Download Math - Geometry - Raffles International School

Learning Ladders
Math Geometry, Shape and Space
Step
28-30
Year
DP
27
11
Geometry, Shape & Space
Pending
Regular Track
Trigonometry
(Benchmarked against IGCSE Extended Section Topic#32)
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Cosine Rules – can find sides and angles from word problems
Area of triangle using sine ( can work out the missing side using algebra)
Solve complex trig problems set in three dimensions
Advanced Track
Trigonometry
(Benchmarked against IGCSE Additional Mathematics Trigonometry Sections Topic
10)
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Draw graphs such as y=aSin(b(x+c))+d; y=aCos(b(x+c))+d;
y=atan(b(x+c))+d where a, b, c and d are positive integers
Use identities
;
;
;
;
in more challenging situations.
Double angle identities for Sin2x and Cos2x (in more challenging
situations)
Solve simple trig equations using the above identities
Vectors
(Benchmarked against IGCSE Additional Mathematics Topic# 13 Vectors)
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26
11
Trigonometry
(Benchmarked against IGCSE Extended Section Topic#32)
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Cosine Rules – can find sides and angles only from given triangles.
Area of triangle using sine
Solve simple trig problems set in three dimensions( finding sides and
angles)
Trigonometry
(Benchmarked against IGCSE Additional Mathematics # Topic 10 Trigonometry)
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25
11
Trigonometry
(Benchmarked against IGCSE Extended Section Topic#32)
Finding Vector Equation of Straight Lines and converting to Cartesian form
and vice versa.
Understand amplitude and periodicity and be able to model given data
with trig graphs
Draw graphs such as y=aSin(b(x+c))+d; y=aCos(b(x+c))+d; where a, b, c
and d are positive integers
Use identities
;
;
;
;
in very simple situations.
Double angle identities for Sin2x and Cos2x ( in simple situations)
Solve simple trig equations using the above identities
Trigonometry
(Benchmarked against IGCSE Additional Mathematics Topic # 10 Trigonometry)
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Can convert word problem of bearings to diagrams
Work with Sine rule ( ambiguous case)
Cosine Rules - can only find the sides
Area of triangle using sine ( when all information is given)
Solve simple trig problems set in three dimensions (can find sides but not
angles)
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Know the six trig functions of angles(sine, cosine, tangent, secant,
cosecant, cotangent)
Understand amplitude and periodicity in very simple situations.
Draw graphs of sinx, cosx and tanx.
Use identities
;
;
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Solve simple trig equations using the above identities
Prove simple identities
Vectors
(Benchmarked against IGCSE Additional Mathematics Topic # 13 Vectors)
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Use vectors in the form (
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Know and use position vectors and unit vectors
Find the magnitude of a vector; add and subtract vectors and multiply
vectors by scalars
Scalar Product (Back tracked from DP)
Vector Equation of Lines (Back tracked from DP)
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24
10
Geometry- Symmetry and Mensuration
(Benchmarked against IGCSE Extended Section #31 and #28 Symmetry)
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Recognize and use rotational and line symmetry (including order of
rotational symmetry) in two dimensions and properties of triangles,
quadrilaterals and circles to arrive at conclusions.
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Volume and Surface Area of Prisms, Cylinders and Cones( compound
shapes and reverse problems)
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Solve problems involving the arc length and sector area of a circle and
reverse.
Angles
(Benchmarked against IGCSE Extended Section#29 Angle Properties)
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Work with angles in polygons
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Can apply skilfully his knowledge of angles in circles such as angles in a
semi-circle; angle between tangent and radius, angle at the centre of
circle is twice the angle at the circumference to find the necessary angles;
angles in the same segment and cyclic quadrilaterals
Trigonometry
(Benchmarked against IGCSE Core Section #32)
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Solve word problems using bearing,
Solve more challenging 3 D problems involving right triangles
and ai + bj
Trigonometry
(Benchmarked against IGCSE Extended Section Topic#32)



