E. Spatial Sense · Angles, Rectangles, Grids and Measurement

Plotting and Reading Coordinates

E1.2About 35 minutes

Learning goals

I can name the x-axis, the y-axis and the origin on a grid.
I can read the coordinates of a point as an ordered pair (x, y).
I can plot a point when I am given its coordinates.
I can explain why the order of the numbers matters.

Words to know

coordinate grid
A grid with numbered lines going across and up, used to describe exactly where points are. It is also called a Cartesian plane.

x-axis
The numbered line that goes across the bottom of the grid.

y-axis
The numbered line that goes up the left side of the grid.

origin
The point where the two axes meet. Its coordinates are (0, 0).

coordinates
Two numbers that tell exactly where a point is, like (4, 2).

ordered pair
Two numbers written in a set order (x, y). The across number always comes first.

plot
To mark a point on a grid in the right place.

Remember from Grade 3

You followed and gave directions on grid maps, moving from square to square with distances and turns.

This year you will learn a new, very exact way to describe where something is: coordinates. Pilots, game designers and map makers all use them.

Let's start with a winter carnival

The town is planning a winter carnival in the park. The map below has a grid on it. How can the organizers tell the volunteers exactly where the hot chocolate stand goes? They can give its coordinates: (5, 1).

A carnival map on a coordinate grid. The skating rink R is at (2, 3), the hot chocolate stand H is at (5, 1), the snow fort F is at (6, 4) and the toboggan hill T is at (1, 5).

Parts of a coordinate grid

The x-axis goes across the bottom. Its numbers start at 0 and get bigger to the right.
The y-axis goes up the left side. Its numbers start at 0 and get bigger going up.
The two axes meet at the origin, which is (0, 0).

Points go where the lines cross, not in the middle of the squares. This is different from the grid maps you used in Grade 3.

Reading an ordered pair

Coordinates are written as an ordered pair: (x, y).

Start at the origin (0, 0).
The first number tells how far to go across (along the x-axis).
The second number tells how far to go up (along the y-axis).

A way to remember: "Across the hall, then up the stairs." You have to walk along the hall before you can climb the stairs!

To plot R (2, 3): start at the origin, go across 2, then go up 3.

Worked example

Example 1: Plot a point

Plot the point S (4, 2).

Start at the origin (0, 0).
The first number is 4. Move across the x-axis to 4.
The second number is 2. From there, move straight up 2 lines.
Make a dot where the lines cross. Label it S.

S is 4 across and 2 up from the origin.

Worked example

Example 2: Read a point

On the carnival map, what are the coordinates of the snow fort F?

Put your finger on F. Look straight down to the x-axis. It lines up with 6.
Now look straight left to the y-axis. It lines up with 4.
Write the across number first: (6, 4).

The snow fort is at (6, 4).

Order matters!

(2, 5) and (5, 2) use the same numbers, but they are different points. Always go across first, then up.

P (2, 5) is 2 across and 5 up. Q (5, 2) is 5 across and 2 up.

Worked example

Example 3: Points on an axis

Where is the point (0, 3)? Where is (3, 0)?

(0, 3): go across 0 (stay at the origin), then up 3. The point is on the y-axis.
(3, 0): go across 3, then up 0 (don't go up at all). The point is on the x-axis.

A 0 for x puts a point on the y-axis. A 0 for y puts a point on the x-axis.

Math talk: check your partner

When you plot a point, say the moves out loud: "Across 4, up 2." If someone plots a point in a different place, compare your moves to find the mix-up. Usually someone went up first!

Just for fun

A rhyme for the order of a coordinate pair: "Along the hallway, then up the stairs." You can't climb the stairs before you walk to them!

Hands-on activity

Hide the snowflake (a coordinate game)

You need: 2 sheets of grid paper (or draw your own grid with a ruler), 2 pencils and a book to hide your grid behind. Play with a grown-up.

Each player draws axes on their grid and numbers both axes from 0 to 6.
Without showing anyone, each player secretly plots 3 snowflakes where lines cross.
Take turns guessing a point by saying its coordinates, like "(4, 1)". The other player says "Hit!" or "Miss".
Plot your guesses on a second grid to keep track. Use a dot for a miss and a star for a hit.
The first player to find all 3 hidden snowflakes wins.

Math talk: "Did anyone mix up across and up? How did you notice?"

Points A, B, C, D, E and G on a coordinate grid, for the questions below.

Your turn

What are the coordinates of point A?

What are the coordinates of point B?

What are the coordinates of point C?

What are the coordinates of point D?

What are the coordinates of point E? What do you notice about its two numbers?

Which point is at (1, 1)?

On grid paper, plot M (5, 3). Describe your moves.

More practice: warm-up

What are the coordinates of the origin?

Which axis goes across: the x-axis or the y-axis?

In (7, 2), which number tells you how far to go up?

On the carnival map, what are the coordinates of the toboggan hill T?

On the carnival map, what is at (2, 3)?

More practice: on your own

Leah plots (3, 6) by going up 3 and across 6. What mistake did she make? Where did her point land?

A point is on the x-axis, 8 units from the origin. What are its coordinates?

Plot (1, 1), (5, 1), (5, 4) and (1, 4). Join them in order and back to the start. What shape did you make?

Which point is farther up: (2, 6) or (6, 2)?

On the carnival map, which is farther right: the hot chocolate stand H or the snow fort F? How can you tell from the coordinates?

Challenge

Three corners of a square are at (2, 1), (5, 1) and (5, 4). What are the coordinates of the fourth corner?

List all the points on a grid where x + y = 4 and both numbers are whole numbers. What do you notice when you plot them?

Max says (0, 5) and (5, 0) are the same point because they both have a 0 and a 5. Use the grid to explain why he is wrong.

Check your understanding

Quiz

In the ordered pair (6, 3), what does the 6 tell you?

What are the coordinates of the origin?

A point is 2 across and 7 up from the origin. What are its coordinates?

Where is the point (0, 4)?

Are (3, 5) and (5, 3) the same point?

Where do you put a point on a coordinate grid?

For parents and teachers

Big idea: The Ontario curriculum (E1.2) asks Grade 4 students to plot and read coordinates in the first quadrant of a Cartesian plane (only the top-right part, where both numbers are 0 or more). In the next lesson they will describe how to move a point from one coordinate to another.

Common difficulties:

Reversing the order. A very common mistake is going up first. Use the saying "across the hall, then up the stairs".
Putting points in squares. In Grade 3, grid maps labelled squares. Coordinates label the crossing points of lines.
Points on the axes. (0, 3) and (3, 0) confuse many children. Act them out: "Across zero means don't move across."

How to help: Play the snowflake game (like Battleship) on grid paper. Many board games and city maps use grids too. Ask your child to give you coordinates to draw a simple picture by joining dots.