There are two.

How many loops does this knot have?

There are three. The following slides have larger knots, but students age 6+ should still be capable of tackling them – certainly collectively if not alone.

How many knots do square knot patterns have? These are actually easier to count because the loops are all like rectangles.

There are six.

This is a 6×7 knot. Students learning about relatively prime numbers, greatest common factors and lowest common multiples could try to come up with a general theory of how many loops are in these knots.

However, younger students can still tackle these puzzles to practice their tracing and counting skills.

This 6×7 knot has only one big loop.

This 6×8 knot has how many loops?

Just two.

This 6×9 knot has how many?

Three. Notice the symmetry.

This is just one of the loops in the previous pattern. Can the junior high student working on symmetry say anything about the symmetry of the loops in an nxm knot.

I’ll leave you with this bigger knot… Don’t go onto the next slide till you’ve solved it. Can you solve it without using paper?

There are more than two loops…

There are more than three loops…

There are four loops.

Three puzzle sheets are included in the pdf below. Here is the first.

Students should also be encouraged to create their own knots. The following sheet is a template that may help. All my knots have loops that alternate going over and under. That should be a rule for an introductory exploration.

Template to create knots…