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All Tied Up In Knots Systems of Equations Exploration Activity

I first experienced the All Tied Up in Knots activity for exploring systems of equations at a Common Core workshop I attended in the summer of 2013. I finally tried the activity in my classroom with my Algebra 2 students, and it was an awesome introduction to solving systems of equations.

all tied up in knots systems of equations activity

All Tied Up in Knots

Each group needs 2 unequal lengths of different size rop, a meter stick, graph paper (or handout), and a graphing calculator (or Desmos).

all tied up in knots system of equations exploration activity algebra

The activity begins by having students measure the length of the first rope without any knots in it. Then, the must follow the process of tying a knot in the rope, measuring and recording the new length, tying a new knot, etc. They repeat this process until they can no longer easily tie a knot. They then repeat the process with the other rope.

students measuring piece of rope with knots tied in it.

When you set this activity up, it is IMPERATIVE that you make sure each group’s thicker rope is the longer rope. If you do not do this, the system will have no solution.

comparison of two ropes in all tied up in knots activity.

Once students have their data, they are instructed to make a scatterplot of the data and sketch in lines of best fit for each data set.

scatterplot instructions.
all tied up in knots scatterplot systems example.

The second side of the handout asks students if the lines intersect and what that point of intersection means. It encourages them to physically prove the point of intersection by tying the appropriate amount of knots in each rope and seeing if they have the same length.

questions from all tied up in knots activity.
all tied up in knots system of equations exploration activity algebra

There are a few things I would tweak before doing the activity again, but I will definitely be doing it in the future.

pile of ropes on desk in classroom.

I didn’t burn the ends of my rope because I’m a major procrastinator and didn’t have time to cut the rope until the morning of the activity, so I ended up having to throw all the rope away. In the future, I will definitely burn the ends of the rope to prevent fraying so I can keep the rope and reuse it from year to year.

students working on all tied up in knots systems of equations activity.

The goal of the activity was to determine what number of knots was required to take two ropes of unequal lengths and make them the same length. The students achieved this by collecting data, creating a scatter plot, drawing in lines of best fit for each rope, and finding the point of intersection. Here’s another explanation of the activity I found online.

students working on all tied up in knots systems of equations activity.

I have scanned and uploaded the handout for this activity that I was given at the Common Core Workshop I attended. We classified this activity as aligning to A.REI.6, S-ID.6, and S-ID.7

Free Download of All Tied Up in Knots Activity for Systems of Equations


All Tied Up in Knots Activity for Systems of Equations (PDF) (1220 downloads )