Year 9 Independent Learning, Term 2
Below is a list of objectives the students will cover in school during term 2. Students should use Hegarty Maths and complete the relevant video and questions. Further guidance will be sent by their class teacher.
Higher: N1, N2, S1, S2, R1 OBJECTIVES:
Angles and Polygons Hegarty Maths Clip Number
Draw and use scales on maps and scale drawings 492 - 496 Solve problems involving bearings including: 869 Mark on a diagram the position of point B given its bearing from
point A;
Give a bearing between the points on a map or scaled plan; Given the bearing of a point A from point B, work out the bearing of B
from A;
Understand a proof that the exterior angle of a triangle is equal to
the sum of the interior angles at the other two vertices; 481, 483 Understand and use the angle properties of parallel lines and find
missing angles using the properties of corresponding and alternate angles, to solve problems giving reasons for each step;
481-483, 488-490 Use geometrical language appropriately and give reasons for angle
calculations;
Explain why the angle sum of a quadrilateral is 360°; 561, 563 Find the size of each interior angle, or the size of each exterior angle,
or the number of sides of a regular polygon, and use the sum of angles of irregular polygons;
562, 564 Calculate the angles of regular polygons and use these to solve
problems;
Explain why some polygons tessellate and others do not; OBJECTIVES:
Pythagoras and Loci Hegarty Maths Clip Number
Understand and draw front and side elevations and plans of shapes
made from simple solids; 837 - 840
Given the front and side elevations and the plan of a solid, draw a
sketch of the 3D solid. 841
Use straight edge and a pair of compasses to do standard
constructions: 683
• understand, from the experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not;
864-868 • construct the perpendicular bisector of a given line; (Recap)
• construct the perpendicular from a point to a line; 660 • construct the bisector of a given angle; (recap) 660
• construct angles of 90°, 45°; 661
Draw and construct diagrams from given instructions, including the
following: 674
• a region bounded by a circle and an intersecting line; • a given distance from a point and a given distance from a line; • equal distances from two points or two line segments; • regions may be defined by ‘nearer to’ or ‘greater than’; Find and describe regions satisfying a combination of loci 675
Use constructions to solve loci problems 676-679
Solve locus problems including bearings. 676-679
Know that the perpendicular distance from a point to a line is the
shortest distance to the line
Calculate the length of the hypotenuse in a right angle triangle 498 Calculate the length of a shorter side in a right angle triangle 499 Solve problems using pythagoras' theorem including: 501 - 504 Given 3 sides of a triangle, justify if it is right-angled or not;
Apply Pythagoras’ Theorem with a triangle drawn on a coordinate
grid;
Calculate the length of a line segment AB given pairs of points; OBJECTIVES:
Surface area and Volume Hegarty Maths Clip Number
Calculate the area of compound shapes made from triangles, rectangles, trapezia and parallelograms using a variety of metric measures;
555 Estimate area and perimeter by rounding measurements to 1
significant figure to check reasonableness of answers. 534, 535 Give an answer to a question involving the circumference or area of a
circle in terms of π; 534, 539
Find radius or diameter, given area or perimeter of a circles; 540 Find the perimeters and areas of semicircles and quarter-circles; 536,541
Calculate perimeters and areas of composite shapes made from circles and parts of circles (including semicircles, quarter-circles, combinations of these and also incorporating other polygons);
536, 537, 542, 543 Calculate arc lengths, angles and areas of sectors of circles; 544, 545
Convert between metric area measures. 700, 701
Convert between metric volume measures; 702, 703
Convert between metric measures of volume and capacity e.g. 1ml =
1cm3. 698,699
Find the surface area of prisms using the formulae for triangles and
rectangles, and other (simple) shapes with and without a diagram; 585 Find the volume of a prism, including a triangular prism, cube and
cuboid; 570
Calculate volumes of right prisms and shapes made from cubes and
cuboids; 571
Estimate volumes etc by rounding measurements to 1 significant
figure;
Find the surface area of a cylinder; 586
Crossover: N3, N4, S3, S4, R2 OBJECTIVES:
3D Shapes and Constructions Hegarty Maths Clip Number
Recognise 3D shapes and their properties and describe the shapes
using the correct mathematical words 829, 830
Understand and draw front and side elevations and plans of shapes
made from simple solids; 837, 838, 839, 840
Given the front and side elevations and the plan of a solid, draw a
sketch of the 3D solid. 841, 842, 843
Use straight edge and a pair of compasses to do standard
constructions:
• understand, from the experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not;
683 • construct the perpendicular bisector of a given line; 660 • construct the perpendicular from a point to a line; 662 • construct the bisector of a given angle; 661
• construct angles of 90°, 45°; 664
Draw and construct diagrams from given instructions, including the
following:
• a region bounded by a circle and an intersecting line; 675, 676, 677, 678 • a given distance from a point and a given distance from a line;
• equal distances from two points or two line segments; • regions may be defined by ‘nearer to’ or ‘greater than’;
Find and describe regions satisfying a combination of loci 674
Use constructions to solve loci problems 679
Know that the perpendicular distance from a point to a line is the
shortest distance to the line 662
OBJECTIVES:
Transformations Hegarty Maths Clip Number
Understand that reflections are specified by a mirror line; 639, 640, 641 Identify correct reflections from a choice of diagrams; 639, 640, 641 Identify the equation of a line of symmetry; 639, 640, 641 Transform 2D shapes using single reflections (including those not on
coordinate grids) with vertical, horizontal and diagonal mirror lines; 639, 640, 641 Describe reflections on a coordinate grid; 639, 640, 641 Understand that distances and angles are preserved under
reflections, so that any figure is congruent under this transformation; 680 Understand that rotations are specified by a centre, an angle and a
direction of rotation; 648, 649
Find the centre of rotation, angle and direction of rotation and
Describe a rotation fully using the angle, direction of turn, and centre; 648, 649 Rotate a shape about the origin or any other point on a coordinate
grid; 648, 649
Draw the position of a shape after rotation about a centre (not on a
coordinate grid);
Identify correct rotations from a choice of diagrams; 648, 649 Understand that translations are specified by a distance and direction
using a column vector; 637, 638
Translate a given shape by a vector;
Describe and transform 2D shapes using single translations on a coordinate grid;
Understand the effect of one translation followed by another, in terms of column vectors (to introduce vectors in a concrete way); Understand that distances and angles are preserved under rotations and translations, so that any figure is congruent under either of these transformations.
