Introduction

Rationale

Stage 5.2 Volume is one of the sub-strand units of the overarching topic of Measurement and Geometry in the NSW syllabus. The study of Volume develops students' ability to visualise and solve life-related problems of three-dimensional objects. We live in a spatial-dimensions where we can move up/down, left/right and forward/backward so it is important that students can see the fundamental importance of volume in their lives.

Examples of Volume in everyday activities:

Building or gardening projects:
- calculating the number of cubic metres of concrete, soil, sand, gravel, mulch that need to be removed for the installation of a swimming pool (NESA, n.d.)
Swimming pools or water tanks
- calculate the appropriate size in litres of water tanks and swimming pools (NESA, n.d.)
Fueling Up
- Determine the volume of gasoline needed to fill up the tank (Welch, March 14)
Cooking and Baking
- The number of measurements using table spoons or cups are linked to Volume (Welch, March 14)

Syllabus Outcomes

A student:

Selects appropriate notations and conventions to communicate mathematical ideas and solutions (MA5.2-1WM)
Interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems (MA5.2-2WM)
Applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders (MA5.2-12MG)

Working Mathematically

Solve problems involving the volumes of right prisms (ACMMG218)

Solve a variety of practical problems related to the volumes and capacities of composite right prisms
- Compare the surface areas of prisms with the same volume (Problem Solving, Reasoning)
- Find the volumes and capacities of various everyday containers, such as water tanks or cartons used by removalists (Problem Solving)

Solve problems involving volume for a range of prisms, cylinders and composite solids (ACMMG242)

Find the volumes of composite solids involving prisms and cylinders, e.g. a cylinder on top of a rectangular prism
- Dissect composite solids into two or more simpler solids to find their volumes (Reasoning)

776 _ NSW Education Standards.pdf

Common Misconceptions

Recognising students' misconceptions will allow teachers to develop and employ strategies that minimises errors and assumptions in their teaching (Sarwadi & Shahrill, 2014, p. 8).

Common misconceptions

A student may:

Using volume formula for surface area (vice versa)
Think area and volume of a shape changes if the shape is rearranged
Treating volume as one-dimensional 'Volume = length x width' hence using the wrong unit of measurement
Counting the faces of unit cubes given in the picture and multiplying that number with 3 because a prism has three dimensions

(Sisman & Aksu, 2016, pp. 1296 -1311)

Mixing up the names e.g. cube and cuboid
Multiplied the number by 2 instead of 3 when calculating the volume of a cube

(Ozerem, 2012, p. 726)

Mixing up ML (megalitres) and mL (mililitres)
m³ is read as 'cubic metre(s)' and not 'metre(s) cubed' or 'metre(s) cube

(NESA, n.d.)

References:NSW Education Standards Authority. (n.d.). Mathematics Year 7-10 Syllabus. Retrieved from: https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10
Özerem, A. (2012). Misconceptions in geometry and suggested solutions for seventh grade students. Procedia-Social and Behavioral Sciences, 55, 720-729.
Sarwadi, H. R. H., & Shahrill, M. (2014). Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research, 2014(2014), 1-10.
Sisman, G. T., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293-1319.
Welch, T. (2014). Uses of Volume in Daily Life Retrieved from: https://sciencing.com/uses-volumes-daily-life-8692308.html

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