Draw Polygons & Compound Figures with a Given Area using Pro-Bot

Can you program the Pro-Bot to draw polygons & compound figures with a given area?

This, again, is an assignment that I designed for our Grade 3 students. It relates to the Common Core Math Standards: Geometric measurement: understand the concepts of area. For this exercise, I highly recommend using graph paper, as it provides a helpful medium for the kids to work out the math problems. Provide at least one sheet per child to work out the problem and then additional sheets as required for the groups to draw the figures using Pro-Bot. Here is a link to a graph paper with 1 cm grid in PDF format; you can make copies for the students to draw on using the Pro-Bot.

Area of a Figure

The area of a figure is the number of squares required to cover it completely, and is specified in square units. Here's an article from math.com that gives a quick overview of the topic.

How do you calculate the area of a given figure? You add the number of squares needed to cover the entire figure. Say you are given a square with sides 3 cm each. You need 9 squares of sides 1 cm x 1 cm to cover it completely. The area of the square is 3 x 3 = 9 sq.cm. Similarly, a 5 cm x 6 cm rectangle has an area of 30 sq.cm.

Can we do the reverse too? Given the area, can we come up with the design for a figure with that area? 

Let's look at an example. Given an area of 9 sq.cm, how many polygons can we draw? We can draw multiple polygons, all with the exact same area of 9 sq.cm. In the figure below, you can see:

• a square 3 cm x 3 cm,
• couple of polygons with an area of 9 sq.cm.

Can you think of more polygons with an area of 9 sq.cm?

Let's now look at a scenario that shows the practical application of the concept of area. And then program the Pro-Bot to draw a few polygons with a given area.

Programming Assignment

You work for an architectural firm, and have been asked to design a single story house with a floor area of 100 square meters (roughly 1076 sq.ft.) You are to draw and present various designs for the floor plan.

1. How many different ways can you draw the floor plan with an area of 100 sq.m.? Provide at least 2 to 3 different designs and make a rough drawing of the figures that you come up with.

2. Classify the figures that you came up with into the various classes of polygons based on the number of sides.

3. Program the Pro-Bot to draw them on graph paper. Use 1 sq.cm. to represent 1 sq.m. in your figures.

4. Assume that the plot of land available for the construction, is a rectangle that is 15 m long and 8 m wide. Can you provide a design(s) to build a 100 sq.m. building in this plot? Program your Pro-Bot to draw the design. 
5. You can program the Pro-Bot to draw other figures with the 100 sq.m. area. Or explore other figures with different areas.

Solutions: Modular Programming with Squares on Pro-Bot

This is a subset of solutions for the assignment Modular Programming with Squares. This is just one way of coding the solutions, there are multiple correct solutions for the same.

Breaking Down Squares

1.  The shape is a square. It can drawn using the code:

Rpt 4 [    
Fd 12
Rt
]

2.  The above square needs to be divided into two equal parts. You can do this with a horizontal or vertical line across the middle or divide the square along the diagonal. The solution below divides the cake along the horizontal line
across the middle.

Rpt 4 [
Fd 12
Rt
]
Fd 6
Rt
Fd 12

3.  The square now needs to be divided into quarters. Two possible solutions, along the diagonals or using horizontal & vertical lines. The solution below divides the cake along the horizontal & vertical lines.

Rpt 4 [
Fd 12
Rt
]
Fd 6
Rt
Fd 12
Bk 6
Lt
Fd 6
Bk 12

4.  Here is another way to divide the cake into quarters, along the diagonals.

Rpt 4 [
Fd 12
Rt
]
Rt 45
Fd 17
Lt 135
Fd 12
Lt 45
Bk 17

5.  You need to divide the 12 x 12 cake into 9 equal pieces in this case.  Each slice is going to be 4cm x 4 cm.  Here is a solution using Nested Loops.

