020. Coordinates on the Number Plane
Learning Intentions
- To know the meaning of the terms number plane (or Cartesian plane), origin and coordinates
- Interpret the location of a point described by its coordinates, e.g.
- plot points on the cartesian plane
Pre-requisite Summary
- Understand horizontal and vertical directions
- Be able to count whole number steps accurately
- Know that ordered pairs are written in brackets with a comma, e.g.
- Understand that the first number tells how far to move across
- Understand that the second number tells how far to move up
- Recognise that the origin is the point where the two axes meet
- Be able to read values from a simple scale on a grid
Worked Examples
Worked Example 1
a) Define the terms number plane, origin and coordinates.
b) State the coordinates of the origin.
c) Explain what the ordered pair
Worked Example 2
Interpret the location of each point:
a)
b)
c)
Worked Example 3
Describe how to plot each point on the cartesian plane:
a)
b)
c)
Worked Example 4
A point is plotted by moving
a) Write its coordinates.
b) Explain how the coordinates show the location.
Worked Example 5
A point has coordinates
a) Describe its location.
b) State whether it lies on an axis.
c) Name the axis if it does.
Worked Example 6
A point has coordinates
a) Describe its location.
b) State whether it lies on an axis.
c) Name the axis if it does.
Problems
Problem 1
a) Define the terms number plane, origin and coordinates.
b) State the coordinates of the origin.
c) Explain what the ordered pair
Problem 2
Interpret the location of each point:
a)
b)
c)
Problem 3
Describe how to plot each point on the cartesian plane:
a)
b)
c)
Problem 4
A point is plotted by moving
a) Write its coordinates.
b) Explain how the coordinates show the location.
Problem 5
A point has coordinates
a) Describe its location.
b) State whether it lies on an axis.
c) Name the axis if it does.
Problem 6
A point has coordinates
a) Describe its location.
b) State whether it lies on an axis.
c) Name the axis if it does.
Exercises
Understanding and Fluency
Exercise 1.
State the coordinates of each point described:
a)
b)
c)
Exercise 2.
Describe the location of each point:
a)
b)
c)
Exercise 3.
Describe how to plot each point:
a)
b)
c)
Exercise 4.
State whether each point lies on an axis:
a)
b)
c)
Exercise 5.
Name the axis if the point lies on an axis:
a)
b)
c)
Exercise 6.
Write the coordinates of each point described:
a)
b)
c)
Exercise 7.
Match each description to a coordinate:
a) on the vertical axis,
b) on the horizontal axis,
c)
Exercise 8.
Mixed practice:
a) What does the first number in
b) What does the second number in
c) What are the coordinates of the origin?
Reasoning
Exercise 9.
Explain why the point
Exercise 10.
A student says the point
Exercise 11.
Explain why
Exercise 12.
Compare the points
Problem-solving
Exercise 13.
A treasure map uses coordinates on a number plane. The treasure is
Exercise 14.
A robot starts at the origin and moves to
Exercise 15.
A point is on the vertical axis and is
Exercise 16.
A point is on the horizontal axis and is
Exercise 17.
Plot the points
Exercise 18.
A point is described by
Potential Misunderstandings
- Students may reverse the order of coordinates and treat
as up first, then across - Students may confuse the origin with any point containing a zero
- Students may not recognise that the origin is
- Students may think the first coordinate tells vertical movement and the second tells horizontal movement
- Students may count grid squares inaccurately when plotting points
- Students may not understand that a point with first coordinate
lies on the vertical axis - Students may not understand that a point with second coordinate
lies on the horizontal axis - Students may confuse the number plane with only the axes rather than the full grid