Solve word problems using bearing
Cosine Rules – can find sides and angles from word problems
Area of triangle using sine ( can work out the missing side using algebra)
Further Trigonometry
(Benchmarked against IGCSE Additional Mathematics Circular Measure Topic # 9)
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Know and use the unit circle to solve problems.
Work with positive and negative angles
Know the sin, cos and tan values of 0, 30,45,60,90 and use these values to
solve problems.
Trigonometric identities ( use and apply in complex situations)
Matrices
(Removed because not in IBDP)
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Find angles between planes
Locus
Not done because not in IBDP
Vectors
(Benchmarked against IGCSE Extended Mathematics Topic # 35 Vectors)
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23
10
Position vectors
Geometry- Symmetry and Mensuration
(Benchmarked against IGCSE Extended Section # 31 and #28 Symmetry)

Recognize rotational and line symmetry (including order of rotational
symmetry) in two dimensions and properties of triangles, quadrilaterals
and circles directly related to their symmetries.
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Volume and Surface Area of Prisms, Cylinders and Cones ( compound
shapes)
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Solve problems involving the arc length and sector area of a circle
Angles
(Benchmarked against IGCSE Extended Section#29 Angle Properties)

Work with angles in circles such as angles in a semi-circle; angle between
tangent and radius, angle at the centre of circle is twice the angle at the
circumference,
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Angles in the same segment are equal; cyclic quadrilaterals
Trigonometry
(Benchmarked against IGCSE Core Section #32)
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Solve simple word problems using bearings
Solve simple 3 D problems involving right triangles.
Find the angle between a line and a plane.
Locus
Not done because not in IBDP
Vectors
(Benchmarked against IGCSE Extended Mathematics Topic # 35 Vectors)

Use the sum and difference of two vectors to express given vectors in
Trigonometry
(Benchmarked against IGCSE Mathematics Extended Section #32)
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Solve simple word problems using bearings
Cosine Rules – can find sides and angles only from given triangles.
Area of triangle using sine ( in-direct situations)
Further Trigonometry
(Benchmarked against IGCSE Additional Mathematics Circular Measure Topic # 9)
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Know and use the unit circle to some extent.
Work with angles between 0≤x≤360
Know the sin, cos and tan values of 0,30,45,60,90
Be able to convert between radians and degrees for all angles.
Trigonometric identities use and apply in simple situations
Matrices
(Removed because not in IBDP)
terms of two coplanar vectors
22
10
Geometry- Symmetry and Mensuration
(Benchmarked against IGCSE Extended Section # 31 and #28 Symmetry)

Recognize line symmetry (including order of rotational symmetry) in two
dimensions and properties of triangles, quadrilaterals and circles directly
related to their symmetries.
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Build on knowledge of Volume and Surface Area of Prisms, Cylinders and
Cones
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Solve problems involving the arc length and sector area of a circle for
semi-circle, quarter circle.
Angles
(Benchmarked against IGCSE Extended Section#29 Angle Properties)

Work with angles in polygons.
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Work with angles in circles such as angles in a semi-circle; angle at the
centre of circle is twice the angle at the circumference.
Trigonometry
(Benchmarked against IGCSE Core Section #32)
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

Trigonometry
(Benchmarked against IGCSE Extended Section #32)




Can convert word problem of bearings to diagrams
Work with Sine rule ( ambiguous case)
Cosine Rules - can only find the sides
Area of triangle using sine ( when all information is given)
Further Trigonometry
(Benchmarked against IGCSE Additional Mathematics Circular Measure Topic # 9)

Know what is a unit circle
o
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Work with angles greater than 90
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Be able to convert between radians and degrees for small angles.
Matrices
(Removed because not in IBDP)
Solve simple word problems involving right triangle using sin, cos and tan
Work with angles of elevation and depression using sin, cos and tan
Can convert word problem of bearings to diagrams
Locus
Not done because not in IBDP
Vectors
(Benchmarked against IGCSE Extended Mathematics Topic # 35 Vectors)

