KS2 Mathematics: Converting Units, Parallelograms, Circles and Nets

Measurement questions on the reasoning papers of the Key Stage 2 mathematics tests rarely ask for one fact on its own: you convert a unit, then calculate, then compare. This material brings together the Year 6 measurement and shape content of the national curriculum that these questions draw on: converting between standard units of length, mass, volume and time using up to three decimal places, converting between miles and kilometres, recognising that shapes with the same area can have different perimeters, calculating the area of parallelograms and triangles, finding the volume of cuboids, naming the parts of a circle and knowing that the diameter is twice the radius, and recognising the 3-D shapes that nets make.

The quiz has twelve questions, with every measurement given in words. You convert grams to kilograms and millilitres to litres, change hours into minutes, use the approximation that 5 miles is about 8 kilometres in both directions, find the area of a parallelogram when a slanted side is also given, find the area of a triangle, choose which rectangle with an area of 24 cm² has the smallest perimeter, count the centimetre cubes that fill a cuboid, find a diameter from a radius, name the circumference and identify the shape made by a net. The wrong options come from the usual slips, such as dividing by 100 instead of 1 000, reading 0.5 hours as 50 minutes, using the slanted side, or forgetting to halve for a triangle.

The flashcards list the conversions and formulae to know by heart: metres and kilometres, grams and kilograms, millilitres and litres, 5 miles and 8 km, the area of a parallelogram and of a triangle, the volume of a cuboid, 1 000 cm³ in a litre, the link between radius and diameter, the parts of a circle and what a net is.

The printable written work has eight problems to set out on paper: a set of metric conversions, time and distance conversions, the area and perimeter of a parallelogram, a triangle and a parallelogram with the same area, rectangles with the same area but different perimeters, the capacity of a fish tank in litres, circles packed in a rectangle, and the net of a cube together with the faces, edges and vertices of a pyramid.

In the oral exam an examiner asks one measurement question at a time and asks you to explain each conversion or formula you use.

The material is written for Year 6 pupils getting ready for the end of Key Stage 2 tests. Circle area and the number pi are not part of Key Stage 2, so they do not appear here: the circle work is about naming parts and the radius and diameter.

• Convert between units of length, mass, capacity and time, using up to three decimal places
• Convert between miles and kilometres using 5 miles is about 8 km
• Calculate the area of parallelograms and triangles from the base and perpendicular height
• Recognise that shapes with the same area can have different perimeters
• Calculate the volume of cuboids and link cubic centimetres to litres
• Name the parts of a circle, use diameter = 2 × radius, and recognise 3-D shapes from their nets

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): measurement (converting units, miles and kilometres, area of parallelograms and triangles, volume) and geometry, properties of shapes (parts of circles, nets).