Math PBL and Real World Resources

Math -- PBL and Real Applications

BIE – The Buck Institute (BIE) is of course is one of the international leaders in PBL. In fact, I am a proud member of their National Faculty. On the front of BIE page you will find a large collection of projects. A simple search through the data base may just land you on that project you have been looking for. Many times the project will contain those essential PBL elements. Enjoy the search!

The New York Times Learning Network – The supplied link happens to bring you right to the math section of this amazing site. Have you ever thought about exploring Driving Questions that ask some of the below mathematical concepts?

  • How is math beautiful?
  • How big is infinity?
  • What happens if we go over a fiscal cliff?
  • Is Algebra necessary?

If these questions spark your curiosity to explore the wonderful world of numbers and computation then the New York Times Learning Network is a must visit! The Learning Network provides teaching and learning materials, ideas, and lesson plans based on New York Times content. Teachers can use or adapt these lessons and even contribute their own ideas. While the lessons may not be a complete PBL unit, they can sure provide the footprint for a new idea or scaffolding for a current project. Take a visit and start reading some of these amazing ideas. I guarantee it will get you looking at math in a different way and might help you generate a completely new idea.

Emergent Math – Looking for ideas that just might spark a PBL math idea? Emergent Math is dedicated to brainstorming interesting and dynamic math problems and projects. The facilitator of the blog is employed by the New Technology Network of Schools. The posts really do allow for real mathspiration (inspirational combined with math). As stated in the blog, “interesting math problem/project can come in the form of a picture, a video, a tweet, something your child says, etc”. This blog really does attempt to use all of the preceding ideas, plus more! The posts generate ideas on how these concepts just might fit in the classroom and/or provide some driving/guiding questions. The best place to begin your exploration is at the first page of the blog and read the index! You will enjoy your immersion in Math!

Less Helpful Math – Many math teachers are familiar with the amazing work of Dan Meyer. Dan has been a high school math and currently studies math education at Stanford University. He speaks internationally and works with textbook publishers assisting in the transformation of print past to digital future. You will be tempted to spend hours, days, and weeks in this amazing blog. In fact, just subscribe so you do not miss a thing. Dan has the wonderful ability to talk in a real world math language. Many of his examples and ideas can be the footprint of scaffolding for either PBL or PrBL (Problem Based Learning). Areas to make sure you explore include blog articles, author’ choice, My Curricula (3 Act Math), My Projects, and of course the Categories! Just don’t watch the clock, there is no way to predict the minutes you will spend in this amazing land of math!

Share My Lesson – This link will land you at the PBL Math Portion of the site. Share My Lesson is a place where educators come together to create and share their very best teaching resources. It was created by teachers for teachers. It is a free platform giving access to high-quality teaching resources.  It provides an online community where teachers can collaborate with, encourage and inspire each other. Many of the math activities and plans will provide ideas to a PBL project, the idea for a PBL project, or scaffolding ideas to reside in a PBL project. Be sure to explore the lessons in Algebra, Geometry, Mathematical Functions, Statistics, and Probability. At last count there were over 3500 combined lessons. Perhaps that is still not enough and you will find something to share!

PBL Pathways – This is a website dedicated to Math and PBL. In the supplied link you are directed to the PBL Projects. Here you will discover some project ideas covering many areas of advanced math. Each is a complete project that you may wish to include. Please be sure to read their Terms of Copyright Statement when using the materials. The site really does contain some outstanding mathematical PBL pathways.

Project Based Instruction in Mathematics for the Liberal Arts – The purpose of this wonderful web site is to provide projects and resources for instructors and students who wish to teach and learn college mathematics or post-algebra high school mathematics via project-based instruction. Many of these projects can be geared toward high school mathematics. Project-Based Instruction in Mathematics for the Liberal Arts (PBI-MLA) was developed at the University of South Carolina Spartanburg (now known as University of South Carolina Upstate). In six years, it developed an amazing 30% higher success rate than traditional textbook-driven sections of College Mathematics. You will find some great ideas as you explore.

CIMS Industrial Mathematics Projects For High School Students – The WPI Industrial Mathematics Project for High School Students developed over twenty industrial mathematics projects for high school students. Best of all these were drawn from a variety of real-world situations. These engaging projects are available for every level of high school mathematics, from Algebra to Calculus and Statistics. The length and scope of these projects is very flexible.  Each project contains enough material for a major, semester-long endeavor, but its component parts can be used in a shorter project of for scaffolding activities. Explore the project database which contains downloadable versions of each of the projects, ready to be assigned to students.

TEDed Math – The TED-Ed commitment to creating lessons worth sharing is an extension of TED’s mission of spreading great ideas. Within the growing TED-Ed video library, one can find carefully curated educational videos, many of which represent collaborations between talented educators and animators. This platform also allows users to take any useful educational video, not just TED’s, and easily create a customized lesson around the video. This link brings you to some amazing Math lessons that can be used for a footprint of a PBL Unit of a scaffold activity.

