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

Grade levels: 3, 4, 5

Hours required: 2 or more

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**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:

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

#### Rectangle:

- Use Pro-Bot to draw a rectangle of sides 4 cm and 6 cm. Each interior angle is 90 degrees.
- Divide the rectangle into thirds along the longer side using Pro-Bot as your drawing tool.
- Divide the rectangle into halves along the shorter side using Pro-Bot as your drawing tool.
- Divide the rectangle into quarters using Pro-Bot as your drawing tool.
- 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:

- 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.
- Divide the rhombus into thirds, using Pro-Bot as your drawing tool.
- 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:

- 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).
- 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?
- 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:

- Use Pro-Bot to draw an equilateral triangle of sides 6 cm. Each interior angle is 60 degrees.
- Divide the triangle into 2 equal triangles, using Pro-Bot as your drawing tool.
- 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.

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