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The content for this section is sub-divided
into the following areas:
Angles
Top
| Content |
Resources |
| distinguish
between lines and line segments |
|
|
understand and use SSS,
SAS, ASA and RHS
conditions to prove the congruence of
triangles using formal arguments, and to verify standard ruler and compass
constructions
|
|
| recall and
use properties of angles at a point,
angles on a straight line (including right
angles), perpendicular lines, and opposite
angles at a vertex |
O
N
N
N angle facts
W
W W
angle facts
|
| distinguish between acute, obtuse, reflex
and
right angles estimate
the size of an angle in degrees |
|
Properties of triangles and other rectilinear shapes
Top
W
shape search
| Content |
Resources |
| use
parallel lines, alternate angles and corresponding
angles |
|
| understand the properties of parallelograms and a proof that the
angle sum of a triangle is
180 degrees |
|
| understand a proof that the
exterior angle of a triangle
is equal to the sum of the interior
angles at the other two vertices |
|
| use angle properties of equilateral,
isosceles
and right-angled triangles |
W
angle facts |
| understand congruence |
W
congruent shapes |
| explain why the angle sum of any
quadrilateral
is 360 degrees |
|
|
use their knowledge of rectangles, parallelograms
and triangles to deduce formulae
for the area of a parallelogram, and
a triangle, from the formula for the area
of a rectangle
|
|
| recall the essential properties of special
types
of quadrilateral, including square, rectangle,
parallelogram, trapezium and rhombus |
A
quadrilaterals
W
shapes
O
parallelogram or trapezium
|
| classify quadrilaterals by their geometric
properties |
A
quadrilaterals
H
shapes
|
| calculate and use the sums of the interior
and
exterior angles of quadrilaterals, pentagons
and hexagons |
|
| calculate and use the angles of regular
polygons |
W
polygons |
| understand,
recall and use Pythagoras’ theorem
in 2-D, then 3-D
problems |
N W
H Pythagoras' theorem |
| understand similarity of triangles and
of other plane figures, and use this to make
geometric inferences |
W
W similar shapes
|
|
understand, recall and use trigonometrical
relationships in right-angled triangles, and use these to solve problems, including those involving
bearings
then use
these relationships in 3-D
contexts, including finding the angles between a line
and a plane (but not the
angle between two planes
or between two skew lines)
|
N
N W
trigonometry
|
| calculate the area of a triangle using
˝ ab sin C |
|
| draw, sketch and describe the
graphs of trigonometric
functions for angles of any
size, including
transformations involving
scalings in either or both the x and y directions |
|
| use the sine and cosine rules to solve
2-D
and 3-D problems |
|
Properties of circles
Top
| Content |
Resources |
| recall the
definition of a circle and the meaning
of related terms, including centre, radius,
chord, diameter, circumference, tangent
and arc, sector
and segment
|
N
words and formulae |
|
understand that the tangent at any point on a circle is perpendicular to
the radius
at that point
|
|
| understand and use the fact that tangents from an external point are
equal in
length |
|
| explain why the perpendicular from the centre
to a chord bisects the chord |
|
| understand that inscribed regular polygons can
be constructed by equal division of a circle
|
|
|
prove and
use the
facts that the angle subtended by
an arc at the centre of a circle is twice
the angle subtended at any point on
the circumference, the
angle subtended at the
circumference by a semi-circle
is a right angle, that
angles in the same segment are
equal and that opposite angles
of a cyclic quadrilateral sum
to 180 degrees
|
|
| prove and use the alternate segment theorem |
|
3-D shapes
Top
| Content |
Resources |
| explore the
geometry of cuboids (including
cubes), and shapes made from cuboids
|
|
| use 2-D representations of 3-D shapes and analyse
3-D shapes through 2-D projections
and cross-sections, including plan
and elevation.
