2.2.1 = 0,4 (1) 2.2.2 (1) 2.3 2.3.1 Let So: (3) [8] QUESTION 3 3.1 8 trucks = 804 litres 11 trucks = litres Owner must supply 1105, 5 litres. (4) [4] QUESTION 4 4.1 (1) 4.2 (1) 4.3 (1) 4.4 (2) 4.5 (4) [9]
Answers Week 2 Lesson 1 Mental Maths Class work Homework Define the following: Angles line close to each other on a line Two angles adding up to Two angles adding up to Angles on opposite sides of a point of intersection of two lines a) and b) Parallel lines don’t intersect c) It implies that the two lines intersect at an angle of [Vertically opposite angles] [adj. angles on line] [Vertically opposite angles] [adj. angles on line] Homework will be given after the second lesson SUBJECT: MATHEMATICS GRADE 9 WEEK 2: LESSON 2
AND/OR HOMEWORK 3 min Calculate the value of p Calculate the value of y. Determine the size of x in each of the following diagrams. Show all steps of working and give reasons. Answers Week 2 Lesson 2 Class work Homework Calculate a, b, c and d. 62° + 88° + c = 180° [∠s on a straight line] c = 180° − 62° − 88° c = 30° a = 88° [vert. opp. ∠s] b = 62° [vert. opp. ∠s] d = 30° [vert. opp. ∠s m + 20°=100°[vert. opp. ∠s] m = 100°− 20° = 80° Calculate the size of: [∠s on a straight line] (b) Calculate the value of p [vert. opp. ∠s] Calculate the value of y. [vert. opp. ∠s] [∠s on a str. line , ]
COMPONENTS TIME TASKS/ACTIVITIES CAPS INTRODUCTION 3 min Continue from Lesson 1 REVIEW AND CORRECTION OF HOMEWORK 5 min Homework will be given at the end of this lesson LESSON and CLASSWORK min Determine the size of in each of the following diagrams. Show all steps of working and give reasons. a) b) Are line segments AB and DE parallel? Prove your answer. Revise and write clear descriptions of the relationship between angles formed by: -perpendicular lines -intersecting lines -parallel lines cut by a transversal -solving problems -solve problems using the
Answers Week 2 Lesson 4 Class work a) [corr. ∠s; DF // GJ] [sum of co-int. ∠s ] Yes. [sum of ∠s on str. line ] and they are corresponding angles. Therefore AB // DE Homework 1. corr. ∠s, BD // FG corr. ∠s, AB // EC [adj. ∠s on straight line] 1 [adj. angles on straight line] [co-interior ∠s and AB//CD [sum of ∠s of a ]
AND/OR HOMEWORK Homework follows at the end of term 2 lesson 6 REFLECTION Answers Week 2 Lesson 5 Class work [adj. ∠s and MN//OP] [vert. opp. ∠s] But [corr. ∠s and MN//OP]
[alt. ∠s and AB//DC] [sum of int. ∠s of ] Hence =2(45 [alt. ∠s and PQ//RS] Homework [vert. opp. ∠s] [suppl. ∠s] [co-int. ∠s and DE//BC] [corr. ∠s and DE//BC] [sum of int. ∠s of ]
The properties of quadrilaterals The properties of triangles COMPONENTS TIME TASKS/ACTIVITIES CAPS INTRODUCTION 4min Allow learners to continue researching and presenting REVIEW AND CORRECTION OF HOMEWORK 5min Presentations to class continue. LESSON 10 min This is a continuation of lesson 3 Question: List the types of triangles List the properties of triangles Learners are now given an opportunity to refer to resources such as DVD or Sasol Inzalo workbooks to find properties of triangles. Please note – it is here that educators should make the necessary arrangements for learners to watch the DVD on the section or allow learners to access their cell phones and or computers to research. Learners prepare the properties of triangles on a chart with diagrams and to present their findings to the class. Identify and write clear definitions or properties of triangles in terms of their sides and angles to distinguish between them *Equilateral triangles *Isosceles triangle Solve for unknown CLASS WORK 10min As per lesson presentation 1min Summarize in workbooks the properties of the different types of triangles.
the third angle. ….. If the exterior angle of a triangle is 1200 and one of the interior opposite angles is 400 then what is the other interior angle. ….. What do we call the line of a right angled triangle that is opposite to the perpendicular angle?……hypotenuse Study the diagram below and answer the following questions: Calculate the size of angle E in terms of : Solve for . 1.1 = 180o – 4 – 3 (Sum of angles of a triangle) = 180o – 7 1.2 ( angles on a straight line) 2. In ∆ABC, AB=AC and = . Determine the size of , with reasons, in terms of . ( angles opposite equal sides) ( sum of angles of a triangle) continues in lesson 8.
