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

Module 1: Numbers ,[object Object],[object Object],[object Object],[object Object]

Introduction ,[object Object],Item F1130 GW 4kg NW 3kg Meas. 22,5x22,5x32 Batch # C33217-003 Pack 01/19/2004 RBG D70745 Work press 100 bar Max press 110 bar Max vol 6l / min T max 40ºC 2006 No 6830001432 230 V 50Hz 1.6kW 92dB Elsewhere on box 360 l/hr

Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

1. USE NUMBERS CORRECTLY ,[object Object],[object Object],[object Object],[object Object],[object Object]

Case study ,[object Object],[object Object],[object Object],[object Object],[object Object]

Case study ,[object Object],[object Object],[object Object]

Case study ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Case study ,[object Object],For Potato Rosti To all intents and purposes, we can presume that there are 40 people, otherwise you’ll end up with half ingredients. 30 Potatoes 10 Onions 10 eggs 150ml + extra 1kg Salmon 10 lemons 10 cartons extra cheese

Case study ,[object Object],Chocolate cheesecake Here we have a bit of a dilemma: We could increase the amount to 40 people (and serve everyone slightly more) or decrease the amount to 36 people (and serve everyone slightly less). While its better in this case to round up, it’s easier to round down. 750 g toasted cereal 167g toasted hazelnuts 13 1/3 tbsp butter 83 g dark chocolate 1167g cream cheese 333g castor sugar 667 ml castor sugar 1 litre double cream 3 1/3 sachet gelatin 10 tbsp water 583.3g dark chocolate 583 g white chocolate

Case study ,[object Object],Assuming that each person would have 2 glasses of fruit juice = 500ml x 40 people =20 litres of fruit juice =10 litres orange and 10 litres grape

Case study ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Case study ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

1.1 Count, order and estimate 9 3 8 5 2 7 6 1 4 6 7 5 4 1 8 2 3 9 2 1 4 9 6 3 8 5 7 7 5 9 3 8 4 1 6 2 3 8 2 1 9 6 7 4 5 1 4 6 2 7 5 9 8 3 4 6 7 8 5 9 3 2 1 5 9 1 6 3 2 4 7 8 8 2 3 7 4 1 5 9 6

Activity 2: Count, order and estimate numbers

Activity 2: Count, order and estimate numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 2: Count, order and estimate numbers ,[object Object],R68 million has been set aside, together with another R570 million totals R638 million. This needs to replace 86 600 taxis. This gives R7367 per taxi. If you say that the government has R570 million to replace 25 720 taxis, then each taxi gets R22 161, which still falls short of the R50 000.

Activity 2: Count, order and estimate numbers ,[object Object],Total taxis scrapped = 13400 + 25720 = 39 120 taxis projected to be scrapped

Activity 2: Count, order and estimate numbers ,[object Object],Percentage of trips not made by taxi = 100% - 35% = 65%

Activity 2: Count, order and estimate numbers ,[object Object],The difficult part of this question is what we do with weekends. One option would be to take only weekdays, which would overestimate the daily value, another option would be to take the whole week, which would underestimate the value earned during a weekday. The proper value would lie somewhere between these two values. For 7 day week: R10.96 million per day For 5 day week: R15.33 million per day

Activity 2: Count, order and estimate numbers ,[object Object],Considering that these taxis are going to be scrapped, R100 000 is a lot of money, probably far too much.

Activity 2: Count, order and estimate numbers ,[object Object],Taxis sold by Toyota: between 900 and 1200. Let’s estimate it to 1000 taxis

Activity 2: Count, order and estimate numbers ,[object Object],The lower bound increases by 33%, and the upper bound by 20%. Here we can settle on 25%.

