pie did he give to his friends?

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  1. Read-Draw-Write: Making Word Problems Less Problematic

    Eureka Math® encourages students to use the Read-Draw-Write (RDW) process as a tool for solving word problems. The RDW process helps students make sense of word problems. Students using the RDW process first read the whole problem to get an idea of what's happening in the story.

  2. Problem Solving the RDW Way. Strategies

    Problem Solving the RDW Way Strategy Eureka Math · Follow Published in Eureka Math · 3 min read · Apr 10, 2015 3 What do you see when you look at this student's work?

  3. Mixed Word Problems with RDW Strategy

    Students will be able to solve mixed operation word problems using the RDW strategy. EL adjustments On Introduction (3 minutes) Display the example problem from the Word Problem Solving Template: Read-Draw-Write (RDW) worksheet.

  4. Read, Draw, Write: A Better Strategy for Solving

    1. Understand the Problem 2. Come up with a Plan for Solving 3. Carry out the Plan 4. Reflect or Check Your Work These steps are better known as Polya's Problem Solving Approach and were developed by George Polya in 1945.

  5. From Read-Draw-Write (RDW) to Modeling-How Students Experience Problem

    Coherence is a key feature of the Eureka Math2® curriculum. The problem-solving process employed in Grade Levels K-9 is a major part of that coherence. In Grade Levels K-5, students know it as the Read-Draw-Write (RDW) process. Starting in Grade Level 6 the process advances to Read, Represent, Solve, Summarize (RRSS) while maintaining ...

  6. What is the READ DRAW WRITE strategy for solving word problems

    3rd Grade Math: The Read Draw Write process (RDW) is a strategy for solving word problems in math. This video breaks down the steps for answering questions, ...

  7. What Is the Read Draw Write Process?

    The Read Draw Write process (RDW) is a strategy for solving word problems in math. This article breaks down the steps for answering questions, including an example of a read, draw, write solution. How the Read Draw Write Process Works Read. The first step in the RDW process is to carefully read the problem.

  8. Two-Step Word Problems with Mixed Operations

    Intermediate. Provide visuals to accompany the names of the games. Label the games with their names in students' home languages (L1). Download to read more. With this lesson plan, students will be able to solve two-step, mixed operation word problems using the Read, Draw, Write (RDW) strategy.

  9. Solution Strategies to Word Problems (solutions, examples, videos

    Lesson 3 Homework. Use the RDW process to solve the problems below. Use a letter to represent the unknown in each problem. 1. Jerry pours 86 milliliters of water into 8 tiny beakers. He measures an equal amount of water into the first 7 beakers. He pours the remaining water into the eighth beaker. It measures 16 milliliters.

  10. Strategies for Solving Word Problems

    1. Read the word problem- reread as needed 2. Draw a picture or diagram that represents the information given 3. Write a number sentence or equation to solve the word problem Let's look at an example: Read Draw Write Strategy For Solving Word Problems Why I Use the RDW Strategy with My Students

  11. Two-Step Word Problems (solutions, examples, videos, worksheets, lesson

    This video shows how to solve word problems using diagrams and an area model. Solve the word problem using the RDW strategy. Show all your work. 4. Mr. Rivas bought a can of paint. He used 3/8 of it to paint a book shelf. He used 1/4 of it to paint a wagon. He used some of it to paint a bird house, and have 1/8 of paint left.

  12. Eureka Math Grade 5 Module 3 Lesson 15 Answer Key

    Eureka Math Grade 5 Module 3 Lesson 15 Problem Set Answer Key. Solve the word problems using the RDW strategy. Show all of your work. Question 1. In a race, the-second place finisher crossed the finish line 1\(\frac{1}{3}\) minutes after the winner. The third-place finisher was 1\(\frac{3}{4}\) minutes behind the second-place finisher.

  13. Read, Draw, Write: A Better Strategy for Problem Solving

    1. Understand the Problem 2. Come up with a Plan for Solving 3. Carry out the Plan 4. Reflect or Check Your Work These steps are better known as Polya's Problem Solving Approach a nd were...

  14. Strategy Alert RDW (Read-Draw-Write) Method for Solving Word Problems

    Does your scholar have a difficult time, solving word problems? Give the RDW method a try!

  15. Solved Date Solve the word problems using the RDW strategy ...

    This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Date Solve the word problems using the RDW strategy. Show all of your work. Christine baked a pumpkin pie. She ate (1)/ (6) of the pie. Her brother ate (1)/ (3) of it and gave the leftovers to his friends.

  16. Word Problems Rdw Teaching Resources

    RDW Word Problem Solving Strategy Posters Chalkboard Themed by Hey Natayle 4.9 (67) $2.00 PDF Elementary math teachers will love these chalkboard themed RDW posters for their math bulletin board. The RDW strategy is a helpful tool students may use when attacking word problems in math.

  17. Rdw Word Problem Worksheets & Teaching Resources

    $10 and up On Sale RDW Word Problem Solving Strategy Posters Chalkboard Themed by Hey Natayle 63 $2.00 PDF Compatible with Elementary math teachers will love these chalkboard themed RDW posters for their math bulletin board. The RDW strategy is a helpful tool students may use when attacking word problems in math.

  18. Word Problem Strategies : Analyzing Word Problems with Free Organizers/Mats

    Using graphic organizers/mats helps break the process down into manageable steps for the students. The free download (available a few sections down) has several different versions to allow you to choose which works best for your students and their needs. Having the different versions will also allow you to differentiate the organizers.

  19. Results for word problems rdw process

    Created by. Sharper Teacher. This 30-second video is ready to use to support students' daily mathematical practices with solving word problems. It takes students step-by-step through the RDW (read, draw, write) strategy for solving word problems. Use the video whole class, small group, and with individual students.

  20. The effects of the RIDE strategy on teaching word problem solving

    mnemonic device on solving word problems for middle school students with Learning Disabilities and to examine the teacher and student satisfaction in teaching and learning using . RIDE. to solve word problems. Two male 8th graders participated in this study. They were both classified as having learning disabilities and were learning mathematics ...

  21. Solve the word problems using the RDW strategy. Show all of

    Solve the word problems using the RDW strategy. Show all of your work. Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave the leftovers to his friends. What fraction of the pie did he give to his friends?

  22. Solve the word problem using the RDW strategy. Show all of your work in

    Solve the word problem using the RDW strategy. Show all of your work in your journal. Cheryl bought a sandwich for 5 1/2 dollars and a drink for $2. 60. If she paid for her meal with a $10 bill, how much money did she have left? Select the answer as a fraction and in dollars and cents. * Advertisement aliibrah8958 is waiting for your help.