1A corresponding relationship is "pairing up"
A corresponding relationship is when one quantity changing means another quantity changes right along with it, as a matched pair. Like the number of tricycles (x) and the number of wheels (y), every x-value is matched with exactly one y-value.
Every time the number of tricycles goes up by 1, the number of wheels always goes up by 3.
2A table reveals the pattern
Writing x and y values side by side in a table makes it much easier to see what pattern the numbers follow. If y grows by the same amount every time you go down a row, that means a rule is hiding in there.
3Plotting the table as dots makes a graph
Plot each x, y pair from the table as a dot, and you'll see the dots trace out a steady path. If the dots line up straight, that's a sign there's a very simple rule between x and y.
Like the number of matchsticks needed to join equilateral triangles in a row, some rules are "multiply by this much, then add this many." Practicing finding the rule yourself by looking at the table is what matters.
4You'll learn this rule again later as a "function"
For now, you're just observing the rule with tables and graphs, but once you get to middle school, you'll learn how to write this rule using letters and equations. That's exactly where functions begin.
5Try this
- Compare several situations. See how the rules differ between tricycles, joined triangles, and joined tables.
- Cover the table and guess the rule. Looking only at y for x=1, 2, 3, guess ahead of time what y will be when x=10.
- Apply the rule yourself in the quiz. Without reading the on-screen rule explanation, challenge yourself to find the answer using only the table's pattern.