One row of a table, one point
Represent an input-output pair as coordinates and read between a table and its points.
Begin with the activity ↓What can you see when a table becomes points?
With input horizontal and output vertical, one row becomes one point. Check this convention in the axis labels.
Suppose you already have one sticker. Let the input be the number of new stickers received. The output is the total, one more than the input. An input of zero still gives an output of one.
Put new stickers in the left column and the total in the right. A row with input 2 and output 3 gives one pair. Do not take the two numbers from different rows.
We choose input on the horizontal axis and output on the vertical axis. The row input 2, output 3 becomes point (2, 3). Column and axis labels tell you which value comes first.
From point (1, 2), find the row with input 1 and output 2. Practise reading pairs back from points, not only plotting them. Reordering rows does not change the corresponding points.
Sticker counts here are whole numbers such as 0 or 1. We have not defined receiving 1.5 stickers, so the plotted points are not joined by a line. Joining points would require knowing what intermediate values mean and how the relationship continues.
We plotted a correspondence whose output is always one more than its input. That does not make it direct proportion. Direct proportion requires a constant multiplier, which the future ratio and proportion course will examine.
Listen one paragraph at a time
Hold on to this distinction
Point to the row input 3, output 4. Move horizontal 3 and vertical 4 to locate (3, 4). Connect one row to the two positions in a pair.
Change it and check
Choose a row to highlight its point. Show the other rows too, then explain why the points are not connected.
One initial sticker + new stickers = total stickers. Reordering the rows does not change the pairs.
| New · input | Total · output |
|---|---|
| 3 | 4 |
| 0 | 1 |
| A: 2 | 3 |
| 1 | 2 |
Input 2 + 1 = output 3. These whole-number counts are not connected by lines.
Here horizontal means input and vertical means output, and sticker counts are whole numbers. Other tables may use different conventions, so always check the labels.
Try with paper and objects
Write rows pairing inputs 0, 1, 2 with outputs 1, 2, 3. Plot them, hide the table and read each input and output back from its point.
Check and explain another example
Check your idea 1
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Apply it in a new setting
Write an answer yourself
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(2, 3) · two numbers: horizontal, then vertical
Write input 2 first and output 3 second: (2, 3).
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 the changed and unchanged coordinates in reflections across the axes.