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K-12 Math Projects:
About Project-Based Learning

A connected world Gif

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Project-based learning is a terrific way to link your curriculum with real world events and applications of concepts that your students are learning.  There are two pages in this section to help you and your learners.


Arrow: You are hereProject Based Learning (Page 1 of 2): An essay

Projects on the Web (Page 2 of 2): Our list of project sites

Also see Technology Integration Resources for Multimedia in Projects, a three part collection with an essay on multimedia and resources for their use.

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About Project-Based Learning

Recent trends in K-12 education include active learning, blended learning, and project-based learning.  Projects help students personalize their learning and are ideal for gaining key knowledge and understanding of content and answering the question: Where am I ever going to use this?  When project-based learning (PBL) is introduced into classrooms, "Teachers and schools can make use of externally developed PBL curricula, they can develop their own PBL approaches, or PBL can be part of a whole-school reform effort" (Condliffe, Quint, Visher, Bangser, Drohojowska, Saco, & Nelson, 2017, p. iii).

Among the greatest benefits of project-based learning (PBL) are gains in students' critical-thinking skills and development of their interpersonal and intrapersonal skills.  PBL is also an ideal way to help learners gain speaking and presentation skills indentified in the Common Core Standards. PBL in mathematics, particularly when completed in teams, helps learners "model with mathematics" as they "apply the mathematics they know to solve problems arising in everyday life, society, and the workplace,"  "use tools strategically,"  and "construct viable arguments and critique the reasoning of others," as noted in the Common Core Standards (2010) for Mathematical Practice.

However, implementation is not without concerns.  As Condliffe and colleagues (2017) noted, math teachers have found it difficult to implement PBL.  In general:

It requires that teachers modify their roles (from directors to facilitators of learning) and that they tolerate not only ambiguity but also more noise and movement in the classroom. Teachers must adopt new classroom management skills and learn how best to support their students in learning, using technology when appropriate. And they must believe that their students are fully capable of learning through this approach. Given these challenges, professional development — both initial training and continuing support — is likely to be essential to the successful implementation of PBL." (p. iii)

Additionally, a major shortcoming in many student projects is that educators tend to assign projects just for the sake of doing them (Goodwin, 2010).  As Bryan Goodwin found in his literature review on PBL, "Educators can avoid this phenomenon and realize the potential of projects to promote students' critical-thinking by framing projects around a driving question" (2010, p. 81).

PBL Gold Standard from BIEThis challenging open-ended driving question or problem is just one of the essential elements of meaningful projects, according to John Larmer and John R. Mergendoller (2010) of BIE.  They updated their PBL model in 2014 to what they called a "gold standard" (See their 2015 blog post on why), and the Gold Standard PBL: Project Based Teaching Practices (Larmer, 2015), which is also the source for the image on PBL).

The Gold Standard PBL: Essential Project Design Elements include:

  1. A challenging problem or question
  2. Sustained inquiry
  3. Authenticity
  4. Student voice & choice
  5. Reflection
  6. Critique & revision
  7. A public product (Larmar, 2020)

Every good project should be tied to standards so that students gain key knowledge and understanding.  Four key areas serve as indicators that PBL is grounded in standards:

  1. Curricular Content
  2. 21st Century Skills
  3. Formative and Summative Learning Opportunities
  4. Intentional, Aligned, Varied, and Constant Assessment (Gorman, 2019, para. 1).

Gorman (2019) noted having a teacher first deliver content and then having a follow-up project is not truly PBL.  "In true Project Based Learning the project uncovers and facilitates the learning of significant content. ... PBL provides the rigor of learning new content along with the engagement apparent in a student-centered program based on deeper learning. The content becomes the “what” while PBL is the “how” " (para. 5).

Students need to perceive the work as meaningful to them.  A clear connection to an entry event adding this meaning might be via almost anything: "a video, a lively discussion, a guest speaker, a field trip, or a piece of mock correspondence that sets up a scenario" (Larmer & Mergendoller, 2010, p. 35).  Students need a voice and choice in fulfilling project requirements, keeping in mind that limited choices be considered and that "teachers should design projects with the extent of student choice that fits their own style and students" (2010, p. 36).  Projects should give students opportunities to build 21st century skills (or success skills) and to use technology that will be useful to them in life and the workplace.  Projects should enable learners to conduct real inquiry.  This has to do with authenticity or how real-world a project is.  With "real inquiry comes innovation--a new answer to a driving question, a new product, or an individually generated solution to a problem" (2010, p. 37).

