Coordinate Grid Worksheets

Coordinate grids use two number lines at right angles to name the position of any point with an ordered pair, such as (5, 7). The nine PDFs on this page ask children to name points, plot points and join them to draw mystery pictures, and every sheet has an answer key. They follow standard 5.G.A.1 of the Common Core standards for grade 5 geometry, and the notes below explain the grid, the ordered pair and the quadrants.

New: try the interactive coordinate plane and print coordinate plane mystery pictures in one or four quadrants.

Across, then up

An ordered pair like (3, 7) gives two directions: the first number says how far to go across (x), the second says how far to go up (y). A simple way to remember: walk along the hall, then climb the stairs. The mystery picture worksheets reward careful plotting with a house, a boat, a star, a fish or a rocket.

Coordinate grids worksheets: what is in the set

There are 9 coordinate grids worksheets on this page, and every one has an answer key except for any cut-out games. The first four sets name and plot points, and the last five are mystery pictures that are drawn by joining the plotted points in order.

Coordinate grids: the words children need

Coordinate grids have a few words that every child needs. The two number lines are called axes, and they meet at the origin. Every point has two coordinates in an ordered pair, and the order matters. Wikipedia’s article on the Cartesian coordinate system explains how this idea, which comes from René Descartes, is used in maps, graphs and computers. This table lists the six words used on the worksheets:

The saying “across the hall, then up the stairs” helps children remember the order: the first number is how far to go across, and the second is how far to go up. The coordinate plane tool on this site lets children plot points on screen and print their own mystery pictures.

Plotting points worksheets: across, then up

The plotting points worksheets give children eight ordered pairs and a blank grid. To plot (5, 7), start at the origin, move 5 to the right along the x-axis, then 7 up, and make a dot. This table shows the eight points from the diagram, with the number of moves from the origin:

Coordinate grid worksheets: how big is the grid?

The coordinate grid worksheets in this pack use a grid from 0 to 10, which is large enough for a picture and small enough to read easily. A grid from 0 to 10 has 121 points where the lines cross, and each one has its own name. A bigger grid has many more points, as this table shows:

Ordered pairs worksheets: why the order matters

The ordered pairs worksheets teach that (3, 7) and (7, 3) are different points. Only when both numbers are the same, as in (4, 4), do the two orders name the same place. On a grid from 0 to 10 there are 11 such points, and they all lie on a diagonal line. This table shows six pairs and their swapped partners:

The other 110 points on the grid each have a different swapped partner, so they form 55 pairs of points that are mirror images of each other across the diagonal. A child who plots both (3, 7) and (7, 3) sees this in the picture at once.

Coordinate grid pictures: how a mystery picture works

The coordinate grid pictures give a list of ordered pairs, and children plot each point and join it to the one before. When all the points are joined, the last point is joined back to the first, and a picture appears. This table shows a simple house with five points, and the length of each side:

The perimeter of this house is about 22.5 units, since the two roof sides are slanted and each is about 4.24 units long. The area is 33 square units: a rectangle of 6 by 4 and a triangle with a base of 6 and a height of 3. The mystery pictures on the worksheets are the house, the boat, the rocket, the star and the fish. The area and perimeter worksheets page shows how to find the area and perimeter of shapes like these.

First quadrant worksheets: the four quadrants

The first quadrant worksheets use only the top right part of the plane, where both numbers are positive. This is the part that grade 5 uses (5.G.A.1 and 5.G.A.2). The full plane has four quadrants, which grade 6 uses when negative numbers are introduced (6.NS.C.6). The Common Core standards for grade 6 the number system describe the next step. This table shows the four quadrants, with an example in each:

A point can also be reflected, or flipped, across an axis, and the ordered pair changes in a simple way. This table shows three points flipped across each axis:

Distance on a coordinate grid

When two points are in the same row or the same column, the distance between them is the difference of the coordinates that are not the same. For (2, 5) and (8, 5) the y values match, so the distance is 8 − 2 = 6. This table shows four pairs:

A rectangle with corners at (1, 2), (7, 2), (7, 5) and (1, 5) has sides of 6 and 3, so its perimeter is 18 and its area is 18. Grade 5 children solve problems like this, and it connects coordinate grids with the work on shapes in the geometry worksheets.

Where coordinate grids are used

Coordinate grids are used all around us, and a short talk about these examples shows children why the idea matters. This table gives five of them:

Common mistakes with coordinate grids

The most common mistake is to reverse the order of the numbers. This table shows five mistakes, what went wrong and the fix:

Coordinate grids word problems

Coordinate grids are used in maps and games. Ask children to draw a grid for each story and plot the points before they answer:

Games and activities for coordinate grids

Children learn coordinate grids best when they play with it. These games use things that are found at home or in a classroom:

• Treasure map: hide a treasure on a grid, and let a partner find it with ordered pairs
• Battleship: play with a grid that has numbers on both axes instead of letters
• Human grid: make a big grid on the floor with tape, and ask children to stand on points
• Join the dots: make up a picture, write the ordered pairs and let a friend draw it
• Robot moves: give instructions such as 3 right, 2 up, and ask where the robot stops
• Mystery picture bingo: a bingo card with ordered pairs and calling cards with points

Extra support and extra challenge with coordinate grids

For children who need more support: use a large grid on the floor and let children walk to each point, saying “across” and “up”. Always start at the origin. Use two colors for the two numbers, such as blue for across and orange for up. Do the first set only, and practice points on the axes after the other points.

For children who need more challenge: ask for the missing corner of a rectangle with three given corners, for the distance between two points in a column, and for a picture of their own with at least ten points. The mystery pictures with the most points are a good challenge.

How to tell that a child is ready to move on from coordinate grids

1. The child plots an ordered pair with the first number across.
2. The child names the ordered pair of a plotted point.
3. The child plots points on the axes, such as (0, 5).
4. The child joins the points in order to make a picture.

When all four are true, move on to the bar graphs page, or the tally charts and picture graphs page.

A 20-minute lesson on coordinate grids

A short lesson is the best way to introduce coordinate grids. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where coordinate grids fits across the grades

No skill stands alone. This table shows what children learn before and after coordinate grids, with the standard that goes with each step:

This page is the first step in coordinate geometry. The whole sequence is on the graphing worksheets page.

Helping at home with coordinate grids

Parents do not need to be experts to help with coordinate grids. These suggestions work well, and each takes only a few minutes:

• Draw a grid on the sidewalk with chalk and walk to points.
• Use a map and ask “what is at B4?”.
• Play Battleship with a grid of numbers.
• Draw a picture on grid paper and write the ordered pairs.
• Check the answers with the answer key and ask the child to explain one point.

How to check progress in coordinate grids

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for coordinate grids

Most children need about a week of short sessions for coordinate grids. This plan follows the order of the worksheets on this page:

When the plan is complete, the child is ready for all four quadrants. The whole sequence is on the graphing worksheets page.