Making connections to other topics within Key Stage 3
Pupils will need to be conversant with a whole range of number topics to support their learning and development within this area. In particular they will need to be secure in operations with integers, fractions, and decimals.
Ratio and proportion
Pupils should be encouraged to see the connections between transformations, enlargements and similar figures in both 2D and 3D and calculations applying the concepts of ratio and proportion.
Pupils should be encouraged to see the links between aspects of substitution of numerical values into formulae used within geometry.
Making connections to this topic in Year 6
In year 6 measurement pupils should be taught to:
- solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
- use, read and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation up to three decimal places
- convert between miles and kilometres
- recognise that shapes with the same areas can have different perimeters and vice versa
- recognise when it is possible to use formulae for area and volume of shapes
- calculate the area of parallelograms and triangles
- calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3].
Notes and guidance on measurement (non-statutory) suggest
- Pupils connect conversion (for example, from kilometres to miles) to a graphical representation as preparation for understanding linear/proportional graphs.
- They know approximate conversions and are able to tell if an answer is sensible.
- Using the number line, pupils use, add and subtract positive and negative integers for measures such as temperature.
- They relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this.
- Pupils could be introduced to compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.
In year 6 Geometry - properties of shapes pupils should be taught to:
- draw 2-D shapes using given dimensions and angles
- recognise, describe and build simple 3-D shapes, including making nets
- compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
- recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
Notes and guidance on Geometry - properties of shapes (non-statutory) suggest
- Pupils draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles
- Pupils describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements
- These relationships might be expressed algebraically for example, d = 2 × r; a = 180 – (b + c)
In year 6 Geometry – position and direction pupils should be taught to:
- describe positions on the full coordinate grid (all four quadrants)
- draw and translate simple shapes on the coordinate plane, and reflect them in the axes
Notes and guidance on Geometry – position and direction (non-statutory) suggest:
- Pupils draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers.
- Pupils draw and label rectangles (including squares), parallelograms and rhombuses, specified by coordinates in the four quadrants, predicting missing coordinates using the properties of shapes. These might be expressed algebraically for example, translating vertex (a, b) to (a – 2, b + 3); (a, b) and (a + d, b + d) being opposite vertices of a square of side d.
Cross-curricular and real life connections
Finding distances outside the classroom, e.g. the height of a tree or building given the distance away and the angle of elevation.
Calculation of the distance to the horizon on a ship (see the NCETM micro-site ‘Maths at Work’)
The mathematics of the race track
(You must register in the National STEM Centre website to access the “Environmental Geometry” document – free registration)
This guide delves deeper in to how the study of the environment can lead to geometrical work. The range of activities discussed in this guide extend beyond experiences with objects in the classroom which the pupil can touch or handle.