Aligned Resources

Introduces students to acute, obtuse, and right angles as well as relationships between angles formed by parallel lines crossed by a transversal.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: acute, adjacent, alternate exterior, alternate interior, angles, corresponding, geometry, intersection, lines, obtuse, rays, right angle, transversal, vertical

Comparing shapes with the same areas but different perimeters.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Geometry

Related Topics: area, comparing, geometry, integers, length, perimeter, polygon, rectangles, right angle, squares, width

This lesson utilizes the concepts of cross-sections of three-dimensional figures to demonstrate the derivation of two-dimensional shapes.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: conic section, geometry, hyperbola, parabola, polygon, pre-calculus, pyramid

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

Introduces students to the ideas involved in understanding fractals.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry, Number and Operations

Related Topics: area, distance, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, iteration, length, limit, lines, multiplication, pattern, percents, perimeter, recursion, scale, segment, self-similarity, sequences, sets

Introduces students to quadrilaterals with an emphasis on defining characteristics of parallelograms, rectangles, and trapezoids.

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

Primary Subjects: Geometry

Related Topics: angles, geometry, parallel, parallelogram, polygon, quadrilaterals, rectangles, rhombus, squares, supplemental, tessellations

Introduces students to lines, rays, line segments, and planes.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Geometry

Related Topics: algebra, axis, coordinate plane, coordinate system, functions, geometry, graph, infinity, lines, number line, planes, rays, segment

Students learn how the Pythagorean Theorem works and how to apply it.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry, Trigonometry

Related Topics: algebra, angles, area, arithmetic, cartesian coordinate, coordinate plane, distance, exponents, geometry, hypotenuse, length, perimeter, pythagorean theorem, right angle, slides, solving equations, squares, triangles, trigonometry

Introduces students to the concepts of surface area and volume.

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

Primary Subjects: Geometry

Related Topics: area, arithmetic, dimension, geometry, integers, length, polyhedra, prisms, surface area, volume

This lesson teaches students how to find the surface area of non-rectangular prisms.

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

Primary Subjects: Geometry

Related Topics: area, dimension, geometry, length, polyhedra, prisms, rectangles, slant height, surface area, triangle, volume

This lesson teaches students how to find the surface area of rectangular prisms.

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

Primary Subjects: Geometry

Related Topics: area, dimension, geometry, length, polyhedra, prisms, rectangles, surface area

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

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

This lesson teaches students how to find the volume of non-rectangular prisms.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: area, depth, dimension, geometry, height, length, multiplication, polyhedra, prisms, rectangles, slant height, squares, surface area, triangle, volume, width

This lesson teaches students how to find the volume of rectangular prisms.

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

Primary Subjects: Geometry

Related Topics: area, depth, dimension, geometry, height, length, multiplication, polyhedra, prisms, rectangles, squares, triangle, volume, width

Learn the relationship between perimeter and area. A shape will be automatically generated with the perimeter that you choose. Calculate the area of this shape. Area Explorer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Geometry

Related Topics: addition, area, arithmetic, assessment, comparing, coordinate plane, geometry, length, perimeter, polygon, rectangles, squares

Explore cross sections of different geometric solids: cone, double cone, cylinder, pyramid, and prism. Manipulate the cross section with slider bars, and see how the graphical representation changes.

Audiences: Grades 9-12, Undergraduate

Primary Subjects: Algebra, Calculus, Geometry, Graphs

Related Topics: algebra, calculus, cartesian coordinate, circles, conic section, coordinate system, ellipse, flyer, graph, hyperbola, parabola, polygon, polyhedra, pre-calculus, prisms, pyramid, radius, rotation, transformation

Build a "floor tile" by dragging the corners of a quadrilateral. Learn about tessellation of quadrilateral figures when the shape you built is tiled over an area.

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

Primary Subjects: Geometry

Related Topics: angles, area, coordinate plane, coordinate system, length, pattern, planes, quadrilaterals, rectangles, reflections, rhombus, rotation, slides, symmetry, tessellations, transformation, translation

Learn the relationship between perimeter and area. A shape will be automatically generated with the area that you choose. Calculate the perimeter of this shape. Perimeter Explorer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Geometry

Related Topics: area, arithmetic, assessment, comparing, coordinate plane, coordinate system, geometry, length, perimeter, polygon, rectangles, squares

This activity operates in one of two modes: auto draw and create shape mode, allowing you to explore relationships between area and perimeter. Shape Builder is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Geometry

Related Topics: area, assessment, comparing, geometry, perimeter

Learn the relationship between perimeter and area. A random shape will be automatically generated. Calculate the area and perimeter of this shape. Shape Explorer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Geometry

Related Topics: area, arithmetic, assessment, comparing, geometry, length, perimeter, polygon, rectangles, squares

Step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

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

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: algebra, area, fractals, fractions, geometric sequences, iteration, pattern, pre-calculus, recursion, recursive functions, self-similarity, sequences

Step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.

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

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: dimension, fractals, fractions, geometric sequences, geometry, iteration, length, pattern, pre-calculus, recursion, recursive functions, self-similarity, sequences, symmetry, triangle

Learn about how the Pythagorean Theorem works through investigating the standard geometric proof. Parameters: Sizes of the legs of the triangle.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry, Trigonometry

Related Topics: algebra, angles, area, coordinate plane, distance, geometry, length, pythagorean theorem, slides, solving equations, squares, triangle, triangles, trigonometry

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

Calculate the area of a triangle drawn on a grid. Learn about areas of triangles and about the Cartesian coordinate system. Triangle Explorer is one of the Interactivate assessment explorers.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Geometry

Related Topics: acute, area, assessment, cartesian coordinate, coordinate plane, distance, geometry, length, pythagorean theorem, triangle, triangles