Estimating Tree Heights For Primary School

Abstract

Measurement is one of the key areas of study in mathematics and features prominently in the Australian Curriculum: Mathematics (ACARA, 2010a) and in the Principles and Standards for School Mathematics in the US (NCTM, 2000). It is also a topic that provides examples of numeracy across the curriculum. In this set of investigations requiring students to estimate indirectly the height of a tree they are encouraged to use the “power of mathematical reasoning” and “apply their mathematical understanding creatively and efficiently” (ACARA, 2010a, p. 1). These aspects of mathematics are recognised in curricula around the world (e.g., NCTM, 2000, pp. 182, 188). Specifically, the various measurement techniques involved in the investigations encourage students to use ratio, proportional reasoning and properties of triangles to calculate something that they are unable to measure directly. In the Australian Curriculum: Mathematics, development of proportional reasoning is encouraged from Year 3 onwards, and ratio is specifically mentioned in Year 7 (ACARA, 2010a, p. 35). Similarly in the US, the NCTM (2000) asks that students in Years 6 to 8 “understand and use ratios and proportions to represent quantitative relationships” (p. 215). Making connections between different types of triangles and using their properties becomes a major focus in the Measurement and Geometry strand from Year 2 onwards (p. 19).