Introduction week 1 Hi all First of all

Introduction- week 1 Hi all First of all I hope you are all keeping safe, healthy and looking after yourselves. Now to the boring bit…. Work… My expectation…. I will be expecting you to be doing 5 hours of maths a week. This is no more than what you do in school so it should be relatively straight forward. Now this can be completed by doing an hour a day or spending a few hours on 2 or 3 days completing the entirety of the work, the choice is yours, however, I will be expecting the work to be completed. There will be 4 lessons of NEW CONTENT a week with the 5 th lesson having to complete questions on everything you’ve just learnt (Each lesson 1 hr long). There will be an instruction of how I expect these questions to be completed when you go to lesson 5. I will be providing you with lessons to go through and will be expecting each of you to take notes and answer any questions which are within the slides to help develop your understanding. The week will be topic based so lesson 1 will help with lesson 2 and 3 and so on, so PLEASE DO NOT skip slides. All the lessons will provide you with material on topics that we were yet to cover during your first year at LEEP. If you feel you get stuck or are confused please do not hesitate to contact me. I will be allocating every Wednesday for you to contact with any questions or concerns and will respond to them as soon as I can on the day. However if you have any questions outside of that day I will get back to you as soon as I possibly can. Email: s. rivera@leep. org. uk Please continue to look after yourselves and work hard to ensure we are not having to play catch up when we are back. Mr Rivera

Timetable: Monday – Lesson 1 material Tuesday – Lesson 2 material Wednesday – Lesson 3 material Thursday – Lesson 4 material Friday – Exam questions

Lesson 1

Please look at these slides in full screen so you get all the content material. Perimeter of compound shapes L. O • Calculate the perimeter of compound shapes made from triangles, rectangles and trapeziums 16 -Jan-22

Starter C/W January 2022 Perimeter of compound shapes Calculate the perimeter of these shapes: a. b. c. 5 cm 7 m 8 cm d. 12 m 9 m e. (Regular hexagon) 11 cm 0. 5 m 25 cm 300 mm f. Q+ 80 cm 2. 5 m 16 -Jan-22

All: Calculate a perimeter where all lengths are known. Most: Calculate a perimeter where at least one side must be derived. Some: Calculate the perimeter of a variety of shapes using their properties. Perimeter of compound shapes What is a compound? What is a compound shape? 5 cm 3 cm 7 cm 8 cm 5 cm 12 cm Keywords: Perimeter, compound shape, properties 16 -Jan-22

All: Calculate a perimeter where all lengths are known. Most: Calculate a perimeter where at least one side must be derived. Some: Calculate the perimeter of a variety of shapes using their properties. Perimeter of compound shapes Copy Finding missing lengths 3 cm 4 cm 6 cm 4 cm Keywords: Perimeter, compound shape, properties 16 -Jan-22

All: Calculate a perimeter where all lengths are known. Most: Calculate a perimeter where at least one side must be derived. Some: Calculate the perimeter of a variety of shapes using their properties. Perimeter of compound shapes Complete the worksheet 1. 34 cm 2. 48 m 3. 11 cm or 110 mm Keywords: Perimeter, compound shape, properties 16 -Jan-22

All: Calculate a perimeter where all lengths are known. Most: Calculate a perimeter where at least one side must be derived. Some: Calculate the perimeter of a variety of shapes using their properties. Perimeter of compound shapes 4. 500 m 5. 56 cm 6. 314 mm Keywords: Perimeter, compound shape, properties 16 -Jan-22

All: Calculate a perimeter where all lengths are known. Most: Calculate a perimeter where at least one side must be derived. Some: Calculate the perimeter of a variety of shapes using their properties. Perimeter of compound shapes 7. 44 m 8. 88 cm 9. 100 mm or 10 cm Keywords: Perimeter, compound shape, properties 16 -Jan-22

Lesson 2

16/01/2022 Area of Compound Shapes LO: . • Calculate the area of compound shapes made from triangles, rectangles, trapezia and parallelograms Keywords: area, compound shape, squared units 13

