Open and closed paths worksheet
A sheet of paths, and one job: tick the box under every closed path. A short teaching panel at the top gives the child both words and what they mean, so the sheet works on its own. Free, no account, no ads.
How hard the ends are to find
Closed paths and open paths look different, and the gap in an open path is easy to see. New version prints a fresh set at the same level.
How many paths
How long the sheet is, not how hard it is. Every path is drawn in the same size box whichever you pick.
Adds a second page for the adult with the two words, a note on why closed is about the two ends meeting, the three mistakes children usually make, and the answer key. The child's page is unchanged.
Open and Closed Paths
Tick the box under every closed path.
Closed paths and open paths look different, and the gap in an open path is easy to see.
It is about the two ends
An open path has two ends and they are in different places. A closed path comes back to where it started, so its two ends are the same point and there is no loose end to find. That is the whole judgement, and it is worth making it the habit early, because it is the version that keeps working later.
Why we do not say it holds a space
It is tempting to tell a child that a closed path is one with something in the middle, and on this sheet that would be true of every closed path printed. That is exactly the problem. A path that crosses itself can still be closed, and there is no clear middle to point at, so a child taught the middle version has to unlearn it the first time they meet one. Every level here sticks to the ends, and the teacher page explains why in full.
Why the levels get harder
Each level takes away a shortcut rather than changing the question. On the first, an open path and a closed one are different sorts of picture and the gap is wide, so one glance is enough. On the second, every open path is a closed path with a piece taken out, so the outline tells you nothing and you have to find the ends. On the third the gap shrinks to the smallest we can print and still be sure it shows.
Where it fits
This sits alongside points and line segments and straight, curved and partly curved paths, which ask different questions about the same family of figures: whether a figure has any length, and how it goes. Any of the three can come first. For plain written practice at any level, you can make a worksheet in seconds.