Rpt 4 [
Fd 12
Rt
]
Rpt 2 [
Rpt 2 [
Fd 4
Rt
Fd 12
Bk 12
Lt
]
Fd 4
Rt
]

Building Up with Squares as the Basic Building Blocks

1.  The square can be drawn using the code:

Rpt 4 [
Fd 6
Rt
]

2.   Here is the code for the rectangle drawn without using Nested Loops:

Rpt 4 [

Fd 6
Rt
]
Fd 6
Rpt 4 [
Fd 6
Rt
]
Fd 6
Rpt 4 [
Fd 6
Rt
]

3.  As seen from the code above, there is a repeating pattern. After drawing each square, you need to move to the starting position for the next square. The above code can be rewritten using Nested Loops as:

Rpt 3 [
Rpt 4 [
Fd 6
Rt
]
Fd 6
]

4. & 5.  To draw the large square that is double the size of the small square, different techniques can be employed. The easiest is to start from the midpoint of the figure. Each time, draw the small square and then turn 90 degrees to the right. Here is the code that uses Nested Loops.

Rpt 4 [
Rpt 4 [
Fd 6
Rt
]
Rt
]

Solutions to the Hopscotch figure:

Rpt 3 [      // Start drawing the rectangular part of the hopscotch from bottom left corner
Rpt 4 [
Fd 6
Rt
]
Fd 6
]
Rt             // Here, you want to try and get to the midpoint of the large square
Fd 3         // 3 cm from the top of the rectangle to the midpoint of large square
Lt
Fd 6         // You have reached the midpoint of the large square now
Rpt 4 [     // Now draw the large square using the previously written code for the same
Rpt 4 [
Fd 6
Rt
]
Rt
]

Breaking Down & Building Up: Modular Programming with Squares on Pro-Bot

We have already worked on drawing squares using Pro-Bot. We used Repeat Loops to create a square in our previous assignment here

Now, let’s work a bit more with squares, first breaking it down into smaller parts and then building up compound figures using squares as our basic building blocks.

Computer Science concepts involved:   Sequential programming, Repeat loops, Nested Loops, Modular programming

Math concepts involved:   Polygons (squares, rectangles), Measurement, Fractions, Compound figures, Angles

Grade levels:   3, 4, 5

Hours required:   2 or more

Breaking Down Squares

1.   You have spent your Sunday afternoon at home baking a delicious chocolate cake. You baked the cake in a square pan that measures 12 cm long on each side. What shape is your cake when you look at it from above? Can you draw this shape using Pro-Bot? 

2.   You plan to share the cake with 2 of your friends. You cut the cake into equal parts for yourself and your friends. Using Pro-Bot can you draw a figure to represent your cake and how you would cut it? What fraction of the cake would each person get? 

3.   One more friend comes along. So, you decide to cut the cake into equal parts for yourself and your 3 friends. Using Pro-Bot can you draw a figure to represent your cake and how you would cut it? What fraction of the cake would each person get now? 

4.   How many different ways can you think of to cut the cake into 4 equal parts? Using Pro-Bot, draw figures to represent each case. What shapes are the fractions in each case? 

5.   Your friend says that a single serving of cake should be no larger than 4 cm x 4 cm in size. How would you cut the cake to get slices of this size? Using Pro-Bot, draw a figure to represent your cake and how you would cut it in this case.  How many pieces can you cut the cake into?

Building Up with Squares as the Basic Building Blocks

1.   Use Pro-Bot to draw a square of sides 6 cm each. (Remember to use Repeat Loops for drawing the square).

2.   Now, let’s create a rectangular shape with the following dimensions, using the above 6 cm square as our building block:  

Length  =  3 x length of one side of the square 

Width  =  length of one side of the square 

Can you write a program for Pro-Bot to draw this figure, using the program for the 6 cm side square that you wrote earlier? 

  

3.   Can we use Nested Loops to draw the above figure? Explain why.

4.   Next, let’s create a bigger square with the following dimensions:       

Side of big square  =  2 x Side of the 6 cm square

Can you write a program for Pro-Bot to draw this figure, using the program for the 6 cm side square that you wrote earlier? 

5.   Can we use Nested Loops to draw the above figure? (Tip: It is easier to start drawing from the midpoint of the figure while using Nested Loops.)

Here is a set of possible solutions to the above assignments.

Modular Programming

From the two examples above, you can see how a small module that performs one distinct function (in this case, our program to draw the 6 cm side square) can be used to build bigger components. The big components that we created in turn can work as modules for an even bigger program. 

