Introduction to Geometry

Teacher Guide by Anna Warfield

Find this Common Core aligned Teacher Guide and more like it in our Elementary School Category!

Student Activities for Introduction to Geometry Include:

In the early grades, students start recognizing, naming, and drawing shapes. As students become more advanced, geometry becomes more complicated. Utilizing storyboards is an excellent way for students to show what they have learned, manipulate shapes, build shapes from segments and other shapes, and create charts or other graphic organizers to arrange information about properties or characteristics.

Geometry is a chance for visual and spatial reasoning skills to develop or flourish. Shifting a shape to a different orientation may give some students the ability to finally see that acute angle or tell if those two sides are really the same length. One benefit to using Storyboard That is that students are able to rotate objects. The rotating tool is great for precise movement, or use the flip or rotate 90 degree buttons to get a quick new look at the same shape.

By the end of this lesson your students will create amazing storyboards like the ones below!

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In the Triangle Chart, it is clear that the shapes stay the same even if they are turned around. Students may turn their papers or notebooks around at any time if they need to get a different view of a shape or angle.

Intro to Geometry - Triangle Chart


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Beginning geometers sometimes struggle making their pencils follow their thoughts. A point of frustration is not being able to create the shape they are trying to make because of lack of practice or difficulties with motor control. While they are learning to draw different shapes, students can use Storyboard That to demonstrate their knowledge. Spider Maps, Frayer Models, or T-Charts are great ways for students to show information they have learned.

Intro to Geometry - Trapezoid Frayer Model


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Introduction to Geometry Lesson Plans, Student Activities and Graphic Organizers

Geometry Terms

In geometry, there is a lot of new vocabulary for students to master. Not only do they need to identify shapes such as rectangle and triangle, but they need to be able to identify parts, such as base, leg, obtuse angle, vertex, and more! Build charts, such as the one below, for students or with students, to help them organize new concepts and have a point of reference for review.

Students recognize squares, circles, and triangles easily enough, but words such as “ray” and “perpendicular” are usually new terms. These unfamiliar words are also fundamental in understanding more complicated geometry. Keep charts clean and simple as much as possible. If the example pictures on the chart are too distracting, try a separate slideshow with multiple examples as you go over new words with your group or class.

Suggested Beginning Geometry Terms

PointA single location in space or on a flat surface
LineA collection of points that continues forever in both directions
Line SegmentA part of a line with two endpoints
RayA part of a line with one endpoint
AngleTwo rays that share an endpoint
Parallel LinesLines that never intersect
Intersecting LinesLines that pass through the same point
Perpendicular LinesLines that intersect and form four right angles

Intro to Geometry - Geometry Vocab


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Polygon Sorting Activity

Students will already be familiar with many, many shapes, but they may not know the mathematical names. One simple way to start is to identify whether or not a shape is a polygon. A polygon is closed figure made up of at least three sides and angles. Triangles, quadrilaterals, pentagons, hexagons, etc. are all polygons. Any shape with curves or open ends is NOT a polygon. Polygons can be weird shapes, have convex and concave sides, and can have any number of sides.

Have students move shapes from a template into the appropriate columns on their own storyboard. Interactive whiteboards or projected computer screens make this an engaging class activity, but students can just as easily work individually or in pairs on a computer.

See also Polygonia and Roundsville for a short math story.

Polygons can be categorized by the number of sides (and therefore angles) they have:

  • Three-sided polygons - triangles
  • Four-sided polygons - quadrilaterals
  • Five-sided polygons - pentagons
  • Six-sided polygons - hexagons
  • Seven-sided polygons - heptagons*
  • Eight-sided polygons - octagons
  • Nine-sided polygons - nonagons*
  • Ten-sided polygons - decagons*
  • Eleven-sided polygons - hendecagons*
  • Twelve-sided polygons - dodecagons*

*These shapes are not required by the Common Core, but it is nice to have the names handy if inquiring minds want to know.

Intro to Geometry - Polygon Sorting


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Special Polygon Names

Both triangles and quadrilaterals are big groups. One of the standards for elementary grades is to be able to recognize shapes and categorize them. There are many things to remember about each polygon, and it can be tricky to keep them all straight.

Categorize Triangles

Triangles can be named by both sides and angles, making seven different types of triangles.
(see TRIANGLE CHART above)
Equilateral Triangles have equal side lengths and equal angle measurements.
Scalene Triangles have different lengths for each side.
Isosceles Triangles have at least two sides with equal length.
(An equilateral triangle is ALSO an isosceles triangle)
Acute Triangles have three acute angles.
Right Triangles have one right angle and two acute angles.
Obtuse Triangles have one obtuse angle and two acute angles

Special Quadrilaterals

Square quadrilateral with four equal sides and four right angles
Rectangle quadrilateral with four right angles
Rhombus quadrilateral with four equal sides
Parallelogram quadrilateral with two sets of parallel sides
Trapezoid quadrilateral with one pair of parallel sides
Kite quadrilateral with two pairs of adjacent congruent sides

Lists like the ones above contain helpful information, but can be too wordy and unclear. Charts with images and labels are sometimes more kid-friendly (or just more friendly in general). Sometimes making chart after chart can become tiresome and muddle the brain, so a little extra ingenuity can go a long way.

Here are some example flyers to help find and identify some common or regular polygons that have gone "missing". Students may also enjoy making Wanted Posters for any law-breaking polygons, or "fashion" reviews of celebrity polygons. To add faces to shapes, type "face" into the search field.

Intro to Geometry - Lost Flyers


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•   (English) Introduction to Geometry   •   (Español) Introducción a la Geometría   •   (Français) Introduction à la Géométrie   •   (Deutsch) Einführung in die Geometrie   •   (Italiana) Introduzione Alla Geometria   •   (Nederlands) Inleiding tot Geometry   •   (Português) Introdução à Geometria   •   (עברית) מבוא גיאומטריה   •   (العَرَبِيَّة) مقدمة في الهندسة