Mathematical Literacy Level 3 Module 1

Mathematical Literacy NQF 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Work with numbers correctly Module 1 Downloaded from hlayiso.com Maths Lit NQF Level 3

Overview 1.1 Revising numbers 1.2 Rounding numbers 1.3 Investigating the possible effect of rounding numbers 1.4 Applying addition and multiplication facts Downloaded from hlayiso.com Maths Lit NQF Level 3

Revising numbers Unit 1.1 Revision of numbers: • Natural numbers: {1; 2; 3; ...} • Whole numbers: {0; 1; 2; 3; ...} • Positive and negative numbers: {1; 2; 3; ...} and {...; -3; -2; -1} • Fractions, decimals and percentages: are all ways to show parts of a whole quantity Downloaded from hlayiso.com Maths Lit NQF Level 3

Revising numbers Unit 1.1 • Some useful equivalent fractions, decimals and percentages: Fractions Decimals Percentages 1 0,01 1% 100 1 0,05 5% 20 1 0,1 10% 10 1 0,125 12,5% 8 1 0,2 20% 5 1 0,25 25% 4 1 0,333... 33 % 3 Downloaded from hlayiso.com Maths Lit NQF Level 3

Revising numbers Unit 1.1 Fractions Decimals Percentages 1 0,5 50% 2 3 0,75 75% 4 4 0,8 80% 5 5 1 100% 5 5 1,25 125% 4 3 1,5 150% 2 4 2 200% 2 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 1.1 Unit 1.1 Complete Exercise 1.1 on page 2 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding numbers Unit 1.2 We round off numbers to make them easier to use and to remember. The population of South Africa is about 56 million. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding numbers Unit 1.2 We round off numbers to make them easier to use and to remember. The distance from Cape Town to Musina is almost 2 000 km. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding numbers Unit 1.2 We round off numbers to make them easier to use and to remember. The distance from the Earth to the Sun is almost 150 million km. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding up or down Unit 1.2 Round down if the number you are rounding is followed by 0, 1, 2, 3 or 4. Example: 79 rounded to the nearest 10 is 80. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding up or down continued ... Unit 1.2 Round up if the number you are rounding is followed by 5, 6, 7, 8 or 9. Example: 114 rounded to the nearest 10 is 110. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding up or down continued ... Unit 1.2 Note: • All the numbers to the right of the place you are rounding to become zeros. • When you work with big numbers, it is important to group them in threes with spaces between. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.1 page 4 Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding off to estimate answers Unit 1.2 to calculations Definition Estimation is a way to find approximate answers to a problem quickly. We can use estimation to: ” 1 Check quickly whether you have enough money to buy what you want. 2 Get a rough idea of the correct answer to a problem. 3 Check whether you have entered numbers into a calculator correctly. You round off, but first decide which digit to round off to, depending on the situation. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding off decimal numbers Unit 1.2 • You need to decide how many decimal places you want in your answer. • Remember that decimal numbers get 10 times smaller each time you move one position to the right. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding off decimal numbers Unit 1.2 1 is 10 times smaller than 10 0,1 is 10 times smaller than 1 0,01 is 10 times smaller than 0,1 0,001 is 10 times smaller than 0,01 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.3 page 7 Unit 1.2 1. Kefilwe calculates the area of a circle with a radius of 7,5 cm. Area = π × r2 = 3,14 × (7,5)2 = 176,71458… Round off her answer to two decimal places. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.3 page 7 Unit 1.2 1. Write down the number and circle the digit you are rounding. 176,71458… The digit to the right is 4. Round down to 176,71 Zeros after the decimal number are not necessary. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.3 page 7 Unit 1.2 2. Round 12,756 off to the nearest tenth. 2. Write down the number and circle the digit you are rounding. 12,756 The digit to the right is 5. Round up to 12,8 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.3 page 7 Unit 1.2 3. Round 101,418 off to the nearest hundredth. 2. Write down the number and circle the digit you are rounding. 101,418 The digit to the right is 8. Round up to 101,42 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 1.2 Unit 1.2 Complete Exercise 1.2 on page 8 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding up or down in practical situations Unit 1.2 In some practical situations, the rounding is determined by the context. 1. There are 203 children in a day-care centre and they all need transport to their concert. A bus can hold 80 children safely. • 2 buses can hold 160 children. • 3 buses can hold 240 children. We need to round up to 3 buses to include all the children. Downloaded from hlayiso.com Maths Lit NQF Level 3

Rounding up or down in practical situations Unit 1.2 In some practical situations, the rounding is determined by the context. 2. You have 31 square metres of cardboard and you need 6 square metres to make a box. You can make 5 boxes and have some cardboard left over. You need to round down the number of boxes down to 5, not up to 6. There is not enough cardboard for 6 boxes. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 1.3 Unit 1.2 Complete Exercise 1.3 on page 9 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Investigating the possible effect of rounding Unit 1.3 numbers • Rounding off makes the answers less accurate. • The larger the decimal place to which we round off, the less accurate the answer is. • It is best to avoid rounding off until the end of a calculation to make it more accurate. Downloaded from hlayiso.com Maths Lit NQF Level 3