Learners should receive feedback to use in revision, as learning that real-world work often involves revision.  Outside experts or mentors can also provide input (Larmer & Mergendoller, 2010).  Teachers should not be the only ones to provide this feedback.  Peer-editing sessions with the aid of appropriate rubrics or checklists can be useful for students to present their rough drafts to each other (Pahomov, 2014).

Authentic Learning in the Digital AgeStudents should publicly present their work, as they will be more motivated to produce a quality product when knowing a real audience will view it (Larmer & Mergendoller, 2015, 2010).  As Larissa Pahomov (2014) pointed out in Authentic Learning in the Digital Age, "Why should students put so much effort into a product that is only going to be viewed by one person?" -- the teacher (p. 92).  Although there might be live presentations to share projects, "they should also be designed to stand on their own, after the formal presentation has ended" (p. 87).  A venue for presenting completed projects might be "as simple a setting up a gallery in the hallway or a landing page for links to projects" (p. 92).  A blog or wiki is ideal for posting online presentations, which elevates projects beyond the school walls.  "What makes this process meaningful, however, is when students have been creating their project with a particular audience in mind and then they target that audience once the content has been posted" (p. 98).  Projects might be entered into contests and competitions, or presented to real-world professionals for feedback.

If projects involve teamwork, educators will need to emphasize commitment to the team as an essential component for success of group work.  Larmer (2014) noted that this may not automatically emerge, but a "sense of responsibility to their peers can be one of the most powerful motivating factors for students working on a project in teams" (p. 45).  To help support teamwork, teachers might consider "constructing list of norms or a rubric with students; having students write contracts for how they will work together; providing them with tools, such as task planners and online collaboration platforms; and teaching them how to resolve conflicts and make decisions. During a project, have team members frequently check in with one another—and the teacher—to be sure things are going smoothly" (p. 45).

Finally, projects should include the element of reflection.  Per Larmer and Mergendoller (2015), "students should reflect on what they’re learning, how they’re learning, and what they have accomplished in a project" (Two new elements section).  Self-Reflection on Project Work from BIE's PBLWorks is one such template.

With the above being said, Volker Ulm (2011) offered teachers some sound advice regarding math project-based learning:

Enriching classroom teaching with projects is certainly the most challenging, but at the same time the most beneficial form of independent learning. It is challenging because it requires high-level skills on the part of the students, e.g. skills in applying methods, self-management, and social competence. So project-based learning should never degenerate into a teacher-centered training course where ultimately the teacher still does all the planning, structuring and organizing, prepares and procures all the materials, or even produces and presents the results. (p. 44)

What do we mean by building 21st century skills?

Question markNumerous documents have referred to the need for this or that activity to build 21st century skills needed for career and college readiness.  However, what does that mean stated in terms that everyone can easily remember?

The National Research Council (2012, p. 2) suggested three broad domains as a way in which to organize competencies--such skills and abilities: cognitive, intrapersonal, and interpersonal.  They are intertwined based on human development and learning, however.

While one might elaborate on specific skills or competencies within each, those domains are easy to remember.  Briefly:

What might not surprise readers, however, is that "Precise definitions of the many terms used for “21st century skills” are not possible at this time, in part because there is little research to support such definitions" (p. 2).


Key Questions

Thus, projects should result from students' attempts to answer essential questions.  They can take many forms: products, presentations, performances.  They might fit any of three structures: interpersonal, information sharing, or problem-solving.  When selecting an existing project, or creating one of your own, consider the following.  In terms of math projects:

  1. Is the project devoted only to mathematics (or a single subject area), or is there a link to other curricular areas?

  2. Is the project tied to standards for the curricular areas addressed, such as those from the National Council of Teachers of Mathematics, the Common Core Standards, or the National Education Technology Standards?

  3. Does the project come with classroom instructional materials (e.g., teacher resources, student activities, rubrics and assessment tools)?

  4. Can all students in your class participate? Projects should not be reserved for your talented and gifted students, as all students should be able to benefit.

  5. What is the total time for project completion?

  6. Is the project collaborative in nature? A collaborative project, particularly involving students outside your own school setting, will take more time and monitoring to help students learn how to be a part of a team and communicate appropriately with others.

  7. How will students benefit both academically and personally from their involvement in the project?  Consider that when students interact with other students and experts across the country or internationally, they get a broader feel for diversity.  Their participation in an actual real world activity might encourage them to do their best work, and see the relevance of mathematics in their daily lives.  If students have input into project selection, and like the topic, they will tend to become more involved and excited about their learning.

  8. Is there a cost involved to participate?


Don't forget the home-school connection!

Friendly reminder GifIf you decide to engage in a project of significance to your learners, parents would appreciate knowing about it.  Consider sending parents a letter to explain PBL, the nature of the project, how learners will be assessed, and what they can do to help.  BIE's PBLWorks has a Template for a Letter to Parents.

