Monday, August 4, 2014

Applying Fractions to Polygons

In this programming assignment, we shall draw polygons and divide them into fractions using Pro-Bot. This assignment can be a follow-up to the one where we learned to draw various polygons using Pro-Bot. We shall use sequential programming for drawing irregular polygons and Repeat Loops to draw regular polygons. Next, we shall divide the polygons into specified fractions using Pro-Bot as our drawing tool.

Computer Science concepts involved:   Sequential programming, Repeat loops

Math concepts involved:   Polygons (regular and irregular), Linear & Angular Measurements, Fractions, Area, Congruence

Hours required:   2 or more

Polygons

In geometry, a polygon refers to a closed, two-dimensional figure formed by a set of straight line segments. The straight line segments are called the polygon’s edges or sides, and the points where two edges meet are the polygon's vertices or corners.

If all edges are equal and all angles are equal, then it is a regular polygon. Else, it is an irregular polygon.

Square:

1. Use Pro-Bot to draw a square of sides 8 cm. Each interior angle is 90 degrees.
2. Divide the square horizontally into quarters (1/4) using Pro-Bot as your drawing tool.
3. Divide the square vertically into quarters (1/4) using Pro-Bot as your drawing tool.
4. Divide the square into 4 equal squares, using Pro-Bot as your drawing tool. What fraction of the large square does each small square occupy?
5. Divide the square into 2 equal sized triangles, using Pro-Bot as your drawing tool. Are the triangles congruent?

Rectangle:

1. Use Pro-Bot to draw a rectangle of sides 4 cm and 6 cm. Each interior angle is 90 degrees.
2. Divide the rectangle into thirds along the longer side using Pro-Bot as your drawing tool.
3. Divide the rectangle into halves along the shorter side using Pro-Bot as your drawing tool.
4. Divide the rectangle into quarters using Pro-Bot as your drawing tool.
5. Divide the rectangle into 2 triangles along a diagonal, using Pro-Bot as your drawing tool. Are the triangles congruent? Are they equal in area?

Rhombus:

1. Use Pro-Bot to draw a rhombus of sides 6 cm. One pair of opposite interior angles is 60 degrees each and the other pair is 120 degrees each.
2. Divide the rhombus into thirds, using Pro-Bot as your drawing tool.
3. Divide the rhombus into sixths (1/6) using Pro-Bot as your drawing tool. Are the fractions congruent shapes? Are they rhombuses? If not, what shapes are they?

Parallelogram:

1. Use Pro-Bot to draw a parallelogram of sides 4 cm and 6 cm. One pair of interior opposite angles is 45 degrees each and the other pair is 135 degrees each (Remember that for a parallelogram, opposite angles are equal).
2. Divide the parallelogram into 2 equal parallelograms, using Pro-Bot as your drawing tool. What fraction of the original parallelogram is occupied by the smaller ones?
3. Considering that the minimum dimension that can be provided by Pro-Bot is 1 cm, what is the maximum number of smaller parallelograms that you can divide up the larger parallelogram into, using Pro-Bot as your drawing tool? What fraction of the larger parallelogram is occupied by each of the smaller units?

Equilateral Triangle:

1. Use Pro-Bot to draw an equilateral triangle of sides 6 cm. Each interior angle is 60 degrees.
2. Divide the triangle into 2 equal triangles, using Pro-Bot as your drawing tool.
3. Divide the triangle into 3 triangles of equal area, using Pro-Bot as your drawing tool. You can do this in a couple of ways:

• Divide one side of the triangle into 3 equal parts. Then draw lines connecting the opposite vertex to the two points that trisect the side.
• Find the centroid: If you draw a line from each vertex to the midpoint of the opposite side, the point at which all three lines meet is the centroid. Draw a line from each vertex to the centroid to divide up the triangle into 3 equal triangles.