Math 1 · Unit 2 · Lesson 2
Connect the Dots: From Points to a Line
Lesson 1 left the dots lined up. Now fill in the gaps: an in-between input like 0.5 or 2.25 has exactly one output too, so it is a point, and it lands on the same line. The line is all of the points at once. Then decide when connecting the dots is honest: continuous (any input is real) or discrete (only whole things).
The big idea
A function promises one output for every input, and that promise does not stop at the whole numbers. Feed in 0.5, or 2.25, or any number at all, and you get one output, one point, and that point sits on the same straight path as the dots from the table. So the line is nothing new: it is every point of the rule at once. Draw it when the in-between inputs are real, which is what continuous means. Leave the dots separate when the input can only be whole things, which is what discrete means. Next unit, this line gets measured and named. For now, it is enough to see that it is really there.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the leap from dots to line, the continuous and discrete rule with an example of each, the words we use, and a worked in-between input. Plus a worksheet with an answer key and a short lesson plan.