In 3rd grade students begin to transition from being able to recognize shapes based on their defining attributes to understanding they can share attributes and belong to multiple categories.
MA.3.GR.1.2 – Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares, and trapezoids.
Defining Attributes of Quadrilaterals
Defining attributes of shapes are components that must be present in order for a shape to be in a certain category. Attributes that are NOT defining include size, color, and orientation or direction. For some shapes, side length is also not a defining attribute.
Defining attributes on a basic level involve the number of straight lines (line segments) a shape has.
The number of sides in a polygon will correspond with its number of angles.
Further attributes students will use to define and categorize shapes include:
- right angles
- perpendicular lines
- parallel lines
Children begin their work in 3rd grade with quadrilaterals, the category of polygons with the most variety. In later grades they will do similar work with triangles and 3-dimensional shapes.
Comparing and Contrasting Quadrilaterals
All quadrilaterals have 4 straight sides and 4 angles. From there, they can be identified more specifically based on other combinations of side length, angle measure, and number of parallel sides.
Quadrilaterals can be organized in two directions: from having the least common attributes to having the most common attributes.
- The quadrilateral has the least number of defining attributes because it just has to have 4 closed line segments and 4 angles.
Rectangles, squares, parallelograms, rhombi, and trapezoids are all examples of quadrilaterals.
There are also quadrilaterals that don’t share defining attributes with any of the sub-categories of quadrilaterals.
Trapezoids
Within the larger categories of polygons and quadrilaterals, trapezoids are quadrilaterals with at least one set of parallel line segments.
One thing to avoid while working with 2-dimensional shapes is to only offer students one representation of shapes like trapezoids. Most commonly, regular trapezoids are used as an illustration, which have a shorter top base, a long bottom base, and two equal diagonal sides. The concern is that students may develop the understanding that all trapezoids look one way.
In fact, trapezoids may have a right angle, only one diagonal line, and be oriented in any direction. Offering multiple representations encourages flexible thinking and deeper understanding of the attributes being studied.
Parallelograms
After quadrilaterals and trapezoids, parallelograms have the next least amount of defining attributes. Then there are more specific shapes that fit within the parallelogram category. Parallelograms have 2 sets of parallel lines and equal opposite sides and angles. Parallelograms have no requirements about angle measure, but some sub-categories of parallelograms do.
Rhombi are parallelograms with 4 equal sides. A rhombus can have a variety of different angle measurements, but the opposite angles will be the same size.
This is where sorting gets fun! A rhombus will always be a parallelogram, but a parallelogram will only be a rhombus if it has 4 equal sides.
Rectangles are also parallelograms, but with the additional defining attribute of four right, or square, angles. Right angles are formed by perpendicular lines. Rectangles have equal opposite side lengths created by 4 perpendicular line segments and 2 sets of parallel lines.
Squares are rectangles with the additional defining attribute of 4 equal sides. At the highest level of categorization, squares also belong to every other category of quadrilateral, while no other shape does.
Standards
Different standard sets for understanding 2-dimensional shapes have different wording for what children should be able to accomplish at a 3rd grade level. The underlying concept is the same, and covering the material in this post will give every 3rd grader a great foundation to build upon in later years.
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