Word (.docx)
Acrobat (.pdf)
Clarifications
Clarification 1: Problems include the use of data in informal comparisons between two data sets in the same units.Clarification 2: Data displays can be represented both horizontally and vertically.
Clarification 3: Circle graphs are limited to showing the total values in each category.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Bar Graph
- Categorical Data
- Circle Graph
- Whole Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to interpret data displayed in scaled pictographs, circle graphs, scaled bar graphs and line plots. Like MA.3.DP.1.1, the purpose of this benchmark builds on data interpretation skills from Grades 1 and 2. In Grade 1, students interpreted data represented with tally marks and pictographs, and in Grade 2, students also interpreted data represented in pictographs and bar graphs. Additionally, students solved addition and subtraction problems using the data representations.- In Grade 3, students will interpret categorical data represented in scaled pictographs and bar graphs, whole-number numerical data represented in line plots, and whole-number category totals in circle graphs (e.g., instead of percentages). To interpret the represented data, they will solve one- and two-step problems from a given data set or compare two data sets in the same units (MTR.5.1).
- Instruction should include opportunities for students to interpret their own numerical and categorical data (MTR.7.1).
- Students could use addition, subtraction, multiplication or division to solve the problems. This benchmark should be taught with MA.3.DP.1.1 (collecting and representing data) (MTR.2.1, MTR.4.1, MTR.5.1).
Common Misconceptions or Errors
- Students may confuse the values in scaled pictographs and bar graphs. They should always utilize the given key when determining frequency of each category.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to determine the values in a scaled pictograph, pointing out the importance of paying close attention to the key of the pictograph. The key outlines how much each of the pictures on the graph will represent. Students connect multiplication strategies to this concept. Instruction includes opportunities to practice counting by 2s, 5s, and 10s, to be successful with this benchmark. To help students see the connection between the key and what each picture represents, a bar diagram may be helpful.
- Instruction includes opportunities to determine the values in a scaled pictograph, pointing out the importance of paying close attention to the key of the pictograph. The key outlines how much each of the pictures on the graph will represent. Students connect multiplication strategies to this concept. Instruction includes opportunities to practice counting by 2s, 5s, and 10s, to be successful with this benchmark. To help students see the connection between the key and what each picture represents, a bar diagram may be helpful.
- For example, students use the key for the pictograph and a bar model to determine the number of sunny days in August.
Instructional Tasks
Instructional Task 1
The pictographs show favorite subjects in third and fourth grades at Palm Elementary School.
- Part A. Write an equation that shows how many fourth graders chose reading as their favorite subject.
- Part B. How many third graders chose social studies as their favorite subject?
- Part C. How many more students prefer math in third grade than fourth grade?
Instructional Items
Instructional Item 1
John surveys his classmates about their favorite foods, as shown in the bar graph. How many more classmates chose pizza as their favorite food than classmates who chose salad?
Instructional Item 2
Molly surveys her class about their favorite ice cream flavors, as shown in the circle graph. How many students picked a favorite ice cream flavor other than vanilla?
*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 Assessment
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
Animal Habitat MEA is where the students will help a pet store choose which habitat they should buy to house their snake and lizard families. The students will solve an open-ended problem and give details on the process that they used to solve the problem.
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 compare multi-digit numbers to create a procedure for choosing the best car for Edward Easy to buy for his driving school. They will have to weigh quantitative and qualitative factors to determine the best car to purchase. Students will present their recommendations and the steps to the procedure they created in writing and orally.
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 time rush to get a haircut, students will add elapsed time to find the total time spent at the hair salon and the time of departure from the salon. They must use this information determine which salon is the best for the new family in the neighborhood. Students will submit a letter to the client explaining their procedure for ranking the hair salons.
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 Model Eliciting Activity, MEA, students will compare different nutritional content of chicken nuggets from many restaurants presented in bar graphs. They will factor in the calories, total fat, and sodium information about the nuggets to create a procedure for ranking the nuggets from healthiest to least healthy.
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 task involves having students look at three different fish tank sizes and determine, using a data list, which fish will fit in these fish tanks based on their size. They will also need to look at other characteristics to determine how to group the fish together. Students will have to either multiply, divide or add repeatedly in order to find different solutions on how to place the fish in each tank size.
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 determine what two snacks should be placed in the school vending machines because the district is asking for healthier and tastier snacks. Factors to consider are calories, fat, protein, sugar, student comments, and cost.
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 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
Using information about the needs of different animals, students will help choose which pet would be best to purchase for a classroom.
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
Rangoli is a traditional Indian art that is used in decorating the entrance of the house to welcome guests. In this activity students will use the concept of lines of symmetry to select the best rangoli design for a school event.
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 Model Eliciting Activity, MEA, students will help the Sweet Donut Shop determine what the newest donut will be. Students are given the cost to make each batch along with the selling price and are asked to determine the profit for each batch. Students create a procedure for ranking the donuts and write a letter explaining the procedure and the ranking. In the “twist” students are provided the starting and finishing times for each batch. They must determine the total amount of time, decide if their procedure should change based on the new information, and write a letter explaining whether the procedure changed and the new ranking of the donuts.
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
Original Student Tutorials Mathematics - Grades K-5
Learn to use the information presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems.
STEM Civics Tutorials and Videos - Grades K-12
United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project.
Learn how to use a bar graph to summarize voting results at school in this interactive tutorial.
This is part 2 in a two-part series. Click HERE to open Part 1.
Student Resources
Original Student Tutorials
Learn how to use a bar graph to summarize voting results at school in this interactive tutorial.
This is part 2 in a two-part series. Click HERE to open Part 1.
Type: Original Student Tutorial
United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project.
Type: Original Student Tutorial
In this video Sam-1 introduces a Model Eliciting Activity (MEA) challenge. Students will take their prior experiences from the properties unit and apply their knowledge of investigating sea turtle nesting temperatures.
Students will develop a hypothesis, design an experiment, and support their reasoning to determine how to best study different methods for cooling sea turtle nesting areas.
Type: Original Student Tutorial
Learn to use the information presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems.
Type: Original Student Tutorial
Problem-Solving Task
After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Tasks
This task adds some rigor to the activity, by collecting actual growth data, providing practice for students in measuring and recording length measurements. Centimeters are an appropriate unit for these measurements, as they provide a good level of precision for these measurements, while being easy enough for students to handle.
Type: Problem-Solving Task
After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.
Type: Problem-Solving Task
The size of the hand makes a difference in some sports that involve throwing or catching and some activities such as playing the piano. Hand span is a measure that has been used for many years. By placing the hand on the edge of a piece of paper and marking the tips of the thumb and little finger, the student can measure a straight line. This is a better method than placing the hand directly on the ruler. Discuss rounding conventions. This could be used as a class activity, or students could gather and plot data on separate line plots from different age groups.
Type: Problem-Solving Task
