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Students learn how to calculate the total surface area and volume of cuboids, prisms and convergent shapes. Throughout the topic students develop their algebraic notation, and application of Pythagoras’ Theorem to aid their problem solving skills. This topic takes place in Year 11 Term 2 for Foundation students and Year 10 Term 5 at higher level.

**Prerequisite Knowledge**

- use standard units of measure and related concepts (length, area, volume/capacity
- know and apply formulae to calculate: area of triangles, parallelograms, trapezia;
- know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes

**Success Criteria**

- know and apply formulae to calculate the volume of cuboids and other right prisms (including cylinders)
- know the formulae to calculate the surface area and volume of spheres, pyramids, cones and composite solids

**Key Concepts**

- To calculate the volume of a prism identify the cross-section and calculate its area. The volume is a product this area and its depth.
- When calculating surface areas encourage students to illustrate their working by either writing the area on the faces of the 3D representation or create the net diagram so all individual faces can be seen.
- While students are not necessarily required to derive the formulae for the volume and surface area of complex shapes they do need to be proficient with substituting in known values.

**Common Misconceptions**

- Students often forget to include units when calculating volumes and areas.
- It is important to differentiate between those which are prisms and those which are not. Encourage students to identify the cross-section whenever possible.

June 5, 2019

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values. Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]