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Geometry and Spatial Relations: Sidewalk Capers

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Geometry and Spatial Relations: Sidewalk Capers

In this math lesson, learners use a variety of manipulatives to explore spatial relationships of squares and their transformations. Learners create a square with 36 square tiles and determine that by sliding several of the pieces both vertically and horizontally, they form an irregular shape that can be tessellated. Learners are given a variety of curved shapes and encouraged to use tape and scissors to reconfigure their shape back into a square. Learners are surprised to learn that all of the different shapes have the same area. Given a variety of measurement tools, learners are also asked to estimate the number of squares tiles (24" x 24”) needed to cover an assigned section of the sidewalk. Finally, learners create a pattern from the square and tessellate it on the sidewalk using chalk.

Quick Guide

Preparation Time:
10 to 30 minutes

Learning Time:
1 to 2 hours

Estimated Materials Cost:
$5 - $10 per group of students

Age Range:
Ages 8 - 11

Resource Types:
Activity, Lesson/Lesson Plan


Materials List (per group of students)

  • 2 squares: 36 square units in size. (One should show an outline of the grid)
  • 36 magnetic square tiles or cut-outs of small squares that can be taped to the board
  • 4 copies of the 36 square unit shape
  • Square Tiles (36 per learner)
  • Activity Sheets: Special Shape (A-E)
  • Activity Sheets: Sidewalk Capers
  • Colored sidewalk chalk
  • Tape measures
  • Tape
  • Rulers
  • Scissors
  • Square units made from paper (approximately 24 in on a side)


  • Mathematics
    • Algebra
      • Patterns
    • Geometry
      • Plane Geometry
    • Measurement
      • Polygons
    • Problem Solving

Informal Categories

  • Outdoor Activity


To use this activity, learners need to:

  • see
  • read
  • be mobile
  • touch

Learning styles supported:

  • Involves teamwork and communication skills
  • Involves hands-on or lab activities


This resource is part of:

Access Rights:

  • Free access



  • All Rights Reserved, PBS, ©2012

Funding Source:

  • US Department of Education


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