Scaffold Projects

Help learners reach project milestones by recording oral feedback along the way using tools such as ScreenPal.  ScreenPal (formerly Screencast-o-Matic) provides free screen capture recording for Windows, Mac, iPad, iPhone, Android, and Chromebook.


The Methodology--PBL models and tips

World Class Learners: Educating Creative and Entrepreneurial StudentsAdding to the above, educators need to decide on what they mean by project-based learning (PBL) and which model is needed.  In World Class Learners: Educating Creative and Entrepreneurial Students, Yong Zhao (2012) noted three forms of PBL, according to J. Robinson (2013): an academic model, a mixed model, and an entrepreneurial model.

Michael Stone (Schwartz, 2016) provided the following tips for success to guide the methodology.

  1. Make projects explicitly tied to standards.  This helps justify the time investment.
  2. Balance clear expectations with open-ended problems.  Stone indicated, "the strength of a project depends heavily on the initial driving question developed by the teacher."  The rubric should be clear about expectations and designed around the driving question.
  3. Assess process alongside content.  Per Stone, process-oriented goals "like collaboration, critical thinking, communication and innovation" should be included on the rubric "alongside the specific content goals."  This demonstrates their equal importance.  Students should document the development of their projects to illustrate their role in achieving process goals.
  4. Anticipate the skills and design scaffolds.  "In addition to thinking through the driving question and the learning standards students would need to answer that question, the teacher also thinks ahead about the likely gaps in skills students are going to have both in content and process."  Scaffold categories might include whole class activities, station activities, workshops, and focus groups.
  5. Transfer accountability to students.  Consider using contracts--"students make contracts with one another about how each member of a group is expected to participate, and students set the consequences for failure to do so."  To illustrate, Stone indicated students have assigned detentions or reduced final project grades when others did not meet the terms of the contract.

As projects should be ongoing, Gorman (2019) suggested that proper scaffolding within a PBL unit "includes both learning activities and effective ongoing assessment. In fact, some of these activities might actually be existing lessons that a teacher has always used. It is even possible and probable that part of the scaffold will include readings, lectures, and even a worksheet, although it is important to keep a balance using all of Bloom’s levels. While assessment is varied, there is nothing wrong with including a summative test" (para. 5).

In order to tie projects to math standards, Andrew Miller (2011) suggested that teachers need to pick or make an appropriate time for projects (e.g., during a three-week unit on a specific math learning target).  Pick a standard with an easy real-life application.

Learn More on Project-based Learning

These resources are for those who need to know more before engaging in projects and inquiry-based learning.

Designing Learning is a section within the Galileo Educational Network Association, which includes a series on the nature of inquiry-based learning.  Learn about what inquiry is all about, choosing a topic, essential questions, inquiry and assessment, and then go to the section for Classroom Examples of projects for elementary, middle, and secondary students and a rubric for assessing inquiry projects.

Framework for High Quality Project Based Learning (2018) "describes PBL in terms of the student experience."  The Buck Institute for Education facilitated the development of the framework with support from Project Management Institute Educational Foundation and the William and Flora Hewlett Foundation (About section).  Key elements of the PBL framework include intellectual challenge and accomplishment, authenticity, creating a public product, collaboration, project management, and reflection.

Thinking Through Project-Based Learning: Guiding Deeper InquiryKrauss, J., & Boss, S. (2013). Thinking Through Project-Based Learning: Guiding Deeper Inquiry provides an overview of PBL including findings on brain development and connections to Common Core Standards; numerous how-tos and sample projects for K-12; strategies for integrating PBL into main subject areas, across disciplines (science, social studies, language arts, math), and with technology and social media; ideas to involve the community and showcasing student work.

Performance Tasks or Projects? Complementary Approaches for Student Engagement: In this article, authors Jay McTighe and John Larmer (2022, June 8) note that performance tasks and projects are not identical.  They provide "Eight key dimensions [that] can help underscore the differences and similarities between performance tasks and projects, so educators know how to use each of them appropriately."

PBL-Online has all the resources you need to design and manage high quality projects for middle and high school students.  You can learn how to design your own project, what project based learning is all about, search for projects developed by others or contribute your own, review research on PBL, and access other web resources on the topic. PBL-Online was created under the leadership of the Buck Institute of Education, with major contributions from the George Lucas Foundation and others.

PBLWorks from the Buck Institute for Education (BIE) has an overview of project based learning (PBL), plus numerous resources for conducting PBL.  Educators desiring to implement PBL will benefit from the following books.


