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Examples
A group of students are playing soccer during lunch. How many students are needed to form four teams with eleven players each and to have two referees?Clarifications
Clarification 1: Instruction includes understanding the context of the problem, as well as the quantities within the problem.Clarification 2: Multiplication is limited to factors within 12 and related division facts. Refer to Situations Involving Operations with Numbers (Appendix A).
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Expression
- Equation
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to apply all four operations to solve one- and two-step real-world problems. This benchmark continues the work done in grade 2 solving real-world problems using addition and subtraction (MA.2.AR.1.1).- Instruction should facilitate students’ understanding of contexts and quantities within word problems.
- The emphasis on teaching problem-solving strategies should focus on the comprehension of problem contexts and what quantities represent in them. Examples of questions that help students comprehend word problems are:
- Teachers should model answering these questions through rectangular arrays, base-ten blocks, counters and think-alouds. In addition, teachers should help students explore estimation strategies to determine reasonable ranges for solutions (e.g., rounding, finding low and high estimates) and teach problem-solving strategies that build comprehension (e.g., Three Reads) (MTR.4.1, MTR.5.1, MTR.6.1).
Common Misconceptions or Errors
- Students may have difficulty creating effective models (e.g., drawings, equations) that will help them solve real-world problems. To assist students, provide opportunities for them to estimate solutions and try different models before solving. Beginning instruction by showing problems without their quantities is a strategy for helping students determine what steps and operations will be used to solve.
- Students may also have difficulty identifying when real-world problems require two steps to solve and will complete only one of the steps. Focusing on comprehension of real-world problems helps students determine what step(s) are required to solve.
Strategies to Support Tiered Instruction
- Instruction provides opportunities for students to estimate solutions and try different models before solving.
- Instruction includes opportunities to create models (e.g., equations, drawings, manipulatives) to help solve real-world problems. The teacher uses guided questioning to support comprehension, considering levels of reading proficiency for students who may struggle with word problems—some students may need to hear the problems read aloud. The teacher provides opportunities to estimate solutions and try different models before solving, beginning instruction by showing problems without their quantities is a strategy to help students determine what steps and operations will be used to solve.
- For example, the teacher reads aloud the following problem: Keisha and Diego are selling pies for a fundraiser. Each pie cost five dollars. If Keisha sells 15 pies and Diego sells 5 pies, how much money did they earn for the fundraiser?
- The teacher uses questioning to ensure comprehension (e.g., “What do you need to find out?” “What do the quantities represent in the problem?” “What will the solution represent in the problem?”).
- The teacher models how to represent this problem using an equation and a drawing:
- For example, the teacher reads aloud the following problem: Keisha and Diego are selling pies for a fundraiser. Each pie cost five dollars. If Keisha sells 15 pies and Diego sells 5 pies, how much money did they earn for the fundraiser?
20 × 5
- The teacher repeats with additional two-step problems, guiding students to create appropriate models to support problem-solving.
- For example, the teacher reads aloud the following problem: Antwan is helping the art teacher get ready for art club. There are a total of 30 paintbrushes. The art teacher asked Antwan to put 6 paintbrushes on each of the 4 tables in the room and then put the rest on the counter. How many paint brushes will he put on the counter?
- The teacher uses questioning to ensure comprehension (e.g., “What do you need to find out?” “What do the quantities represent in the problem?” “What will the solution represent in the problem?”).
- The teacher models the problem using counters, prompting the students to demonstrate each step of the problem while writing the corresponding equations for each step.
30 − 24 = 6
- The teacher repeats with additional two-step problems, guiding students to create appropriate models using manipulatives to support problem- solving. Some students may benefit from “ acting out” the story in the problem to support the problem-solving process.
- Instruction includes guided practice identifying and completing two steps in a real-world problem. The teacher uses guided questioning to support comprehension considering levels of reading proficiency for students who may struggle with word problems—some students may need to hear the problems read aloud. The teacher uses explicit prompts for each step.
- For example, the teacher reads aloud the following problem: Suni is taking piano lessons. Her piano teacher told her to practice for 90 minutes this week. On Monday, she practiced for 15 minutes. She practiced 20 minutes on Tuesday and 25 minutes on Wednesday. How much more time does she still need to practice this week?
- The teacher uses guided questioning and prompts to help students identify the steps (e.g., “ What do you already know?” “ What do you need to find out?” “ What do we need to do before we can find out the remaining time she has left to practice?”). Through questioning, the teacher guides students to identify the first step: adding the amount of time Suni has already practiced.
- The teacher uses a model to represent the problem and an equation to represent the first step.
15 + 20 + 25 = 60 - After students complete the first step, the teacher uses questioning to prompt the next step (e.g., “ What does the sum we just found show us?” “ What do you need to find out to solve this problem?” “ What should we do next?”). The problem may need to be reread aloud.
