Horizontal first, vertical second
Read points as ordered pairs and check what changes when the order is reversed.
Begin with the activity ↓Are (2, 3) and (3, 2) the same position?
Write the horizontal position first and the vertical position second. (2, 3) means horizontal 2, vertical 3.
Write the two positions as a pair, such as (2, 3). The first number gives the horizontal position and the second gives the vertical position. A pair with a specified order is an ordered pair.
The horizontal and vertical reference lines are axes. Their intersection is the origin, written (0, 0). The horizontal axis is also called the x-axis and the vertical axis the y-axis.
To locate (2, 3), find horizontal 2 from the origin, then go up to vertical 3. The comma separates the two values, and parentheses group them as one pair. Do not add 2 and 3 into a single number.
Reversing the order gives (3, 2): horizontal 3, vertical 2. The same digits can locate a different point. But (2, 2) remains the same pair when reversed.
Coordinates describe where a point is. Moving horizontally and then vertically is a way to locate it, not a record of the route actually travelled. Coordinates alone do not give a total path length.
We are now ready to describe positions in opposite directions from zero on both axes. Next we use negatives for leftward and downward positions. The reading order stays the same.
Listen one paragraph at a time
Hold on to this distinction
Read the first number horizontally and the second vertically. Locate (1, 4) and (4, 1) to see why order matters.
Change it and check
Choose a pair and swap its order. Compare examples with different values and equal values.
This activity uses integer coordinates from 0 to 4. It does not ask for the sum of the numbers or distance from the origin.
Try with paper and objects
Mark (1, 3) and (3, 1) on paper. Point to each and identify its horizontal number.
Check and explain another example
Check your idea 1
Check your idea 2
Apply it in a new setting
Write an answer yourself
Return to the explanationCompare with a solution
(3, 1) · two numbers: horizontal, then vertical
Horizontal comes first and vertical second: (3, 1).
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
Continue, or pause here
Distinguish negative directions on both axes and read signed coordinates.