Volume and surface area

Overview

During these lessons students will learn how to calculate and use volume and surface area of solids. 

Students will:

• compare and order three-dimensional objects based on the concept of volume 

• use measuring instruments to record the dimensions of three-dimensional object 

• calculate the surface area and volume of a range of solids 

• apply calculations of the surface area and volume of a solid to make practical decisions.

Outcomes:

• MA4-14MG uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume 

• 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 

• MA5.3-3WM uses deductive reasoning in presenting arguments and formal proofs 

• MA5.3-13MG applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids 

• MA5.3-14MG applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids

Students will:

• Collect and order objects from around their home based on volume 

• Check their order by filling any empty containers they have chosen with water, sand, rice or pasta and pouring between solids.  

• Establish approximate relationships between containers, for example between those that appear to have three times the volume of others 

• Classify chosen containers by their approximate features, defining them as a prism, pyramid, cylinder, cone or sphere.  

• Measure the dimensions of chosen containers and calculate the volume of each container to verify and modify the order they have chosen.  

Outcomes:

• MA4-14MG uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume

• 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 

• MA5.2-2WM 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 

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

• MA5.3-3WM uses deductive reasoning in presenting arguments and formal proofs

• MA5.3-14MG applies formulas to find the volumes of right pyramids, right cones, spheres and related composite solids

Students will:

• investigate nets of a variety of solids

• practice drawing nets

• calculate the surface area of solids.

Outcomes:

• 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

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

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

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

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

• MA5.3-3WM uses deductive reasoning in presenting arguments and formal proofs

• MA5.3-13MG applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids 

Students will:

• apply their knowledge of solid surface area and volume to design a dog kennel

• apply their knowledge of solid surface area and volume to calculate the cost of the materials needed to build a dog kennel

• apply their knowledge of solid surface area to calculate the cost of the paint needed to complete a dog kennel.

Outcomes:

• 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 

• MA5.2-2WM 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

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

• MA5.3-3WM uses deductive reasoning in presenting arguments and formal proofs 

• MA5.3-13MG applies formulas to find the surface areas of right pyramids, right cones, spheres and related composite solids 

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