| 1 |
Study Plan |
Study plan – Topic 5 – Geometry |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Coordinate Geometry-the plane |
Distance formula. |
| Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. |
| 3 |
Coordinate Geometry-midpoint, slope |
Mid-point formula |
| Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. |
| 4 |
Coordinate Geometry-gradient |
Gradient |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. |
| 5 |
Coordinate Geometry-gradient |
Gradient formula. |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. |
| 6 |
Coordinate Geometry-straight line |
The straight line. |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. |
| 7 |
Coordinate Geometry-slope, etc. |
Lines through the origin. |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. |
| 8 |
Coordinate Geometry-equation of line |
General form of a line and the x and y Intercepts. |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. |
| 9 |
Coordinate Geometry-intercept |
Slope intercept form of a line. |
| Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. |
| 10 |
Coordinate Geometry-point slope |
Point slope form of a line |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. |
| 11 |
Pythagoras |
Find the hypotenuse |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. |
| 12 |
Pythagoras |
Pythagorean triples |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
| 13 |
Pythagoras |
Find the hypotenuse Part 2 |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. |
| 14 |
Pythagoras |
Calculating a leg of a right-angled triangle |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. |
| 15 |
Pythagoras |
Proofs of Pythagoras theorem |
| Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem |
| 16 |
Trigonometry-ratios |
Trigonometric ratios. |
| Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op |
| 17 |
Trigonometry-ratios |
Using the trigonometric ratios to find unknown length. [Case 1 Sine]. |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. |
| 18 |
Trigonometry-ratios |
Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. |
| 19 |
Trigonometry-ratios |
Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. |
| 20 |
Trigonometry-ratios |
Unknown in the denominator. [Case 4]. |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. |
| 21 |
Trigonometry-practical |
Trigonometric ratios in practical situations. |
| Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. |
| 22 |
Trigonometry-ratios |
Using the calculator to find an angle given a trigonometric ratio. |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. |
| 23 |
Trigonometry-exact ratios |
Trigonometric ratios of 30., 45. and 60. – exact ratios. |
| Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. |
| 24 |
Trigonometry-cosine rule |
The cosine rule to find an unknown side. [Case 1 SAS]. |
| Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. |
| 25 |
Trigonometry-cosine rule |
The cosine rule to find an unknown angle. [Case 2 SSS]. |
| Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. |
| 26 |
Trigonometry-sine rule |
The sine rule to find an unknown side. Case 1. |
| Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. |
| 27 |
Trigonometry-sine rule |
The sine rule to find an unknown angle. Case 2. |
| Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. |
| 28 |
Trigonometry-areas |
The area formula |
| Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. |
| 29 |
Area |
Problems with area. |
| Objective: On completion of the lesson the student will be able to solve problems with area. |
| 30 |
Volume/capacity |
Problems with volume/capacity. |
| Objective: Problem Solving: problems involving volume/capacity |
| 31 |
Surface area |
Surface area of a cube/rectangular prism. |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. |
| 32 |
Surface area |
Surface area of a triangular/trapezoidal prism. |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. |
| 33 |
Surface area |
Surface area of a cylinder and sphere. |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. |
| 34 |
Surface area |
Surface area of pyramids |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. |
| 35 |
Surface area |
Surface area of cones |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul |
| 36 |
Surface area |
Surface area of composite solids |
| Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. |
| 37 |
Geometry-angles |
Measuring angles |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. |
| 38 |
Geometry-angles |
Adjacent angles |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. |
| 39 |
Geometry-angles |
Complementary and supplementary angles |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. |
| 40 |
Geometry-angles |
Vertically opposite angles |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. |
| 41 |
Geometry-angles |
Angles at a Point. |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. |
| 42 |
Geometry-angles |
Parallel Lines. |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. |
| 43 |
Geometry-problems |
Additional questions involving parallel lines |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. |
| 44 |
Geometry-triangles |
Angle sum of a triangle |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. |
| 45 |
Geometry-triangles |
Exterior angle theorem |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. |
| 46 |
Special triangles |
Special triangles |
| Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles. |
| 47 |
Geometry-quadrilaterals |
Quadrilaterals |
| Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. |
| 48 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 49 |
Geometry |
To identify collinear points, coplanar lines and points in 2 and 3 dimensions |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. |
| 50 |
Geometry – angles |
To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. |
| 51 |
Geometry-constructions |
Angle bisector construction and its properties (Stage 2) |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. |
| 52 |
Geometry-constructions |
Circumcentre and incentre (Stage 2) |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. |
| 53 |
Geometry-constructions |
Orthocentre and centroids (Stage 2) |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. |
| 54 |
Geometry-quadrilaterals |
Midsegments of Triangles |
| Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. |
| 55 |
Geometry-quadrilaterals |
Classifying Quadrilaterals |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. |
| 56 |
Geometry-quadrilaterals |
Using the Properties of a Parallelogram |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. |
| 57 |
Geometry-quadrilaterals |
Proving a Shape is a Parallelogram |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. |
| 58 |
Geometry-quadrilaterals |
Properties of the Rectangle, Square and Rhombus |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. |
| 59 |
Geometry-quadrilaterals |
Properties of the Trapezium and Kite |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. |
| 60 |
Geometry-quadrilaterals |
The quadrilateral family and coordinate methods in geometry |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. |
| 61 |
Geometry-locus |
Constructions and loci – single condition |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. |
| 62 |
Geometry-locus |
Constructions and loci – multiple conditions |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. |
| 63 |
Geometry problems |
More difficult exercises involving parallel lines |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log |
| 64 |
Geometry-reasoning |
Further difficult exercises involving formal reasoning |
| Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information. |
| 65 |
Geometry-polygons |
Angles of regular polygons |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. |
| 66 |
Geometry-congruence |
Congruent triangles, Test 1 and 2 |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. |
| 67 |
Geometry-congruence |
Congruent triangles, Test 3 and 4 |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. |
| 68 |
Geometry-congruence |
Proofs and congruent triangles. |
| Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent. |
| 69 |
Similar triangles |
Similar triangles |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. |
| 70 |
Similar triangles |
Using similar triangles to calculate lengths |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. |
| 71 |
Overlapping triangles |
Examples involving overlapping triangles |
| Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. |
| 72 |
Geometry – triangles |
Triangle inequality theorem |
| Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. |
| 73 |
Exam |
Exam – Topic 5 – Geometry |
| Objective: Exam |