This activity provides a quick peek into modular programming, a principle that is widely used in most programming languages. Modular programming is the process of dividing a program into smaller, separate sub-programs. 

Let's look at an example that is familiar to you. Do you play with Lego construction sets? A lot of times, when you buy Lego sets, the box comes with several small bags inside of it, each labeled with a number. There will be an instruction booklet that tells you how to use the tiny pieces inside each bag to create a small component of the big toy that you plan to make. Once you have created a couple of such components from the different bags, the book tells you how to put them together to create a slightly bigger unit... and the process goes on till you get to the completed product... 

Just like you build large Lego toys using multiple smaller units, each of which in turn was made of still smaller pieces, we can build large programs using smaller components or modules, which in turn can be made of even smaller modules.

So, why do we prefer to use modular programming rather than develop one giant program? Here are some reasons...

• Reusing the code. You write a module just once, but it can be used multiple times by different programs. In the above examples, you wrote the code for the 6 cm side square just once, but you used it multiple times while developing two different programs. 
• Breaking up the program into smaller modules makes it easier to maintain the program. For example, if you decide to change the larger programs to be using 10 cm side squares, all you need to do is make one change in your smallest module for the square from 6 cm to 10 cm. The change is easily reflected in all the bigger modules that use it. 
• It is easier to find and fix errors in smaller modules. 
• Smaller modules ensure that the code is short, simple, easy to read and understand.
• It makes it easier for different people to develop different modules independent of each other. You could have one person write the program for the 6 cm square, another person write the program for the rectangle using the 6 cm square and yet another person write the program for the bigger square. And then, all of these could be put together to create an even bigger program as seen below...

1.   Elmo and his friends are planning to play hopscotch. Elmo suggests a figure that looks like the following and draws it out using Pro-Bot. Each square in this hopscotch figure has 6 cm sides. Can you write a program for Pro-Bot to draw this figure? Can you re-use the programs that you wrote above to draw this figure?

• You can also store each of the programs that you wrote above (for the rectangle and the big square) as separate Procedures and call them from your Main program for Pro-Bot to draw the hopscotch figure.

A Different Approach to the above Program

If you have an even number of students/ groups working on this project, you could try the following exercise with the hopscotch figure:

• Divide the class into an even number of teams, so that each team pairs with another.  Let’s call the teams in each pair as Team A & Team B.
• Team A in each pair would create the procedure for the big square. Team B in each pair would create the procedure for the large rectangle.
• The pairs then exchange the Pro-Bots.
• So now, each team has the procedure that they created themselves plus the procedure that was created by the other team. They do not need to know how the other team created their procedure;  they just need to know what it does (a black box).
• Each team shall give clear instructions to their partner team as to how their procedures work. They can even draw a picture to show what their procedure would create, specifying the start & end points, and give it to the other team.
• Each team now integrates the procedures/modules (their own work + the other team’s work) to create the required final result & test it.
• This could be a good activity to introduce the kids to the concepts of real world engineering projects: division of work among different teams, testing & integration of results.

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

Grade levels:   3, 4, 5

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.

Drawing Polygons using Pro-Bot given Area or Perimeter

In this programming assignment, we shall draw polygons using Pro-Bot, given the area or perimeter of the polygons. Your first task is to figure out the dimensions of the polygons from the given data and your second task is to write programs to draw the polygons using Pro-Bot. You can use either sequential programming or Repeat loops to draw the polygons, depending on whether they are irregular or regular.

