Simple and self-intersecting paths worksheet
A sheet of paths, and one job: tick the box under every path that crosses itself. A short teaching panel at the top shows the child both cases and what to look for, so the sheet works on its own. Free, no account, no ads.
How hard the crossings are to spot
A path that crosses itself looks different from one that does not, and it is easy to see where it goes back over itself. 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 both mathematical terms, the note that a crossing does not split one path into two, why every path here is open, the three mistakes children usually make, and the answer key. The child's page is unchanged.
Which Paths Cross Themselves?
Tick the box under every path that crosses itself.
A path that crosses itself looks different from one that does not, and it is easy to see where it goes back over itself.
Follow the path, do not judge the tangle
A path crosses itself when, tracing it from one end to the other, you pass back over a place you have already been. That is the whole judgement. It is worth making it a habit of following rather than glancing, because a busy-looking path may never cross at all and a plain-looking one may cross once.
A crossing does not make two paths
Where a path crosses, it is still one path. It has two ends, and you can trace the whole thing from one to the other without lifting your finger. The crossing is a place the line passes through twice, not a join and not a split. It does not make a shape or a hole either, which is why nothing here asks what is inside anything. The teacher page says all of this in full for the adult.
Why the levels get harder
Each level takes away a shortcut rather than changing the question. On the first, the two kinds of path look different and a crossing is easy to spot. On the second, every path bends by the same amount, so the outline tells you nothing and you have to follow. On the third the paths also come back on themselves at the same angle, so even how squarely the two strands meet stops being a clue.
Where it fits
This sits alongside points and line segments, straight, curved and partly curved paths and open and closed paths, which ask different questions about the same family of figures: whether a figure has any length, how it goes, and whether its two ends meet. Any of the four can come first. For plain written practice at any level, you can make a worksheet in seconds.