Use vectors in the form (

Find the magnitude of a vector; add and subtract vectors and multiply
vectors by scalars
Represent vectors by directed line segments;
Use the sum and difference of two vectors to express given vectors in
terms of two coplanar vectors-in straight forward simple situations
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21
9
and ai + bj
Geometry: measurements
9Gs7
Know and use Pythagoras’ theorem to solve two-dimensional problems involving right-angled triangles
9Mt1
Solve problems involving average speed
IGCSE Topic 32
Introduction to Sin(e), Cos(ine) and Tan(gent) in 2D and 3D shapes
IGCSE Topic 26
Similarity and Congruence-Proofs
Geometry: this part of Geometry not covered, because not in IBDP
20
9
9Gs3
Draw 3D shapes on isometric paper
9Gs4
Analyse 3D shapes through plans and elevations
9Gs5
Identify reflection symmetry in 3D shapes
9Gp9
Find by reasoning the locus of a point that moves at a given distance from a fixed point, or at a given distance from a fixed straight line
Geometry: angles
9Gs2
Solve problems using properties of angles, of parallel and intersecting lines, and of triangles, other polygons and circles, justifying inferences and explaining
reasoning with diagrams and text
Geometry: measurements
19
9
9Gp7
Use bearings (angles measured clockwise from the north) to solve problems involving distance and direction
9Ml1
Solve problems involving measurements in a variety of contexts
9Mt2
Use compound measures to make comparisons in real-life contexts, e.g. travel graphs and value for money
9Ma4
Calculate lengths, surface areas and volumes in right-angled prisms and cylinders.
IGCSE Topic 31
Surface area and Volume of Prisms, Cylinder, Spheres, Cones and Pyramids
IGCSE Topic 26
Similarity and Congruence-Simple Proofs
Geometry: measurements
9Ma2
Know that land area is measured in hectares (ha), and that 1 hectare = 10 000 m²; convert between hectares and square metres
9Gp1
Tessellate triangles and quadrilaterals and relate to angle sums and half-turn rotations; know which regular polygons tessellate, and explain why others will not
IGCSE Topic 31
Surface area and Volume of Prisms and Cylinders
IGCSE Topic 32
Find area and perimeter of Sectors
Use converse of Pythagoras’ theorem.
Geometry: angles
9Gs1
Calculate the interior or exterior angle of any regular polygon; prove and use the formula for the sum of the interior angles of any polygon; prove that the sum of
the exterior angles of any polygon is 360°
IGCSE Topic 29
centre
Angles in circles-angles in a semicircle, angles in the same segment, angles in a cyclic quadrilateral, angle between radius and tangent, angle at the
Geometry: construction
IGCSE Topic 27
9Gs6
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18
8
8
Use a straight edge and compasses to:
construct the perpendicular from a point to a line and the perpendicular from a point on a line
inscribe squares, equilateral triangles, and regular hexagons and octagons by constructing equal divisions of a circle
Geometry: measurements
8Gp1
17
Construct quadrilaterals with a compass.
Find the midpoint of the line segment AB, given the coordinates of points A and B
Geometry: measurements
8Gs3
Know that the longest side of a right-angled triangle is called the hypotenuse
8Gs7
Draw simple nets of solids, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prism
8Ml1
Choose suitable units of measurement to estimate, measure, calculate and solve problems in a range of contexts, including units of mass, length, area, volume or
capacity
8Ml2
mile
8Ma2
Derive and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound 2D shapes, and lengths, surface areas and volumes
of cuboids
8Ma3
Use simple nets of solids to work out their surface areas
9Ma1
Convert between metric units of area, e.g. mm² and cm², cm² and m² and volume, e.g. mm³ and cm³, cm³ and m³; know and use the relationship 1 cm³ = 1 ml
9Gs7
Know and use Pythagoras’ theorem to solve two-dimensional problems involving right-angled triangles
8Gp4
Interpret and make simple scale drawings
9Gp8
Make and use scale drawings and interpret maps
Geometry: angles
8Gs1
Know that if two 2D shapes are congruent, corresponding sides and angles are equal
8Gs2
Classify quadrilaterals according to their properties, including diagonal properties
8Gs4