Computer Science concepts involved:  Sequential programming, Repeat loops

Math concepts involved:  Polygons (regular and irregular), Area, Perimeter, Measurement, Angles

Grade levels:  4, 5

Hours required: 3 - 4

Draw Polygons using Pro-Bot given the perimeter:

1. The perimeter of a regular, 4 sided polygon is 32 cm. The interior angles are all 90 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
2. The perimeter of a regular, 4 sided polygon is 32 cm. A pair of opposite interior angles are 60 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
3. The perimeter of a regular 3 sided polygon is 18 cm. The interior angles are all 60 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
4. The perimeter of a 3 sided polygon is 24 cm. The interior angle between the shortest sides is 90 degrees. The interior angle between the shortest and longest sides is 54 degrees. The sum of the lengths of the shortest sides is 14 cm. The difference between the lengths of the shortest sides is 2 cm. What kind of a polygon is it? Can you write a program for Pro-Bot to draw this polygon? 
5. The perimeter of a 4 sided polygon is 24 cm. Two of its sides are parallel to each other and the other two are not. The sides that are not parallel are equal in length. Both the angles coming from a parallel side are equal: the pair of angles coming from the longer parallel side is 54 degrees each and the pair of angles coming from the shorter parallel side is 126 degrees each. The sum of the lengths of the parallel sides is 14 cm. The shorter of the parallel sides is 4 cm. Can you identify the polygon? Can you write a program for Pro-Bot to draw this polygon?
6. The perimeter of a 4 sided polygon is 24 cm. Both sets of opposite sides are parallel. What kind of a polygon do you think it is? The ratio of the shorter side to the longer side of this polygon is 1/2; i.e.; each shorter side is half the length of the longer side. One pair of interior opposite angles is 60 degrees and the other pair of interior opposite angles is 120 degrees. Can you write a program for Pro-Bot to draw this polygon?
7. The perimeter of a 5 sided regular polygon is 25 cm. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it? What is the value of each interior angle?

Drawing Polygons using Pro-Bot given the area:

1. The area of a regular, 4 sided polygon is 24 square cm. The interior angles are all 90 degrees each. Can you write a program for Pro-Bot to draw this polygon? What kind of a polygon is it?
2. The area of a 4 sided polygon is 24 square cm. The opposite sides are equal in length and the interior angles are all 90 degrees each. The longer side measures 2 cm more than the shorter side. The sum of the lengths of the long side and the short side is 10 cm. Can you write a program for ProBot to draw this polygon? What kind of a polygon is it?
3. The area of a 3 sided polygon is 24 square cm. The interior angle between the shortest sides is 90 degrees. The interior angle between the shortest and longest sides is 54 degrees. The sum of the lengths of the shortest sides is 14 cm. The difference between the lengths of the shortest sides is 2 cm. What kind of a polygon is it? Can you write a program for ProBot to draw this polygon? 
4. The area of a 4 sided polygon is 24 square cm. Both sets of opposite sides are parallel to each other. What kind of a polygon is it? The distance between the longer parallel sides is 4 cm. The perimeter of this polygon is 20 cm. One pair of interior opposite angles is 60 degrees and the other pair of interior opposite angles is 120 degrees. Can you write a program for ProBot to draw this polygon?

Solutions: Drawing Polygons using Pro-Bot

Here is a subset of the possible solutions for drawing the polygons in this assignment. Please keep in mind that there are multiple correct ways of programming each of these figures.


The following programs draw the polygons without using Repeat Loops.

1. Square of sides 8 cm:

Fd 8
Rt
Fd 8
Rt
Fd 8
Rt
Fd 8

2. Rectangle 4 cm x 6 cm: 

Fd 4
Rt
Fd 6
Rt
Fd 4
Rt
Fd 6

3. Parallelogram 4 cm x 6 cm:

Fd 4
Rt 45
Fd 6
Rt 135
Fd 4
Rt 65
Fd 6

4. Rhombus 6 cm:

Fd 6
Rt 60
Fd 6
Rt 120
Fd 6
Rt 60
Fd 6

5. Equilateral Triangle of sides 6 cm:

Fd 6
Rt 120
Fd 6
Rt 120
Fd 6 

6. Right Triangle of sides 3 cm, 4 cm, 5 cm:

Fd 3
Rt 126
Fd 5
Rt 144
Fd 4 

Drawing Regular Polygons using Repeat Loops in Pro-Bot

All of the regular polygons below have sides of 6 cm.

1. Equilateral Triangle

Rpt 3 [
Fd 6
Rt 120
]

2.  Square

Rpt 4 [
Fd 6
Rt 90
] 

// You can also use the instruction "Rt", instead of "Rt 90" in the code above,                                           // as the default turn is 90 degrees for Pro-Bot.