Activity 2: Count, order and estimate numbers ,[object Object]

Activity 2: Count, order and estimate numbers ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 2: Count, order and estimate numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],50 dogs R90 (actual R90.70) R351 R310 (actual R310)

Activity 2: Count, order and estimate numbers ,[object Object],[object Object],[object Object],[object Object],6 chalets 8 chalets

Activity 3 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

1.2 Positive and negative numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 4 ,[object Object],[object Object],[object Object],[object Object],12 145,42 1315,50 5692,61 12 308,06 6494,61

Activity 4 ,[object Object],-3.5  C

Activity 4 ,[object Object],[object Object],[object Object]

Activity 4 ,[object Object],[object Object]

Activity 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 4 ,[object Object],[object Object],[object Object],[object Object]

1.3 Normal fractions, decimal fractions and percentages 8 2 1 6 5 7 . 3 2 4 800 000 + 20 000 + 1000 + 600 + 50 + 7 + 0.3 + 0.02 + 0.004

1.3 Normal fractions, decimal fractions and percentages ,[object Object],[object Object],[object Object],[object Object]

1.3 Normal fractions, decimal fractions and percentages ,[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],1.3 Normal fractions, decimal fractions and percentages 0, 825 =

1.3 Normal fractions, decimal fractions and percentages ,[object Object],[object Object],[object Object]

Activity 5 ,[object Object],0.375 37.5% 5/8 62.5 0.333 33.33% 0.8 80% 3/4 75% 0.25 25% 72.65% 0.528 66 / 125 0.8 80% Common fraction Decimal fraction Percentages 3/8 0.625 15/45 16/20 0.75 25/100 1453/2000 0.7265 52.8% 4/5

Activity 5 ,[object Object],[object Object],[object Object]

Activity 5 ,[object Object],[object Object],50%; R221,24

Activity 5 ,[object Object],[object Object]

Activity 5 ,[object Object],[object Object],129/1; 45/1; 467/1; 1 528/1.

95324/716243 30440/716243 42730/716243 12050/716243 10105/716243 121087/716243 121087/716243 75492/716243 105309/716243 14784/716243 37772/716243 13,30% 4,25% 5,97% 1,68% 1,41% 49,49% 16,91% 10,54% 14,70% 2,06% 5,27%

165213/716243 16775/716243 5651/716243 14624/716243 2775/716243 71281/716243 54107/716243 40302/716243 655283/716243 54960/716243 6000/716243 716243/716243 23,07% 2,34% 0,79% 2,04% 0,39% 9,95% 7,55% 5,63% 91,49% 7,67% 0,83% 100%

World maps and international time zones ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

World maps and international time zones ,[object Object],[object Object],[object Object],[object Object]

Activity 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],04:00 19:00 13:00 0:00 13:00 18:00

Activity 5 ,[object Object],8 time zones

Activity 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],N45 E0º S35; E150 S30; E50 S65; E60 N10; E50

Activity 5 ,[object Object],[object Object],[object Object],[object Object],12:15 49 minutes 11:20

Activity 6 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 6 ,[object Object],[object Object],[object Object],[object Object],Stage 1: 5hr 25; Stage 2: 14hr50; Stage 3: 6hr55; 6hr05 15h40 + 7hr45 = 23hr25 Cape Town – Christchurch = 47hr55min

2. ACCURATE ANSWERS TO PROBLEMS / SOLVE PROBLEMS ACCURATELY ,[object Object],[object Object],[object Object],[object Object],[object Object]

2.1 Estimation and approximation / rounding ,[object Object]

2.1 Estimation and approximation / rounding ,[object Object],[object Object],[object Object],[object Object],[object Object]

How to round off: ,[object Object]

Activity 7 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 8 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],15 hours 3hr20min 1hr40min 16 days day x R900 = R19 800 48 sheets

Activity 8 ,[object Object],65 000 000 126 000 000 100 000 400 000 70 000 670 000 498 625 32 453 567,896 64,490

Activity 8 ,[object Object],[object Object],[object Object],[object Object],135bpm No

Activity 8 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Yes R63.63

Activity 8 ,[object Object],[object Object],[object Object],Up; 9 busses Up; 4 packets

Activity 8 ,[object Object],25 000 visitors

1.2.2 Calculations ,[object Object],[object Object],[object Object]

Example ,[object Object],[object Object]

Memory keys ,[object Object],[object Object],[object Object],[object Object],[object Object]

Memory keys ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Constant functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 9 ,[object Object],[object Object],[object Object],[object Object],[object Object],173 007 161 016 2 962 404 20572.25

Activity 9 ,[object Object],Price of one item Price of 22 of these items R1 235,68 R252,75 R398,52 R549,87 Total amount owed Keystroke sequence: R27 184,96 R5560,50 R8635,44 R12 097.14 R53 478.04

