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Examples
Given the data of the softball team’s hat size represented on a line plot, determine the fraction of the team that has a head size smaller than 20 inches.Clarifications
Clarification 1: Instruction includes using any of the four operations to solve problems.Clarification 2: Data involving fractions with like denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100. Fractions can be greater than one.
Clarification 3: Data involving decimals are limited to hundredths.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Numerical Data
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to use data sets as real-world context for doing arithmetic with whole numbers, fractions and decimals beyond finding measures of center and spread.- Instruction includes having students solve one- and two-step problems from a given data set or by comparing two data sets in the same units.
- Instruction includes problems that involve addition, subtraction, multiplication or division.
- This benchmark should be taught with MA.4.DP.1.1 and MA.4.DP.1.2 (collecting and representing data). Students should have a strong command of creating and interpreting line plots and stem-and-leaf plots to be successful with the interpretation these data displays.
Common Misconceptions or Errors
- Students can make errors when writing equations used to solve problems with numerical data. During instruction, expect students to justify their equations and solutions.
Strategies to Support Tiered Instruction
- Instruction includes visualizing word problems. The Three-Reads Protocol is a strategy to help students conceptualize what the question is asking. Students draw pictures or models to represent what is happening in the word problem. These pictures and models are used to help students write equations for the problem they are solving.
- Instruction includes breaking down word problems into smaller parts. Students use a highlighter to emphasize the important information in the word problem. Also, students paraphrase the word problem so the teacher can determine if the student understands what the question is asking.
Instructional Tasks
Instructional Task 1 (MTR.7.1)
Collect 10 used pencils from people in your class. Measure the length of each pencil to the nearestinch and record the lengths on a line plot. What is the difference in length of the longest pencil and the shortest pencil?
Instructional Items
Instructional Item 1
The last 5 putt lengths, in feet, for the 18th hole of a golf tournament are shown below.
- a. 8 feet
- b. 9 feet
- c. 12 feet
- d. 15 feet
*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
Teaching Idea
STEM Lessons - Model Eliciting Activity
Students will help a track coach determine which shoe is the best to purchase for his team. Students will be required to convert measurements initially and then rank the shoes from best to worst based on the data provided.
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
This MEA asks fourth grade students to collaborate with their classmates to solve a problem. They have to use their previous knowledge of the area formula and apply it to a real world problem using a given data set. They will also be asked to reevaluate their solutions when additional data is added.
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
Students will be given specifications (specs) about a house and have to determine which house would be the best one for the client according to the families needs.
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
Students will think like chess club members to make two wish lists on how to spend $75 on chess related materials. Then they have to make two new wish lists on how to spend $750 on chess related materials.
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
Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies. Students will use multiplication and division of whole numbers to plan for how many packages to order.
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.
In this MEA, students will convert fractions into decimals and then compare the decimals to decide which donut a donut shop should add to their menu.
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
Growing Green, Inc. is planning to expand their business into Florida. The client has specific criteria for selecting a good location to set up their new fertilizer manufacturing plant. This project will familiarize students with some of Florida's natural resources (with a great emphasis on phosphate) and will present students with opportunities to interpret different types of maps.
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
Students will work in groups to assist a client in purchasing different fish for a fish pond. From a data table, they will need to decide which type of fish and how many fish to purchase according to the size of the each pond. After, they will need to revisit a revised data table to make different selection of fish and calculate costs for the purchase of the fish.
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
This Model Eliciting Activity is written at a 4th grade level. In this open-ended problem, students must consider how to rank potting soil based on factors like fraction of ingredients, price, and eco-friendliness. In teams, students determine their procedures and write letters back to the client.
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 MEA, students will rank t-shirt companies from the best price to the worst price by considering data such as purchase price, shipping fees, sizes, colors, etc. as well as notes regarding the amount of students enrolled. In the twist, students will be given information on additional requirements from the principal for specific shirt colors for each grade as well as the additional add-on of the school's logo (an elephant).
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
This MEA allows students to explore the creation of a model to rank hotels. Students are presented with the first part of the problem and the data which includes cost, meals served, pet friendly, and closeness to highway. They will determine which hotel will receive their highest recommendation. The second part of the task adds two hotels and additional data related to discounts. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which hotels they might stay in as they travel.
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
The Park by the Bay is having its grand opening soon and your students are needed to help figure out what playground equipment to use. 4th grade students will look at a data set and make decisions as to how to rank the playground equipment. Also, students will practice their area and perimeter skills by calculating the area and perimeters for the different playground equipment.
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
The students will use mathematical skills and problem solving skills to recommend which current starting pitcher will be replaced once one of the pitchers is back on the active roster for the Miami Marlins. They will write a letter on the computer and print it out to respond to the assistant coach's letter.
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
This MEA asks students to take on the job of a tennis pro and decide which factors are most important in choosing a facility to take tennis lessons. Students will perform math calculations, create a two-column table for hours and minutes, develop a procedure to rank facilities, and provide written feedback through letters to a parent whose child needs group tennis lessons and writes letters to ask for advice. They will rank their choices from "best to worst" tennis lesson facilities. Students will provide a detailed written explanation for how they decided to rank factors and their solution for rating tennis lesson facilities.
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
This MEA allows students to calculate the area of tents in order to determine if they will hold a given number of people. Students will determine which tent is best for the customer by analyzing each tent's specific features, calculating space for each family member, and using deductive reasoning and key details from the reading passages.
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 main problem students will encounter in this MEA is determining the appropriate placement of required furniture in a classroom with a new school that is being constructed. The MEA provides students the opportunity to use their knowledge of Measurement and Geometry in order to work as an engineer in solving a realistic problem. The students will need to review and incorporate the usage of Mathematical formulas and sketching in order to help make their final determination to the client within the MEA. The students may need to reconsider their initial thinking once they encounter a problem with the specifications.
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 students are ranking the building of a new park according to the criteria that the town wants. They need to determine the total area of the space and how it is being used.
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 MEA students will have to find the right rental for a client as they use their knowledge of numbers and some reasoning. Students will read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
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
During this activity, students will look at data from a fictional town, Thrift Town and develop a strategy of choosing which material would be the best to help insulate an ice cream container. The students will utilize higher order thinking skills, as well as deduction to find a solution.
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), students will be need to help a travel agent come up with the best vacation hotel package for a family of four. They need to take into consideration all the amenities, prices, perks, and reviews into consideration. A twist comes in when the travel agent will need to provide vacation hotel packages for families of 5 members.
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
Students will be asked to rank the different floor tiles for the playrooms in activity centers throughout community parks. They will need to take certain factors into consideration when making their rankings. They will also need to calculate the costs of installing the floor tiles using the given measurement of the playroom and the floor tiles. The "twist" will be that the client now needs to include a storage room for some of the playroom's equipment. They will need to decide if to use the same floor tile or different from the playroom and the additional cost of the storage closet. After, they will add the total costs of the playroom and the storage closet. They will report their findings and reasons by writing letters to the client.
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 analyze data presented in a line plot and solve problems related to the data.
Students are asked to analyze data presented in a line plot and solve problems related to the data.
Students analyze data presented in a line plot and solve problems related to the data.
Students are asked to analyze data presented in a line plot and solve problems related to the data.
Original Student Tutorials Mathematics - Grades K-5
Learn how to create a line plot and analyze data in the line plot in this interactive tutorial. You will also see how to add and subtract using the line plot to solve problems based on the line plots.
Student Resources
Original Student Tutorial
Learn how to create a line plot and analyze data in the line plot in this interactive tutorial. You will also see how to add and subtract using the line plot to solve problems based on the line plots.
Type: Original Student Tutorial
