Lesson 14 Tents

# Tents

Overview Resources
An activity approaches the ratio indirectly through exploring the relationship between the radius and half the circumference of a circle. This starts with strings and/or flexible strips rather than formal measurement. The issue of accuracy possible for arises naturally and allows consideration of its representation in calculators and computers, and irrational numbers. Worksheet 1

Lengths of string or stiff but flexible materials for ‘measuring’ lengths. Rulers or measuring tapes

Worksheet 2 (Optional).Large paper circle (Optional). Compasses (Optional).Prepared semicircles (Optional)

Board compass. Calculators
• Construct the idea of a constant ratio between the radius and the length of its semicircular arc,
• Recognise that all measurements are approximate,
• Recognise that some numeric values can be more accurate than others but remain not exact.
• Pi ratio,
• Meaning of measurement with different levels of accuracy,
• Geometric reasoning.
• EPISODE 1
The tent in a semicircle
Many pupils’ difficulties with the circle result from premature formalisation. The symbol z of the circle ratio is sometimes ‘given’ to the pupils and used in an algorithmic manner when they haven't sufficient grounding in experience of the linear relationship it describes.

A real-life context of simple tents made of fabric stretched around a semicircular frame focuses pupils’ attention on the mathematical properties of a semicircle. The pupils identify what is and is not a semicircle, and hence define a semicircle and identify the radius and the half-circumference curve as the main variables.
EPISODE 2