Ropes of Different Thickness and Equal Length - Knot

When we tie a knot in a rope we use up a bit of that rope. I took two ropes of different thicknesses and asked my students to guess too low, too high and best guess for how much rope would get used up if we tied a knot.

Groups then collected data to get how many centimeters per knot.

 As a class we took each group rates and averaged them to get a class rate per knot. We decided on the question shown on this whiteboard.

 

And some student work to solve this problem.

 

 

And some of my work to consolidate with the students how to use the equations to solve this problem.

 

 

 

 

 So we got 30 knots and a length of 4 meters when both ropes would have the same length.

This is what it looked like when we tied the 30 knots in each of the ropes.

 

And here is a close up of the lengths.

 

 

 Great discussion at this point about our model and how averaging the entire classes rates made it better. Students loved this.

Of course I could knot resist and we decided to look at figure 8 knots.

It took a little while for groups to figure out figure 8 knots. Data collection from various groups.

The class average.

  And some student work.

 I was knot prepared to do 60 knots.

 

 Knotted up for equal lengths!!!!!