When to round off when calculating Unit 1.3 VAT • When prices are entered into a shop's computer system, the VAT is added to find the selling price. • The computer rounds off to the nearest cent after VAT is calculated. • You could have this table of VAT charged for different sale amounts. Price before VAT (R) VAT (R) Price including VAT (R) Selling price (R) 5,95 0,833 6,783 6,78 R6,783 rounds to R6,78 10,50 1,47 11,97 11,97 20,75 2,905 23,655 23,66 R23,655 rounds to R23,66 31,83 4,4562 36,2862 36,29 55,51 7,7714 63,2814 63,28 78,75 11,025 89,775 89,78 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.4 page 10 Downloaded from hlayiso.com Maths Lit NQF Level 3

Map scale and rounding errors Unit 1.3 • Rounding off measurements on a map or plan makes the number easier to work with, but less accurate. • Example: If the rounding error is 1 mm on the map, error in actual distance is multiplied by the scale factor of the map. Scale of map 1 : 200 1 : 2 000 1 : 20 000 1 : 200 000 1 : 2 000 000 Error in result 200 mm 2 000 mm or 2 m 20 000 mm or 200 000 mm or 200 m 2 000 000 mm or 20 m 2 km Downloaded from hlayiso.com Maths Lit NQF Level 3

Map scale and rounding errors Unit 1.3 • Example: • David measures the space available for a couch on a room plan is 9 mm. He rounds this off to 10 mm. • With a scale factor of 200, he calculates 10 mm × 200 = 2 000 mm = 2 m is available for the couch. Downloaded from hlayiso.com Maths Lit NQF Level 3

Map scale and rounding errors Unit 1.3 • The rounding off error on a room plan with scale 1 : 200 is about 100 mm or 10 cm. • This error can result in buying carpets or furniture that do not fit into the room! • Rounding errors on a world map can be much larger and cause bigger inaccuracies. Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.5 page 12 continued ... Unit 1.3 1. Maria measures the distance between two cities on a map as 16 cm, rather than a more accurate 15,75 cm. She needs to multiply by 10 000 000 to find the actual distance. How inaccurate is her measurement? Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.5 page 12 continued ... Unit 1.2 1. Maria’s measurement: 16 cm x 10 000 000 = 160 000 000 cm = 1 600 000 m = 1 600 km Actual distance: 15,75 cm x 10 000 000 = 157 500 000 cm = 1 575 000 m = 1 575 km Error of 1 600 km - 1 575 km = 25 km Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.5 page 12 continued ... Unit 1.3 2. A builder sees on a floor plan that he needs to fit cupboards into a certain space. The space is slightly less than 2 cm wide on the plan, so he rounds off to 2 cm. The plan is 100 times smaller than the actual distance. The space in the room is 1,96 m. Will his cupboards fit? Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.5 page 12 continued ... Unit 1.2 2. He measures 2 cm. This is 2 x 100 = 200 cm = 2 metres in actual distance. The space is only 1,96 m wide. So the cupboards will be 2 m - 1,96 m = 0,04 m too wide. This is 4 cm too wide. The cupboards will not fit. Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 1.4 Unit 1.3 Complete Exercise 1.4 on page 12 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

Applying addition and multiplication Unit 1.4 facts • Calculators and computers make our lives much easier, but we still need to be able to calculate quickly and on the spot. Definition Estimation is a way to find approximate answers to a problem quickly. ” Downloaded from hlayiso.com Maths Lit NQF Level 3

Applying addition and multiplication Unit 1.4 facts We can use estimation to: 1 Check quickly whether you have enough money to buy what you want. 2 Get a rough idea of the correct answer to a problem. 3 Check whether you have entered numbers into a calculator correctly. Rounding off numbers is a good way to estimate. Downloaded from hlayiso.com Maths Lit NQF Level 3

The order of operations Unit 1.4 Downloaded from hlayiso.com Maths Lit NQF Level 3

Addition and multiplication facts Unit 1.4 Commutative property of addition and multiplication: These can be done in any order. 3 + 15 = 15 + 3 3×4×6=4×6×3 Distributive law: Use it to break up a number and then multiply the parts. (25 × 86) × 4 = (25 × 4) × 86 = 100 × 86 = 8 600 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.7 page 14 Unit 1.4 1. Bottles of salon shampoo are sold at R85 each. Dikeledi needs to calculate the price of 21 bottles quickly. Write down a calculation to help her. 1. 85 × 21 = (85 × 20) + 85 × 1 = 1 700 + 85 = R1 785 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.7 page 14 continued ... Unit 1.4 2. Sipho is putting products on the shelf in the hairdressing salon. He can put 3 rows of 75 bottles on each shelf. There are 2 shelves. How many bottles will fill the space? Simplify this calculation so he can do it while working. 2. 3 × 75 × 2 = 3 × (75 × 2) = 3 × 150 = 450 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.7 page 14 continued ... Unit 1.4 3. Write down a simple way to calculate 132 × 23. 3. 132 × 23 = (132 × 20) + (132 × 3) = 2 640 + 396 = 2 640 + 400 - 4 = 3 040 - 4 = 3 036 Downloaded from hlayiso.com Maths Lit NQF Level 3

Example 1.7 page 14 continued ... Unit 1.4 4. It cost R96 for a bottle of hair conditioner. How could calculate the cost of 43 bottles quickly? 4. The answer will be about R4 300 because the cost of one bottle is close to R100. 43 × R96 = 43 × (100 - 4) = (43 × 100) - (43 × 4) = 4 300 - 172 = R4 128 Downloaded from hlayiso.com Maths Lit NQF Level 3

Exercise 1.5 Unit 1.4 Complete Exercise 1.5 on page 15 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

VIDEO: Application in the workplace Downloaded from hlayiso.com Maths Lit NQF Level 3

Module assessment Module 1 Complete Module assessment on page 17 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 3

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