ELEMENTARY 

 From Illuminations:

• Tree Talk Lesson 
  If a tree could talk, we could ask it how old it is. Here is a mathematical way to estimate the age of your schoolyard trees. Students will measure circumference of trees in order to find diameter and calculate age of local trees using a growth rate table.

 From Teaching Children Mathematics journal:

• Collecting Data Outdoors: Making Connections to the Real World    
  Carol G. Basile
  September 1999, Volume 6, Issue 1, Page 8
  Abstract: Describes a process of data collection with young children using the outdoors as a mathmatical context.
• Bird Station Investigation    
  Julie R. Poth
  October 2006, Volume 13, Issue 3, Page 174
  Abstract: This article describes how the real-world application of measurement skills within an integrated science unit can strengthen the engagement level of students and improve their critical thinking and problem-solving skills.
• Trailblazers    
  Lyn D. English, Steve Humble and Victoria E. Barnes
  March 2010, Volume 16, Issue 7, Page 402
  Abstract: You, too, can design and implement math trails to promote active, meaningful, real-world mathematical learning beyond your classroom walls.
• How Many Blades of Grass Are on a Football Field? 
  Christina M. Nugent
  February 2006, Volume 12, Issue 6, Page 282
  Abstract: This article discusses the use of a problem-based instructional task in an elementary classroom. After estimating the number of blades of grass on a football field, students write letters to explain the results of their research.
• A Physical Situation as a Way to Teach Angle    
  Valerie Munier, Claude Devichi and Hélène Merle
  March 2008, Volume 14, Issue 7, Page 402
  Abstract: An experimental sequence to teach angle concept in elementary school shows how children abstract this concept from a real-life physical situation to connect physical and geometrical knowledge. Article describes the four-part lesson used in the study of 3rd and 4th graders. 
• Designing Math Trails for the Elementary School    
  Kim Margaret Richardson
  August 2004, Volume 11, Issue 1, Page 8
  Abstract: This article explains how to construct a multi-level math trial exploring mathematics in the environment.  
• Problem Solvers: A Visit to Your School and Solutions to the Walk for the Paws Problem 
  May 2009, Volume 15, Issue 9, Page 516
  Abstract: Problem Solvers: A Visit to Your School edited by Sarah Bunten, Brian Schad, and Joseph Georgeson. Solutions to the Walk for the Paws Problem edited by Mark Ellis and Cathery Yeh. “Problem Solvers” is a department of the journal that typically features a new problem for students and then discusses the results of presenting a previous problem to students. 
• Investigations: Sun Catchers
  Aaron D. Isabelle and Karen N. Bell
  April 2007, Volume 13, Issue 8, Page 414
  Abstract: Edited by Cornelis de Groot. "Investigations", a regular department of the journal, highlights activities that develop conceptual understanding of mathematics topics.

  MIDDLE SCHOOL  

 From Illuminations:

• Building Height Lesson
  Students will use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class will compare measurements, talk about the variation in their results, and select the best measure of central tendency to report the most accurate height.
• Bouncing Tennis Balls Lesson
  Students develop their skills in collecting and recording data using the real-world situation of a bouncing tennis ball. They use the data collected to formulate the relationship between the dependent and independent variable in their experiment.

 From Figure This!: 

• Oh, Which Way do I Go? Challenge #6 
• Have You Ever Seen a Tree Big Enough to Drive a Car Through? Challenge #15 
• What Shape is at the Very Top of a Fire Hydrant? Challenge #35 
• When Should You Buy Block Ice or Crushed Ice? Challenge #62  

 From Mathematics Teaching in the Middle School journal:

