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Celtic Knot

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Celtic Knot


A Celtic knot pattern $4\times4$ looks like this. You can see how it is built up on a grid.



A Celtic knot pattern $8\times8$ looks like this on a grid.



A Celtic knot pattern $6\times6$ looks like this.

Can you build it up? There is a copy of the design to download here.

You can do it by making a set of cards to use on a $6\times6$ grid in a $24$ cm square with four copies of this sheet. There is also a second page with two copies of the design.

Or you could try doing it using this interactivity.
Full screen version
This text is usually replaced by the Flash movie.

 

Why do this problem?

This problem requires learners to look closely at a design, and see how it can be divided into squares, and built up from simple pieces. It will involve mathematical language, using words such as 'curved' and 'straight', 'vertical', 'horizontal' and 'diagonal'. It should encourage useful discussion between those working together.

Possible approach

You could start by showing the group the problem as it is given, show a bit of the interactivity and then challenge them to continue.

Alternatively, you could show them this snippet from YouTube as a start. [You may prefer to show this faster version from YouTube.] Then show the group the simplified knot used in this problem and then go on from there.

Here is a copy of the design.

Learners can then continue in pairs either using the interactivity or these cards. Four copies of the first sheet will be needed to make a complete set of the cards. The design is more easily and satisfactorily built up on a $24$ cm square divided into a six by six grid. This will just fit on a sheet of A3 paper. There is also a second page of the download with two copies of the design itself.

At the end of the session bring the group together again and discuss their findings. Ask what they found easiest to do and most difficult in building up the knot. How many different strands are there in this particular Celtic knot? If they have not already seen it, the piece from YouTube might make an interesting ending to the lesson.
Some learners may like to read about Celtic knots. This article or this in Wikipedia may be found useful and interesting.

Key questions

Which pieces do you think go where?
Are you remembering that the line turns at the edges?
What do you notice about the way that the lines pass each other?

Possible extension

Learners could be challenged to make an $8$ by $8$ Celtic Knot on squared paper. Or, alternatively, attempt some of the designs shown in this article. Some may also like to try Drawing Celtic Knots.

Possible support

Suggest finding the four corner pieces and putting them in place. The pieces with curves then go next. Follow the design from this sheet.