Starter - Area of simple 2 D shapes Find the area of these shapes 5 cm 3 cm 6 cm ½ base X perpendicular height ½ X 6 X 3 = 9 cm 2 16/01/2022 2 cm height 2 X base X 6 = 12 cm 2 14

Area of Compound Shapes Work out the area of this compound shape in two different ways. 6 cm Another way is …. . 6 X 5 =30 cm 2 5 cm 10 cm 7 cm 10 X 6 =60 cm 2 7 X 52 =35 cm 2 5 X 13 =65 cm 13 cm Area of of the compound shape == 30 60 ++ 65 35 == 95 cm 22 16/01/2022 15

Find the area of this Compound Shape ½ (6 X 5) =15 cm 2 8 X 6 =48 cm 2 Total = 48 + 15 = 63 cm 2 16/01/2022 16

3 m 4 m 3 m 3 X 4 =12 m 2 3 X 2 = 6 m 2 2 m Total area = 12 + 6 = 18 m 2 16/01/2022 17

Checkpoint - AFL As a manager of a local football club, you need to re-turf the playing field for an important international match. It costs £ 1. 50 to turf 1 m 2. Find the cost of re- turfing the pitch. Area of the playing field = 90 X 40 = 3600 m 2 40 m The cost of re-turfing the pitch = 1. 5 X 3600 = £ 5400 90 m 16/01/2022

Find the area of this Compound Shape 10 cm 20 cm Rectangle = 20 X 10 =200 cm 2 Triangle = ½ (4 X 20) = 40 cm 2 Total = 200 – 40 = 160 cm 2 16/01/2022 19

Find the area of this Compound Shape Trapezium = ½ (a + b) h 3 cm = ½ (3 + 7) 4 = ½ (10 X 4) = 20 cm 2 6 cm Rectangle = 6 X 7 = 42 cm 2 10 cm 7 cm Total = 42 + 20 = 62 cm 2 16/01/2022 20

Compound Shape GCSE question The diagram shows a room in Mr Bains’ house. He wants to carpet the entire floor. Carpet costs £ 5 per m². Calculate the total cost for Mr Bains to carpet this floor. 8 m A 16 m B 11 m 5 m Area A = 8 x 5 = 40 m 2 Area B = 11 x 2 = 22 m 2 Total Area = 40 + 22 = 62 m 2 Cost = 62 x 5 = £ 310 2 m (4 marks)

Compound Shape GCSE question * The diagram shows the plan of a swimming pool. Harry wants to tile the bottom of the swimming pool. Each pack of tiles cover 6 m². How many packs of tiles does Harry need to buy? 2 m A Area A = 2 x 5 = 10 m 2 5 m Area B = 6 x 8 = 48 m 2 Total Area = 10 + 48 = 58 m 2 11 m B 8 m 6 m Packs of tiles = 58 ÷ 6 = 9. 66 So, he needs 10 packs (4 marks)

Plenary - How could we find the shaded area? 1) Area of Trapezium 2) Area of rectangle 11 cm 10 cm 7 cm 3 cm 4 cm 3) Area of triangle 4) Total shaded area

Lesson 3

16/01/2022 Circles L. O Recall definition of a circle and name and draw parts of a circle • Recall and use circumference formulae and the area enclosed by a circle STARTER Work out the following Mathematical anagrams: REPRMEITE SADRIU AIDETERM Perimeter Radius Diameter EXTENSION Develop your own Mathematical anagrams

NAMING CIRCLE PARTS TASK MATCH THE CARDS AT THE BOTTOM WITH THE EMPTY BOXES TANGENT CHORD SECTOR DIAMETER SEGMENT RADIUS 16/01/2022 CIRCUMFERENCE

NAMING CIRCLE PARTS ANSWERS RADIUS SECTOR DIAMETER CIRCUMFERENCE SEGMENT TANGENT CHORD 16/01/2022

Finding the Area You can find the area of a circle by using the formula- Area= π x Radius 2 For Example 7 cm Area= π x 72 = π x 49 = 153. 93804 = 153. 9 (to 1 dp) cm 2 16/01/2022

