Math class without numbers?

You are joking right? Surely that is not possible in a high school?

In an attempt to re-engage my students with sequences and series, I invited them to create a sequence using only paper and scissors. I explicitly told them that they are not allowed to write any numbers, but can model and explain their sequence using words in everyday language.

After a few moments of staring at the pieces of paper in front of them, ideas started to emerge and the previously disengaged class was not only engaged and the most surprising, the students that I struggle with most in terms of engaging, was the most engaged! Not only were they ‘hands-busy’, cutting away, they were ‘heads-busy’, as I would often hear conversations about whether this particular piece was indeed a sequence or not. 

Here is some of the work they’ve created: 

Each time the paper is folded open, it produces the sequence 1, 2, 4, so as this student commented, that if it was a infinite piece of paper, this would have produced a geometric sequence.

Considering you are starting (with the man in the middle) each additional layer, would provide a +1, so therefore this student created an arithmetic sequence.

We had discussions that ranged from what makes a pattern a sequences, and when it is a ‘normal’ arithmetic sequence and when it is a recursive arithmetic sequence. They could correct themselves on the terminology we so easily get tripped up on, one student started “this is a series of circles, oh no! I’m not adding, the pattern repeats. This is a sequence of circles…”.  (As seen below). 

One of the students referred to different terminology - she explained “this is my pattern of triangles, but when I fold my paper and bend it down, I introduce a line of symmetry”. 

Another student, produced smaller cut-outs that they arranged and re-arranged every time to create various different sequences (both arithmetic and geometric).

The verdict: This is a fun way to either introduce or reflect on sequences in mathematics. It is not very time consuming, but involves great amounts of fun! Fantastic to get students talking about what they created without feeling the 'pressure'. Highly recommended!