Graph Paper

The gray lined graph paper is most useful if you need to draw over top of the existing lines and highlight your own figures. For example, for a measurement lesson, rectangles of different sizes could be outlined in a word problem like the following: "Draw as many rectangles as you can with whole number dimensions that have an area of 36 square centimeters."

This paper uses fractions of inches for those who are used to measuring using the U.S. or Imperial system of measurement. Perhaps you might consider using this graph paper for learning multiplication facts. To multiply 5 by 6, for example, a student would make a rectangle that is five squares by six squares and find out how many squares were contained within. You might also solve a problem like the following using grid paper, "Find the area of forest on a rectangular property that is 9 miles by 7 miles if the entire property is forested except for an estate with a house and open area that is 3 miles by 2 miles."

Multi-line graph paper has many applications including everything that you can accomplish on single-line graph paper. We'll leave the potential to your imagination, but here are a couple ideas to get you started. A three line graph paper worksheet with 2.5 cm, 1.25 cm and 0.25 cm lines ends up having smaller boxes of 25 squares and larger boxes of 100 squares. There are also small rows and columns of 5 squares. This is very similar to the decimal money system that is used in many countries. Therefore, you could model counting coins using this particular three line graph paper. The boxes of 25 and 100 and the rows and columns of 5 make it easy to get a total in the end. Multi-line graph paper also makes most graphing activities easier because students can skip count rather than having to count each line. For example drawing a bar on a bar graph that required a height of 28 would be easier if you had every 4 lines marked with a thicker differently colored line just like you'll find on the two line graph paper with 1 inch major lines and 1/4 inch minor lines.

Dot paper can be useful in a variety of mathematical situations. For example, it is quite useful for drawing side views of connecting cube structures or other rectangular based figures. One very interesting use of dot paper is to find the area of irregular polygons using Pick's Formula (named after Georg Alexander Pick). You could decompose an irregular polygon into regular polygons, find the area of each polygon and add the areas, or you could use the much easier Pick's Formula which is to add the number of interior dots to half of the boundary dots and subtract one.

Dot paper can actually be used for just about anything for which grid paper can be used. Dot paper is grid paper without the line segments in between the vertices. Some people prefer dot paper as the page is less busy and allows better definition of anything that is drawn on the page.