HOT: Project-Based Learning: A Resource for Instructors and Program Coordinators from the National Academy Foundation and Pearson Foundation provides comprehensive coverage on this topic.  You'll find a definition of PBL, questions to consider for when to use PBL, conditions and research supporting PBL, PBL examples and links to resources and training.  Commentary on PBL includes: "The best projects skillfully weave together opportunities for students to engage in classroom activities (Level 1) that address content standards (Level 2) while encouraging them to develop habits of mind (Level 3) and the ability to take responsibility of their own learning (Level 4)" (p. 12).  The 6 A's of PBL are addressed: Authenticity, Academic Rigor, Adult Connections, Active Exploration, Applied Learning, and Assessment Practices.  Finally, within Project Delivery you'll learn about the scaffolding that teachers must consider when implementing sophisticated projects in their classrooms.

Project-Based Learning Professional Development Guide at from the George Lucas Educational Foundation can be used as a two- to three- hour learning module, or expanded to day-long workshops.  Find out what project based learning is, why it is important, how it works, and get some supporting resources.  Also see Edutopia's Project-Based Learning section.

Project Based Learning explained by Common Craft is a short video with an easy explanation of PBL.

Project Approach to Teaching and Learning in school addresses the foundation theory for using projects, strategic planning, and project development structure.  This is an award winning site by Sylvia Chard of the University of Alberta, Canada. You might also be interested in the interview of Dr. Chard addressing project-based learning, which is Edutopia of the George Lucas Educational Foundation.

In Using the Internet to Promote Inquiry-Based Learning, authors D. Jakes, M. Pennington, and H. Knodle describe a structured approach to inquiry-based learning that uses the World Wide Web.  They address an intuitive 8-step process that begins with an essential question and ends with a knowledge product produced by students, typically completed in a cooperative setting. They discuss the skills that students and teachers require to make inquiry-based learning and the Internet a successful endeavor; and the components of a Project Page, which include the scenario, task, resources, product students will build, and assessment.

The Comprehensive Guide to Project-Based Learning: Empowering Student Choice through an Effective Teaching Method from New Tech Network provides an in-depth overview of this method.

PBL in Math

Yetkiner, Z. E., Anderoglu, H., & Capraro, R. M. (2008). Research summary: Project-based learning in middle grades mathematics. Also available at


Teaching the Common Core Math Standards with Hands-On Activities, Grades 6-8

Teaching the Common Core Math Standards with Hands-On Activities, Grades 6-8 by Judith, Gary, and Erin Muschla (2012) has over 100 activities correlated to the CCSS math standards.

Hands-On Math Projects With Real-Life Applications: Grades 6-12

Hands-On Math Projects With Real-Life Applications: Grades 6-12 by Judith and Gary Muschla (2006) contains 60 math projects.

Math Projects: 50 Hands-On Projects that Correlate to Specific Math Concepts, Grades 5-8+

Math Projects: 50 Hands-On Projects that Correlate to Specific Math Concepts, Grades 5-8+ (2011) by Joyce Stulgis-Blalock is aligned to Common Core and NCTM standards.

MathART Projects and Activities (Grades 3-5)

MathART Projects and Activities (Grades 3-5) by Carolyn Brunetto contains dozens of projects within standards for geometry, number & computation, measurement, patterns, statistics, fractions.  You can also find them by season and holiday.

Project Based Learning in the Math ClassroomProject Based Learning in the Math Classroom by Chris Fancher and Telannia Norfar (2019) for grades 6-10 includes three sections.  Section 1 addresses Understanding PBL in a Math Classroom; section 2 includes strategies for designing inquiry-based tasks and PBL units; section 3 provides multiple examples of inquiry-based tasks and PBL units.  The authors also have 2021 books by the same name for grades 3-5 and for grades K-2 with similar content.


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Design Your Own Math Project or WebQuest

Tony Frontier (2021) provided the following valuable insights about projects if you decide to design your own.

"Designing projects that allow students to be engaged and demonstrate evidence of the most important skills and understanding from a unit of study requires alignment among three elements:

  1. The prioritized standard or learning goal.
  2. Standards-aligned success criteria.
  3. Observable, standards-based evidence from the project that can be described using the most important success criteria." (Three Key Elements section)

At step 2, "Focus on the verbs in the standards such as compare, analyze, describe, design, evaluate, and justify."  Further, "Ensure success criteria focus on the most important, transferable elements of the standards."  (Potential of Projects section)

Frontier (2021) also pointed out some perils of projects to be aware of.

The point of this last question is why have students do the project if it does not relate to what should have been learned from that unit, such as the concepts, skills, and vocabulary (Frontier, 2021).


