Encourage students to attempt the Extension Problem.Have them to write up their work, making sure that they have carefully explained their arguments. Share and discuss the students’ answers.If a number of students are struggling, a brainstorming session may help.Check on group progress as they work. Encourage them to set up equations and reduce the number of dependent variables to one.To use a table they will have to find some equations.
Make string available to those who want to model the situation. Let the class investigate the problem in any way that they want.Have them consider how they might approach it. If he makes a rectangular run, how big an area can he enclose? He has 20 metres of wire to put round the run. The farmer is putting a new chicken run up against a brick wall. These problems explore maximum and minimum perimeters for a given area. The second set includes: Karen’s Tiles, Measurement, Level 5 and Karen’s Second Tiles, Algebra, Level 6. These show the non-link between rectangles’ areas and perimeters, including showing that among all quadrilaterals with a fixed perimeter, the square has the largest area. The final problemexplores the areas of regular polygons with a fixed perimeter and shows that they are ‘bounded above’ by the circle with the same perimeter. The first set includes: Peters’ String, Measurement, Level 4, Peters’ Second String, Measurement, Level 5, Peters’ Third Stringand Polygonal String ProblemAlgebra, Level 6. There are seven problems related to perimeter and area. Though some problems have a set procedure or a formula that can be used to solve them, the most worthwhile problems require the use of known mathematics in a novel way. Thinking and creating are at the heart of the subject. Mathematics is more than doing calculations or following routine instructions.
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