Examples of using BODMAS calculations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 10 ,[object Object],Answer Answer 148 – 12 x 7 + 28 (148 -12) x (7 + 28) 6222 +148 ÷ 2 -25 6222 + (148 ÷ 2) - 25 1600 ÷ (135 -25 -23) 1600 ÷ 135 – (25-23) 400 – (60 – 18) 400 – 60 - 18 1000 x (30 + 65) 100 x 30 + 65 5 x (8 + 5) 5 x 8 + 5 x 5 (7 + 3) x 13 7 x 13 + 3 x 13 92 6271 21.33 358 95 000 65 130 4760 6271 9,85 322 30 065 65 130

Activity 10 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 10 ,[object Object],[object Object],[object Object],[object Object],[object Object]

5,43% 4,01% 2.25% 43,89% 17.90% 19,82% Breakfast items Price in 1995 Price in 2000 One dozen eggs $1,29 $1,36 One pound of bacon $2,49 $2,59 Half a gallon of milk $0,89 $0,91 A stack of pancakes $3,19 $4,59 Can of frozen orange juice $1,17 $1,37 Total $9,03 $10,82

Activity 10 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 11 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

2.3 Ratio and proportion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 12 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],2:25 13:310 1c : 6c 2 min : 5 min 8 min : 1 min 1c : 9c 4m : 1m 1c : 4c 1kg: 2kg

Activity 12 ,[object Object],[object Object],[object Object],[object Object],R14 565 R18 783.08 R12 127.50

Activity 12 ,[object Object],[object Object],1kg pea flour; 1,5 kg oats

Activity 12 ,[object Object],[object Object],[object Object],4km

Activity 12 ,[object Object],Worker 1: R2 141,81; Worker 2: R3212,72; Worker 3: R6425.45

Activity 12 ,[object Object],21.63cm

Activity 12 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],73440 drops 514 080 drops 15 422 400 drops 187 639 200 drops

2.3 Ratio and proportion ,[object Object],[object Object],[object Object],[object Object]

Activity 13 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1200mm = 1,2 metres 1000mm = 1,0 metres 17,38m 2

Activity 13 ,[object Object],Imperial measurement Metric measurement 56 inches 1 900 yards 650 miles 32 pints 74 gallons 85 ounces 25 tons 142.24 1737.36 1045.85 18,1856 280.12 litres 2,409 kg 25 tons

Currency rates ,[object Object],[object Object],[object Object],[object Object]

Monetary unit R1 equals One foreign unit equals R 14/10/05 20/03/08 14/10/05 20/03/08 US $ 0.1515 0.1227 6.6019 8.1520 British £ 0.0863 0.0619 11.5889 16.1549 Euro € 0.1262 0.0794 7.9223 12.5957

Activity 14 ,[object Object],Price per kg Quantity Price in ZAR Price in GBP Price in EUR Price in US$ Apples @ R2.50 2t Pears @ R3 1,5t Grapes @ R4 750 kg Oranges @ R1.50 3t R5 000 R4 500 R3 000 R4 500 £309.50 £278.55 £185,70 £278,55 € 397.00 € 357.30 € 238.20 € 357.30 $613.50 $522.15 $368.10 $522.15

Activity 14 ,[object Object],Rands USD GBP EUR R10 000 R4 509 R 6 558 $1 515 $683,11 $993,54 £619 £279,10 £405,94 € 794 € 358.01 € 520.71

Activity 15 ,[object Object],[object Object],[object Object],[object Object],1:22 368; 10 min 1,07 km 939m

Activity 16 – Case study ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(R99 + R135 x 9) = R1 314 5,66: 1:1

Activity 16 – Case study ,[object Object]

Activity 16 – Case study ,[object Object],Cost of calls = 85 calls x R1,15 x 1 minute = R97.75 Cost of peak calls = 15 calls x 2,75 x 1 minute = R41.25 Cost of SMS = 0.75 x 15 = R11,25 Total cost = R150,25 Saving = 150,25 – 135,00 = R15,25

Activity 16 – Case study ,[object Object],[object Object],Cost of calls = 85 calls x R1,40 x 1 minute = R119 Cost of peak calls = 15 calls x 2,85 x 1 minute = R42,75 Cost of SMS = 0.75 x 15 = R11,25 Total cost = R173

Activity 16 – Case study ,[object Object],Cost per minute = R20 + R1,80 = R21,80 Cost per call = R21,80 x 6,5minutes = R141,70

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

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