Identify alternate angles and corresponding angles (and co-interior angles, IGCSE)
8Gs5
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Understand a proof that:
the angle sum of a triangle is 180° and that of a quadrilateral is 360°;
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the exterior angle of a triangle is equal to the sum of the two interior opposite angles
8Gs6
Solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and special quadrilaterals, explaining reasoning with
diagrams and text
Geometry: construction
IGCSE Topic 27
16
8
Construct angles of 30°, 60°, 120° and 150° with a compass
8Gs9
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Use a straight edge and compasses to construct:
the midpoint and perpendicular bisector of a line segment;
the bisector of an angle
8Gs10
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Use a ruler and compasses to construct
circles and arcs
a triangle, given three sides (SSS)
a triangle, given a right angle, hypotenuse and one side (RHS)
Geometry: measurements
8Mt1
Draw and interpret graphs in real life contexts involving more than one component, e.g. travel graphs with more than one person
9Ma3
Solve problems involving the circumference and area of circles, including by using the π key of a calculator.
IGCSE Topic 31
Find the area of a kite and rhombus
IGCSE Topic 31
Find Volume of prisms with a cross-sectional shape of parallelogram, trapezium, kite, circle, rhombus using formula V= Area of Cross Sectional x h
Understand the link between capacity of liquids and capacity of solids and convert units within the metric system for capacity and volume
Geometry: angles
IGCSE Topic 29
Recognize if two (or more) angles are adjacent complementary or supplementary (IGCSE)
Geometry: transformations
9Gp5
Recognise that translations, rotations and reflections preserve length and angle, and map objects on to congruent images, and that enlargements preserve angle
but not length
9Gp6
15
7
Know what is needed to give a precise description of a reflection, rotation, translation or enlargement
Geometry: measurements
7Ma1
Know the abbreviations for and relationships between square metres (m²), square centimetres (cm²), square millimetres (mm²)
7Ma4
Calculate the surface area of cubes and cuboids from their nets
Geometry: angles
7Gs7
14
7
Solve simple geometrical problems by using side and angle properties to identify equal lengths or calculate unknown angles, and explain reasoning
Geometry: measurements
7Mt1
Draw and interpret graphs in real life contexts involving more than one stage, e.g. travel graphs
7Ma3
Derive and use the formula for the volume of a cuboid; calculate volumes of cuboids
8Ma1
Know the definition of a circle and the names of its parts; know and use formulae for the circumference and area of a circle
Geometry: angles
7Gs3
Name and identify side, angle and symmetry properties of special quadrilaterals and triangles, and regular polygons with 5, 6 and 8 sides
7Gs5
Start to recognise the angular connections between parallel lines, perpendicular lines and transversals
7Gs6
Calculate the sum of angles at a point, on a straight line and in a triangle, and prove that vertically opposite angles are equal; derive and use the property that the
angle sum of a quadrilateral is 360°
Geometry: transformations
8Gp2
Transform 2D shapes by rotation, reflection and translation, and simple combinations of these
8Gp3
Understand and use the language and notation associated with enlargement; enlarge 2D shapes, given a centre of enlargement and a positive integer scale factor
8Gs8
Identify all the symmetries of 2D shapes
9Gp2
Use the coordinate grid to solve problems involving translations, rotations, reflections and enlargements
9Gp3
Transform 2D shapes by combinations of rotations, reflections and translations; describe the transformation that maps an object onto its image
9Gp4
Enlarge 2D shapes, given a centre and positive integer scale factor; identify the scale factor of an enlargement as the ratio of the lengths of any two
corresponding line segments
Geometry: construction
IGCSE Topic 27
Construct angle of 30, 60 and 90 degrees with the compass.
IGCSE Topic 27
Construct a perpendicular and parallel line using a compass.
IGCSE Topic 27
Construct a perpendicular bisector of a line using a compass.
IGCSE Topic 27