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills AREA OF CIRCLES AND SEMI-CIRCLES Self Manager Which ones are you using? radius EXAMPLES (a)Find the area of the circle: (b) Find the area of the circle: 4 cm 14 m diameter Area of circle = 3. 14 x 4 Area of circle = 50. 2 cm 2 (1 d. p. ) Area of circle = 3. 14 x 7 Area of circle = 153. 9 m 2 (1 d. p. ) (c)Find the area of the semi-circle: Area of semi-circle = 20 cm Area of semi-circle = 2 2 Area of semi-circle = 157 cm 2 16/01/2022 Team Worker

PLT Skills AREA OF CIRCLES AND SEMI-CIRCLES TASK EXTENSION 1) Calculate the area of the circles below: (a) (b) (c) 1) Calculate the area of the semi-circles below: (b) (a) 2 cm 1. 5 cm 6 cm 13 cm 9 cm 2)Calculate the area of the circles below: (a) (b) (d) (c) 3 cm 8 cm 20 cm 7 cm 12 cm 2)Calculate the area of the quadrant below: 3) Find the area of one face of the following coins. Give your answers to 1 decimal place. a) 1 p coin, radius 1 cm b) 2 p coin, radius 1. 3 cm c) 5 p coin, diameter 1. 7 cm d) 10 p coin, diameter 2. 4 cm 16/01/2022

Practice working backwards 16/01/2022

Answers 16/01/2022

Creative Thinker Effective Participator Independent Enquirer Reflective Learner PLT Skills AREA OF CIRCLES AND SEMI-CIRCLES Self Manager Which ones are you using? MINI-PLENARY A point B moves so that it is always a distance of 5 cm from a fixed point A. Draw the locus and calculate the area. Area of circle = 3. 14 x 5 Area of circle = 78. 5 cm 2 5 cm 16/01/2022 Team Worker

PLENARY ACTIVITY EXAM STYLE QUESTION Calculate the area shaded black. Area of big circle = 3. 14 x 5 Area of small circle = 3. 14 x 3 Area of big circle = 78. 5 cm 2 Area of small circle = 28. 26 cm 2 Area shaded black = 78. 5 - 28. 26 = 50. 2 cm 2 (1 d. p. ) 16/01/2022

Lesson 4

16/01/2022 Composite Shapes Learning Objective • Calculate perimeters and areas of composite shapes made from circles and parts of circles Compound Area Keywords Trapezium Circle

Work out perimeter/circumference of a circle C=2 xπxr Or Diameter x π

Starter . Calculate the area and perimeter of each circle: 2. 1. 3. 3. 5 cm 11 m 12 cm Calculate the perimeter and area of each shape 6. 5. 4. 20 cm 4 cm 16 cm Challenge: Calculate the perimeter and area of this shape

Example – find the shaded area 1) Draw two separate circles out 2) Area of big circle 3) Area of smaller circle 4) Area of shaded part

Compound Shapes with Circles GREEN Calculate the area and perimeter of the following shapes: 2 cm 6 cm 12 cm 20 cm 11 cm 2 cm 17 cm 4 cm 6 cm 5 cm 12 cm 10 cm 5 cm 10 cm 20 cm

Find the shaded areas

The top of this enormous circular table has a radius of 10 m. Find its area. 10 m Area of a circle = r 2 = 3. 14 X 10 m 2 = 3. 14 X 100 = 314 m 2 16/01/2022 43

Here are two concentric circles. Find the area of the shaded portion. Leave your answer in 2 d. p. Area of a circle = r 2 2 cm Bigger circle = 3. 14 X 32 1 cm = 3. 14 X 9 = 28. 27 cm 2 Smaller circle = 3. 14 X 22 = 3. 14 X 4 = 12. 56 cm 2 Shaded area = 28. 27 – 12. 56 =15. 70 cm 2 16/01/2022 44

Inscribed circle Find the area of the part shaded blue. Square = 20 X 20 =400 m 2 Area of a circle = r 2 20 m = 3. 14 X 10 m 2 = 3. 14 X 100 = 314 m 2 20 m Shaded area = 400 – 314 =86 m 2 16/01/2022 45

