om
.c
s
er
ap
eP
m
e
tr
.X
w
w
w
Scheme of work – Cambridge IGCSE® Mathematics (US) 0444
Unit 6: Geometrical measurement (Core)
Recommended prior knowledge
To understand definitions of length, area and volume and how to find the area by counting squares and the volume by counting cubes
To know the definitions of solids
To be able to multiply and divide by 10, 100 and 1000
To have made solids from nets
Context
This is the third geometry unit of five. This unit can be taught as a whole or be broken down into small bits and spread throughout the course. The only unit that
needs to precede this is Unit 1. Students who are following the extended syllabus will move through this faster but need to have all these skills in place before
working on the extended units. It may be useful to have 3 dimensional models both solid and skeleton framed to support the learning.
Outline
Within the suggested teaching activities ideas are listed to identify and remediate misconceptions and to pull learning through to the required standard. By the end of
this unit students should have good understanding of how to find a variety of perimeters, areas and (surface areas), volumes, of simple and compound shapes and
be able to express them in appropriate units and convert between units. The learning resources give both teaching ideas, summaries of the skills and their
sequencing and investigative problems to develop the problem solving skills and a depth of understanding of the mathematics, through exploration and discussion.
v1 2Y01
Cambridge IGCSE Mathematics (US) 0444
1
Syllabus ref
Learning objectives
CCSS:
N-RN1
6.1
Units: mm, cm, m, km
mm2, cm2, m2, ha,
km2
mm3, cm3, ml, cl, l, m3
g, kg
Suggested teaching activities
Learning resources
General guidance
This resource gives a good overview of the developmental steps within the
unit. Specific pages are referred to at the relevant point. It has a variety of
interesting problems to use.
Notes and exemplars
All units will be metric; conversion between units is expected.
Units of time as given in Unit 1.10.
www.counton.org/resources/ks3framework
/pdfs/measures.pdf
General guidance
Students need to
1. be able to multiply and divide by 10, 100 and 1000 thinking of this as
sliding left and right across the place value system not moving the
decimal point.
2. know the connection between the units and to think ‘milli’ and ‘Kilo’ as
relating to 1000 and ‘centi’ as 100.
3. be aware of the relative sizes so to know that there will be more
millimetres than cm enabling them to realise they will need to multiply
when converting cm to mm and so on
www.bbc.co.uk/schools/ks3bitesize/maths/
measures/use_of_measure/revise1.shtml
www.bbc.co.uk/schools/gcsebitesize/math
s/shapes/measuresact.shtml
www.counton.org/resources/ks3framework
/pdfs/measures.pdf
pages 228 and 230
There is often confusion about the 1000cm3 as 1 litre and 1 m3 as 106 cm3 so
ensure the area and metric units are devised from first principles.
Ensure students know which units are for length, area, volume, mass and
capacity.
Teaching activities
Once students know the definitions and connections a quick mental starter on
regular occasions can consolidate the conversions by putting a variety of
measures (of say length) as headers and values scattered in the table in their
appropriate columns. Completing the rows against the clock.
This can also reinforce standard index form if all the units have to be
expressed in that format too.
When setting problems in other sections of this unit ensure that problems are
expressed in a mixture of units requiring conversion to a single unit.
6.2
v1 2Y01
Perimeter and area of
rectangle, triangle,
and compound
Notes and exemplars
Formula will be given for area of triangle.
Cambridge IGCSE Mathematics (US) 0444
www.youtube.com/watch?v=bK53Wn4Jdp
c
2
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
shapes derived from
these
General guidance
Students need to:
http://nrich.maths.org/7534
http://nrich.maths.org/7283
http://nrich.maths.org/1841
http://nrich.maths.org/1883
http://nrich.maths.org/2293
http://nrich.maths.org/271
http://nrich.maths.org/498
Area of trapezoid and
parallelogram
6.3
CCSS:
G-C5
Circumference and
area of a circle
Arc length and area of
sector
1. Understand the difference between perimeter and area
2. Know how the areas of parallelograms, triangles and trapezoids are
linked to their formulae
3. Practice at cutting compound shapes into rectangles and triangles,
finding missing measurements and finding the areas, or completing a
rectangle around a shape and subtracting the unwanted parts
4. Link to substitution in formula (2.5) unit 2
Teaching activities
Work with problems to finding lengths given areas (or perimeters) and one of
the dimensions or in the case of the square none of the dimensions, to assess
understanding.