3. Pentagon

Rpt 5 [
Fd 6
Rt 72
]

4. Hexagon

Rpt 6 [
Fd 6
Rt 60
]

5. Octagon

Rpt 8 [
Fd 6
Rt 45
]

6. Nonagon

Rpt 9 [
Fd 6
Rt 40
] 

7. Decagon

Rpt 10 [
Fd 6
Rt 36
]

A Circle using a Repeat Loop

Rpt 360 [
Fd 1                 // Move 1 cm
Rt 1                 // Turn 1 degree
]

An Algorithm for Drawing Regular Polygons using Repeat Loops 

From the pieces of code above for various regular polygons, the relation between the number of sides of a regular polygon and the angle of turn can be deduced to 360/N where N is the number of sides of the polygon.

The generalized algorithm for drawing regular polygons is:

Rpt N [
Fd X
Rt 360/N
]

where N is the number of sides of the regular polygon, X is the length of each side of the polygon.  

Drawing Polygons using Pro-Bot

In this programming assignment, we shall draw polygons using Pro-Bot. We shall start by using sequential programming to draw the polygons. Next, we shall look at some regular polygons and learn how to use Pro-Bot’s Repeat Loops to draw them. We shall also develop a generalized algorithm to draw regular polygons using Pro-Bot. We can store programs for the polygons as Procedures on Pro-Bot.

Computer Science concepts involved:  Sequential programming, Repeat loops, Algorithm development

Math concepts involved:  Polygons (regular and irregular), Linear & Angular Measurements, Interior angles, Supplementary angles

Grade levels:  3, 4, 5

Hours required:  3 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.

We see polygons of different types all around us in our daily lives. Here is an interesting article that I found on mathforum.org, as to where we see different types of polygons in our daily lives.

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.

Rectangle:

Use Pro-Bot to draw a rectangle of sides 4 cm and 6 cm. Each interior angle is 90 degrees.

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.

Note: Remember that for a parallelogram, opposite angles are equal. 

In the figure of the parallelogram above, angles marked ‘a’ are equal; they are opposite angles. Similarly, angles marked ‘b’ are equal; they too are opposite angles. The angles ‘a’ and ‘b’ add up to 180 degrees; ‘a’ and ‘b’ are supplementary angles.

Note: Remember that when Pro-Bot has to draw a 45 degree interior vertex, it would have to turn 135 degrees and not 45 degrees, assuming it was moving in the forward direction before making the turn. Similarly for the 135 degree vertex, Pro-Bot would have to turn 45 degrees. Can you see why?

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. 

Next, use Pro-Bot to draw a rhombus of sides 6 cm. One pair of opposite interior angles is 90 degrees each. What shape do you get?

Equilateral Triangle:

Use Pro-Bot to draw an equilateral triangle of sides 6 cm. Each interior angle is 60 degrees.

Note: Remember that when you draw an equilateral triangle using Pro-Bot, at each vertex Pro-Bot has to turn 120 degrees (supplementary angle), and not 60 degrees, assuming it was moving in the forward direction before making the turn. Can you see why?

Right Triangle:

Use Pro-Bot to draw a right triangle of sides 3 cm, 4 cm and 5 cm. The interior angle between the 4 cm and 5 cm sides is 36 degrees. The interior angle between the 3 cm and 5 cm sides is 54 degrees. The interior angle between the 3 cm and 4 cm sides is 90 degrees.

Note: Remember that when you draw a right triangle using Pro-Bot, at each vertex Pro-Bot has to turn at its supplementary angle, and not the interior angle, assuming it was moving in the forward direction before making the turn. 

Drawing Regular Polygons using Repeat Loops in Pro-Bot

For the various shapes above that you drew using ProBot, you could see that in the case of programs for for the regular polygons (polygons with equal sides and equal interior angles), there is a pattern of instructions that keeps repeating multiple times. 

You can rewrite your programs for the square and the equilateral triangle using Repeat Loops in Pro-Bot. 

Use Pro-Bot to draw each of the shapes below. Use Repeat Loops to write your programs.

