Defining Attributes of Shape Categories

Students at the 3rd grade level build on their work in earlier grades where they identified and described shapes before starting to look at their attributes (e.g. number of sides). By the end of 3rd grade they should understand that shapes in different sub-categories (e.g. rhombus, rectangle) share the same attributes (e.g. 4 sides) and that shapes with these shared attributes can belong to a broader category (e.g. quadrilaterals)

Terms

Some of these terms might seem obvious to you but just assuming they are familiar to your children may lead to difficulties.

Side

A line segment linking two angles together – an edge of a shape*

An annotated illustration of what a side is

Angle

The shape formed by two lines or rays diverging from a common point (the vertex)*

An annotated illustration of what an angle is

Vertix

(Plural is vertices) The corner or a point where lines meet.*

An annotated illustration of what a vertix is

Equal length

Having the same distance between endpoints

An annotated illustration of what an angle is

Right Angle

An angle whose measure is exactly 90°*

An annotated illustration of what a vertix is

Parallel Lines

Remain the same distance apart over their entire length, no matter how far you extend them, they will never meet.*

An annotated illustration of what an angle is

Opposite Sides

Do not have a common (shared) vertex

An annotated illustration of what a vertix is

*Page, John D. "Math Open Reference" www.mathopenref.com

Discuss the above words and terms with your children. Encourage them to lead as you work through the list. The concepts of perpendicular and parallel lines and angle measurement in degrees are typically studied in 4th grade so they need not be mastered in 3rd grade although the ability to identify a right-angle is required.

Polygons/ non-polygons

A polygon is a two-dimensional shape with sides made of line segments that join at their endpoints. Your children should already have been introduced to polygons and they should be able to distinguish them from "non-polygons." Use this polygon/ non-polygon worksheet for practice with making the distinction.

Six shapes or figures that are not polygons

Categories of Polygons

Quadrilaterals are 4-sided polygons. Review the quadrilaterals shown and described below with your children. Ask them to describe them to you. Encourage them to talk about the sides, vertices, and angles and to identify the defining attributes. Good questions for you to ask include:

  • What is the relationship between the number of vertices and the number of sides?
  • What are the differences between [name of a shape] and a rectangle?
  • Describe a [name of a shape] to me so that I can draw it without hearing the name.
3 different sized quadrilaterals

Quadrilateral

2 different sized squares

Square

2 different sized rectangles

Rectangle

3 different sized parallelograms

Parallelogram

3 different sized trapezoids

Trapezoid

3 different sized rhombi

Rhombus

Defining attributes

Check that your children can distinguish between attributes that define a category of shape (e.g. number of sides, vertices, angles, congruence) and other attributes such as size and color.

Have your children draw and categorize their own shapes using this worksheet.

Quadrilateral Hierarchy

Help your children to identify attributes that are shared by different categories and discuss how this means a shape can belong to a larger category. For example, a square is a special type of rectangle and a rectangle is a special type of parallelogram. The diagram below illustrates the hierarchy.

A venn-type diagram showing the hierarchy of quadrilaterals

Activity

  • Print out this chart and then have your children:
    1. Draw on the chart a variety (maximum of 6 variations ) of each of the quadrilateral sub-categories illustrated above (i.e. square, rectangle, parallelogram, trapezoid, & rhombus)
    2. Cut out the different variations and sort them into their sub-categories.
    3. Repeat the sorting exercise and suggest sorting into other categories. e.g. "yes these are squares but they are special types of rectangle." Or "yes these are rectangles but they are also special types of parallelogram".
  • Discuss with your children why these polygons belong to more than one category.
  • If your children suggest categories such as small, large, wide, or tall, then sort using them but be sure to discuss that these attributes do not define the shape’s category.
2 different sized traingles

Things to watch out for:

  • Your children may need support to recall shape names as they are learning about them. Use this chart for reference and make it available when needed. You can challenge your children to recall the names from memory as they work through the exercises on this page. Having them draw and label shapes will help to commit the shape names to memory. Use this blank chart to help.
  • There can be a tendency to assume polygons have to be regular to qualify for a category
2 pentagons. 1 regular and 1 irregular

More Math Help

All Geometry 24 Worksheets Terms/ Definitions Formulas/ Equations 2D Shapes Defining Attributes 3D Shapes Quadrilaterals Measuring Angles Using a Protractor Adding and Subtracting Angles Angle Properties Finding Angles Symmetry Area Volume Surface Area Perimeter Coordinate System Coordinate Graphing Pythagoras' Theorem Distance Between Two Points Congruent Triangles Similar Triangles Transformations Dilations
By Subject > Geometry > 2D Shapes