1. Give an example of how a level 1 understanding of rectangles is different from a level 0 understanding of rectangles.
A level 0 understanding would compare a shape to a prototypical rectangle: a door, or a rectangle on a poster. A level 0 understanding can often recognize properties, but they aren't the most important thing for identifying something as a rectangle or not a rectangle.
A level 1 understanding would focus more on properties: 4 sides, 4 square corners. It might include ideas of how to count the sides or decide that the corners were square. A level 1 understanding should allow the person to accept things as rectangles that look different from most rectangles they have worked with (for example, much longer and skinnier or tilted at an angle)
2. Give an example of how a level 2 understanding of rectangles is different from a level 1 understanding of rectangles.
A level 1 understanding of rectangles includes a lot of information about properties rectangles have: square corners, 4 sides, it can be turned around
A level 2 understanding includes recognizing that some groups of shapes are subsets of others, and will recognize that rectangles are also parallelograms and quadrilaterals. A child at level 2 understanding will understand a property-based explanation of why squares are considered special kinds of rectangles.
A child at level 2 would be able to explain how some properties are related to other properties, or explain why some properties are true for all rectangles (eg. why opposite sides are the same length)
3. Give an example of something children should learn about geometric attributes and properties in grades 1-3.
They should learn that geometric attributes don't change when the whole shape gets larger or smaller or is turned. They should know several examples of geometric attributes (for example: having two equal sides or having a right angle)
4. Give an example of an activity that involves children thinking about shapes and their attributes.
Shape sorting; guess my rule for shape sorting; drawing a shape with given attributes.
5. Explain the term "orientation" as used in standard: K.G.A.2 Correctly name shapes regardless of their orientations or overall size
orientation means how a shape is rotated to appear on the page (which side is up)
6. Explain the term "attributes" as used in the geometry standards. Give some examples.
an attribute is a property that a shape has. Examples: having two equal sides, having a right angle, having an obtuse angle.
7. Give an example of shapes in different categories that share an attribute that is different from the examples given in: CCSS.Math.Content.3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
triangles, quadrilaterals, pentagons and hexagons all are closed figures that have straight sides, so they are all polygons.
8. Describe the activity Sorting Shapes. Explain the teacher's role in directing the activity for learning about shapes and attributes.
An important thing that the teacher does is to focus childrens attention on geometric attributes. Asking about how children chose to sort the shapes makes the attributes more explicit, and in class discussions, the teacher can explain and/or lead a discussion about which attributes are about shape (not color or texture) and don't change when the size or orientation of the shape changes.
9. Describe the progression in what children should learn about shapes and attributes in grades K-3.
Children first need to learn names of shapes if they don't already know them. Teaching names should begin with exploring examples of the shapes, and should include a wide variety of the shape being named.
Throughout, the teacher should help children recognize attributes of the shapes, and help children recognize which attributes are most important for defining the shapes.
Children should learn which attributes are the important ones for defining shapes
Children should use and be able to describe geometric attributes of shapes
Children should draw shapes based on definitions and properties
Children should recognized that some shapes are special kinds of other named shapes.