### Description of Graph Paper

Graph paper is a writing paper that is pre-printed with fine lines that make up a squared grid. There are several ways to achieve this, but the grids are often coming with composing of vertical and horizontal lines. The grid lines are used to drawing curves, plotting co-ordinates, calculate some experimental data, and functions of graphs.

Most of the people are familiar with the use of ruled paper that comes up with horizontal lines to write on the paper neatly. In the similar way, grid papers or squared paper provides support to solve your math based problem in two dimensions rather just once.

Suppose you are a student as a beginner, you can use graph paper to visually represent the addition, subtraction, multiplication or division of the numbers. It is easier to use grid paper to draw geometric figures on the XY-plane, maps relation on it rather than ruled paper or blank paper. Finally, any king of graphs such as geometric curve drawing, plotting co-ordinate, any schematic or any drawing that needs to be scale precisely is much easier to do with grid paper.

However, graph paper can also be used for making fun. It is perfect for formatting complex designs such as embroidery design, quilting, interior design, beading and kitting. Grid paper is also a very common tool for making games that has the features of strategic divisions of space for example, most of the character playing games uses graph papers to find out the characters of each other in the relation to the plat, and to the enemies.

Figure. 1. Repeating pattern design in a complex textile by using graph paper.

### 10 Popular Types of Printable Graph Paper

There are standard versions of different types of graph papers those are come up with squares. This papers are used to graph mathematics projects such as graphing lines, plotting coordinates or functions, developing symmetrical graphs, repeating designs and science projects such as creating format for experimental outcomes of a problem.

### Quad-Ruled Graph Paper

Quad ruled graph paper, also referred to as quadrille paper and is made up with Small Square. This is the ordinary form of graph paper having sparse grid and printed with the colour of grey or light blue from the right to the edge of the graph paper. In general, it has two squares, four squares or five squares inch detail for work in the Canada and U.S. Sparse grid in the metric paper has one square or two squares in each centimetre.

Figure. 2. Quad ruled graph paper

### Quad-Ruled Graph Paper with XY-Coordinates

The quad ruled graph paper that has an XY axis is commonly used to plot coordinate in mathematical geometry. The XY coordinates grids are further divided into two ways in the graph paper: half page coordinate grids and full page coordinate grids.

Figure. 3. Half page coordinate grids

Figure. 4. Full page coordinate grid

### Millimetre Paper

The millimetre paper template is filled with ten squares grid in each centimetre. This can be used to drawing technical expressions.

### Normal-Probability Paper

This is another type of graph paper featured with variable widths of rectangles. This paper is form so that “the graph of the normal distribution function is represented on it by a straight line”. Therefore it can be used to plot the normal probability distribution functions for a straight line.

### Engineering paper

An engineering paper, sometimes referred to as an engineer’s pad, is printed with light green in a traditional manner, a translucent paper. It consists of four squares, five squares or ten squares in each centimetre. The front side of the page shows the faintly lines and on the back side of each page the grid lines are printed. The grid lines do not display the resultant copy of the paper whenever it scanned, so that it allows the work with uncluttered and neat appearance. Some of the engineering professors in the Canada and U.S., they provide the homework to the student that required to be done base on engineering paper. Thesis papers is considering as a general purpose papers. This type of paper templates can be applied in various ways. Most of the engineering students used this template to plotting mathematical functions or expressions.

Figure. 5. Engineering paper

### Multi-Line Graph Paper

This graph paper made up with a standard ¼inch square grid in the intervals of four or five square and overlaid with smaller heavier lines. This type of paper template can be used to learn skip counting of discovering first numbers, represent different kinds of data visually and also make it easy to create bar graphs.

Figure. 6. Multi-line Graph Paper

### Isometric (Triangle Grid) paper

The isometric paper grid is filled up with equilateral triangles rather than squares. It is sometimes referred to as 3 dimensional graph paper that uses certain guidelines to forming small triangles grids of 60°. The triangular-graph paper templates are used to create 3 dimensional graphs for designing interior planning, plotting graphs on an XY axis, space planning or graphing woodworking plans. The triangles are arranged in a group to form a hexagon. The functionality of this graph paper including pseudo 3 dimensional views or isometric views as the name suggests, also used in the design of triangle point embroidery and used to create angles properly.

Figure. 7. An isometric graph paper

Figure. 8. An example of drawing 3D image on Isometric Paper

### Dot Paper

The dot paper is another kind of graph paper which is used to marks the corners of the square grid only and leaves their sides out. The dot paper can be used for charts, designs with less visibly cluttered outcomes. Since the paper is made up with dots only, the lines you are drawing won’t be completed with pre-printed lines that the standard quad consists of.

Figure. 9. Dot Paper

### Hexagonal Paper

The hexagonal paper template provides the hexagons rather than squares. This graph paper can be used for tessellated designs or used to map geometric expressions such as tiled.

### Logarithmic Paper

The logarithmic paper template has variable widths of rectangles drawn in the graph paper. This can be associates with logarithmic scales to draw log-log plots or semi log plots.

Figure. 10. Log-log graph paper

Figure. 11. Semi-log graph paper

### Polar Coordinate Paper

The polar coordinate graph paper has made up with concentric circles, which is divided into pie wedges or small arcs. This type of graph paper can used to plotting polar coordinates.

Figure. 12. Polar Coordinate Graph Paper

In addition, graphs basically showing grids which are sometimes referred to as Cartesian graphs since the squares on the graph paper are used to mapping the measurement in form of a Cartesian (X Cartesian Y) axis system. It can also be done without drawing lines, but you have to draw a dot at point of intersection.

### Expert Tips for Using Graph Paper in Math Accommodation

This paper provides guidance for beginner students. The various productive ways of using graph paper are given below:

The number of lines: To draw some lines of number on a graph paper automatically spaces each segment correctly. You can use it to draw intersection of lines which illustrate units, fives or tens.

Addition of numbers: By using various colour pencils you can add squares into the whole. Alternatively, different number of lines can be used to show the addition that you are moving up.

Subtraction of numbers: By using various colour pencils you can subtract squares from the whole. Alternatively, different number of lines can be used to show the subtraction that you are moving down.

Multiplication of numbers and Division of numbers: You can use different rectangular shapes to describe the same outcomes that 3×8 given by plotting 3 rows of 8 as 4×6 given by plotting 4 rows of 6. Hence able to count the outcomes of the squares.

Fractional Numbers: The concept is to divide a rectangle in a variety of fixed parts, then using various colour pencils to show the different parts of the rectangle that forms the whole.

Mapping to the Environment: This can be used making a map between 3 dimensional worlds to 2 dimensional space which shows you are in the room or in the street.

These are the examples of some advanced level learning using graph paper. The automatic use of the graph paper: it is easier to represent mathematical problems with graph papers. For example, to figure out the geometric expressions where you have need to point out several coordinate, and you have to deals with XY coordinate on the graph paper.

The graph paper is an effective tool to makes the best scratch paper: the grid paper can be used as a scratch paper for calculating mathematical problems and it will helps to draw more precise and neater graph while reducing formulas, organizing proofs and so on.

## References

https://blog.prepscholar.com/free-printable-graph-paper