Problem: Article: This is for her upper skull. Make sure that you are using a pencil for the draft sketch so you can erase it afterwards to make it neat. Draw a vertical line in the middle of the head so you know the center of the face. You can draw on a different angle for her pose. Add an L-shaped line for her jaw guide. For her torso, draw an inverted triangle. For her cheeks, just connect the head with the L-shaped line. Draw a circle at the pointed end of the triangle for her hips. For her neck just draw a rectangle to connect the body to her head. For the limbs and legs, just draw some lines. It all comes to the artist’s preference. To complete her neck, draw 2 huge bolts at each side. For the hands, just draw rounded ovals. Also, don’t forget to add her legs. By now, you should have her basic skeleton. Basically, Frankie’s hair is straight but tends to meet up at the ends, you might want to keep that in mind when drawing her hair. Aside from that, it’s just simple lines and curves. For her bangs, draw some curvy and wavy lines. Add some sleeve puffs and her necktie. Frankie likes wearing gothic dresses so let’s add some ruffles for her skirt. On the center of the face,  draw her small nose and large lips. Make sure to make the lower lip big and the upper lip thin. Add two almond-shaped figures for her eyes. Make the eyes skew a little from the center. Put in mind the overlapping lines and parts that should be hidden. For her limbs and legs, just add some width from the bone. It doesn’t matter if your legs look weird. The drawing style for Monster High defies logic and proportional rules. The lineart might not look perfect and crisp but it should look neat when the pencil is erased. You can add details like jewelry and different accessories. Don’t forget to add some eyelashes and the inside lens (which is just 2 small circles overlapping a big one). Also, never forget her body stitches. She’s got one on her face, neck, two on her right arm, and one on the other. For her legs, she’s got one set of stitches each leg. Try to add more if needed. Don’t be afraid to add more lines than what is necessary.  You can add lots of trinkets on her clothes. When coloring her, notice that she has different-colored eyes.
Summary: Draw a big circle. Add guidelines for the face. Add her torso and cheeks. Add neck and hips. Draw her limbs and thigh. Complete neck and add hands. Add hair. Draw some clothing details. Draw the face. Using a pen, draw on top of your sketch. Erase the pencil sketch and add details. Color Frankie.

Problem: Article: You may need to first identify how many sides are present in the polygon. Each polygon has a prefix that indicates the number of sides it has. Here are the names of polygons with up to twenty sides:  Quadrilateral/tetragon: 4 sides Pentagon: 5 sides Hexagon: 6 sides Heptagon: 7 sides Octagon: 8 sides Nonagon/Enneagon: 9 sides Decagon: 10 sides Hendecagon: 11 sides Dodecagon: 12 sides Triskaidecagon/tridecagon: 13 sides Tetrakaidecagon/tetradecagon: 14 sides Pentadecagon: 15 sides Hexadecagon: 16 sides Heptadecagon: 17 sides Octadecagon: 18 sides Enneadecagon: 19 sides Icosagon: 20 sides Note that a triangle has no diagonals. If you wanted to know how many diagonals were present in a square, you would start by drawing the square. The easiest way to find diagonals and count them is to draw the polygon symmetrically, each side has the same length. It’s important to note that even if the polygon is not symmetrical, it will still have the same number of diagonals.  To draw the polygon, use a ruler and draw each side the same length, connecting all of the sides together. If you’re unsure what the polygon will look like, search for pictures online. For example, a stop sign is an octagon. A diagonal is a line segment drawn from one corner of the shape to another, excluding the sides of the polygon. Starting at one vertex of the polygon, use a ruler to draw a diagonal to every other available vertex.  For a square, draw one line from the bottom left corner to the top right corner and another line from the bottom right corner to the top left corner. Draw diagonals in different colors to make them easier to count.  Note that this method gets much more difficult with polygons that have more than ten sides. There are two options for counting: you can count as you draw the diagonals or count them once they have been drawn. As you count each diagonal, draw a small number above the diagonal to denote that it has been counted. It is easy to lose track while counting when there are a lot of diagonals crossing each other.  For the square, there are two diagonals: one diagonal for every two vertices.  A hexagon has 9 diagonals: there are three diagonals for every three vertices. An octagon has 20 diagonals. Past the heptagon, it gets more difficult to count the diagonals because there are so many of them. Each vertex may have multiple diagonals, but that doesn’t mean that the number of diagonals is equal to the number of vertices times the number of diagonals. Take care when counting the diagonals to count each one only once. For example, a pentagon (5 sides) has only 5 diagonals. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals. This is incorrect because you would have counted each diagonal twice! Draw some other polygons and count the number of diagonals. The polygon does not have to be symmetric for this method to work. In the case of a concave polygon, you may have to draw some of the diagonals outside the actual polygon.  A hexagon has 9 diagonals. A octagon has 20 diagonals.
Summary: Know the names of polygons. Draw the polygon. Draw the diagonals. Count the diagonals. Beware of counting a diagonal more than once. Practice with some examples.

Problem: Article: These are the vertical and horizontal lines that form basic outline of the histogram. If you have trouble making the right angle where the axes meet, go ahead and cheat: use a corner of a sheet of paper! In a histogram, the data is visualized in groups. These groups are evenly distributed, so you'll need to make set marks along your lower axis. For example: 0-4 apples, 5-9 apples, 10-14 apples, etc at 1", 2", and 3" along the axis. The vertical axis in a histogram is always for frequency. What measure of time is necessary, though, is up to your data of course (but the numbers will still need to be equally spaced). Just be sure to leave extra room at the top to make your chart easier to read.  If the upper limit of your histogram is 54, for example, you should make the highest number on the axis 60. If the frequency doesn't start until a fairly high number, you can cut out many of the numbers below it. For example, if the first frequency is 32, you can start the chart at 25 or 30. Draw the horizontal top line for each interval or group lightly, at the level that data was measured. Then, draw in the bars centered over the data point they represent. Make sure the bars are even and the same width as each other. Generally, histogram bars are supposed to touch, but if you have no results for a particular group, then don't worry about it. Add different colors to the histogram rectangles with colored pencils, markers, or crayons to help differentiate among the intervals.
Summary:
Using a ruler, draw out the basic axes. Measure out the groups. Measure out the vertical axis. Draw the bars. Add some color.