Real-World Application in Mathematics

Real-World Application

   Project-based learning, internships, and civic engagement makes learning relevant.

Real-World Application refers to learner-centered instruction that helps learners acquire a deeper knowledge through exploration of real-world challenges and problems. It requires collaboration between students, teachers, and community resources. It is often defined as “Learning WHILE Doing” rather than “Learning THEN Doing.”  The learning occurs throughout the course of a project, not just after the project’s completion. It is an active style of learning that provides learners the opportunity to learn about a content standard by investigating and responding to a problem, challenge or complex question. The key element in Real-World Application is that the learning is RELEVANT to the student.
What is Real-World Application in Mathematics?
Evidence shows that hands-on learning and real-world applications are more effective at engaging student interest in and recall of material. This effective interest actually starts in pre-K and kindergarten with the physical and mental engagement of basic blocks. It continues through elementary and secondary grades with use of manipulatives, projects, research, explorations, etc.  Research shows that math needs to be relevant to the individual student and experience based.  We must strive for a balance between skill work and application work.  Without application, the skill seems meaningless to students.
Below are great resources to help build your understanding around real-world application in mathematics.
How is Real-World Application directly connected to the student Standards for Mathematical Practice and Effective Mathematics Teaching Practices?

There is an iterative and complex relationship between the Standards for Mathematical Practices, the Effective Mathematics Teaching Practices and Real-World Applications. There is not a one-to-one correlation or a simple stimulus-response relationship.  Teachers should implement the Effective Mathematics Teaching Practices, which encourage students to develop co-academic knowledge, attitudes and skills that are woven into the Standards for Mathematical Practice.


Throughout the 2017 Kansas Mathethmatics Standards the words “real world” appear MANY times.  If we are truly building conceptual understanding of mathematics, our standards must be able to apply these understandings to their “real world.”
Effective Real-World Mathematics Applications involve:
  • Tasks that promote problem solving and reasoning
  • Mathematical discourse
  • Purposeful questioning
  • Productive struggle
  • Connected representations
  • Evidence of student thinking
  • Persevere in solving problems
  • Abstract and Quantitative reasoning
  • Construct viable arguments
  • Model Mathematics
  • Attend to precision
Are there limitations within this area for mathematics? Are there instructional practices that should be avoided for mathematics?
  • Real world problems need to be at an appropriate DOK level.  We must push students to the levels of Strategic Thinking and Extended Thinking.
  • Learning needs to be blended with application and skill.
  • Soft skills need to be taught in conjunction with math skills.
  • Avoid debilitating struggle, students must build up their perseverance through problem solving.
  • Be cautious with offering too much direct / procedural instruction.  Allow students to learn WHILE doing.
  • Always know that there will be a need for SOME direct instruction opportunities.  However, these opportunities need to have a purpose within the context of the Real-World Application.  Learning a skill with no application is simply a skill to be forgotten.
What does Real-World Application look like in the mathematics classroom?
The following productive actions apply to Real-World Application.

   Likewise, the following unproductive actions often do not apply to Real-World Application.
 Productive Practices
 (What it IS)
 Unproductive Practices
(What it is NOT)
A balance of grouping for students - whole group / small group / individual
Teacher lead discussions
Mathematical discourse with engagement
Silent classrooms with compliance
Teachers facilitate the discussion, allowing conversations off “planned” path and intervene only as needed
Teacher asks few questions, often answering them himself/herself
Primary focus is rich mathematical tasks or projects that promote understanding and relevance
Primary focus is computation problems and practice
Community partners to make connections to mathematical concepts
Isolated algorithms and formulas with no connections
Teachers pose questions that promote productive struggle for learning
Teachers assign students easy problems that they will get right
Assessment encourage students to reason about the units or rounding that makes sense for the situation
Assessment directions specify units or rounding directions
Honor and learn from mistakes
Reward “correct” answers
Tasks chosen based on state standards, student interest and relevance
Tasks based on great project idea without regard to the standards


