Real world knots and Celtic knots at the Curious Minds Club (St Thomas of Canterbury Primary School, 29 November 2019)

This week at the Curious Minds Club we started by trying some more real world knots. I used the NetKnots website to learn these knots which I showed to the children: Clove Hitch, Transom Knot, Constrictor Knot, Highwayman’s Hitch, Barrel Hitch and Cat’s Paw.

Some children played a game called Knotted. The person who created this game put it online to download for free. I did this and printed it on thick card. I tried the rules but decided to adapt them to my version, in which the winner is the first player to lay a continuous path from their side of the board to the opposite side.

knotted2

All the children had a go at making a Celtic Knot pattern. I had created some patterns of my own which I asked the children to copy to get them familiar with the different pieces and how they fit together. I then challenged them to come up with their own design. Here are three examples:

Two strands interlinked (Year 2 girl):

Y2girl_rotate

Two separate strands (Year 6 boy):

Y6boy

One continuous strand (Year 6 girl):

Y6girl

The symmetry of shoelaces and real world knots at the Curious Minds Club (St Thomas of Canterbury Primary School, 22 November 2019)

A move away from mathematical knots this week at the Curious Minds Club, and a look at real world knots. We started with a look at the symmetry of shoelaces. I made some ‘shoes’ out of felt and threaded them with one blue lace and one yellow lace. The instructions asked the children to make the base knot with the lace on the left leading first, then make the actual shoe lace knot with the lace on the right leading; this resulted in a neat and tidy, balanced knot with two types of rotational symmetry. I then asked the children to take the other shoe and make the base knot with the lace on the right leading, then make the actual shoe lace knot as above (right lace leading). This lack of alternation resulted in an ugly knot with one part facing the toes and the other part facing the heel; this is the knot which is much more likely to come apart. Ian’s Shoelace Site has more information and really good diagrams.

I then showed the children how to make some actual knots, specifically some loops and some bends.  I used the NetKnots website to learn these knots. The loops we tried were: Slip, Bowline, Hanson and True Lover’s. The bends we tried were: Square (Reef), Flemish and Fishermen’s.

To end the session, one group of children played the Knot Game. Another group had a go at solving some of Adrian Fisher’s Celtic Knot Playing Card puzzles:

adrian fisher

Unknots, Reidemeister moves and crossing numbers at the Curious Minds Club (St Thomas of Canterbury Primary School, 15 November 2019)

Another week exploring Knot Theory. The first activity was to look at a page of knots and work out which ones were actually unknots. Some children could do this by looking at the knot, and other children made the knot and manipulated it. The second activity was to learn the Reidemeister moves then look at some pairs of knots and decide which Reidemeister move had been used to turn picture one into picture two. The last activity was to learn about crossing numbers, and to look at pictures of knots and see if they could be simplified in order to decide what their true crossing number was.

reidemeister

We ended the session by playing the Knot Game.

knot game

Knot theory and the handcuffs puzzle at the Curious Minds Club (St Thomas of Canterbury Primary School, 8 November 2019)

We started Knot Theory in this week’s Curious Minds Club. The first activity was the Handcuffs Puzzle: in pairs both children had a length of rope attached to their wrists in such a way that they were linked to their partner; the challenge was to untangle themselves. It looks like the length of rope forms a closed loop for each child, but the solution lies in realising that there is a gap under each wrist: if a loop is threaded through in the right direction, passed over the fingers and back over the wrist again then the two pieces of rope do become detached. The children had fun trying this out, but I did need to show them the solution.

The next activity was to challenge the children to tie a knot in a length of rope without letting go of either end. I demonstrated that holding a length of rope in each hand forms a closed loop and that if you do not let go you end up tying your arm into the knot. The children were pleased when I showed them there is a solution which involves tying your arms into a knot before picking up the rope, then unknotting your arms. This works on the principle of the transference of curves: when you unknot your arms you transfer the knot that was on your arms onto the rope.

The final activity was to start to explore some mathematical knots. I had attached velcro to the ends of some shoelaces so that the ends could be joined. The children made the 3,1 (the trefoil) then the 5,1 and the 7,1. They made one crossing change and saw how this allowed them to transform their knot into the previous one in the series.