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

FSMQ Level 2 Shape and Space scheme of work

Before starting this Higher (Level 2) FSMQ students should be able to:

  • measure lengths in and understand common metric and imperial units (millimetres, centimetres, metres, inches, feet)
  • be able to use a protractor to measure angles
  • understand basic ideas of area and volume including use of correct units such as cm2 and cm3
  • be able to interpret drawings including the use of basic plans and elevations drawn to scale.

A suggested work scheme showing topic areas and methods to be covered is given below. This recommends a total of 60 guided learning hours that could be used in a variety of ways, such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, or 5 hours per week for 12 weeks. Although the topic areas are listed separately below, it would be beneficial at times to use a variety of skills within a piece of work. For example the Nuffield resource ‘Costing the Job’ involves taking measurements from scaled drawings as well as finding areas and working out the cost of painting a house.

Some terms and techniques should be introduced as soon as possible and used throughout the course. These include:

  • geometrical terms: parallel, perpendicular, bisect, perpendicular bisector, mid-point, horizontal, vertical, line segment, line, similarity, congruence, regular, irregular, polygons (triangles including obtuse-angled, acute-angled, right-angled, equilateral, isosceles and scalene, quadrilaterals including rectangle, square, parallelogram, rhombus, trapezium and kite, pentagon, hexagon, octagon), circle (including circumference, arc and sector), cuboids, prisms (including triangular), cylinders, spheres and hemispheres, cones.
  • using appropriate instruments (including ruler, tape measure, protractor) to take measurements to appropriate levels of accuracy with appropriate units and correct notation
  • using a calculator effectively and efficiently (including memory facilities) - includes finding percentages and fractions
  • checking calculations using estimation, inverse operations and alternative methods.

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.    

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 been updated. These are included for possible use as classroom activities but will not form part of the assessment of this FSMQ.

Topic area

Content

Nuffield resources The links below go to pages from which you can download the resources, some recently revised.

Plans and elevations
(2 hours)

 

Identify and sketch objects from plans and elevations.

Sketch plans and elevations of objects.

Include sufficient dimensional information to allow drawings to be correctly interpreted.

Points of view   
Introduces the representation of objects by plans and elevations.  Includes use of dotted lines for hidden edges.

Measure lengths and calculate using scales
(5 hours)

Measure lengths using appropriate tools and degrees of accuracy.
Calculate lengths from scale drawings using scales given in the forms a:b, a to b, a/b for all a and b (and forms related to students’ other work).

Use scale drawings to solve problems, deciding on the correct arithmetic to use (including addition, subtraction, multiplication, division of lengths).

Paper sizes (AMP)
Learners consider the relationships between paper sizes within one range and the relationships between ranges (A and B series of international paper sizes).

Plans 
Choose from seven plans with scales of varying difficulty.

Ratios   
Activities giving learners practice in simplifying ratios.

Draw scale diagrams
(8 hours)

Draw plans and elevations of 3-dimensional situations using scales such as 2:5, 1:150, 10:1, 2 to 5, 1/3 (such as plans of rooms or elevations of front of buildings). Use dashed lines to show hidden detail and shading for cross-sections.  Include the use of a ruler and set-square to draw parallel and perpendicular lines where appropriate.

Emergency shelter (AMP)
Design a shelter to protect three people from the wind and rain.

 

Topic area

Content

Nuffield resources The links below go to pages from which you can download the resources, some recently revised.

Convert measurements
(4 hours)

Convert within and between metric and imperial systems, including inches, feet, yards, miles.  Include the use of conversion factors and formulae

(such as L = 3.28l for converting metres to feet).

Solve problems by carrying out calculations with measurements.

Convert lengths  
Bingo and dominoes games providing practice in length conversions.

Convert it!   
Interactive spreadsheet for practice in converting metric lengths and distances.

Plane shapes
(6 hours)

Recognise and classify plane shapes.

Irregular and regular polygons with special cases (e.g. rectangles, squares, parallelograms, trapezia, rhombi, kites as special quadrilaterals).

Know and use internal and external angle sums of triangles, quadrilaterals and other polygons.  Solve problems involving angle calculations.

