Welcome teachers!

While the Box is designed to be student-led, we have some advice based on our own experience of running this activity with many groups of people over the years, as well as some tips from other teachers who have used the Box.

• Talk about the concept of topology and the Möbius Strip before beginning the craft activity (and before handing out the craft materials). In particular, emphasise the key terms such as side and edge. A key concept is orientability, and we encourage you to get your own head around this using pages 14-15 of the Teacher Zine. Once students start exploring their creations, it can be hard to re-capture their attention. The Zine features a beautiful and accessible introduction to topology and the Möbius Strip on pages 6-17.

• Pose some questions about topology and prompt students to make hypotheses (predictions) before they start each craft process, and discuss reasons for their ideas. There are plenty of reflection exercises throughout the Zine to keep students thinking during and after the craft activity.

• Work through a few (say 2–4) experiments per lesson. Students could work in small groups, pairs, or as individuals. Students working in pairs or groups should still do each experiment themselves. Much of the learning in this task comes from making and physically manipulating mathematical objects.

• It will be up to you whether you try to bring the groups back together for classroom discussions before moving on to the next experiment, which will keep the class moving forward together, or let them progress at their own pace. Both methods are good - you will know what will be best for your students in this regard!

We designed the Box to be flexible for use in classes of different sizes. The craft activity is well-suited to group work, and in fact we recommend that within a class, small groups share a Zine and work together to discuss their thoughts. When supporting groups, emphasise the value of making hypotheses about what will happen and discussing reasons for these. It is of most benefit that each student still do each experiment themselves, within their group. Students will make the most of this learning opportunity if they do the physical experiments, read the Zine in full, and pause to reflect and make predictions when prompted by the Zine. Failed hypotheses can be particularly enlightening, so encourage students whose hypotheses were wrong. Errors are often useful ways to deepen understanding and aid progress. Students who are used to getting things right every time may struggle the most with this idea!

We would love to hear of your experiences using the Box with classes of different sizes, so please email us at box@mathscraftnz.org.

Although not common, there are a few reasons why students may not want to try the activity. Here are some issues that we have encountered and suggestions on how to address them:

• "I'm no good at craft." This activity is designed to be entry-level and accessible to all! Often students find that they are better than they thought and/or rapidly improve after a bit of practice. There are plenty of paper strips to try again!

• "It's not the maths I'm used to." Sometimes students who are already doing well in mathematics can find this new approach daunting. Reassuring them that it is "real" and "serious" mathematics can help to alleviate their concerns. We use this same activity with some deeper theory in our final year university mathematics course, so it is definitely real mathematics!

• "Why is this maths?" We are so conditioned to see mathematics as equations or word problems that it can be hard to see maths in new contexts. But maths is everywhere! Being able to think mathematically means learning to appreciate this. This is where the Zine can help. The Zine guides students through an introduction to topology and then a set of exercises to help them engage mathematically with their creations. There are also extension activities for those students who want to go deeper.