NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 2 Part 1

Module 2: Patterns and relationships

Module 2: Patterns and relationships ,[object Object],[object Object],[object Object],[object Object]

1. IDENTIFY AND EXTEND PATTERNS FOR DIFFERENT RELATIONSHIPS IN THE WORKPLACE ,[object Object],[object Object],[object Object],[object Object]

1.1 Numerical and geometric patterns investigated and extended y = 2x Input value (x) 1 2 3 4 Output value (y) 2 4 6 8

Example ,[object Object],[object Object],[object Object],Input value 1 2 3 4 Output value 6 12 18 Formula y =

Activity 1: Arithmetic patterns ,[object Object],[object Object],[object Object],[object Object],Cost of ticket = R25 + 0,75 x (no of km) Km travelled 100 200 300 400 500 600 1000 Cost (R) R100 R175 R250 R325 R400 R475 R550

Activity 1: Arithmetic patterns ,[object Object],[object Object],[object Object],[object Object],[object Object],12 x m 2 R35,4 x m 2 It will take him 25 days. He will need 2 additional helpers, which will allow them to complete it in 8 1/3 days Number of sq metres of pavements 1 2 3 4 5 10 50 Number of face bricks Cost per square metre 12 24 36 48 60 120 600 R35,40 R70,80 R106,20 R141,60 R177 R354 R1770

Activity 1: Arithmetic patterns ,[object Object],[object Object],[object Object],$0.1305 76,60 766,00 7 660 76 600 766 000 7 600 000 Value in US$ 1 10 100 1000 10 000 100 000 1000 000 Amount in ZAR 7.66

Geometric patterns ,[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 2 – constant difference patterns and constant ratio patterns ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1250 1500 1750 2000 2000 4000 8000 16 000 32 000 336.025 402,628 442,890 487,179 13 310 14 641 16 105,1 17 715,61 19 487,17 19 487 171 1 715 561 121 11 1

Activity 2: Constant difference patterns and constant ratio patterns ,[object Object],[object Object],[object Object],[object Object],0,5358; 0,5383; 0,5408; 0,5433; 0,5458; 0,5483; 0,5508 6,375 million; 12,750 million; 12,500 million; 25,500 million; 51million; 102 million 10:10; 10:50; 11:30; 12:10; 12:50

Activity 2: Constant difference patterns and constant ratio patterns ,[object Object],11 000 12 100 13 310 14 641 16500 18150 19965 R41772,48 R21961,5 R62658,72 22000 24200 26620 29282 83554,96 Amount of deposit Amount after one year Amount after two years Amount after three years Amount after four years 15 th term 10 000 1,1 x 10 000 1.1 2 x 10 000= 1.1 3 x 10 000= 1.1 4 X10 000 15 000 1,1 x 15 000 1.1 2 x 15 000= 1.1 3 x 15 000= 1.1 4 X 15 000 20 000 1,1 x 20 000 1.1 2 x 20 000= 1.1 3 x 20 000= 1.1 4 X 20 000

Activity 2: Constant difference patterns and constant ratio patterns ,[object Object],R1000 R2000 R3000 R15000 R1500 R3000 R4500 R22500 R2000 R4 000 R6 000 R 30 000 Loan amount Cost of loan for 1 year Cost of loan for 2 years Cost of loan for three years Cost of loan for 15 years 10 000 0,1 X 10 000 x 1 0,1 X 10 000 x 2 0,1 x 10 000 x 3 15 000 20 000

Activity 3 – Patterns in Asanda’s working day ,[object Object],[object Object],[object Object],[object Object],[object Object],56 per week 2920 per year R3066 per year Week number 1 5 10 15 20 25 50 Total

Activity 3 – Patterns in Asanda’s working day ,[object Object],[object Object],[object Object]

1.1.2 Direct and inverse relationships and trends ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 4 ,[object Object],10 20 Price of house by estate agent in one year (R) R8 500 000 R4 250 000 R1 700 000 R850 000 R425 000 Number of the specific houses sold per year 1 2 5

Activity 4 ,[object Object],Inverse 60 30 20 15 10 Speed (km/h) 20 40 60 80 100 120 Time of journey 12

Activity 4 R148,50 R445,50 R594,00 Direct litres of petrol 1 15 45 60 Total cost 9,90

Activity 4 Direct R79,20 R99,00 R118,80 R138,60 Petrol consumption 8 10 12 14 Cost per 100km

