AgendaAgenda

Mathematical PracticesMathematical Practices1. Make sense of problems and persevere in

solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

GeometryGeometryReason with shapes and their attributes. 2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

3.G.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.

Van Hiele Levels of Van Hiele Levels of Geometric ThoughtGeometric Thought

Level 0: Visualization

DescriptionSee geometric shapes as a whole; does not focus on their particular attribute

ExampleA student would identify a square but would be unable to articulate that it has four congruent sides with right angles.

Teacher ActivityReinforce this level by encouraging students to group shapes according to their similarities

Shape SortShape Sortvan Hiele

• This is a level 0 activity because students are operating on shapes they see in front of them.

• These shapes may “change” or have different properties as they are rearranged or rotated.

The object of this activity is to begin to see that there are likenesses and differences in shapes.

van Hiele Levels of van Hiele Levels of Geometric ThoughtGeometric Thought

Level 1: Analysis

DescriptionRecognize that each shape has different properties; identify the shape by that property.

ExampleA student is able to identify that a parallelogram has two pairs of parallel sides, and that if a quadrilateral has two pairs of parallel sides it is identified as a parallelogram.

The products of thought at level 1 are the properties of shapes.

Property Lists for Property Lists for QuadrilateralsQuadrilaterals

Work in groups of 3 or 4.List as many properties as you can that are applicable to all the shapes on their sheet.

•Use an index card to check right angles.•Use rulers to compare side lengths and draw straight lines.•Look for lines of symmetry.•Use tracing paper for angle congruence.•Use the words “at least” to describe how many of something.

Does the property apply to all the shapes in the category?

Math Talk VideosMath Talk Videos

van Hiele Levels of van Hiele Levels of Geometric ThoughtGeometric Thought

Level 2: Informal Deduction

DescriptionSee the interrelationships between figures

ExampleGiven the definition of a rectangle as a quadrilateral with right angles, a student could identify a square as a rectangle.

Teacher ActivityCreate hierarchies (i.e. organizational charts of the relationships) or Venn diagrams of quadrilaterals to show how the attributes of one shape imply or are related to the attributes of others.

Minimal Defining ListsMinimal Defining Lists Work in your group to find “Minimal Defining Lists”.

A Minimal Defining List (MDL) is a subset of the properties for a shape that is defining or minimal.

Defining means that any shape that has all the properties in the MDL must be that shape.

Minimal means that if any single property is removed from the list it is no longer defining.

Find two or three MDLs for your shape.

A proposed list can be challenged as either not defining or not minimal by giving one counterexample.

Quad SquadQuad Squad AIMS Activity – See Directions

square (rectangle with equal sides or rhombus with

congruent angles)