- For example, the teacher reads aloud the following problem: Suni is taking piano lessons. Her piano teacher told her to practice for 90 minutes this week. On Monday, she practiced for 15 minutes. She practiced 20 minutes on Tuesday and 25 minutes on Wednesday. How much more time does she still need to practice this week?
- The teacher repeats with additional two-step problems, guiding students to identify and solve each step.
- For example, the teacher reads aloud the following problem: Rahim is learning about instruments in music class. He learns that guitars have six strings and mandolins have four strings. If there are three guitars and four mandolins in the classroom, how
many strings are there altogether on the guitars and mandolins?
- The teacher uses guided questioning and prompts to help students to identify the steps (e.g., “ What do you already know?” “ What do you need to find out?” “ What do we need to do before we can find out the remaining time she has left to practice?”). Through questioning, the teacher guides students to identify the first step: Multiplying the number of strings by the number of each instrument.
- The teacher guides the students to create a model (using manipulatives such as counters) with corresponding equations.
- After students complete the first step, the teacher uses questioning to prompt next step (e.g., “ What have we learned about the numbers of strings?” “ What do you need to find out to solve this problem?” “ What should we do next?”). The problem may need to be reread aloud. 18 + 16 = 34 total strings
- The teacher repeats with additional two-step problems, guiding students to identify and solve each step using manipulatives. Some students may benefit from “ acting out” the story in the problem to support the problem-solving process.
Instructional Tasks
Instructional Task 1
Solve the problem. Oak Hill Elementary third-grade students are taking a field trip to the zoo. There are 71 students who paid to attend the field trip. Of those that paid, 8 students cannot go on the day of the trip. There needs to be 7 groups at the zoo and each group must have an equal number of students. How many students will be in each group on the field trip?
Instructional Items
Instructional Item 1
For a school food drive, three students bring in cases of canned goods to donate. Uriel brings 4 cases, Paola brings 6 cases, and Mika brings 5 cases. Each case contains 8 canned goods. How many canned goods in all does the school collect?
Instructional Item 2
A bookstore has 8 boxes of books. Each box contains 10 books. On Monday, the bookstore sold 16 books. How many books remain to be sold?*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Teaching Idea
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options. Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
This MEA asks students to work as a team to figure out which candidate is the best possible choice for the 8th grade boys' basketball coach. They will have to analyze data, decide on a procedure, and create a ranking system to choose the best candidate. They are also given multiplication and division problems based on the data.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
The principal needs help planning the school lunch schedule! Students will plan a lunch schedule to accommodate all of the students in the school. However, there can only be 100 students in the cafeteria at a time and only 20 students can sit at a table. Students will figure out how to arrange the lunch schedule so that every class eats together and so that certain grade levels are not together at the same time.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this MEA, students will rank pets from most family-friendly to least family-friendly by considering data such as purchase price, cost to feed, cleanliness, etc. as well as notes regarding the physical description of the pet. In the twist, students will be given information on additional pets as well as information on cleanliness and life expectancy. Students may need to make trade-offs in regards to cost to adopt, feed, and house along with life expectancy, ease of clean up, etc.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, The Junior League needs the students' help to determine which table rental company to use for their Charity Auction. With a tight budget, limited time, and a mistake in the order, students must create a procedure for determining the best rental company, write an explanation about their procedure, and present their recommendations to the class.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this model eliciting activity students use data about the temperature and water requirements of plants to figure out when the plants should be planted. They also use data such as space requirements and time until harvest to make judgments about which plants would best suit the needs of students planning a school garden in Florida.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
MFAS Formative Assessments
Students solve a two-step word problem involving addition and division and then write an equation to represent the problem.
Students solve a two-step word problem involving multiplication and subtraction and then write an equation to represent the problem.
Students are asked to model an equal groups and an array problem in which the product is unknown with multiplication or division equations and then solve each problem.
Students are asked to model an equal groups and an array problem in which the group size is unknown with multiplication or division equations and then solve each problem.
Students are asked to model an equal groups and an array problem in which the number of groups is unknown with multiplication or division equations and then solve each problem.
Students solve a two-step problem requiring multiplication and addition and then write an equation to represent the problem.
Students are asked to solve a division equation and then interpret the quotient by writing a word problem that can be modeled by the equation.
Students solve a two-step word problem involving subtraction and division and then choose an equation that represents the word problem.
Original Student Tutorials Mathematics - Grades K-5
Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.
Student Resources
Original Student Tutorial
Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.
Type: Original Student Tutorial
Problem-Solving Tasks
For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.
Type: Problem-Solving Task
The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.
Type: Problem-Solving Task
The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.
Type: Problem-Solving Task
