How to Teach the Geometric Properties of Shapes

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  • 0:04 Learning About Geometry
  • 1:01 2-D & 3-D Shapes
  • 3:10 Using Manipulatives
  • 4:32 Incorporating Problem Solving
  • 5:27 3-D Shapes from 2-D Shapes
  • 6:46 Lesson Summary
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Instructor: Deb Maxwell

Deb has an MA in education and 15 years of elementary classroom experience.

When teaching the geometric properties of shapes, it is important to be as hands-on as possible. Students will comprehend better with concrete examples.

Learning About Geometry

Whenever starting a new topic, it's a good idea to explain the ways it will directly relate to student's lives. When it comes to geometry, there are many jobs that require at least basic geometric knowledge such as builders, architects, interior designers, fashion designers, engineers, and many others. Even if you're not in any of these careers, it's important to be able to communicate ideas that may involve the use of geometric shapes.

Creating connections between ideas and words is crucial to developing understanding. When teaching students the words, it's helpful to have them organized in a logical way. Consider guiding the students through making a flipbook that they can use as a reference tool. Sorting the vocabulary words will help the students make connections between the words, and drawing and labeling shapes is extremely engaging and results in deeper learning. Remember to use these terms consistently through all of your lessons. Here's an example of how information could be organized.

2-D Shapes

First, let's review 2-D shapes, also known as polygons. Polygons have height and width and sides, vertices, and angles. They include the circle, triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, and decagon, and they can be regular with equal sides and angles or irregular with varied sides and angles.

All triangles have three sides, but there are many special types. Equilateral triangles have three equal sides. Isosceles triangles have two equal sides. Scalene triangles have zero equal sides. Right triangles have a 90-degree angle. Obtuse triangles have an angle that measures more than 90 degrees. Acute triangles have all angles measuring less than 90 degrees.

There are also many types of quadrilaterals, which have four sides. Here are some different kinds:

  • Parallelogram have two sets of parallel sides, and the opposite angles are equal
  • Trapezoids have one set of parallel lines
  • Rectangle have four right angles, and the opposite sides are equal
  • Rhombuses have four equal sides, and the opposite angles are equal
  • Squares have four equal sides, and four equal angles

3-D Shapes

Now let's review the properties of 3-D shapes. They have height, width, and depth and faces, vertices, and edges. They include prisms, pyramids, cones, cylinders, and spheres.

Prisms have two polygonal faces and two parallelograms. Types of prisms include:

  • Triangular prisms
  • Rectangular prisms
  • Cubes
  • Pentagonal prisms
  • Hexagonal prisms

Pyramids have a polygonal face and a point. Think about the pyramids of Ancient Egypt. Types of pyramids include:

  • Triangular pyramids
  • Square pyramids
  • Pentagonal pyramids

Curved shapes are what they sound like: geometric shapes with curves. Here are some common curved shapes:

  • Cones have one circular face, curved edges, and one vertex
  • Cylinders have two circular faces, curved edges, and no vertex
  • Spheres have no faces, no edges, and no vertices

Using Manipulatives

There are many ways to make geometry hands-on. Students usually enjoy building with real-world materials, such as toothpicks and marshmallows, or dry spaghetti noodles and clay. Materials like these provide the opportunity to use vocabulary in a meaningful way.

For example, have students build a square, then have them push opposite vertices closer together to make a rhombus. Ask questions that require students to communicate their observations and discoveries. For example, what similarities and differences do you notice between a square and a rhombus? Students will learn to use words like sides, vertices, and angles. They will notice they need a word to explain the wider and narrower angles and the 90-degree angles.

After some exploration with flat shapes, students can start building and creating three-dimensional shapes. This is a wonderful way to guide student discovery. Have students construct two congruent triangles side-by-side, then have them transform one into a prism and the other into a pyramid. Ask students to determine the number of faces, edges, and vertices for each one.

After giving students the opportunity to make some discoveries with the materials, have a post-lesson discussion where you engage them in a discussion about the new vocabulary terms. Adding a kinesthetic component like having students demonstrate kinds of angles with their hands and draw them on paper with labels will solidify learning.

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