Show:
General Geometry
Shapes & Properties
Location
Transformation
Visualization
100
What is a polygon?
A 2-D shape with sides made of straight lines
100
At Level-0 Thinkers, with respect to sorting and classifying, what should teachers be prepared for students to notice?
Students will notice features that teachers do not consider to be “real” geometric attributes, such as “dented” or “looks like a tree”. Children at this level will attribute to shapes ideas that are not part of the shape, such as “points up” or “has a side that is the same as the edge of the board.”
100
What are the introductory concepts to use when teaching locations?
Introductory concepts are everyday positional descriptions – over, under, left, right, between.
100
Transformations are changes in position or size of a shape. What are the ways three ways in which we can alter shapes?
These transformations are referred to as translations (slides), reflections (flips), and rotations (turns).
100
What is visualization?
Being able to create mental images of shapes and then turn them around mentally, thinking about how they look from different perspectives.
200
What are the van Hiele levels of geometric thought?
A five level hierarchy decribing how we think about spatial ideas. These five levels are visualization, analysis, informal deduction, deduction and rigour.
200
Children need to freely explore how shapes fit together to form larger shapes and how larger shapes can be made of smaller shapes. What are the best known two-dimensional shapes for these activities of composing and decomposing shapes?
Pattern blocks and tangrams.
200
What are the subjects supported by using a grid system to specify location?
Geometry, measurement, and algebra are all supported by using a grid system to specify and understand location.
200
What is a combination of two or more transformations?
It is referred to as a composition, where a figure can be reflected over a line, then that figure could be rotated. Compositions do not have to involve different types of transformation; for example, a rotation can be followed by another rotation.
200
How do level 0 students understand visualization?
At level 0 students are bound to thinking about visualization in terms of the way shapes look.
300
What does level 0 instruction involve?
Sorting classifying, putting together and taking a part shapes.
300
How can students and teachers go about building three-dimensional shapes?
A) Plastic coffee stirrers with modelling clay or twist ties. B) Plastic drinking straws. C) Rolled newspaper rods.
300
What are level-1 thinkers capable of?
Level-1 thinkers can think of grid systems in an analytic manner; extending to negative and positive numbers.
300
If a shape can be folded on a line so that the two halves match, they have mirror or line symmetry. What is rotational symmetry?
A shape has rotational symmetry (also known as point symmetry) if it can be rotated on a point and land in a position exactly matching the one in which it began, such as a square or equilateral triangle.
300
What is one of the key differences between level 0 and level 1 thinking in visualization?
At level 1, students will be able to identify and draw a 2-dimensional image of a 3-dimensional figure as well as build 3-dimensional figures from 2-dimensional images.
400
What does level 1 instruction involve?
Level 1 instruction involves a focus on properties of figures and applying ideas to entire classes of figures.
400
As students move to Level 1 thinking, attention turns to what?
Attention turns to properties possessed by the traditional classifications of shapes. During this period, it makes sense for students to learn the proper names for shapes and their properties.
400
What are geometric concepts that are supported by the use of a grid?
Slides, transformations, rotations. Using a grid helps students to concretely visualize the movements related location.
400
A pentomino is an arrangement of 5 unit squares (or sometimes cubes) that are joined along their edges as in the popular game Tetris. What classroom applications could this activity have?
The pentomino puzzle is a popular choice for a classroom manipulative that facilitates learning how shapes can be transformed or arranged in a predefined shape and space by simple rotation, reflection, and translation.
400
What are slices?
Slices occur when a solid is cut or sliced into two parts.
500
What does level 2 instruction involve?
Level 2 involves an encouragement of hypothesizing and informal proofs.
500
At level 2, the focus shifts from simply examining properties of shapes to what?
To explorations that include logical reasoning.
500
What is the transition to level two thinking?
To transition from level 1 to level 2 thinking you need to apply logical thought to coordinate activities.
500
Tessellations are created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Which three types of tessellations exist?
A regular tessellation is made of a single tile that is a regular polygon (checkerboard), semi-regular tessellations combine two types of polygons that share a common corner and an Escher type tessellation is constructed by modifying a regular polygon’s color and shape.
500
What are students at level 2 ready to do?
Students at level 2 are ready for a challenge. Allow them the opportunity to predict possible slices that may occur. Supporting their hypotheses is also important at this level.