Do you need help on getting started?

Designing Authentic Performance Tasks and Projects: Tools for Meaningful Learning and AssessmentIn Designing Authentic Performance Tasks and Projects: Tools for Meaningful Learning and Assessment, authors Jay McTighe, Kristina Doubet, and Eric Carbauch (2020) offer proven tools and templates for designing performance tasks and projects for all grade levels and subject areas so that they address academic standards and 21st century skills.  ASCD has a webinar associated with this book.  McTighe provided a four-page handout at his website taken from the book with Technology Tools for Performance Tasks and Projects.

If you are planning your own project, CT4ME provides an essay on project development phases and tips at our page Technology Integration: Multimedia in Projects: About Multimedia and Project Development.

Project Pals includes free ebooks among its resources, such as PBL 101: A Beginner's Guide to Project-Based Learning.

Friendly reminder GifBeyond Google ...

If you decide to allow your learners to design their own projects in which they will need to use internet resources, read Patricia Deubel's article, Conducting Research-based Projects in Elementary Grades with Safety in Mind, published July 26, 2017 in THE Journal.


Do you need project ideas?

Volker Ulm (2011) had several ideas for potential math projects.  Selection, of course, depends on the skills of your learners for meaningful project-based learning:

Use the following to get other ideas:

Applied Math Science Fair Projects posted at included illustrative images of projects and is searchable by grade level.  You can then download the project.

Math Project Ideas: Examples of Project-Based Learning, posted by EdTecher Heidi Reina at HubPages, includes an extensive collection of engaging projects for all grade levels from general math to money and finance, algebra, geometry, pre-calculus, calculus.  Many have cross-curricular connections.

Origami Resource Center includes project ideas and resources on this topic.  It's easy to connect origami, the art of paper folding, to math and geometry, in particular.  If you think the idea is just for elementary students, view The Origami Revolution (2017, about 50 minutes) from  You'll learn how "engineers and designers are applying its principles to reshape the world around us—and even within us, designing new drugs, micro-robots, and future space missions" (Program description section).

PBLWorks from the Buck Institute for Education includes a database of projects in multiple subjects, including for math.  You can search by subject area, grade level, standards including the Common Core.  Additional resources include articles, blogs, videos, planning tools, rubrics, and student handouts.

Project Ideas for Mathematics and Project Examples, Resources, and Websites are from the American Federation of Teachers.


Here's a project idea!

Good Idea

Use Desmos to have learners connect math to art.  Create equations associated with your drawing, add color and so on.  Art can range from simple to complex, depending on your math skills.

See the many image examples on the web with a search phrase such as "demos art with equations."

Get some how-to's with the following:

Desmos Art Tutorials on YouTube.

Desmos Art: The Definitive Guide to Computational Sketching at Math Vault.


Do your learners know what tools to use to design their own math project?

There are multiple tools in a variety of categories on the Web for project-bbooased learning activities.  Certainly, to help them get started, learners will benefit from a list of resources that you anticipate they will need.  Deal (2009) included specific examples within categories such as collaboration suites, course management systems, dedicated project management tools, wikis, web-conferencing tools for real-time communications, collaborative concept mapping tools, presentation and slide sharing tools, online collaborative writing tools, and task management tools.  The choice would depend on the objectives of the assignment and whether or not the project is to be completed by individual learners or collaboratively within groups. 

In addition consider: is a free web application that allows groups to brainstorm online and create mind maps.  You can embed the map in a blog or website, or save the mind map as an image.  This is a great way to start projects.

Tools for Creativity and Innovation

Infographics templates--15 free templates from, including how to make an infographic.

Infographics as a Creative Assessment from Kathy Shrock includes a list of multiple tools for creating infographics, samples, a general overview of this topic, and more.

Makey Makey--an invention kit.  "Turn everyday objects into touchpads and combine them with the internet."

Scratch--a programming language for kids (ages 8 to 16) to create stories, games, and animations, which was developed by MIT.  It is free.  Note: Members of the ScratchEd research team at the Harvard Graduate School of Education developed a free guide, Creative Computing: An Introductory Computing Curriculum for Scratch.  The version for educators includes plans, activities, and strategies for using Scratch and the workbook version for learners has activities and reflection question templates.

Tynker helps learners ages 5-18 to learn how to program.  It promotes itself as "an online platform that easily and successfully teaches students how to code through the activities they already love: games and stories. Students learn the fundamentals of programming and design through Tynker's intuitive visual programming language without the frustrations of traditional syntax" (FAQ section: What is Tynker?).  School pricing is also available.