Scale a shape on a grid (without a centre specified); 642, 643, 644, 645, 656, 657 Understand that an enlargement is specified by a centre and a scale
factor;
Enlarge a given shape using (0, 0) as the centre of enlargement, and enlarge shapes with a centre other than (0, 0);
Find the centre of enlargement by drawing;
Describe and transform 2D shapes using enlargements by: - a positive integer scale factor;
- a fractional scale factor;
Identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides, simple integer scale factors, or simple fractions;
611, 612, 613, 614 Understand that similar shapes are enlargements of each other and
angles are preserved – define similar in this unit; 611, 612, 613, 614
OBJECTIVES: Hegarty Maths Clip Number
Solve problems involving calculating areas of rectangles, squares, triangles, parallelograms and trapezia, using a variety of metric measures
554, 555, 556, 557, 558, 559 Work backwards given the area of a shape to find a missing
dimension
Calculate the area of compound shapes made from triangles, rectangles, trapezia and parallelograms using a variety of metric measures;
Recall and use formulae for the circumference of a circle and the area enclosed by a circle circumference of a circle = 2πr = πd, area of a circle = πr2;
534, 535, 536, 537, 538, 539, 540, 541, 542, 543 Find circumferences and areas enclosed by circles;
Give an answer to a question involving the circumference or area of a circle in terms of π;
Find radius or diameter, given area or perimeter of a circles; Find the perimeters and areas of semicircles and quarter-circles;
Calculate the volume and surface area of a right prism 568-571 (Volume) & 584-585 (Surface Area) calculate the volume and surface area of a cylinder 572-574 (Volume) & 586
Foundation: N5, N6, S5, S6, R3, R4 Objectives shown in Red are extension objectives OBJECTIVES:
Properties of Shapes and Angle facts Hegarty Maths Clip Number
Estimate reflex angles 455, 457
Draw and measure reflex angles (these were introduced in year 8) 458, 459, 460, 461
Use geometric language appropriately; 456
use letters to identify points, lines and angles; 456, 821 Mark parallel lines on a diagram and use their properties; Understand ‘regular’ and ‘irregular’ as applied to polygons (met
briefly in year 7)
Recall the properties and definitions of special types of quadrilaterals,
including symmetry properties; 824, 825, 826,
Name all quadrilaterals that have a specific property; 824, 825, 826, Identify quadrilaterals from everyday usage;
Given some information about a shape on coordinate axes, complete the shape;
Classify quadrilaterals by their geometric properties; 824, 825, 826, Draw circles and arcs to a given radius or given the diameter;
Recall the definition of a circle;
Identify, name and draw parts of a circle including tangent, chord and
segment; 592
Calculate missing angles in special triangles, and solve simple 2-step
problems involving angles in triangles 484, 485, 486, 487 Use the fact that angle sum of a quadrilateral is 360°; 560
Understand and use the angle properties of quadrilaterals to solve
angle problems 560
OBJECTIVES:
Perimeter and Area Hegarty Maths Clip Number
Know that measurements using real numbers depend upon the
choice of unit;
Convert between units of measure within one system, including time; Make sensible estimates of a range of measures in everyday settings; 691
convert between metric and imperial units given the approximations 705, 706 Find the perimeter of parallelograms and trapezia using their
properties; 549, 550, 551
Work out the area and perimeter of shapes made from rectangles
and triangles 549, 550, 551, 554, 555
Find the area of a parallelogram; 556
OBJECTIVES:
3D Shapes Hegarty Maths Clip Number
Draw sketches of 3D solids; 829, 830
Use 2D representations of 3D solids 829, 830
Identify and sketch planes of symmetry of 3D solids; OBJECTIVES:
Transformations Hegarty Maths Clip Number
Understand that reflections are specified by a mirror line; 827, 639 Identify correct reflections from a choice of diagrams; 827 Transform 2D shapes using single reflections (including those not on coordinate grids) with vertical, horizontal and diagonal mirror lines; 827 Describe reflections on a coordinate grid; 639 Understand that distances and angles are preserved under
reflections, so that any figure is congruent under this transformation; Understand that rotations are specified by a centre, an angle and a
direction of rotation; 648, 649
Find the centre of rotation, angle and direction of rotation and
describe rotations; 648, 649
Describe a rotation fully using the angle, direction of turn, and centre; 648, 649 Rotate a shape about the origin or any other point on a coordinate
grid; 648, 649
Draw the position of a shape after rotation about a centre (not on a
coordinate grid); 648, 649