Golden Rectangles

This Bowland assessment task takes students back to the American ‘gold rush’ of the 19th century. Prospectors can rent an area of land. Each explorer is given four pegs and a 100m length of rope and can make a rectangle shape of whatever dimensions they choose. Students explore what is the maximum area they can make. The task is extended by asking students to explore whether two adventurers working together, making a rectangle with a perimeter of 200m, gives a larger area than both adventurers making their individual rectangles. The task is extended further by considering more than two adventurers working together. Students have to draw various rectangles with a given perimeter, find areas of rectangles, maximise the area and explain why it is advantageous for adventurers to cooperate and work together. Teacher guidance includes concepts which may be discussed with students, examples of probing questions which may be useful and assumptions that students need to make when completing the task. The assessment guidance consists of a progression table detailing how students may improve in each of the key processes. The resource concludes with a number of examples of students' work, together with comments, probing questions and feedback.