Practice: Math Projects
Practice in Action
Math Projects are experiences that connect mathematical concepts and procedures to engaging realworld activities that extend for more than one lesson. Key to the projects concept is that the mathematics—content and process—emerge from students' own investigation of an authentic situation, rather than a classroom exercise. This helps students see ties between mathematics and reallife experiences.
Begin by connecting to the schoolday teacher to find out what math concepts, skills, and standards students are studying, and what kinds of activities might lend themselves to Math Projects. For example, building and racing model cars can extend what students are learning about measurement, geometry, and algebra. Or, combine math and science activities by working on an interdisciplinary project that requires data collection and analysis related to the environment.
Work with students to choose an idea or project that interests them. Then discuss the project, identify what students will do, make a project plan and timeline, identify resources you will need, and conduct the project. It works best when students can work on projects in a regular, ongoing way, as some can take several days. Determine how you and your students will present and evaluate their projects. A culminating activity, such as a final product or presentation, is a typical way to wrap up a project.
Projectbased learning in math works because students are directly involved in their own learning as they develop problemsolving skills, learn new math content, and apply what they learn in authentic, realworld situations. Through this work, students learn new mathematical content and applications as they solve a problem or complete a project. They also experience the connections between the math they have learned in school and realworld situations, and gain skill in transferring and applying this knowledge.
Planning Your Lesson
Great afterschool lessons start with having a clear intention about who your students are, what they are learning or need to work on, and crafting activities that engage students while supporting their academic growth. Great afterschool lessons also require planning and preparation, as there is a lot of work involved in successfully managing kids, materials, and time.
Below are suggested questions to consider while preparing your afterschool lessons. The questions are grouped into topics that correspond to the Lesson Planning Template. You can print out the template and use it as a worksheet to plan and refine your afterschool lessons, to share lesson ideas with colleagues, or to help in professional development sessions with staff.
Lesson Planning Template (PDF)
Lesson Planning Template (Word document)
Grade Level
What grade level(s) is this lesson geared to?
Duration
How long will it take to complete the lesson? One hour? One and a half hours? Will
it be divided into two or more parts, over a week, or over several weeks?
Learning Goals
What do you want students to learn or be able to do after completing this activity? What skills do you want students to develop or hone? What tasks do they need to accomplish?
Materials Needed
List all of the materials needed that will be needed to complete the activity.
Include materials that each student will need, as well as materials that students
may need to share (such as books or a computer). Also include any materials that students or instructors will need for record keeping or evaluation. Will you need to store materials for future sessions? If so, how will you do this?
Preparation
What do you need to do to prepare for this activity? Will you need to gather
materials? Will the materials need to be sorted for students or will you assign students to be "materials managers"? Are there any books or instructions that you need to read in order to prepare? Do you need a refresher in a content area? Are there questions you need to develop to help students explore or discuss the activity? Are there props that you need to have assembled in advance of the activity? Do you need to enlist another adult to help run the activity?
Think about how you might divide up groups―who works well together? Which students could assist other peers? What roles will you assign to different members of the group so that each student participates?
Now, think about the Practice that you are basing your lesson on. Reread the Practice. Are there ways in which you need to amend your lesson plan to better address the key goal(s) of the Practice? If this is your first time doing the activity, consider doing a "run through" with friends or colleagues to see what works and what you may need to change. Alternatively, you could ask a colleague to read over your lesson plan and give you feedback and suggestions for revisions.
What to Do
Think about the progression of the activity from start to finish. One model that
might be useful—and which was originally developed for science
education—is the 5E's instructional model. Each phrase of the learning
sequence can be described using five words that begin with "E": engage, explore, explain, extend, and evaluate. For more information, see
the 5E's Instructional Model.
Outcomes to Look For
How will you know that students learned what you intended them to learn through this
activity? What will be your signs or benchmarks of learning? What questions might you ask to assess their understanding? What, if any, product will they produce?