• An Investigation of Solar Noon
  H. Bruce Stewart, Maria E. Reininger and Walter A. Smudzinski
  October 2008, Volume 14, Issue 3, Page 140
  Abstract: This article describes an activity done by eighth grade students using data that was gathered from sun-shadow observations. 
• Making Mathematics Real: The Boston Math Trail
  Matthew M. Rosenthal and Clement K. Ampadu
  November 1999, Volume 5, Issue 3, Page 140
  Abstract: Students discover the mathematical side of Boston on a day-long field trip. 
• Take Time for Action: Students' Geometric Thinking about Rotations and Benchmark Angles 
  Melfried Olson, Fay Zenigami and Claire Okazaki
  August 2008, Volume 14, Issue 1, Page 24
  Abstract: Article discusses a lesson that uses a problem solving approach to explore and compare similar figures using ratios. 
• Laying Siege to Parabolic Understanding
  John W. Rick
  November 2009, Volume 15, Issue 4, Page 198
  Abstract: An attack on a domino castle using a trebuchet is one way to help students storm a wall of understanding while learning about medieval mathematics.
• Quick Reads: Another Good Idea: Capture the Flags
  September 2010, Volume 16, Issue 2, Page 72
  Abstract: Students work in teams on a project that uses a form of triangulation to find relative positions of flags that have been set out in a field.
• Ramping Up on Fractions
  Ana C. Stephens, Brian A. Bottge and Enrique Rueda
  May 2009, Volume 14, Issue 9, Page 520
  Abstract: This article describes a technology-based and hands-on instructional intervention designed to advance middle school students’ understandings of fractions.

 HIGH SCHOOL  

• Human Conics Lesson
  In this lesson students use sidewalk chalk and rope to illustrate the locus definitions of ellipses and parabolas. Kinesthetics, teamwork, and problem solving are stressed as students take on the role of focus, directrix, and point on the conic, and figure out how to construct the shape.

 From Mathematics Teacher journal:

• Cooking with Quadratics
  Luajean N. Bryan
  November 2010, Volume 104, Issue 4, Page 308
  Abstract: Using basic properties of a parabola, students collect and analyze temperature data and construct a three-dimensional model from a quadratic equation—to cook marshmallows!
• Poles, Parking Lots, and Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics
  Seán P. Madden, Jocelyn M. Comstock and James P. Downing
  September 2006, Volume 100, Issue 2, Page 94
  Abstract: This article describes how a series of lessons might be used to allow students to discover the size of the Earth, the distance to the Moon, the size of the Moon, and the altitude of Mount Piton on the Moon. Measurement with a sextant, principles of geometry and trigonometry, and historically important scientists and mathematicians are discussed.
• Technology Tips: Why Are Shot Puts Thrown at 31 degrees? Using Autograph for Applications of the Parabola
  Douglas Butler
  May 2010, Volume 103, Issue 9, Page 689
  Abstract: Edited by Kathleen Lynch-Davis and Tracy Goodson-Espy. Why is the angle of elevation for a shot-put 31 degrees and not 45? The author answers this and other questions.
• Parabolas under Pressure
  Seán P. Madden
  May 2009, Volume 102, Issue 9, Page 660
  Abstract: The author and his algebra 1 students explore the quadratic behavior behind the parabolic shape of fountains at the local family splash park. In this hands-on discovery project, students gathered data on and used graphing calculators to analysis of the beautiful symmetry of these fountains. This experience served as a capstone project for a unit on quadratic equations. 
• How Far Up Am I? The Mathematics of Stadium Seating
  Rebecca McGraw, David Romero and Robert Krueger
  November 2006, Volume 100, Issue 4, Page 248
  Abstract: This article describes a lesson in which students collect data related to their school's stadium seats and use this data to create tables, draw graphs, and write equations.
• The Human Body’s Built-In Range Finder: The Thumb Method of Indirect Distance Measurement
  Michael Wong
  May 2006, Volume 99, Issue 9, Page 622
  Abstract: Students get a fun challenge from puzzling over an old, seemingly magical distance measurement technique. 
• Projects: The National Math Trail
  Racquel Skolnik
  January 2002, Volume 95, Issue 1, Page 78
  Abstract: During the past few school years, teachers and students across the country have been taking virtual walks along the National Math Trail. The K-12 Internet-based project invites students and teachers to submit community-based mathematics problems, along with photographs, illustrations, audio or video content, or Web pages. These submissions are posted to the National Math Trail map throughout the year. International submissions are also being solicited, and appropriate maps are created.