GCSE Functional question 1. * Mr Weaver’s garden is in the shape of a rectangle. 1) Area of the grass (inc. circles) In the garden: there is a patio in the shape of a rectangle and two ponds in the shape of circles with diameter 3. 8 m. 2) Area of circle The rest of the garden is 18 grass. m 3) Method for area of the grass 12 m 4) Area of the grass 3 m Mr Weaver is going to spread fertiliser over all the grass. One box of fertiliser will cover 25 m² of grass. How many boxes of fertiliser does Mr Weaver need? You must show your working. 5) How many boxes? (Total 5 marks)

M 1 for (17 – 2. 8) × 9. 5 (=134. 9) or 17× 9. 5 – 2. 8× 9. 5 ( = 161. 5 – 26. 6 = 134. 9) M 1 for π × (3. 8 ÷ 2)2 (= 11. 33 – 11. 35) M 1 (dep on M 1) for ‘ 134. 9’ – 2 × ‘ 11. 34’ A 1 for 112 - 113 C 1(dep on at least M 1) for 'He needs 5 boxes' ft from candidate's calculation rounded up to the next integer

Plenary - GCSE Functional question 2. * Mrs Hills garden is in the shape of a rectangle. 1) Area of the rectangle There is a triangular section of patio and a semi circle of patio too. . The rest of the garden is grass. 2) Area of triangle 3. 5 m Patio Grass 3) Area of semi circle 11. 5 m 6 m Patio 6 m 4) Method for area of grass 15 m Mrs Hill is going to spread fertiliser over all the grass. One box of fertiliser will cover 45 m² of grass. How many boxes of fertiliser does Mrs Hill need? You must show your working. 5) Area of grass 6) How many boxes? (Total 6 marks)

t s e o i s i v e R u Q n s n io

Questions with answers Please complete all the questions. If you leave a question use another colour pen to ensure you highlight this as an area to work on. Do not look at the answers until all questions are complete on each individual slide. Look through the lesson slides to complete the questions you didn’t know. Check answers and make changes with another colour pen.

Find the Perimeter of these shapes 8 cm 5 cm 4 cm 5 cm 8 cm 9 cm 8 cm 4 cm 8 cm Answers 1. 21 cm 2. 17 cm 4 cm 9 cm 7 cm 12 cm 3 cm 15 cm 11 cm 10 cm Answers 1. 26 cm 2. 26 cm 3. 30 cm 4. 25 cm 5. 36 cm Answers 1. 16 cm 2. 25 cm 3. 72 cm 5 cm 12 cm 13 cm 4. 39 cm 3 cm 5. 96 cm 6. 110 cm 11 cm 7. 42 cm All of these shapes are regular 4 cm 8 cm

Area of Triangles 1. Find the area of the triangles on the left 2. Find the missing lengths of the triangles Answers: on the right 1. 10 m 2. 14 m 3. 6 m 4. 10 m 5. 10 m 6. 3 m 7. 20 m Answers: 1. 6 m 2 2. 24 m 2 3. 3 m 2 4. 20 m 2 5. 12 m 2 6. 35 m 2 7. 44 m 2 8. 15 m 2 9. 31. 5 m 2 10. 72 m 2

Finding the Area of Circles You can find the area of a circle by using the formula- Area= π x Radius 2 7 cm For Example. Area= π x 72 = π x 49 = 153. 93804 = 153. 9 (to 1 dp) cm 2 ANSWER 2 a S 12. 6 b c d e f g h 78. 5 15. 2 380. 1 314. 2 153. 9 100. 5 28. 3

Circumference 1 2 23 cm 11 cm 5 3 6 30 cm 9 30 cm 4 cm 7 20 cm 10 9 cm 4 8 3 cm 11 12 5 cm 4 cm 8 cm 6 cm Answers: 1. 34. 6 cm 2. 72. 3 3. 25. 1 cm 4. 44. 0 cm 5. 77. 1 cm 7 cm 6. 51. 4 cm 7. 10. 7 cm 8. 17. 9 cm 9. 95. 1 cm 10. 23. 4 cm 5 cm 11. 51. 0 cm 12. 81. 4 cm 12 cm 6 cm 14 cm 18 cm