This jellyfish crop circle appeared in an Oxfordshire field in June 2009.

2. Some people believe that crop circles are the work of aliens, but many people have confessed to creating these elaborate designs by flattening the corn and using rope tied to a stake to ensure that their circles are perfect. This jellyfish crop circle appeared in an Oxfordshire field in June 2009.

3. If you were to mark out a crop circle, you’d need to ensure that straight lines were perfectly straight, that right angles were exactly 90º, that equilateral triangles were exactly equilateral, that squares were perfectly square, that your circles were perfect… all without being able to see what you were doing from above.

4. Crop circles usually feature a combination of equilateral triangles, squares, circles and other regular geometric shapes. How do they get them so perfect?

5. Up2d8 mathsCrop circles Teacher Notes

6. Crop circles Introduction: A huge jellyfish shape recently appeared in a field of crops in Oxfordshire – who did it and how did they do it? This Up2d8 resource uses the context of crop circles to explore geometric reasoning and construction on a grand scale. Content objectives: • use straight edge and compasses to construct triangles, given right angle, hypotenuse and side. • use ICT to explore constructions of triangles and other 2D shapes • use and interpret maps and scale drawings in the context of mathematics and other subjects. Process objectives: These will depend on the amount of freedom you allow your class with the activity. It might be worth considering how you’re going to deliver the activity and highlighting the processes that this will allow on the diagram below:

7. Activity:Students are introduced to the appearance of crop circles through the news story about the jellyfish that appeared in the Oxfordshire field. Using this context, it is possible for students to engage in a range of practical construction activities on paper, in your classroom or on your school field. It is important to stress the accuracy of each of the images in the Powerpoint. Activities based on this context might include: • students drawing an accurate version of one of the crop circle on the slides on paper • students constructing an accurate version of one of the crop circles on the slide using dynamic geometry software such as Cabri, Geometers’ Sketch Pad or Geogebra • students draw their own crop circle then work in pairs where one describes their design to their partner, who tries to draw it without seeing it • students design their own crop circle and then construct it on the school field/playground or in the sports hall, using chalk or string to create their design. Differentiation:You may decide to change the level of challenge for your group. To make the task easier you could consider: • restricting the shapes that are used to create the crop circle. Only using circles would make a crop circle relatively simple to construct while creating perfect equilateral triangles or 90° angles might be more challenging • allowing students to ‘get away with some measurements being done by eye (such as a 90° corner) rather than constructed • providing them with a simple crop circle to construct • providing notes on how to carry out some constructions, such as a 60° or 90° angle • using squared paper or graph paper • allowing the use of board compasses and large angle measurers etc. To make the task more complex, you could consider: • scaffolding less, allowing the students free reign to design the crop circle as they wish (though it might be worth reminding them that they have to construct it accurately!) • insisting that each crop circle contains at least one circle, one equilateral triangle and one square • insisting that each length and angle is accurate to a given tolerance but not providing measuring equipment (or limiting the measuring equipment allowed). This resource is designed to be adapted to your requirements. Outcomes:You may want to consider what the outcome of the task will be and share this with students according to their ability. As well as the finished crop circle, you might like to ask for a set of instructions to allow anyone to create the same crop circle. Working in groups: This activity lends itself to paired or small group work and, by encouraging students to work collaboratively, it is likely that you will allow them access to more of the key processes than if they were to work individually. You will need to think about how your class will work on this task. Will they work in pairs, threes or larger groups? If pupils are not used to working in groups in mathematics, you may wish to spend some time talking about their rules and procedures to maximise the effectiveness and engagement of pupils in group work (You may wish to look at the SNS Pedagogy and practice pack Unit 10: Guidance for Groupwork). You may wish to encourage the groups to delegate different areas of responsibility to specific group members. Assessment:You may wish to consider how you will assess the task and how you will record your assessment. This could include developing the assessment criteria with your class. You might choose to focus on the content objectives or on the process objectives. You might decide that this activity lends itself to comment only marking or to student self-assessment. If you decide that the outcome is to be a presentation or a poster, then you may find that this lends itself to peer-assessment.

8. Probing questions:Initially students could brainstorm issues to consider. You may wish to introduce some points into the discussion, which might include: • how might you make sure that a right angle is exactly 90°? • what shapes are going to be easy to construct on a large scale? • what shapes will be exceptionally difficult to construct on a large scale? • how might you make a semicircle? (this might lead to helping create a right angle) • how might Pythagoras’ Theorem help to create a large scale right angle? You will need: The PowerPoint display which you might read through with your class to set the scene at the beginning of the activity. There are just four slides: The first two slides set the scene and explain what crop circles are. The first slide shows a news story about a jellyfish that appeared in an Oxfordshire field, the second mentions a little of the mythology around crop circles. It is useful to point out the accuracy of each circle when discussing the jellyfish. The third slide focuses on the accuracy needed to produce a crop circle which could be tens of metres across. The fourth slide poses the question, ‘How did they do it?’