Bisect an angle with the compass.
7Gs10
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Use a ruler, set square and protractor to: (covered in Steps 16 and 17)
measure and draw straight lines to the nearest millimetre;
measure and draw acute, obtuse and reflex angles to the nearest degree;
draw parallel and perpendicular lines;
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13
7
construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA);
construct squares and rectangles;
construct regular polygons, given a side and the internal angle)
Geometry: measurements
7Ml1
Choose suitable units of measurement to estimate, measure, calculate and solve problems in everyday contexts
7Ml2
Know abbreviations for and relationships between metric units; convert between
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kilometres (km), metres (m), centimetres (cm), millimetres (mm)
kilometres (km), metres (m), centimetres (cm), millimetres (mm);
tonnes (t), kilograms (kg) and grams (g);
litres (l) and millilitres (ml)
7Ml3
Read the scales on a range of analogue and digital measuring instruments
7Mt2
Know the relationships between units of time; understand and use the 12-hour and 24-hour clock systems; interpret timetables; calculate time intervals
7Ma2
Derive and use formulae for the area and perimeter of a rectangle; calculate the perimeter and area of compound shapes made from rectangles
Geometry: angles
7Gs1
Identify, describe, visualize and draw 2D shapes in different orientations
7Gs2
Use the notation and labelling conventions for points, lines, angles and shapes
7Gs4
Estimate the size of acute, obtuse and reflex angles to the nearest 10°
7Gs8
Recognise and describe common solids and some of their properties, e.g. the number of faces, edges and vertices
IGCSE Topic 27
Recognize if two (or more) angles are adjacent complementary or supplementary (IGCSE)
Geometry: transformations
7Gs9
Recognise line and rotation symmetry in 2D shapes and patterns; draw lines of symmetry and complete patterns with two lines of symmetry; identify the order of
rotation symmetry
7Gp1
Read and plot coordinates of points determined by geometric information in all four quadrants
7Gp2
Transform 2D points and shapes by:
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reflection in a given line;
rotation about a given point;
translation
Know that shapes remain congruent after these transformations
12
11
10
6
6
5
6Gs3
Identify and describe properties of quadrilaterals (including the parallelogram, rhombus and trapezium), and classify using parallel sides, equal sides, equal angles
6Gs4
Recognise and make 2D representations of 3D shapes including nets
6Gs6
Check that the sum of the angles in a triangle is 180°, for example, by measuring or paper folding; calculate angles in a triangle or around a point
6Gp1
Read and plot co-ordinates in all four quadrants
6Gs1
Classify different polygons and understand whether a 2D shape is a polygon or not
6Gs2
Visualise and describe the properties of 3D shapes, e.g. faces, edges and vertices
6Gs5
Estimate, recognise and draw acute and obtuse angles and use a protractor to measure to the nearest degree
5Gs2
Recognise reflective and rotational symmetry in regular polygons
5Gs3
Create patterns with two lines of symmetry, e.g. on a pegboard or squared paper
5Gs4
Visualise 3D shapes from 2D drawings and nets, e.g. different nets of an open or closed cube
5Gs6
Understand and use angle measure in degrees; measure angles to the nearest 5°; identify, describe and estimate the size of angles and classify them as acute,
right or obtuse
9
5
5Gs7
Calculate angles in a straight line
5Gp2
Predict where a polygon will be after reflection where the mirror line is parallel to one of the sides, including where the line is oblique
5Gp3
Understand translation as movement along a straight line, identify where polygons will be after a translation and give instructions for translating shapes
5Gs1
Identify and describe properties of triangles and classify as isosceles, equilateral or scalene
5Gs5
Recognise perpendicular and parallel lines in 2D shapes, drawings and the environment
5Gs6
Understand and use angle measure in degrees; measure angles to the nearest 10 degrees; identify, describe and estimate the size of angles and classify them as
acute, right or obtuse
