Exam 16: Developing and Extending Geometric Concepts and Systems

Why is it important for a child to develop spatial sense?

Use paper figures to derive the area formulas for a triangle and a parallelogram from the area formula of a rectangle.

A parent asks why geometry is taught in the elementary school curriculum when students do not yet know their basic facts and therefore should be spending time on learning them instead. How would you reply to this parent?

Explain the differences between the four geometry systems that are taught in the elementary school curriculum (topological, Euclidean, transformational, and coordinate geometry).

The legs of a right triangle are 5 cm and 12 cm. The length of the third side is:

If a child can isolate alternate interior angles in a complex drawing, that child is said to possess the visual skill known as:

If a child can distinguish between the similarities and differences of rectangles and squares, that child is said to have the skill called:

Illustrate each of the following geometric figures or concepts with a quick sketch. Label the sketches as needed. Point, ray, line segment Congruency and similarity Regular polygon Irregular Polygon Open/closed figure Three kinds of angles Two tessellations Three different triangles Line symmetry Rotational symmetry A slide A flip A turn A pantomime shape that will fold into an open box A pentomino shape that will not fold into an open box

If children stand in a tight circle, then slowly expand the circle by walking backwards, then reverse their positions by walking forward to the tight circle again, they are practicing with a topological geometry relationship known as:

Which of the following combinations of regular polygons will tessellate?

The research of Dina van Hiele-Geldof and Pierre Marie van Hiele suggests that:

A three-dimensional object which has four congruent faces the same shape and size, four vertices, and six edges is:

Research about spatial sense has established all of the following except for :

What are some activities you could use to introduce children to three-dimensional geometry? Explain how these activities encourage the development of these geometric concepts.

Use pattern blocks to demonstrate and represent each geometric concept. A) tessellation B) line symmetry C) rotational symmetry D) similarity E) congruence

Identifying whether an object is inside or outside of a fence is a basic concept associated with:

How many lines of symmetry are there in a regular hexagon?

Explain the differences between translations, rotations, reflections, and dilations.

Classifying squares by the size of their angles is a basic concept associated with:

The following translation will move point Q from (3, − 4)to ______.