VRMath 2.0VRMath 2.0 allows users to create virtual worlds and artifacts.  It "utilises 3D technologies and powerful Web 2.0 ideas for teaching and learning mathematics particularly in geometry. The simple aim of this VRMath 2.0 application is to utilise affordable and innovative technologies to allow learners to freely express their ideas and make meanings of mathematics through multiple knowledge representations (signs, semiotic resources) and interpretations (semiosis). The use of technology is not merely to amplify existing ways of thinking and doing, but to provide an environment and opportunity to re-organise one's thinking and doing about mathematics" (About section).  There are numerous STEM examples to provide project ideas, plus tutorials and help in a wiki, a discussion forum, and an option to share creations.

Tools for Group Projects

Group Project Tools from Carnegie Mellon include team contracts, team roles, self assessments, peer assessments, and group assessments.

iBlocks Project-Based Learning: Per its description, "An iBlock is a 10-part sequence of student-led, teacher-guided lessons and activities that center on technology and culminate in a capstone project.  Students drive the learning and tackle the project as a team, while the teacher facilitates, providing guidance and coaching as students engage in skills-building, career-based exploration."

What is a real WebQuest?


Web Quest GifConsider a WebQuest, an inquiry-oriented activity in which most or all of the information used by learners is drawn from the Web.

Dr. Surhat Kurt (2021) elaborated on the renewed interest in WebQuests in his article WebQuest: An Inquiry-oriented Approach in Learning.  Learn about the long-term and short-term types, benefits for collaboration, versatility, differentiation, and steps for building your own webquest. 

Math WebQuests help students to develop reasoning and critical thinking skills, as advocated in the the Common Core math practice standards.  ZUNAL has an extensive database of WebQuests, including math WebQuests for K-12, to give you ideas.


According to Tom March (2003) in The Learning Power of WebQuests, there are six elements of a real WebQuest:

  1. a scaffolded learning experience,
  2. use of links to essential resources on the World Wide Web,
  3. an authentic task to motivate students' investigation,
  4. open-ended questions,
  5. development of individual expertise, and
  6. participation in a group process that transforms newly acquired information into a more sophisticated understanding.

Some activities may be designed to use Internet resources to produce a product, but can't be classified as WebQuests.  These non-WebQuest activities are those that enable learners to gather information that can go from a browser directly to a product without altering or involving students' understanding, and reflection on their own metacognitive processes.  To assess the real value of a WebQuest, ask "Is this WebQuest real, rich, and relevant?"

Webquest Tutorials, Templates, and Project Examples

Creating a WebQuest: It's Easier Than You Think! from Education World.

WebQuest 101 from will help you get started.

WebQuest Template by Patricia McGee and Deborah Claxton is posted on a Google site.  It includes directions within the sections: Introduction, Task, Process, Evaluation (Rubric), and Conclusion.

WebQuest Maker from includes a template.  Fill-in the steps and then the site will generate your webquest.

WebQuests in Online Learning posted at the University of Hawaii will help you to create your own.  In opening statements, the developers noted: "A WebQuest is an inquiry-based, on-line learning activity. The objective of the activity is to promote “transformative” learning outcomes, accomplished through the reading, analysis, and synthesis of online resources. WebQuests use the internet to present content and are often structured to help develop students’ problem-solving and decision-making skills."

ZUNAL is free web-based software for creating WebQuests.  An evaluation rubric is included.  There's also a database of WebQuests, including math WebQuests for K-12, to give you ideas.


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Project Assessment

Check mark for project assessmentAssessment plays a key role in PBL.  If the nature of your project is collaborative, Ashley Deal (2009) noted that three areas can be assessed.  "Instructors can evaluate the process students use in approaching a given problem and finding solutions; they can assess the final product or end result of the project; or they can evaluate the individual student’s learning outcomes" (p. 4).  However, a single approach to assessment of group work poses a problem, as "a satisfactory final product does not necessarily indicate that students approached the problem according to the preferred process. Similarly, even using the correct process to arrive at a satisfactory final product does not indicate that individual students grasped relevant concepts" (p. 4).  So, more than one level of assessment is recommended.

Grading and Group Work: How do I assess individual learning when students work together?Susan Brookhart (2013a) provided valuable advice in Grading and Group Work: How do I assess individual learning when students work together? noting the struggle that many teachers have between the need for learners to engage in cooperative learning and the need to provide individual grades.  "Many teachers use group work in the general sense, assigning students to collaborate in groups that result in one undifferentiated product.  But true cooperative learning requires individual accountability.  No matter what kind of cooperative learning or group work you employ, it is important not to give group grades" (Does group work have to mean group grades? section).  She further explains what's wrong with group grades and grading cooperative work versus group work.  She answers: How can I assess learning and process skills?  How can I assess and grade individual students' achievement?  How can I adapt group projects to enable individual grading?

