Nuffield Mathematics teaching resources are for use in secondary and further education

# Using spatial techniques

##### FSMQ Level 1 scheme of work

A suggested work scheme for this Level 1 (Foundation) AQA FSMQ is given below.  This recommends a total of 60 guided learning hours, such as 2 hours per week for 30 weeks.

4 hours per week for 15 weeks, 5 hours per week for 12 weeks).  There is plenty of scope for varying the order and time allocation as many of the mathematical techniques can be introduced/revised in several different topic areas.  The following should be introduced as soon as possible and used throughout the course:

• geometrical terms: parallel, perpendicular, right angle, bisect, mid-point, line, line segment, regular, congruent, polygons (triangles including obtuse-angled, acute-angled, equilateral, isosceles, scalene and right-angled, quadrilaterals including rectangle, square, parallelogram, rhombus, trapezium and kite, pentagon, hexagon, octagon), circle, radius, chord, cuboid, cylinder, prism (including triangular prism).

• using appropriate instruments (ruler, tape measure, micrometer, protractor) to make measurements to appropriate levels of accuracy with appropriate units and correct notation

• recording measurements on diagrams or in tables, as appropriate

• using a calculator effectively and efficiently and checking calculations using estimates, inverse operations and different methods.

Note that the assessment of this AQA FSMQ is by examination only and you should disregard any references to Coursework Portfolio requirements in the assignments which have not yet been updated. These have been included for possible use as classroom activities but will not form part of the assessment of this FSMQ.

Also note that the AMP resources in the list below were not written especially for this FSMQ and may include some topics that are not in the FSMQ specification.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Plans and elevations (3 hours) Identify and sketch objects from plans and elevations. Sketch plans and elevations of objects. What is it?   Identify everyday objects from photos, sketch objects from plans and elevations and sketch plans and elevations from 3D sketches of objects. Measure lengths (2 hours) Use ruler, tape measure, micrometer to measure objects using metric and imperial units (m, cm, mm, in, ft, yd)  · to the nearest whole unit · to an appropriate level of accuracy Record dimensions in tables and in diagrams (including plans and elevations). Measure it    Presentation to demonstrate and check that students can measure in centimetres and millimetres.  Worksheet for recording measurements. Drawing shapes in Word Shows students some of the basic drawing techniques available in Word. Paper sizes (AMP activity)   Learners consider the relationships between paper sizes within one range and the relationships between ranges (A and B series of international paper sizes). Make your own shapes in Word   Activity showing students how to draw their own shapes in Word, with and without gridlines. Measure and calculate using scales (5 hours) Carry out calculations with scaling represented in the forms 1:n, 1 to n or 1/n  where n is 2, 5, 10, 50, 100, 500, 1000 (or other appropriate scales). Understand that scaling alters lengths but not angles Plans   Choose from seven plans with scales of varying difficulty. Ratios    Activities giving learners practice in simplifying ratios. Convert measurements (3 hours) Convert within a system: metric (mm, cm, m, km), imperial (inches, feet, yards, miles) Conversion using scale factors. Convert lengths    Bingo and dominoes games providing practice in length conversions. Convert it!    Interactive spreadsheet for practice in converting metric lengths and distances.

 Topic area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Use protractor and compass and calculate with angles (4 hours) Measure and draw angles in degrees.  Draw circles accurately. Angles at a point, on a straight line, angle sum of triangle and quadrilateral. Angles   Presentation and activity measuring and classifying angles. Draw scale diagrams (5 hours) Draw plans of rooms, elevations of front of buildings and other situations/objects. Use simple scales in the form 1:n, 1 to n or 1/n  where n is 2, 5, 10, 50, 100, 500, 1000 (or other appropriate scales). Arranging the furniture   Measuring furniture, considering arrangements and drawing a scaled plan. Emergency shelter (AMP activity)   Design a shelter to protect three people from the wind and rain. Wheelchair access (assignment)    Assessing and designing work area for use by a disabled person. Calculate perimeters and areas of 2D shapes (6 hours) Use measurements of length to calculate: · Perimeters · Circumference of circle = $\pi&space;\times$ diameter · Area of circle = $\pi&space;\times$ radius2 · Area of rectangle = length $\times$width · Area of triangle = (½ base $\times$perpendicular height) (use $\pi$ button on calculator or 3.14) Shapes formed by combining two rectangles or triangles or one of each.  Use mm2, cm2, m2 etc Perimeter and area     Presentation, information sheet and worksheet covering the perimeter and area of rectangles and shapes made from rectangles. Also 24 sets of three cards for learners to match. One card gives the dimensions of a rectangle or shape made from rectangles, one gives its perimeter and one its area. How much will it cost?   Taking measurements from scaled elevations of a house, then finding area and cost of painting. Circle matching cards    Twelve sets of three cards for learners to match. One card shows a real object with its diameter, one gives its circumference and one its area. Design a table (AMP activity)   Students use given body measurements to design a table for five people which can be extended for use by eight/ten people. Calculate surface area and volume of 3D shapes (5 hours) Find surface area and volume of cuboids, triangular prisms and cylinders, using volume formula: · volume = area of cross-section $\times$ length (use $\pi$ button on calculator or 3.14) Use mm2, cm2, m2, mm3, cm3, m3 etc. Volume     Students find the volume of a variety of cuboids in real life contexts. Solve problems (5 hours) Solve problems (involving angles, lengths, areas and/or volumes) with more than one stage, deciding on the correct arithmetic to use (adding, subtracting, multiplying, dividing) Length problems Twelve problems set in a range of real contexts to solve.

 Topic Area Content Nuffield resources The links below go to pages from which you can download the resources, some recently revised. Recognise and classify plane shapes (5 hours) · triangles including obtuse-angled, acute-angled, equilateral, isosceles and right-angled, · quadrilaterals including rectangle, square, parallelogram, rhombus, trapezium and kite, · other polygons including pentagons, hexagons, octagons (understanding that regular polygons have equal sides and equal angles) Use rulers, set squares and protractors to draw shapes accurately (including rectangles, squares  and triangles). Name the shape Presentation and activity naming and classifying shapes. What am I?    24 pairs of cards for learners to match. One card gives a 2D or 3D shape and its name, the other a description. Tessellations in Word     Activity showing students how to draw tessellations in Word, with and without gridlines. Tessellation shapes   Collection of shapes to print on card and laminate. Recognise and classify symmetry  (5 hours) Lines of symmetry Rotational symmetry including centre and order. Crop circles   Sketching and describing crop circles from websites, describing symmetries then producing designs. Suncatchers   Describe then design suncatchers. Symmetry (AMP) Learners make different symmetrical shapes, using one or more of three given shapes. Symmetry in Word   Students use the Rotate and Flip options in Word to draw symmetrical figures. Constructions (5 hours) Use a ruler and compasses to construct: · a line perpendicular to a given line through a given point ·  the mid-point of a line segment · the perpendicular bisector of a line segment · a regular hexagon inscribed in a circle · an equilateral triangle inscribed in a circle · the bisector of an angle. If there is time, students could construct models from information given on diagrams or sketches and perhaps design and build their own models. Geometrical design  Describe a design then use constructions to create a design. Money bags (AMP activity) Learners design a wallet, purse or credit card holder, and explain the reasons for their design Revision (7 hours) Revise topics and try past papers. Discuss data sheet – make up and try questions based on it. Working in 2 and 3 dimensions Revision guide

Page last updated on 02 August 2017