Circles 1: Definitions and Construction
From Teach
Lesson Details
- Class: 8A3 (30-31 pupils)
- 15-16 boys, 15 girls
- Date: 5th November 2009
- Time: 13.55-14.45
- Room: T3
- Lesson number: 6th in the day
- National Curriculum (or other syllabus) area: KS3 Y8 Module 14: Shape and Measure
- Target level(s) Grades: This is a relatively low ability set.
In-Class Support
- Role of in-class support by others (where applicable): Emma Bray will be in the class monitoring this, my first lesson. If required, she can help them with the worksheet(s).
Prior Knowledge of Pupils
- Pupil prior knowledge or experience:
- Symmetry of shapes
- Rotation of images
- Measure lengths in cm using a ruler
- Parallel and Perpendicular lines
- Right, acute and obtuse angles
- Measure angles using a protractor
- Sum of angles of a triangle
- Isosceles, equilateral and right-angled triangles
- Types of Quadrilateral
Pupils may have not yet been taught
- area: the space enclosed by a flat shape. (Think in terms of carpet covering a floor. And if you needed to paint a wall, the bigger the area of the wall, the more paint you would need.)
- perimeter: the perimeter of a shape is the total distance around its edges.
Learning Objectives
- Learning objectives/outcomes:
- Understand the key terms used in circle geometry.
- Use compasses to draw a circle with a prescribed radius.
- Construct complex, circle-based shapes using ruler and compasses.
Class management objectives
- Get through my first lesson without too much stress for anyone.
ECM outcome
- Ensure everyone leaves the lesson feeling they have achieved something.
Demonstrating Learning
- How will your pupils demonstrate successful learning?
- Answers to worksheet.
- Construction of circles in their exercise books
Mis-conceptions
- Possible pupil mis-conceptions
- Confusion over definitions
Resources
- Mrs Bray's geometry bag
- Whiteboard pens
- EW pen
- Plumb line
- Worksheets and answer sheets
Risk
- Risk/safety assessment:
- Improper use of compasses. (Count number handed out and write that number on the board.)
Assessment Opportunities
- Talking to the students on a one-to-one basis.
- Moving around the classroom.
- Using Questioning as part of lesson.
Relationships
- Developing good working relationships:
- Helping the pupils with their learning.
Differentiation
- Opportunities for differentiation:
- Some will have done area before. Some may have previously encountered Pi.
- Clever students: ask to do rest of Exercise 7B.
- Not-so-able students: Diameter/radius exercise.
- SEN: Give the diameter/radius exercise.
National Frameworks
- Issues related to or derived from National Strategies/Frameworks (in particular, approaches to literacy):
- Design and Technology
- Art
- Engineering
- Architecture.
Other terms they need to know
- perimeter: the perimeter of a shape is the total distance around its edges.
- area: the space enclosed by a flat shape. (Think in terms of carpet covering a floor. And if you needed to paint a wall, the bigger the area of the wall, the more paint you would need.)
Proposed Schedule and Content
Entry and Administration
Entry into Classroom
- 2 mins: Get them to line up quietly outside the classroom, then sit in the same seats that Mrs Bray used yesterday.
- "Ladies and gentlemen, can everyone wait in a line against the left-hand wall?"
- "We won't go into the classroom until everyone is quiet."
- "Can everyone please sit in the same desks that were assigned by Mrs Bray for yesterday's lesson?"
Introduction and Registration
- 10 min: Introduce myself and take the register. (Ask each of them to say one interesting thing about themselves -- about your family, your pets, what you do at the weekend etc. The rule is that no-one is allowed to comment on anyone else's interesting fact. The only person I want to hear talking is the person whose name I have called.)
- "I'm Mr Wilson. Most of you know me already as the occasional teaching assistant to Mrs Bray and Mrs Howe. I will now be taking all four of your maths lessons that you would normally have with them each week until the end of term."
- "After that, I'll be going back to Kingston University and so you may never see me again, unless they offer me a job here at the end of my course."
- "I already have a university degree in Maths, so I should know what I'm talking about. But that was 29 years ago, so I may occasionally be a little rusty. For the past 29 years, I was working for a computer company called IBM. Has anyone heard of IBM?"
- "I need to warn you that during the next few weeks, I need to practise various teaching styles. For the past two weeks, I have been trying to be tolerant and friendly. But I may well have to become tough and mean very quickly. You will have to decide for yourself which is the real me."
- "One thing I know: I do not want to spend all my time shouting. If nothing else, we will have quiet in these classes, unless you're working in groups."
- "Just for this particular registration, I'm going to use your full names, so that you can tell me if I am pronouncing your surname properly."
Syllabus and Module Introduction
- 5 mins: introduce the Syllabus for the next few weeks.
- "For the next few weeks, we'll be doing Shape, or what is now called Geometry. Can anyone spell geometry?"
- "We will be doing parts of a circle, and constructing circles using compasses."
- "We will also be constructing triangles, using ruler and compasses and protractor. Do you all have these instruments? Can you make sure you bring them with you to the next lesson?"
- "We will also be bisecting angles and constructing perpendiculars using compasses."
- "We'll be looking at simple solid shapes, and showing how to create nets on paper which you can cut out and make into some of those solids."
- "We'll also be showing how to draw plans and elevations of 3D objects."
- "And finally we'll make sure we can all convert from metric measures, such as kilometres, to imperial measures, such as miles."
- "So whether you plan to be an architect or a designer for your career, or whether you want to go to Europe and know how far you've travelled, there should be something for everyone in this module."
Circles
- "Today's topic is the circle, and the starter is intended to find out how much you already know about circles."
- "On the left hand side are six incomplete sentences. The final word is missing from each sentence, and I would like you to write in the correct word from the list of six words on the right hand side."
Starter
- 5 mins: hand out the starter.
- 5 mins: pupils attempt the starter.
- 10 mins: review their answers; make sure they know the correct terms; hand out the answer sheet. Assess the terms causing most problem, and the pupils having most difficulties.
Rest of Main Body of Lesson
Use of Circles in the Real World
- If there is time, use the PowerPoint.
Circle Construction with Compasses
- 10 mins: Hand out compasses where needed. Count them out. Write the number on the board.
- Ask how doesn't have rulers. Hand out any needed. Count them out. Write the number on the board.
- Hand out worksheet, asking them to do Example 1.
- Instruct how to use compasses. Set circle construction task, 3cm radius.
Radius / Diameter exercise
- If there is time, hand out exercise 26a.
Plenary and Dismiss
- 5 mins:
- "Do you feel you have learnt something today?"
- "How confident do you feel that you know the difference between:
- radius and diameter,
- circumference and arc,
- tangent and a chord?"
- Mastermind Quiz?
- Get compasses back.
- Get rulers back.
- No homework, but it will help your understanding if you have a go at constructing the rest of the circle-based shapes.
- In a future lesson, we will be discussing something called PI, which is mentioned on the worksheet, and is vital to calculating the circumference and area of a circle.
