Plotting on this sheet
The x-axis runs across the page and the y-axis up the middle. They cross at the origin, (0, 0), and every point is an ordered pair (x, y): count x squares right from the origin (left if x is negative), then y squares up (down if y is negative). The axes split the plane into four quadrants, numbered I to IV counterclockwise from the top right: both coordinates are positive in quadrant I, x is negative in II, both are negative in III, and y is negative in IV.
The Common Core math standards introduce this in two steps. In grade 5, students graph points in the first quadrant and read what the coordinates mean in a real problem (standard 5.G.A.2). In grade 6 the axes extend to negative numbers: students graph points in all four quadrants, find distances between points that share a coordinate, and see that points such as (3, 2) and (−3, 2), which differ only by a sign, are reflections of each other across an axis (6.NS.C.6 and 6.NS.C.8).
Choosing a scale
One square doesn’t have to mean one unit. Before you plot a table of values, find the largest number each axis has to reach and divide by the squares you have: on Letter there are 20 squares above the origin, so if y goes up to 200, let each square stand for 10. Write the scale on both axes, and keep it the same across an axis, even if x and y use different scales.
For graphing a line, plot at least three points from a table of values. If they don’t line up, one of them is miscalculated, which is easier to catch on paper than on a calculator screen.
Worksheets and tests
- Several copies: set Pages to the number of students and download one PDF.
- Name line: type something like
Name ________ Period ____into Title and it is printed above the grid. - Photocopies: pick black lines at Medium weight so the grid survives a copier; the axes are always drawn dark.
- Polar equations need a different grid: use polar graph paper. For lab graphs with fine divisions, the millimetre graph paper has a centimetre grid instead of axes.
How this page sets up the sheet
- Square grid, x and y axes through the middle, numbered.
- In inches: 1/4 in (6.35 mm) squares, 4 per inch.
- In millimetres: 5 mm (0.197 in) squares, 2 per cm.
It opens in inches in the US and other countries that use Letter paper, and in millimetres everywhere else (or in whichever unit you last used on this site). The paper size follows your browser too: Letter in the US, A4 elsewhere. Everything stays editable. Your own page settings, such as margins, are remembered for next time; the grid itself always opens as set up here. To start from a blank setup, use the graph paper generator.