5Gp1
8
4
Read and plot co-ordinates in the first quadrant
4Gs1
Identify, describe, visualise, draw and make a wider range of 2D and 3D shapes including a range of quadrilaterals, the heptagon and tetrahedron; use pin boards
to create a range of polygons. Use spotty paper to record results.
4Gs2
Classify polygons (including a range of quadrilaterals) using criteria such as the number of right angles, whether or not they are regular and their symmetrical
properties
4Gs3
Identify and sketch lines of symmetry in 2D shapes and patterns
4Gs4
Visualise 3D objects from 2D nets and drawings and make nets of common solids
4Gs5
Find examples of shapes and symmetry in the environment and in art
7
6
4
3
4Gs5
Find examples of shapes and symmetry in the environment and in art
4Gp1
Describe and identify the position of a square on a grid of squares where rows and columns are numbered and/or lettered
4Gp2
Know that angles are measured in degrees and that one whole turn is 360° or four right angles; compare and order angles less than 180°
4Gp3
Devise the directions to give to follow a given path
3Gs1 Identify, describe and draw regular and irregular 2D shapes including pentagons, hexagons, octagons and semi-circles
3Gs3 Identify, describe and make 3D shapes including pyramids and prisms; investigate which nets will make a cube
3Gs5 Draw and complete 2D shapes with reflective symmetry and draw reflections of shapes (mirror line along one side)
3Gs7 Identify 2D and 3D shapes, lines of symmetry and right angles in the environment
3Gs8 Identify right angles in 2D shapes
5
3
3Gp3
Use a set square to draw right angles
3Gp4
Compare angles with a right angle and recognise that a straight line is equivalent to two right angles
3Gs4 Classify 3D shapes according to the number and shape of faces, number of vertices and edges)
3Gs6 Relate 2D shapes and 3D solids to drawings of them
3Gs7 Identify 2D and 3D shapes, lines of symmetry and right angles in the environment
4
3
2
2
3Gp1
Use the language of position, direction and movement, including clockwise and anti-clockwise
3Gp2
Find and describe the position of a square on a grid of squares where the rows and columns are labelled
2Gs1
Sort, name, describe, visualise and draw 2D shapes (e.g. squares, rectangles, circles, regular and irregular pentagons and hexagons) referring to their properties;
recognise common 2D shapes in different positions and orientations
2Gs2
shapes
Sort, name, describe and make 3D shapes (e.g. cubes, cuboids, cones, cylinders, spheres and pyramids) referring to their properties; recognise 2D drawings of 3D
2Gs3
Identify reflective symmetry in patterns and 2D shapes; draw lines of symmetry
2Gs4
Find examples of 2D and 3D shape and symmetry in the environment
2Gp1
Follow and give instructions involving position, direction and movement
2Gp2
Recognise whole, half and quarter turns, both clockwise and anti-clockwise
2Gp3
Recognise that a right angle is a quarter turn
2Gs1
Sort, name, describe, visualise and draw 2D shapes (e.g. squares, rectangles, circles, regular and irregular pentagons and hexagons) referring to their properties;
2
1
2Gs2
Sort, name, describe and make 3D shapes (e.g. cubes, cuboids, cones, cylinders, spheres and pyramids) referring to their properties;
2Gs4
Find examples of 2D and 3D shape and symmetry in the environment
2Gp1
Follow instructions involving position, direction and movement
1Gs 2 Name and sort common 3D shapes (e.g. cube, cuboid, cylinder, cone and sphere) using features such as number of faces, flat or curved faces. Use them to make
patterns and models
1Gs 3 Recognise basic line symmetry
1 Gp1 Use everyday language of direction and distance to describe movement of objects
1
1
1Gs 1Name and sort common 2D shapes (e.g. circles, squares, rectangles and triangles) using features such as number of sides, curved or straight. Use them to make
patterns and models.
1 Gp1 Begin to use everyday language of direction and distance to describe movement of objects
P
KG
Uses mathematical vocabulary to describe shape pictures ( “This triangle has 3 sides and 3 corners”)
Match some shapes by recognizing similarities and orientation
Identifies and names 3D and 2D shapes
Understands and uses positional language appropriately (under, over, behind, in front of, inside, outside, next to)