SelfEvaluation
After you conduct the activity, take a few minutes to reflect on what took place.
How do you think the lesson went? Are there things that you wish you had done differently? What will you change next time? Would you do this activity again?
Sample Lessons
Students learn about various types of patterns as they make paper flowers, and learn about different aspects of fundraising by selling the flowers.
Peddling Petals (K2)
Duration: 3 to 4 weeks
 Work in cooperative groups
 Use problemsolving strategies
 Recognize patterns, relations, and functions
 Represent mathematical ideas through charts and tables
 Create inviting areas (centers) where students have access to all the materials they will need.
 Mix objects in a large bowl or bag at each center and place a handful on a plate for each student.

This project includes many activity descriptions that provide specific instruction on how to focus on the mathematics behind this craft and fundraiser activity.
Specific math components including asking students to create a table illustrating the number of triangles that will be needed to make the flowers. Students are also asked to create tables illustrating the various prices of the flowers; each of these charts is then used during the flower sale. Students will need guidance in developing the charts and assembling the flowers. For complete lesson descriptions, including activity sheets and guides for instructors,
follow the PBS Online link above.
 The ability to successfully work with group members to complete activities
 Students use mathematical vocabulary to discuss processes and procedures
 An understanding of the basic properties of shapes and patterns among objects and the ability to communicate this understanding through drawings and words
Resources
Another approach for projects is to tap the Internet as a resource for students to explore mathematical concepts and their real world applications. For example, allow students to use the Internet to participate in an online scavenger hunt through an inquiryoriented math activity.
Check out the mathematics section of the "Best Web Quests" Web site for activities that help students to apply the skills they are learning in school to other settings.
www.nctm.org
Global Schoolhouse collaborative Learning Projects
www.gsn.org
KIDPROJ
www.kidlink.org/kidspace/start.php?HoldNode=614
The Genesis Mission
genesismission.jpl.nasa.gov/educate/
I*Earn (International Education and Resource Network)
www.iearn.org
The WebQuest Page
http://webquest.sdsu.edu/
Buck Institute for Education
http://www.bie.org/
PBS TeacherSource
http://www.pbs.org/teachersource/math.htm
Alexander, D. (2000). The learning that lies between play and academics in afterschool programs. Retrieved August 29, 2005 from http://www.niost.org/pdf/learning_article.pdf (PDF).
Boaler, J (1999). Mathematics for the Moment or the Millennium? Education Week Commentary, 29 (XVIII) March 31, pp 30 and 34.
Buck Institute for Education. (2003). ProjectBased Learning Handbook: A Guide to StandardsFocused ProjectBased Learning for Middle and High School Teachers. Novato, California.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Mergendoller, J. R., Thomas, J. W. Managing projectbased learning: principles from the field. Retrieved August 29, 2005 from http://www.bie.org/research/study/principles_from_the_field (PDF).
Miller, B. M. (2003). Critical hours: Afterschool programs and educational success. Brookline, MA: Miller Midzik Research Associates for the Nellie Mae Education Foundation. Retrieved June 15, 2003, from http://www.nmefoundation.org/research/time/criticalhoursafterschoolprogramsandeducation.
Policy Studies Associates. (1995). Extending the learning time for disadvantaged students: An idea book. Volume 1, summary of promising practices. Washington, DC. (ERIC Document Reproduction Service No. ED 389094)
Public Broadcasting Service (19952005). Peddling petals. Retrieved September 15, 2005, http://www.pbs.org/teachersource/mathline/lessonplans/.
Wheeler, J. L., Miller, T. M., Halff, H. M., Fernandez, R., Halff, L. A., Gibson, E. G., & Meyer, T. N. (1999). Web places: Projectbased activities for atrisk youth. Current Issues in Education [Online], 2(6). Retrieved August 29, 2005 from http://cie.asu.edu/ojs/index.php/cieatasu/article/view/830/255.