8'4 and 8'5

1
8.4 and 8.5

• 5 Reasoning levels
• Level 0 -(Recognition) A child recognizes shapes
  holistically without paying attention to their
  component parts.
• For Example Here are different forms of triangles

2
More Examples
Not a Triangle
Triangle
3

• Level 1 (Analysis) Component parts of a figure
  are used like its sides and angles.
• For example a child at this level will recognize
  that a square is a figure with four equal sides
  and 4 square corner.
• So the child will identify both the following
  figures as squares

4
Both figures are Squares
Both figures are not rectangles?
5

• Level 2 (Relationships) Child understands
  relationships.
• For example A child at this level will
  understand that a rectangle is 4 sided figure
  with 4 square corners, a rhombus is a 4 sided
  figure with all equal sides and therefore a
  square is both a rectangle and a rhombus.

6
Rectangles
Squares
Parallelograms
7

• Level 3 (Deduction) Child understands the notions
  of mathematical postulates and theorems and can
  write formal proofs
• Level 4 (Axiomatics) Highly abstract and does not
  necessarily involve concrete pictorial models.
  Postulates or axioms become object of intense
  rigorous scrutiny. (Not necessarily appropriate
  for Elementary or middle school).

8
Sides and Angles

• Line Segment are formed by joining two points in
  the shortest possible way.
• Triangles are closed figures composed of exactly
  three line segments, called sides.
• Quadrilaterals are closed figures composed of
  four line segments.

9

• An angle is the union of two line segments with a
  common endpoint called a vertex.
• Triangles have 3 angles and Quadrilaterals have 4
  angles.
• Right angle is an angle identical to one formed
  by a horizontal and a vertical line segments.
• Two line segments that form a right angle are
  called perpendicular.

10

• A triangle with at least two equal sides is
  called an isosceles triangle.
• A triangle with all three equal sides is called
  an equilateral triangle.
• A triangle with all three sides of different
  lengths is called a scalene triangle.

11

• A quadrilateral with four sides of same length
  and four right angles is called a square.
• A quadrilateral with four right angles is called
  a rectangle.
• A quadrilateral with two pairs of parallel sides
  is called a parallelogram.

12

• A quadrilateral with at least two distinct pairs
  of consecutive sides congruent or equal is called
  a kite.
• A quadrilateral with four equal sides is called a
  rhombous.
• Two lines segments are called congruent line
  segments if they have the same length.

13

• Any figure whose sides are congruent is called
  equilateral.
• Two angles are congruent angles if they have the
  same opening, that is, one angle is an exact
  copy of the other except possibly for the lengths
  of the sides.
• A figure all of whose angles are congruent is
  called equiangular.

14

• A quadrilateral with exactly one pair of parallel
  sides is called a trapezoid.
• If the non parallel sides of a trapezoid are
  congruent, it is called an isosceles trapezoid.

15
THE END