LESSON and CLASSWORK 22 min The educator presents the lesson and allows learners to work at the problem at intervals. ( Thus incorporating classwork) Use the following to show the properties of quadrilaterals: The diagonals AC and BD of parallelogram ABCD intersect at point E. Measure the length of the diagonals. Measure the length of the line segments from E to each corner (BE, DE, CE, and AE). Use your protractor to measure the angles that the diagonals make with each other. What do you notice? Make a conjecture about the diagonals of a parallelogram. By construction, investigate sides, angles and diagonals in quadrilaterals, focusing on the diagonals of rectangles, squares, rhombi and kites. AND/OR HOMEWORK 3 min Homework follows at the end of term 2 week 3 lesson 2 REFLECTION Answers Week 4 Lesson 1 parallelograms
INTRODUCTION 5 min This is a continuation lesson REVIEW AND CORRECTION OF HOMEWORK This is a continuation lesson LESSON and CLASSWORK 22 min The following examples are done by the educator and learners are then asked to continue with the classwork. . Example 1 Fill in the sizes of all the angles in the following Solution: Example 2 Solution: By construction, investigate sides, angles and diagonals in quadrilaterals, focusing on the diagonals of rectangles, squares, rhombi and kites. AND/OR HOMEWORK 3 min Find all the angles marked with letters: REFLECTION
each circle with the intersection points of the circles. Join AB. Construct the perpendicular bisector of AB. What do you notice? Do the diagonals bisect each other? Complete the sentence: The diagonals of a rhombus will always….. Expected answers: 1.The diagonals intersect 2.Yes 3.The diagonals of a rhombus will always bisect each other at right angles. sides, angles and diagonals in quadrilaterals, focusing on the diagonals of rectangles, squares, rhombi and kites. CLASSWORK 10min Learners summarise the properties of rectangles and rhombi using the following diagrams: Properties of a rhombus AND/OR HOMEWORK This lesson will continue in week 4 lesson 4 REFLECTION
3. 4. REFLECTION Answers WEEK 5 Lesson 2 Mental Maths Class work Homework The minimum conditions for two triangles to be congruent are the following: Three sides (SSS) Two sides and an included angle (SAS) Two angles and the corresponding side (ASA) A right angle, hypotenuse and a side (RHS) 1. 2. All congruent SSS SSS SAS (vertically opposite angles included) SSS
The properties of triangles COMPONENTS TIME TASKS/ACTIVITIES CAPS INTRODUCTION 5 min O is the centre of the circle and . Prove that AC = CB p. 136 REVIEW AND CORRECTION OF HOMEWORK 10min 1. 2. 2.1 2.2 LESSON AND CLASSWORK 16min Educator allows learners to do one rider at a time and marks each one at 3-5 minute intervals. 1. In , AB = AD and BC = DC By construction, explore the minimum conditions for triangles to be congruent and/or
CLASSWORK The two polygons are similar. Write a proportion and solve for x. AND/OR HOMEWORK 1 min Calculate the length of the unknown sides if JKL /// PQR REFLECTION Answers WEEK 6 Lesson 1 Mental Maths Class work Homework Scalene/acute angle triangle Right angle triangle
We are now going, by accurate constructions, try to find out what is the minimum information needed to have congruent triangles. Each time use only the information provided. You will now determine what sets of measurements will give only one possible triangle. Use a ruler, compass and protractor to construct the following triangles. Question 1: Minimum dimensions are given each time: 1.1 If three sides are given: side, side, side (S,S,S): (4) ΔDEF with DE = 7 cm, DF = 6 cm and EF = 5 cm. 1.2 If three angels are given: angle, angle, angle (: (4) ΔABC with = 80°, = 60° and = 40°.