Mathematical Moments – Authenticity is important in Math PBL. It seems that Math educators are always looking for ways they can show how math is used in the world around us. Discover a site that will help you achieve this goal of real world application. The site is cleverly titled Mathematical Moments and it is well worth the time! It contains free printable posters that are 8.5″ x 11″ PDF documents. These informational posters are available on many different topics in science, nature, technology, and human culture. As you take a closer look many of these posters note that many have a  link to some short feature podcast interviews with experts in the field. These posters and podcast could spark the idea for a PBL math unit that brings authenticity into your math teaching.

The PBL Academy – The PBL Academy at Indiana University provides outstanding project based learning instruction, structure, and on-going support for K-12 educators.  The provided link focuses on the numerous Math Projects hosted at the Academy. You will find them in the Math Matters Area. Each project is developed by participating teachers. Along with the elements of PBL, each project must also address an actual local ‘need’ which may include an on-going business process or an enhancement of a municipal program, etc. Of course these ideas can be adopted and assimilated into just about any community. When landing on the site you can sign up or log in as a guest.

Real World Math – This site contains a collection of free math activities for Google Earth designed for students and educators. There are some outstanding connections to PBL! As you know, mathematics is much more than a set of problems in a textbook.  Students will find that in the virtual world of Google Earth, concepts and challenges can be presented in a meaningful way. While this link will take you to the PBL section be sure to explore other areas of the site that can be used as you scaffold existing PBL units.

Intel PBL – Intel stresses that PBL puts assessment and content standards at the forefront of learning. It is with projects that students can be engaged in authentic work and develop 21st- century skills of collaboration, problem solving and critical thinking. A well-designed, project-based curriculum can yield high quality results for students and a rewarding experience for teachers. The provided link opens the door to some great Math projects from Intel.

Exploring Space Through Math – This amazing NASA site promotes inquiry through real world applications. Students assume the role of NASA scientists, engineers and researchers who work in teams to accomplish tasks. These projects promote cooperative learning, problem-solving and the use of technology. The problems in this project follow the 5-E’s Instructional Model with a segment for each phase of instruction – Engage, Explore, Explain, Extend and Evaluate. The projects cover the scope of Algebra I, Algebra II, Geometry, and Precalculus.

Curriki Algebra – This is an Open Education Resource (OER) Algebra course that consists of five units aligned to the Common Core. Each of the units culminates in a project that utilizes mastery of conceptual understanding taught in the individual lessons. These units include:

  • Unit 1: Relationships between Quantities and Reasoning with Equations
  • Unit 2: Linear and Exponential Relationships
  • Unit 3: Descriptive Statistics
  • Unit 4: Expressions and Equations
  • Unit 5: Quadratic Functions and Modeling

Teach 21 – This resource rich site was designed by teachers to assist colleagues in planning and delivering effective 21st century instruction in West Virginia. While it enables educators to quickly access 21st Century Content Standards, Learning Skills and Technology Tools for WV Schools the provided link indexes the Math PBL projects for grades 3 -12. There are over 50 potential projects to explore!

Annenberg Learner Math Lessons – Annenberg Learner uses media and telecommunications to advance excellent teaching in American schools. This mandate is carried out chiefly by the funding and broad distribution of educational video programs with coordinated Web and print materials for the professional development of K-12 teachers. The math lessons could be a footprint to a PBL unit or scaffolding for an entire PBL. While at the site… take a look at the interactives.

MIT Blossoms – All of the lessons in the MIT Blossoms library have been contributed by BLOSSOMS partners from around the world. There is a watch the Teacher’s Guide Video Segment included with each lesson to learn more about it. The final segment of each BLOSSOMS video lesson is a one-on-one conversation between the teacher and the “virtual teacher.” Best of all, these lessons can be part of a PBL unit. The provided link brings you to the Math (English Language) Section.

Figure This - This wonderful site is the work of the National Council of Teachers of Mathematics, in cooperation with the National Action Council for Minorities in Engineering, Widmeyer Communications, and the Learning First Alliance.  Its mission is to challenge middle school mathematics and emphasizes the importance of high-quality math education for all students. While it was created to allow for family interaction, it is also figures into the Math PBL classroom. The site allows students to have the opportunity to face some every day real life math challenges. These challenges feature:

  • Descriptions of the important math involved
  • Notes on where the math is used in the real world
  • Hints on how to get started
  • Complete solutions to the challenge
  • A “Try This” section for formative learning
  • Some additional related problems with answers
  • An assortment of questions to think about with each challenge
  • Really fun facts related to the math
  • A database of resources for further exploration.

Suffolk Math – This is an amazing site from the United Kingdom. This site was established  in 2004 with the aim of providing up to date resources and documents to support the high quality teaching of Mathematics. The link will lead you to an area of the site rich with PBL ideas and scaffolding activities. This really is a wonderful resource from across the water!

