Further surface area and volume

This is the teacher notes page identifying the outcomes addressed in these lessons. Copy each lesson link and send it to your students. For printable versions of these materials log into the teacher information section of the Department of Education.

Introduction

During these lessons, students will develop an understanding of the relationships between perimeter and area, the similar relationship between edges, surface area and volume and how measurement, space and shape influence one another.

Students will:

• calculate the perimeter and area of a variety of shapes 

• investigate the meaning of edges and their length in a rectangular prism 

• calculate volume of rectangular prisms 

• investigate the different areas formed by rectangles with the same perimeter 

• investigate the different volumes formed by rectangular prisms with related dimensions 

• investigate the features of shapes that influence the area, and the features of solids that influence the volume 

• calculate the surface area of right prisms and compare with the volume 

• consider the function of real containers and spaces in the world and the impact of changes to their shape and dimensions.  

Outcomes:

• MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts 

• MA5.1-2WM selects and uses appropriate strategies to solve problems 

• MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context 

• MA5.1-8MG calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-11MG calculates the surface areas of right prisms, cylinders and related composite solids  

• MA5.2-12MG applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders

• MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

• MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently  

1. Maximum area

Students will:

• calculate the perimeter and area of a variety of two-dimensional figures

• construct and investigate different rectangles with the same perimeter 

• generalise that the rectangle with a given perimeter that has the largest area is always a square.

Outcomes:

• MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts 

• MA5.1-2WM selects and uses appropriate strategies to solve problems 

• MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context 

• MA5.2-1WM selects appropriate notations and conventions to communicate mathematical ideas and solutions 

• MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems 

• MA5.2-3WM constructs arguments to prove and justify results 

• MA5.2-12MG applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders

• MA5.3-1WM uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

• MA5.3-2WM generalises mathematical ideas and techniques to analyse and solve problems efficiently