|
W
solids and nets
O
O B
isometric grids
|
| solve problems involving surface areas
and volumes of prisms, cylinders, pyramids, cones
and spheres |
W
cylinders |
| solve problems involving more complex shapes and solids,
including segments of circles
and frustums of cones. |
|
Specifying transformations
Top
| Content |
Resources |
| understand
that rotations are specified by a centre
and an (anticlockwise) angle
|
|
| use any
point as the centre of rotation |
W
rotations |
| rotate a shape about the origin |
|
| measure the angle of rotation using right angles
and simple fractions of a turn |
|
| understand that reflections are specified by a
mirror line, using a line parallel to an axis |
|
| understand that translations are specified by
a distance and direction (or vector), and |
|
| enlargements by a centre and positive scale
factor |
|
Properties of transformations
Top
| Content |
Resources |
| recognise and
visualise rotations, reflections
and translations, including reflection
symmetry of 2-D and 3-D shapes,
and rotation symmetry of 2-D shapes
|
O
examples
B
blank co-ordinate grids
H
T
transformations
W
rotations and reflections
W
translations |
|
transform triangles and other 2-D shapes by
translation, rotation, reflection and combinations of
these transformations, recognising
that these transformations preserve
length and angle, so that any figure
is congruent to its image under any of
these transformations
|
W
rotations
|
| solve problems involving more complex shapes and solids,
including segments of circles
and frustums of cones. |
|
| distinguish properties that are preserved under particular
transformations |
|
| recognise, visualise and construct enlargements
of objects using positive scale
factors greater than one |
|
| understand from this that any two
circles and any two squares
are mathematically similar,
while, in general, two rectangles are
not |
|
| use
positive fractional scale factors |
W
enlargements |
| recognise that enlargements preserve angle
but not length |
|
| identify the scale factor of an
enlargement as the ratio of
the lengths of any two corresponding
line segments and apply this
to triangles |
|
| understand the implications of enlargement
for perimeter |
|
| understand and use the effect of enlargement on areas and volumes of
shapes
and solids |
|
| use
and interpret maps and scale drawings
|
|
| understand the difference between formulae for perimeter,
area and volume
by considering dimensions |
|
Coordinates
Top
| Content |
Resources |
| understand
that one coordinate identifies a point
on a number line, two coordinates identify
a point in a plane and three coordinates
identify a point in space, using the
terms ‘1-D’, ‘2-D’ and ‘3-D’
|
W
3-D co-ordinates |
| use axes and coordinates to specify points in
all four quadrants |
O
W W
co-ordinate grids
W
co-ordinate fred
W
co-ordinate pictures
W
orc co-ordinates
|
| locate points with given coordinates |
|
| find the coordinates of points identified by geometrical
information
|
|
| calculate
the length AB, given the coordinates of A and B |
|
Vectors
Top
| Content |
Resources |
| understand
and use vector notation
|
|
| calculate, and
represent graphically the sum
of two vectors, the difference of two vectors and a scalar multiple
of a vector |
|
|
calculate the resultant of two vectors
|
|
| understand and use the commutative
and associative properties of
vector addition |
|
| solve simple geometrical problems in 2-D using vector methods. |
W
vector problems |
Measures
Top
| Content |
Resources |
| know
that measurements using real numbers
depend on the choice of unit
|
|
| recognise
that measurements given to the
nearest whole unit may be inaccurate
by up to one half in either direction |
W
measure is approximate |
| interpret
scales on a range of measuring instruments,
including those for time and mass
|
|
| convert measurements from one unit
to another |
N
metric units
W
decimals
|
| know rough metric equivalents of pounds, feet,
miles, pints and gallons |
A
Who wants to be a milionaire
N
W
W metric and
imperial units
|
| make sensible estimates of a range of measures
in everyday settings |
|
| understand angle measure using the associated
language |
|
|
use bearings to specify direction
|
W
bearings |
| understand and use speed |
|
Construction
Top
| Content |
Resources |
| measure and
draw lines to the nearest millimetre,
and angles to the nearest degree
|
|
| draw triangles and other 2-D shapes using a
ruler and protractor, given information about
their side lengths and angles |
O
accurate drawing |
| understand, from their experience of constructing
them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA
triangles are not |
|
| construct cubes, regular
tetrahedra, square-based
pyramids and other 3-D shapes
from given information |
|
| use straight edge and compasses to do standard
constructions, including an equilateral
triangle with a given side,
|
|
| the midpoint and perpendicular bisector of
a line segment, the perpendicular from a
point to a line, the
perpendicular from a point on
a line, and
the bisector of an angle |
W
loci |
Mensuration
Top
| Content |
Resources |
| find areas of
rectangles, recalling the formula,
understanding the connection to counting
squares and how it extends this approach
|
W
W
W
Area and perimeter
A
who wants to be a millionaire
|
| recall and use the formulae for the area of a
parallelogram and a triangle |
O
parallelogram and trapezium |
| find the surface area of simple shapes using
the area formulae for triangles and rectangles |
|
| calculate perimeters and areas of shapes made
from triangles and rectangles |
O
W
W
W W
W Area and perimeter
W
Area, perimeter, angles puzzle
A
who wants to be a millionaire
|
|
find volumes of cuboids, recalling the formula
and understanding the connection to
counting cubes and how it extends this approach
|
|
| calculate volumes of right prisms and of
shapes made from cubes
and cuboids |
H
prisms
W
cylinders
|
| find circumferences of circles and areas enclosed
by circles, recalling relevant formulae |
W
circles
W
circles - shaded area
T
circles test
|
| convert between area measures, including square
centimetres and square metres, and volume
measures, including cubic centimetres
and cubic metres.
|
|
| calculate the lengths of arcs and the areas of
sectors of circles |
|
Loci
Top
| Content |
Resources |
| find
loci, both
by reasoning and by using
ICT to produce shapes and paths |
|
|