Answers Week 7 Lesson 1 Mental Maths Class work Homework Or 1. 92 + 402 = AC2 81 + 1600 = AC2 1681 = AC2 AC = 41 2. 82 + 152 = Df2 289 = DF2 17 = DF 3. 122 + 162 = GI2 144 + 256 = GI2 400 = GI2 20 = GI This is the first lesson of a new section thus no homework. SUBJECT: MATHEMATICS GRADE 9 WEEK 7: LESSON 2 TOPIC: THEOREM OF PYTHAGORAS CONCEPTS AND SKILLS TO BE ACHIEVED
LESSON and CLASSWORK 10min Informal Assignment (See worksheet on the next page) Pythagorean Theorem Assignment Calculate the measure of in each. Where necessary, round your answer to one decimal place. Complete on a separate piece of paper.
Learners to do the classwork in pairs and exchange with another pair of learners to mark the work. A trapezium is a quadrilateral with one pair of opposite sides parallel. If we tessellate (tile) two trapeziums as shown in the diagram below, we form a parallelogram. (The yellow trapezium is the same size as the blue one. The base of the parallelogram is equal to the sum of the parallel sides of the trapezium.) We can use the formula for the area of a parallelogram to work out the formula for the area of a trapezium as follows: Area of parallelogram = base × height = (side 1 + side 2) × height Area of trapezium ∴ Area of a trapezium Only one pair of opposite sides is parallel For isosceles trapezium, one pair of opposite sides is equal Example: a) Calculate the area of the following. A = ½ (sum of parallel sides )x height between SI units, to solve problems and calculate the perimeter and area of: Polygons Circles
PRIOR KNOWLEDGE The properties of quadrilaterals The difference between the perimeter and the area of a figure The use of formulae to calculate perimeters and areas of squares, rectangles, triangles and circles (From Grade 8). To solve equations by inspection. COMPONENTS TIME TASKS/ACTIVITIES CAPS INTRODUCTION 5 p.139 -140 REVIEW AND CORRECTION OF HOMEWORK 2. A = r2 = (13.5)2 = 572,55 units2 LESSON 15 min The educator presents the following example: EC2 = 52 - 42 =25 – 16 = 9 EC = 3cm. Total area = = 12 x 4 + ½ (3 x 4 ) = 52 cm2 Use appropriate formulae and conversions between SI units, to solve problems and calculate the perimeter and area of: Polygons Circles CLASSWORK 14min Calculate the total area of the shape below:
REVIEW AND CORRECTION OF HOMEWORK FD2 = 262 -102 (Pythagoras) FD = 24 cm Area of figure = Area of rectangle + Area of triangle = 20 x 30 + ½ (20 x 24) cm2 = 840cm2 Perimeter = 5m +5m +3m +6m+3m = 22m LESSON and CLASSWORK 10 min INVESTIGATION: SCALE FACTOR: ENLARGEMENTS AND REDUCTIONS 1. 1.1 Plot the following points on the Cartesian Plane given: A(1;1); B(1;3); C(4,3); D(4;1) 1.2 Now plot the following: A’(2;2) B’(2;6) C’(8;6) D’(8;2) Use appropriate formulae and conversions between SI units, to solve problems and calculate the perimeter and area of: Polygons Circles
10.1 Write down the wording of the Theorem of Pythagoras. …………………………………………………………………………………….. …………………………………………………………………………………….. …………………………………………………………………………………….. (2) 10.2 Calculate the length of AC correct to the nearest m. Show all working. …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… ……………………………………………………………………………………. (4) 10.3 An aeroplane flying at a height of 10km was directly above a house. If the owner of the house was 1 200m from his house at that time, how far was he from the aeroplane? Complete the sketch and write your answer correct to two places. (5)
(6) [12] QUESTION 5 5.1.1 Calculate BD. (4) 5.1.2 Calculate the area of this equilateral triangle, correct to one decimal digit (4) 5.2 Calculate, correct to two decimal digits: 5.2.1 JG (4) 5.2.2 KJ (3) [15] QUESTION 6 Show that (4) [4] TOTAL: 50