Understand and use ideas of tessellation.

 

Drawing Shapes in Word  
Shows students some of the basic drawing techniques available in Word.

Make your own shapes in Word 
Activity showing students how to draw their own shapes in Word, with and without gridlines.

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.

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.

Shape sorter  
Design a shape sorter, using scale drawings, plans, elevations and geometrical terms.

Constructions
(4 hours)

Use a ruler and compasses only 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 
· the bisector of an angle 
· a regular hexagon inscribed in a circle 
· an equilateral triangle inscribed in a circle

Use ruler, compasses and protractor  to construct:
· triangles from information such as 2 base angles and the length of the base or from 3 lengths

 

Pentagon construction  
Instructions for constructing a regular pentagon.

 

Topic area

Content

Nuffield resources The links below go to pages from which you can download the resources, some recently revised.

Perimeters, areas, surface areas and volumes
(7 hours)

 

Calculate (in both metric and imperial units), using formulae in words and symbols and the \pi button on a calculator or the approximate value 3.14 (to 2 decimal places):

· circumference of circle from C = \pi \times d = 2 \pi r

· arc length for fractions of a circle

· area of circle from A = \pi r^2

· area of sector of a circle

· perimeters and areas of rectangles, triangles, parallelograms, trapezia and composite shapes

· surface areas and volumes of cuboids, prisms (including triangular), cylinders, spheres, hemispheres, cones and composite shapes (not frustums)

Recognise that a measurement expressed to a given unit has a maximum error of half a unit and calculate upper and lower bounds to problems involving addition, subtraction and multiplication of lengths.

Use formulae together with known values to find one unknown length.

How much will it cost
Taking measurements from scaled elevations of a house, then finding area and cost of painting (also used for level 1)

Costing the job 
Students take measurements from scaled elevations of a house to find the wall area to be painted and then work out the cost.

Volume 
Students find the volume of a variety of cuboids in real life contexts.

Errors 
Slide presentation showing errors in measurements and how errors accumulate in calculations involving measurements.  Accompanying notes and worksheets.

Design a table (AMP)  
Students use given body measurements to design a table for five people which can be extended for use by eight/ten people.

Symmetry and transformations
(8 hours)

Recognise, visualise, specify and transform shapes by means of:
· enlargement using positive, negative and fractional scale factors and a centre of enlargement
· reflection
· rotation using a centre of rotation and positive (anticlockwise) and negative (clockwise) angles
· combinations of these.

Recognise and classify reflection and rotational symmetry in both 2D and 3D, using lines and planes of symmetry and defining the order and centre of rotation.

Understand ideas of similarity in terms of enlargement and scale factors. 

For two similar shapes, use ratio to find the lengths of unknown sides.

Calculate for a given length scale factor (including fractional scale factors), the effect on area and volume and vice versa.

 

Crop circle geometry 
After sketching and describing crop circles found on websites, students construct a geometrical design, describe symmetries and transformations then produce their own designs.

Suncatchers  
Stained glass suncatchers for students to describe and design.

Symmetry (AMP)  
Learners make different symmetrical shapes, using one or more of three given shapes.

 

Victorian tiles  
Students look for geometrical shapes and symmetry in encaustic tile patterns then design a tessellation using geometrical shapes themselves.

Symmetry in Word  
Students use the Rotate and Flip options in Word to draw figures with line and rotational symmetry.

Pythagoras' Theorem
(4 hours)

Solve problems in two dimensions using c2 = a2 + b2 to calculate unknown lengths.

Pythagoras  
Slide presentation, notes and worksheet. 
Links to useful websites.

 

Topic area

Content

Nuffield resources The links below go to pages from which you can download the resources, some recently revised.

Design and/or make models 
(4 hours)

Construct models from information given on diagrams or sketches.
Design and build own models.

(Omit this section if short of time.)

Money bags (AMP)  
Learners design a wallet, purse or credit card holder, and explain the reasons for their design.

 

Revision
(8 hours)

Revise topics and try past papers.

Discuss data sheet – make up and try questions based on it.

 

 

 

Page last updated on 22 March 2012