In a recent article, Planning for Fair Group Work, Susan Brookhart and Amir Rasooli (2021) provided four recommendations to implement and assess group work fairly.

  1. Establish a clear purpose for working in groups.
  2. Use heterogeneous groups, but offer choice if possible.
  3. Use flexible seating and design tasks so everyone contributes.
  4. Grade individual learning and assess collaboration separately.

The State University of New York at Albany's Institute for Teaching, Learning, and Academic Leadership also developed a useful guide for group projects: How can I design, implement, and grade group projects that ensure student learning?  The guide includes examples of elements of effective group project assignments, including those that can be completed individually contributing to the project.  Of value is the following grading scheme as an example, which focuses on individual assessment:

How can I assess group work? from the Eberly Center at Carnegie Mellon University delves into the challenges and includes samples of group project assessment tools.


Mary Allen (2003) noted that rubrics can be used to evaluate the quality of “virtually any product or behavior, such as essays, research reports, portfolios, works of art, recitals, oral presentations, performances, and group activities. Judgments can be self-assessments by students; or judgments can be made by others, such as faculty, other students, or field-work supervisors. Rubrics can be used to provide formative feedback to students, to grade students, and/or to assess programs” (para. 1).  Essential features include "evaluative criteria, quality definitions, and a scoring strategy" (Popham, 1997, Rudiments section).

There are three common types of rubrics: analytic, developmental, and holistic.  McTighe, Brookhart, and Guskey (2024) noted that all three types share three elements essential to rubrics, but render them in different ways.  That is, as an assessment tool, a rubric consists of "1) a set of criteria aligned to learning goals; 2) a performance scale typically consisting of three or four levels, and 3) descriptors that differentiate the levels of performance on the scale" (para. 3).  

An analytic rubric is often designed in column format with multiple performance criteria listed in the first column and the quality indicator levels, which vary on a continuum, listed in the first row across remaining columns.  Each quality level might contain one point value or a range of points that can be assigned.  Each criteria might also be accompanied by a comment space for additional feedback on the element.  Cells within the rubric might be blank or contain elaborations of each performance criteria for the specific quality level.  The developmental rubric is a subset of the analytic rubric and is based on a theory of development.  It is useful when the goal is to determine a level of development (e.g., of a skill, value, ability, etc.) rather than the quality of a final product.  When using a holistic rubric, a single score (e.g., from 1-4 points on a scale, or 1-6 points on a scale) is assigned based on the overall quality of work in consideration of all criteria.  The evaluator matches the student's work to a single description of it.  For example, ratings might be above average, sufficient, developing, needs improvement with elaborations on criteria for selecting each (DePaul University, Teaching Commons, Types of Rubrics, n.d.).

Students benefit from access to a rubric while they are working on a project.  Knowing the criteria on which they will be assessed is a plus to help them develop, evaluate and tweak their own work prior to submitting it.

Rubrics are valued because they enable objectivity in assessment.  However, when educators design their own rubric or select an existing one, they need to consider the potential increase in cognitive load it might present when actually using it.  The greater the number of criteria and granularity within quality levels, the longer it takes to apply the rubric for one project.  Ranges of point values within a quality level also add a degree of subjectivity to using the rubric.  Then consider the number of projects to be assessed.  Per Popham (1997), if a rubric is to be instructionally useful, its length makes a difference.  Teachers will avoid using overly detailed rubrics, particularly for routine tasks.

Rubrics that include quality indicators requiring evaluators to count errors before assigning a point-value also increase cognitive load and require a level of granularity in grading that not all educators are willing or even able to do.  Of course, this would depend on the objective of the assignment or project.  Scores derived from a rubric might also be affected by terms within quality levels that might be understood differently among evaluators who use the rubric.  Quality elements that differ by only a word or two are particularly challenging to use.  For example, consider quality levels such as: … is not stated, … is stated, …. is clearly stated, … is clearly and concisely stated.

Rubrics might also pose a challenge if the numeric score obtained from it will be translated into letter-grades.

Learn how to create rubrics to help measure quality and student performance on projects with these additional resources. Or, use an existing rubric.

How to Create and Use Rubrics for Formative Assessment and GradingHow to Create and Use Rubrics for Formative Assessment and Grading by Susan Brookhart (2013b) includes two sections.  In Section 1, Brookhart lays out the basics of rubrics, explains their importance, discusses common misconceptions, and how to write or select effective rubrics.  She identifies various kinds of rubrics and their essential components.  In Section 2, she explains how to use rubrics for formative assessment and grading.

