NZ Level 3
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The Number Plane (Q1 with symbols)
Lesson

You may be able to find the place you live on a map but how would you describe it to somebody else on the other side of the world who didn't know where to find your town? Well, we can use a number plane to help us describe a position.

We can describe the position of any point using two values which are called a pair of coordinates

 

Features of a Number Plane

A number plane is made up of a horizontal and a vertical axis.

  • The horizontal axis, called the$x$x-axis, is like a number line you have seen previously that runs from left the right.
  • The vertical axis, called the $y$y-axis, is a number line that runs up and down.
  • The two lines meet at the origin, which has coordinates $\left(0,0\right)$(0,0).

Let's look at an example of a number line now.

 

Reading and Writing Coordinates

Writing Coordinates

To write coordinates, we write the horizontal value, then the vertical value that a point is away from the origin. For example, in the picture below, the coordinates on the smiley face are $\left(10,1\right)$(10,1) because it is $10$10 units to the right of the origin and then $1$1 unit up.

Reading Coordinates

We read coordinates in the same way as we write them. Let's say I asked you what shape was at $\left(1,4\right)$(1,4). To work this out, you'd start at $\left(0,0\right)$(0,0), move $1$1 space to the right, then $4$4 spaces up. Where would you land? On the heart.

 

Plotting Points on a Plane

Now that we can read coordinates, we can plot (draw) the points on a number plane. Play with the applet below and practice plotting points.

Remember!

Coordinates are written as:

(horizontal number, vertical number)

 

Worked Examples

Question 1

Here is a number plane.

  1. What is at coordinate $\left(1,4\right)$(1,4)?

    Heart

    A

    Cloud

    B

    Circle

    C

    Smiley face

    D

    Heart

    A

    Cloud

    B

    Circle

    C

    Smiley face

    D
  2. What is at coordinate $\left(10,1\right)$(10,1)?

    Pentagon

    A

    Smiley face

    B

    Cross

    C

    Rectangle

    D

    Pentagon

    A

    Smiley face

    B

    Cross

    C

    Rectangle

    D

Question 2

Here is a number plane.

  1. Write the coordinate of the circle.

    $\left(\editable{},\editable{}\right)$(,)

  2. Write the coordinate of the moon.

    $\left(\editable{},\editable{}\right)$(,)

Question 3

Here is a number plane.

  1. What is at coordinate $\left(6,2\right)$(6,2)?

    Smiley face

    A

    Diamond

    B

    Cloud

    C

    Circle

    D

    Smiley face

    A

    Diamond

    B

    Cloud

    C

    Circle

    D
  2. Write the coordinate of the crown.

    $\left(\editable{},\editable{}\right)$(,)

Outcomes

NA3-8

Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.

GM3-5

Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.

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