Mathalicious – While this is a paid site you will find several free projects on the homepage. Perhaps you will find that the paid lessons are really well worth it!  This site does demonstrate that math is about more than just numbers and equations. Students find that math is a tool to explore the world around us. Mathalicious provides teachers with lessons that help them teach math in a way that engages their students–in a way that helps students understand how the world works. Lessons are aligned to Common Core Standards and explore real life questions.

Get The Math –  An amazing site that combines video and web interactivity to help middle and high school students develop algebraic thinking skills for solving real-world problems. Lessons can be made that draw on conventions of popular reality TV shows. The video segments begin with profiles of young professionals, who then pose challenges connected to their jobs to two teams of teens. Students are encouraged to try the challenges themselves using interactive tools provided on the Get the Math website. This can be the start of some PBL of PrBl.  After their best attempt, students return to the video to see the teams’ solutions.  To expand learning, students can further explore the same, as well as extended algebraic concepts through additional interactive challenges on the website.

Math and Sports – What an amazing website from Cambridge University! These free online mathematical resources explore math and science through sports. These resources include activities designed to develop problem-solving and mathematical reasoning skills for students aged 5 to 18. You will also find  articles aimed at older students. Also, be sure to visit  video maths challenges which is produced with input from Cambridge by BBC Two Learning Zone. Another must visit site includes activities on Maths and Football (European style). It is possible to discover articles and activities that are arranged by Key Stage. The site also allows the user to access  tabs at the top of the page, or view content by sport or topic.

Plus Magazine – That is right… it is a magazine. Another plus… it is free. Most important it is all about the world of Math. This is a wonderful resource that will bring the authentic world of math to your students. Stories and activities can be a scaffold in a PBL Unit or possibly the catalyst for an entire project. This is one that I could have spent an entire post on. In fact read their own quote!

“Plus is an internet magazine which aims to introduce readers to the beauty and the practical applications of mathematics. A lot of people don’t have a very clear idea what “real” maths consists of, and often they don’t realize how many things they take for granted only work because of a generous helping of it. Apparently, some people even have the idea that it’s boring! Weird. Anyway, we hope that even if you’re such a person now, you won’t be after looking through one or two issues of Plus, and that you’ll come back and read future issues as they come out.”

You will find that Plus provides articles and podcasts many areas of mathematics. These topics include but are not limited to art, medicine, cosmology and sport. Be sure to visit the  news section, showing how recent news stories were often based on some underlying piece of math. You can also check out  reviews of popular maths books, and puzzles that will help  to sharpen your students, and your wit. There is also a regular interview with someone in a maths-related career. In these interviews students are  shown the wide range of uses of math  in the real world. Listen to a podcast that will open up real world math or read one of the new Ebooks! Last, for those  real PBL enthusiasts you just might discover the basis for an entire unit in the area called packages. In fact, you will find this online magazine to be a wonderful collection of packages just waiting for you and your students to open.

NRICH – The slogan of this site is “Enriching Mathematics” As one tours the site it is evident that math can be rich! The aim of NRICH is to focus on the problem solving aspect of math. In the PBL world this could be construed as PrBL (Problem Based Learning). This difference can be discussed in a future article. In short… PrBL is shorter and may not contain all of the 8 elements of PBL. It can be turned into a full PBL or could be a scaffolding piece in a PBL.  The belief of teaching Math using problem solving and inquiry is stated by NRICH in the following:

  • Our activities can provoke mathematical thinking.
  • Students can learn by exploring, noticing and discussing.
  • This can lead to conjecturing, explaining, generalizing, convincing and proof.
  • In a classroom, the students’ role is to focus on the mathematics while the teacher focuses on the learners.
  • The teacher should aim to do for students only what they cannot yet do for themselves.

It is especially exciting to see that last statement, allowing students to own their learning. All of the materials is built into age appropriate categories. It is certain that exploration at NRICH will lead on a path to some wonderful math richness! Enjoy the journey to a real home of rich mathematics.

BBC Bitesize Math – OK… this may not have full scale PBL in its design, but there are some amazing scaffolding activities that will  fit into a PBL unit. Add in the opportunity for some formative assessment, and you have an outstanding math site for educators. Explore this provided content:

  • Algebra: Formula  and equations, inequalities, graphs, quadratic equations, sequence
  • Statistics and probability: Collecting data, averages, representing data, probability
  • Number: Number, fractions, decimals and ratios, factors, powers and roots
  • Geometry and measures: Shapes, coordinates, transformations and vectors, calculating lengths, areas and angles, measurements

Please note that you will find activities for all age groups. Perhaps you wish to start at the Activity Page. You are sure to find some great Math resources and be sure to incorporate them as part of your Project Based Learning in Math!

Mathematics, Learning, and Web 2.0 – You may not have noticed but the last four resources have come from the UK. I really don’t want to switch countries or continents so I will conclude this post with an amazing Math Blog from the UK; “Mathematics, Learning, and Web 2.0″ is written by Colleen Young. Her posts provide thoughts and ideas in a very math practical manner. It is a wonderful blog that will allow any math teacher to dream up a new PBL, or scaffold an activity inside an existing project!. Not only that… it is just wonderful reading… so enjoy!

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