The following existing rubrics from various locations are of value in projects:

Teach-nology: Rubric Makers allow you to make grading rubrics by filling out a simple form. The materials are made instantly and can be printed directly from your computer.  You can also customize your own rubric.  Rubrics of interest include homework, class participation, math projects, oral presentations, WebQuests, team work, writing, research reports, and reading.

Tech4Learning: Rubric Maker includes a free version.


Help your students to understand the beauty of mathematics found in nature and everyday life.

Often students have difficulty seeing the math that is around them everyday or they lack motivation for studying mathematics because they don't see the connection of it to everyday life.  One way to help them is to show them the beauty of math found in nature and in everyday life.  Another is to listen to the variety of TED Talks on the Topic of Math from experts around the world, which is sure to capture the interest of your learners.  Many of these can also provide great topics for projects.

View The Great Math Mystery (2015, about 50 minutes) from  Per the program description:

"Join NOVA on a mathematical mystery tour—a provocative exploration of math's astonishing power across the centuries. We discover math's signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the prediction and discovery of the Higgs boson and the successful landing of rovers on Mars. Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond. It all leads to the ultimate riddle: Is math a human invention or the discovery of the language of the universe?"

Fibonacci series golden section imageThe image shown is of the Fibonacci series Golden section proportion.  The golden section occurs in nature.  See 14 Interesting Examples [and Images] of the Golden Ratio in Nature: flower petals, seed heads, pine cones, shells, spiral galaxies, hurricanes, faces, animal bodies, and more.

View the short video, Nature by Numbers, created by Cristóbal Vila, which was inspired by numbers (e.g., Fibonacci and Golden Ratio), geometry, and nature.  This is truly beautiful and eye-opening.  Then visit:

The Exploratorium in San Francisco features the Geometry Playground, which will change how you view geometry in nature.  It contains three sections: The Geometry of Seeing with a photo exhibition of the invisible geometry of light; The Geometry of Moving on the arcs, angles, and shapes created when people and things are in motion; and the Geometry of Fitting Things Together.  Each includes hands-on activities for grades K-8.  The Geometry Garden features curiosities found in nature from crystals to seashells to sculptures.  The site was made possible by the National Science Foundation and the Gordon and Betty Moore Foundation.

A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and ScienceImagery: A Key to Understanding Math by Holly Korbey at Mindshift (2013, October 31) is a quick eye-opener to helping students find the beauty in math and overcome math anxiety.  It leads one to a valuable book by Michael Schneider (1995) on the topic: A Beginner's Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science.  Schneider focuses on the numbers 1-10 and provides a fascinating historical discussion of their relationship to geometry found in nature, art, science, architecture, and so on over time.  Using a compass, straightedge, and pencil he demonstrates how you can introduce this beauty to your learners.  For example, "ancient philosophers conceived that the Monad [The First] ... creates all subsequent numbers (11111111 x 11111111 = 12345678987654321)" (p. 3).  And the circle "represents a wonderful first glymph into nature's alphabet" (p. 4).

Learn about fractals.

Water FractalWhat is a fractal? The Fractal Foundation defines a fractal as a "never-ending pattern that repeats itself at different scales."  Fractals are found in nature and in math.  This site features "fractivities," which "are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs."  The activities are free and align with the Common Core standards in math and English language arts.  You'll also find an Educators' Guide and free fractal software to make your own fractal.

The PBS television series , NOVA, has a one-hour program about fractals called Hunting the Hidden Dimension. There are five chapters, which can be viewed separately.  Learn about fractals in nature, including those in the human body.  There are links and books, a teacher's guide, and an email newsletter for learning more.  You can also design your own fractal using NOVA's interactive generator.

Fractals are explored in Wikipedia.

Fern will benefit high school learners and above.  The developer provides tutorials to learn more about fractals and how to create fractal art.  Users can download free fractal software programs and view some fractal art galleries.

Pomegranate Software offers the program called Fractals, which is designed for use on iPad and iPhone.  It “renders as you move and pinch to explore Mandelbrot and Julia set fractals in real-time.”  See the exciting displays and learn more about fractals at this site.

If you wish to generate fractals, there are many free possibilities.  For other examples, see the Online Fractal Generator for 2D, Untra Fractal, and Frax.  Frax is by Iter9, LLC.


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Brookhart, S., & Rasooli, A. (2021, July 1). Planning for fair group work. Educational Leadership, 78(9).

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Binoculars GifLearn about the technical side of creating multimedia projects, including working with images and video.

See CT4ME Technology Integration: Multimedia in Projects