Notes and exemplars
Formulae will be given for circumference and area of a circle.
From sector angles in degrees and simple examples only.
General guidance
Students have difficulty with area and circumference even when they are
given the formulae as they mix squaring a number with multiplying by 2 and
do not always correctly identify whether the given information in a problem
states the diameter or the radius. Problems should be set that challenge and
identify whether students are prone to these misconceptions and remediation
put in place.
Arc length and area of sector should be linked to the proportionality model in
Unit 1 (1.4).
www.counton.org/resources/ks3framework
/pdfs/measures.pdf
pages 234 and 236
www.counton.org/resources/ks3framework
/pdfs/measures.pdf
pages 235 and 237
www.counton.org/resources/ks3framework
/pdfs/applying.pdf page 19 and bottom of
page 3
Teaching activities
Draw around a number of circular objects on cm squared paper and cut out.
Fold in half to find the diameter. Count the squares for the area and put string
around the edge and measure the string for the circumference. Record in a
table and let students notice the ratio of diameter to circumference is
approximately 3 and that the area divided by radius squared is also
approximately 3 as an introduction to pi.
Find diameters and radii, given areas and circumferences to test
understanding.
v1 2Y01
Cambridge IGCSE Mathematics (US) 0444
3
Syllabus ref
Learning objectives
Suggested teaching activities
Learning resources
Look at problems with a practical context. e.g. distance travelled by 20 wheel
turns, or the number of wheel turns required to travel a given distance.
6.4
CCSS:
G-GMD3
Surface area and
volume of prism (in
particular cuboid, and
cylinder)
Surface area and
volume of sphere
If the average head circumference is 54.47cm and a witch’s hat is made by
rolling a sector of a circle, what size circle is need for if 2, 3, or 4 hats are to
be made from the circle. Which is the best option to go for? Work out the
area of a brim 5 cm wide for all the hats.
Notes and exemplars
Formulae will be given for the curved surface area of cylinder and sphere, and
the volume of prism, cylinder and sphere.
General guidance
Students need to
1. have experienced folding nets into solids
2. link the area of nets to areas of compound shapes
3. think of wallpapering the outside of solids to find their surface areas
and to be aware of the polygon faces for each the solids
4. be able to work out the dimensions of the solid from the net of the
solid
5. be aware of the way the a definition of a prism and links to where the
slices would be cut in order to indentify the perpendicular height and
the cross section
6. to be able to make links between the definitions of letters in the
formulas and to identify the relevant lengths from diagrams
7. know which units to use for area and volume
Past Paper 33 June 2011 Q9
(syllabus 0580)
www.counton.org/resources/ks3framework
/pdfs/measures.pdf pages 239 - 241
http://nrich.maths.org/7535
http://nrich.maths.org/4919
http://nrich.maths.org/749
http://nrich.maths.org/2664
Teaching activities
1. Collect a variety of tins and work out the dimensions of a carton to
pack 40 tins (2 x 4 x 5 tins)
2. Fix a volume and the height and ask for possible dimensions for the
other two dimensions of triangular prisms, cuboids, or the radius of
the cylinder. Find the surface areas and try to maximise
3. Find the volume of icing (0.5cm thick) to cover the top and sides of a
20cm round cake 8cm high. Give the dimensions of a pack of ready
icing and the weight and ask them to work out the number of packs
needed to ice the cake. Then ask the students to create a table for
cakes of different diameters
v1 2Y01
Cambridge IGCSE Mathematics (US) 0444
4
Syllabus ref
Learning objectives
Suggested teaching activities
6.6
Use geometric
shapes, their
measures, and their
properties to describe
objects
7. Co-ordinate
geometry—Core
curriculum Notes /
Exemplars
Notes and exemplars
e.g., modelling a tree trunk or a human torso as a cylinder.
CCSS:
G-MG1
v1 2Y01
Learning resources
Teaching activities
Decide the minimum quilt size to go over people of different circumferences
and heights.
Estimate the volume of air inside buildings – based on a brick size or a door
height of 2m.
Volume of vases, jugs and then check by filling with water and pouring into
measuring jugs. (some sort of estimate from a maximum and a minimum
model as a range created by surrounding with a cylinder or cuboid or a
combinations of two of these for separate parts of the shape)
Paint tins often give an area of coverage. Research a number of different
qualities of emulsion and their coverage and work out which is the cheapest
and dearest for emulsioning the walls and ceiling of the classroom.
Cambridge IGCSE Mathematics (US) 0444
5