1. Equilateral Triangle:   Use Pro-Bot to draw an equilateral triangle of sides 6 cm. Each interior angle is 60 degrees.
2. Square:    Use Pro-Bot to draw a square of sides 6 cm. Each interior angle is 90 degrees.
3. Pentagon:   Use Pro-Bot to draw a pentagon of sides 6 cm. Each interior angle is 108 degrees.
4. Hexagon:    Use Pro-Bot to draw a hexagon of sides 6 cm. Each interior angle is 120 degrees.
5. Octagon:    Use Pro-Bot to draw a octagon of sides 6 cm. Each interior angle is 135 degrees.
6. Nonagon:   Use Pro-Bot to draw a nonagon of sides 6 cm. Each interior angle is 140 degrees.
7. Decagon:   Use Pro-Bot to draw a decagon of sides 6 cm. Each interior angle is 144 degrees.

After drawing the various polygons, ask the students to identify a few examples of where they might see these shapes in their daily lives. For example: a sandwich cut in half is a triangle, roof trusses are triangles, a STOP sign is an octagon, a YIELD sign is a triangle, cells in beehives/ honeycombs are hexagons, etc.

Here is a set of solutions for this assignment.

Develop an Algorithm for drawing Regular Polygons using Pro-Bot

Now that you have written programs for Pro-Bot to draw various regular polygons, let us develop a generalized algorithm for the same.

1. Is it more efficient to use Repeat Loops or Sequential Programming when you write programs for regular polygons on Pro-Bot?
2. From your programs above, can you identify a technique to find the angle at which Pro-Bot should turn at each vertex for a regular polygon?
3. Given the length of a side of a regular polygon and the angle you found using your above technique, can you write a program for drawing a regular polygon of N sides (N being any whole number) using Pro-Bot?
4. Can you now generalize your method and write down the various steps involved, as an algorithm.

Experiment more with Regular Polygons using Pro-Bot:

1. While developing your algorithm, did you notice that as the number of sides of the polygon increases, the shape of the polygon tends to a circle? What happens to the interior angle of the polygon in this case; does it increase or decrease?
2. What happens to the angle at which Pro-Bot has to turn as the number of sides of the polygon increases? Does it increase or decrease?
3. What is the smallest measurement of angle that you can use on Pro-Bot? What is the smallest length that you can draw using Pro-Bot?
4. Using the algorithm that you developed above for Pro-Bot, draw a regular polygon using that uses the smallest angle and the smallest length that Pro-Bot can provide as its dimensions. What shape do you get? 
5. Draw a regular polygon using Pro-Bot, just like the one in the previous question, that uses the smallest degree of angle, but with the length of the side increased by 1 unit. What shape do you get? 
6. What happens to the shape if you keep increasing the length of the side by 1 unit at a time, but keep the angle constant at the smallest value?
7. What happens if you increase both the length and the angle by 1 unit each time? What difference do you see?

Challenge Question: 

1. Can you write a program for Pro-Bot to draw a circular maze (a spiral shape) using all of the ideas that you learned from the above questions? It is easier to start the spiral from inside and start moving outwards. Start the spiral with the smallest length and angle that Pro-Bot can provide and then build outwards.

Solutions: Art with Pro-Bot - A Soccer Game

The soccer game picture is a follow-up to the "Art with Pro-Bot: A Dancing Robot" exercise, with one of the figures being the exact same as the Dancing Robot and the other being its mirror image.

Let's name the figure on the left as Team A and the one on the right as Team B. You would recognize from the figure that both Team A and Team B share some parts in common, such as the head and the neck. So, it's easier for the programmer to write the code for these parts just once and store it as a procedure; it can then be used multiple times. 

// Proc 1 - procedure for the neck and head

Fd 1

Lt

Fd 1

Rt

Rpt 3 [

Fd 2

Rt

]

Fd 1

Team A:  

// Program written in Main and using the above procedure. The Start point is marked in the figure.

Rpt 4 [

Fd 10

Bk 4

Rt

]

Fd 3

Lt

Proc 1

Team B:

// Program written in Main and using the above procedure. The Start point is marked in the figure.

Rpt 4 [

Fd 10

Bk 4

Lt

]

Fd 3

Rt

Proc 1