Level 5: Prisms, cylinders and units

Measurement · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 4 you filled boxes with cubes. In this level one idea, "area of the base times the height", gives the volume of every prism and every cylinder, from a tent to a water tank, and unfolding solids into flat nets gives their surface area. Then you learn why converting square and cubic units needs the factor squared or cubed, and how to move safely between the metric units and the imperial units Canadians still meet every day.

Lesson	You will be able to
Volume of prisms	Explain with stacked layers why any prism's volume is base area × height, and find the volume of triangular, trapezoidal and leaning prisms
Volume of cylinders	Find the volume of a can or tank with \(\pi r^2 h\), convert to litres, and explain why doubling the radius gives four times as much
Surface area of prisms	Draw a net, find the surface area of boxes and triangular prisms, and work out paint and wrapping paper
Surface area of cylinders	Unroll a label into a \(2\pi r\) by \(h\) rectangle, and find the surface of cans, cups, pipes and tanks
Converting area and volume units	Convert m² to cm², m³ to cm³ and litres, and land to hectares, and explain why the factor is squared or cubed
Imperial units in Canada	Convert inches, feet, miles, pounds, cups and °F to metric using 1 in = 2.54 cm, with units that cancel

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