What instructional strategies are appropriate for Real-World Application in mathematics?
Project Based Learning
Project Based Learning is a teaching method in which students gain knowledge and skills by working for an extended period of time to investigate and respond to an authentic, engaging, and complex question, problem, or challenge. (
The real emphasis for Project Based Learning in the mathematics classroom must be “Learn While Doing” not “Learn Then Do”.  Teachers must be very specific about the standard being emphasized and then allow students to learn these standards while completing a question, problem, or challenge.
It is important in the mathematics classroom that there be an opportunity for “on time” direct instruction of the mathematical concepts and specific skills.  Students discover the need and application of the skills and concepts, but there must be opportunity for direct instruction as needed.
The Buck Institute model has a great foundation for PBL, BUT not all mathematical standards are easily  addressed through Project Based Learning.
Problem Based Learning
Problem Based Learning is both a teaching method and an approach to the curriculum.  It consists of carefully designed problems that challenge students to use problem solving techniques, self-directed learning strategies, team participation skills, and disciplinary knowledge.  (
Like Project Based Learning, the emphasis in the mathematics classroom must be to “Learn While Doing” rather than “Learn Then Do.”  Teachers must be very specific about the standards being taught and assessed through the problem.
The two primary differences between Problem Based Learning and Project Based Learning are 1) Problem Based Learning focuses on the solution of a problem, not necessarily the creation of a product and 2) Often the time frame for the Problem Based Learning activity is shorter.
Rich Mathematical Tasks   
Rich mathematical tasks engage students in sense-making through deeper learning that requires high levels of thinking, reasoning, and problem solving.  Rich mathematical tasks provide students with the opportunity to investigate and analyze the mathematics in the task and apply their learning to new situations.
There are many great resources for Rich Mathematical Tasks listed in the resource section.
Kagan Strategies to encourage mathematical discourse.
Academic Discourse is critically important in the mathematics classroom as students build their neurological pathways concerning mathematical ideas and structures.  One great resource for strategies that encourage academic discourse are the Kagan Cooperative Structures.
These structures are instructional strategies designed to promote cooperation and communication in the classroom, boost students’ confidence and retain interest in classroom interaction. (  These structures can be adapted to multiple grade levels and subject areas.  See below for resource link.
Partnering with local professionals to add relevance and expertise to the mathematics that students are learning
A powerful strategy that is often overlooked is right in your community.  Partnering with local professional and business people adds a real world component that most educators cannot supply because of our limited experiences in the world of business and industry.  Many communities are very interested in retaining the youth of the community in the community and are very willing to assist the schools in building relevance for students’ learning.  Be willing to reach out to the community for help.
Resources for Real-World Application in Mathematics
Click on column header to sort.
Mathematics and the Real WorldArticleThis NCTM post talks about two different approaches to the importance of Real World math. 1. use real world problems as a stepping stone to the math 2. approach is to use authentic math problems and apply math concepts to learn about our world
Seven Essentials for Project-Based LearningArticleThe article is written to give information about PBL. It is for all subject areas.
2018 Kansas Mathematics Flip BooksPDFThis project attempts to pull together, in one document some of the most valuable resources that help develop the intent, understanding and implementation of the Kansas Mathematics Standards.
When Math HappensWebsiteMore links to 3-Act Math problems.
Project PhenomenaWebsiteThis database supplies links to scientific phenomena for projects. The resources are sorted by science standard and grade level.
Three Act Math Task - Dan Meyer's file cabinet of 3-Act math tasks WebsiteThis link takes you to a spreadsheet of Myer’s 3-Act problems and identifies the standards addressed.
Robert Kaplinsky's Problem-based Lesson Search EngineWebsiteThis Robert Kaplinsky resource will take you directly to a search engine, where you can search any topic and the search engine will give you a list of possible projects and the standard that they represent!
PBL Works - Project Based Learning informationWebsiteThis website is from the Buck Institute. It gives basic information about PBL is and project resources. The site is for all subject areas.
Graphing StoriesWebsiteThe site supplies videos of real world situations that can be graphed on a coordinate plane.
Graham Fletchers SiteWebsiteGraham Fletcher provides a list of 3-Act problems as well as videos that can be used for professional development about the progressions of mathematical topics.
Greg TangWebsiteGreg Tang’s website has resources that will help generated word problems by standard.
Mathematics Assessment Project WebsiteThis link takes you to the MARS project website. There you will find several lessons that draw upon real world applications to teach a mathematical concept.
Illustrative Mathematics WebsiteIllustrative Math gives teachers multiple problem examples and tasks that can be used in the classroom. All problems and tasks are divided by content standard.
Contact Information


Marcia Fiorentino
Mathematics Program Consultant
(785) 296-3486

  Michelle Irvine
Senior Administrative Assistant
(785) 296-2078


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