Aligned Resources

Students consider the patterns that emerge from agent models and geometric fractals.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Geometry, Modeling

Related Topics: agent modeling, fractals, pattern, recursion, self-similarity

Explores lines, planes, angles, and polygons in tessellations.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: angles, area, flips, geometry, glides, hexagon, length, lines, pattern, perimeter, planes, polygon, rectangles, reflections, regular, rotation, slides, squares, symmetry, tessellations, triangle

Students learn to identify a variety of patterns using sequences and tessellations.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Geometry, Number and Operations

Related Topics: addition, arithmetic, arithmetic sequences, geometric sequences, hexagon, iteration, multiplication, pattern, planes, polygon, recursion, recursive functions, sequences, squares, symmetry, tessellations, triangle

Examines plane symmetry.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: angles, area, geometry, glides, hexagon, illusion, length, pattern, planes, polygon, rectangles, reflections, regular, rotation, segment, squares, symmetry, tessellations, transformation, translation, triangle

This lesson shows elementary students how they can know, for certain, that rigid motions like reflections, rotations, and translations create a shape congruent to the original.

Audiences: Grades 3-5

Primary Subjects: Geometry

Related Topics: congruent, reflections, rotation, transformation, translation

Introduces students to concepts of transformations.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Geometry

Related Topics: angles, cartesian coordinate, coordinate plane, coordinate system, dimension, distance, flips, geometry, glides, graph, hexagon, image, parallelogram, pattern, planes, polygon, pre-image, reflections, rotation, squares, symmetry, tessellations, transformation, translation, transpose, triangles

Explore the mathematical nature of art and tilings and looks at the role of math in nature and our culture.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: angles, area, contrast, geometry, glides, graph, hexagon, hue, illusion, length, lines, pattern, planes, polygon, rectangles, reflections, regular, rotation, segment, squares, symmetry, tessellations, transformation, translation, triangle, value

Build your own polygon and transform it in the Cartesian coordinate system. Experiment with reflections across any line, revolving around any line (which yields a 3-D image), rotations about any point, and translations in any direction.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Calculus, Geometry, Graphs

Related Topics: angles, calculus, coordinate, coordinate plane, coordinate system, flips, geometry, glides, graph, polygon, polyhedra, reflections, rotation, symmetry, transformation, translation, transpose

Create a tessellation by deforming a triangle, rectangle or hexagon to form a polygon that tiles the plane. Corners of the polygons may be dragged, and corresponding edges of the polygons may be dragged. Parameters: Colors, starting polygon.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: angles, area, flips, geometry, glides, hexagon, length, pattern, planes, polygon, reflections, rotation, slides, squares, symmetry, tessellations

Explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms. Parameters: Shape, x or y translation, x or y reflection, angle of rotation.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry, Graphs

Related Topics: cartesian coordinate, coordinate plane, coordinate system, flips, geometry, glides, graph, hexagon, image, polygon, pre-image, reflections, rotation, symmetry, transformation, translation, transpose, triangle

Build your own polygon and transform it in the Cartesian coordinate system. Experiment with reflections across any line, rotations about any point, and translations in any direction. Parameters: Shape, x or y translation, x or y reflection, angle of rotation

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Geometry, Graphs

Related Topics: angles, cartesian coordinate, coordinate, coordinate plane, coordinate system, flips, geometry, glides, graph, image, linear equations, polygon, pre-image, reflections, rotation, symmetry, transformation, translation, transpose