Lesson 14 Tents

# Episode 1

Reasoning Resources: Worksheet 1
Whole class preparation
A real-life context is often a necessary start for most pupils to hang mathematical concepts on.

The challenge is sorting out what ensures a semicircle.

The teacher as a mediator circulates around groups listening to discussion and prompting more critical thinking by appropriate questioning.

Tell the class this story to set up the context. After leaving school, Joe decided to make cheap tents for pupils joining national camping competitions. His tents are made by stretching fabric over a frame of flexible rods. The rods form a semicircle. He has won an award for his simple design.

The smallest tent that he sells allows two people to sleep side by side. He has worked out that each person needs about 7 metre across the tent to be comfortable. All tents are the same length, 2 metres. Ask: What is a semicircle?

Record all ideas without indicating the ‘right answer’ These initial ideas set up the class for the pairs/small group work.
Pair and small group work
Before he decided on the semicircular design he sketched a number of other shapes for the tent. Worksheet 1 shows his ideas.

Give out Worksheet 1.The pupils work in pairs to agree a statement about each shape. From this they decide how we can be sure what a semicircle is.

Ask pairs of pupils to compare their answers with another pair to come up with ready sentences.
Whole class sharing and discussion
Progressive focusing on the three elements: radius, diameter and the semicircle as half of a circumference.

The tension in the sharing phase is between celebrating engagement by all pupils, and the need to move up the cognitive challenge.
Invite groups of four to report back on which shapes are semicircles, Record all the ideas and note any disagreements. Ask pupils to resolve disagreements if possible. Possible responses:

• 'Same length/distance from centre of the bottom line to the curve'
• ‘The height is the radius'
• ‘If we reflect the semicircle about the base we get a circle with no bumps in the circumference.’

Ask the question: How can we be sure that a shape is a semicircle? to focus responses toward a useful set of characteristics. These can be in pupil-speak at this stage, but the idea of radius and a centre from which the radius traces out the arc of the semicircle is needed for Episode 2.