Activity 4 ,[object Object],Cash loan amount R4 000 R6 000 R8 000 Monthly loan repayment options Within 12 months R466 R679 R892 Within 24 months R290 R421 R551 Within 36 months R234 R339 R443

Activity 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Constant difference Inverse R443 x 36 months = R15948 R15948 ÷ 8000 x 100 = 199.35

Activity 4 ,[object Object],R13 260 R16 334 R19 692 R3 260 R6 334 R9 692 Repayment period 12 months 24 months 36 months R10 000 loan R1 105 R681 R547 Actual repayment amount = months x monthly repayment amount Cost of the loan

Activity 4 ,[object Object],[object Object],[object Object],[object Object],Negative 12 months, the loan is cheaper since you pay less interest

1.1.3 Putting patterns into words an the other way around ,[object Object],[object Object],[object Object],[object Object],[object Object]

1.1.3 Putting patterns into words an the other way around ,[object Object],[object Object],[object Object]

1.1.3 Putting patterns into words and the other way around Input values 0 300 600 900 1200 1500 1800 2100 2400 Output values 50 110

Activity 6 ,[object Object],[object Object],R310 R370 R430 R490 R730 Input value (R) = customers amount Output value (r) = earnings of waitress 300 x0.2 +250 = 600 900 1200 2400

Activity 6 Metro bus ticket: 1,75 - 4,25 4,25 – 5,75 5,75 – 7,25 7,25 – 8,75 8,75 – 10,25 0-5 km = zone 1 x0.5 +1.75 = 5-8 km = zone 2 8-11km = zone 3 11-14km = zone 4 14-17km = zone 5

Activity 6 ,[object Object],[object Object],[object Object],30 55 80 105 130 155 180 205 230 input 1 2 3 4 5 6 7 8 9 output

Activity 6 ,[object Object],[object Object],[object Object],1/3 5 5x + 3 110 140 170 200 230 260 x-value 5 15 25 35 45 55 65 75 85 y-value 20 50 80

Activity 6 ,[object Object],[object Object],[object Object],5 3 5x + 3 73 88 103 118 133 x-value 3 6 9 12 15 18 21 24 27 y-value 13 28 43 58

1.1.4 Make representations of the relationships ,[object Object],[object Object],[object Object],[object Object]

Activity 8: Sketch the relationship ,[object Object],Taxable income Tax rate <0 – 112 500 18% of the amount 112 501 – 180 000 20 250 + 25% of the amount above 112 500 180 001 – 250 000 37 125 + 30% of the amount above 180 000 250 001 – 350 000 58 125 + 35% of the amount above 250 000 350 001 – 450 000 93 125 +38% of the amount above 350 000 450 001 and above 131 125 + 40% of the amount above 450 000

Activity 8: Sketch the relationship ,[object Object],[object Object],[object Object],People who earn less than R43 000 do not pay tax

0 R12 600 R18 000 R24 625 R32 125 R40 125 R49 125 R58 125 R68 625 R79 125 R89 625 R100 725 R112 125 R123 525 R135 125 R147 125 R271 125 R551 125 R751 125 Annual earnings of individual Income tax amount (R) 40 000 70 000 100 000 130 000 160 000 190 000 220 000 250 000 280 000 310 000 340 000 370 000 400 000 430 000 460 000 490 000 800 000 1 500 000 2 000 000

Activity 9 ,[object Object],[object Object]

Activity 9 ,[object Object],[object Object],One way fares Sleeper-6 Sleeper 4 Cape Town to Johannesburg R320 R495 Cape Town to Kimberly R210 R325 Cape Town to Durban R210 R325 Johannesburg to Durban R155 R250 Johannesburg to Kimberly R110 R170

Activity 9 ,[object Object],KMB CPT DBN EL JHB PE KMB 968 811 780 476 743 CPT 968 1753 1079 1402 769 DBN 811 1753 674 557 984 EL 780 1079 674 982 310 JHB 476 1402 557 982 1075 PE 743 769 984 310 1075

Activity 9 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 9 ,[object Object],[object Object],324 399 474 549 624 699 849 999 Months 0 1 2 3 4 5 6 7 8 10 12 Cost 99 174 249

Activity 9 ,[object Object],Voice Calls Select75 (Peak) Select75 (Off peak) Select150 (Peak) Select150 (Off peak) TKS to TKS 2.10 0.95 1.85 0.90 TKS to landline 2.10 0.95 1.85 0.95 TKS to other cell phone 2.75 1.15 2.70 1.15

NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 2 Part 1

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NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 2 Part 1