Circles, frustums and cylinders revision/Document

Lesson Ideas & Pedagogic Rationale

This resource offer students the opportunity to measure and calculate with large size cylinders and frustum. The challenge for students is to work with ‘real life’ numbers where scale factors are not rounded, and where sectors have unconventional angle sizes such as 187 degrees. Teachers have the opportunity to assess students’ work using questioning. It is also a fantastic opportunity to assess students’ ability to communicate the maths to peers. The pedagogical purposes are to revise all circle material, and to introduce the challenge of working with less conventional measures and numbers.

Pedagogical techniques

This lesson brings great opportunity for small group dialogical teaching. Open-ended and closed questioning opportunities can be used to recall existing knowledge and extend students’ understanding. The ground rules for talk is simple: students should be encouraged to discuss and share their ideas with their group as they work and tackle a task.

This lesson supports students’ learning by getting them to recall complex formulae and procedures. It supports multiple kinds of learning, in particular: collaborative, enquiry-based, revision, exploration, hands-on experience, consolidation, extension to new more challenging problems, communication and reasoning skills. Pitfalls: it is very important to establish the appropriate behaviour expectations from students. Teachers must emphasise that students are allowed to talk about the maths, and only about the maths. If using expensive and fragile kit such as samba drums, students should be encouraged in advance to handle equipment with care.

Teachers Notes

Background:

This lesson is aimed at year 11 GCSE students in top sets who understand the definition of prisms, and have 'had a go at' calculating volumes and surface areas of prisms. The questions are deliberately challenging and some have a few calculation stages. At the beginning of the lesson each group of students should be assigned a drum. They are then required to complete the set of questions associated with that drum, before starting to work on another drum (Something like circle training). It is a good idea to have a few spare drums for those who are quick to complete their task and are keen to move on.

Recommendation:

Students should be working in groups of up to 4 although I found working in groups of 3 is ideal. It is recommended to remind students ahead of the lesson to bring their calculators to the lesson, as completing the tasks without one can take an unreasonable amount of time.

Lesson Preparation:

• Photocopy attached worksheet – one copy per student.
  
• It would be hard to use the resource in a conventional size classroom, as the drums and large objects do take a lot of space. Students need to be able to walk around objects and measure comfortably. Book a large classroom space or a hall, in which students can move freely. I ran this lesson successfully in a quiet area of the school field.

The challenges:

• Students do find it hard to measure a large acute angle on the caxia drum. They cannot really use the protractors from their pencil cases. Ask them how they would go about measuring the angle.

• Students find it confusing to communicate about or work with a scale factor which has many decimal figures. Seize the moment to present them with the question as to when it is reasonable to round numbers.

• Challenge the students to give their answers in centimetres or meters for both volume and surface area questions.

• Ask students if their answers make sense, and if they can justify them.