Mathematical Literacy Level 4 Module 11

Mathematical Literacy NQF 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Patterns in the workplace Module 11 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 11.1 Describing patterns 11.2 Using written information and formulae to generate patterns 11.3 Writing formulae for linear number patterns Downloaded from hlayiso.com Maths Lit NQF Level 4

Describing patterns Unit 11.1 Number Patterns • Number patterns are lists of numbers that follow a sequence or pattern. • We can see that the numbers increase or decrease in a regular way that we can begin to predict. The pattern shows a relationship between the numbers. ” Downloaded from hlayiso.com Maths Lit NQF Level 4

Describing patterns Unit 11.1 > Example 11.1 page 219 • Dumisa works at an insurance firm. He says there is a pattern in the phone calls about taking out new insurance policies. • He says: “There is a peak in the number of callers in January every year. Then there are smaller peaks before the holidays, like the July holiday. We see the same pattern every year.” • This is an example of a pattern that has regular increases and decreases. It changes as the time of year changes. Downloaded from hlayiso.com Maths Lit NQF Level 4

Describing patterns Unit 11.1 > Example 11.2 page 219 • Thabang is a hairdresser. She charges R80 for a haircut. These are the amounts of money she receives per day during one week: R720; R320; R400; R560; R640 • They are all multiples of R80, because there is a fixed relationship between the number of haircuts and the money she receives. • Here is the relationship between the numbers in table form: Number of 1 2 3 4 5 6 7 8 9 haircuts Income (R) 80 160 240 320 400 480 560 640 720 • The rule for this pattern is “multiply by 80”. Downloaded from hlayiso.com Maths Lit NQF Level 4

Increasing or decreasing relationships Unit 11.1 We look at number patterns to see how one quantity changes compared to another quantity. The pattern shows increasing or decreasing relationships. Examples: • Dumisa notices how the number of insurance policies taken out changes with the change in the time of year. • Thabang notices an increasing relationship between number of haircuts and income. • Sometimes we say we are looking at one quantity against another, e.g. income against the number of haircuts. Downloaded from hlayiso.com Maths Lit NQF Level 4

Dependent and independent variables Unit 11.1 Independent Variables Dependent Variables An independent variable stands A dependent variable depends on alone and is not changed by other the independent variable. A change variables. This is the input value. in the independent variable affects the dependent variable. This is the output value. Downloaded from hlayiso.com Maths Lit NQF Level 4

Dependent and independent variables Unit 11.1 How much does it cost to print these books? That depends on how many you print, what kind of paper you use, and whether you want to print them in colour, how you bind them, etc. The cost of printing a manual is dependent on the kind of paper, the quality of binding, the colour of the manual, and so on. Dependent variable: Cost of printing a manual Independent variable: The kind of paper, the quality of binding, the colour of the manual Downloaded from hlayiso.com Maths Lit NQF Level 4

Establish a specific pattern Unit 11.1 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 11.1 Unit 11.1 Complete Exercise 11.1 on page 220 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 11.3 page 222 Unit 11.1 1. Kyle starts a ‘pay it forward’ idea for Mandela Day. He helps 3 friends and then asks those 3 friends to do something similar for 3 other people. The number of people helped changes as in the table below: a) What kind of pattern has he created? Explain. b) What is the constant difference or constant ratio? 1. a) Geometric or constant ratio pattern. The number of people helped is multiplied by 3 each time. b) The constant ratio is 3. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 11.2 Unit 11.1 Complete Exercise 11.2 on page 222 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Direct proportion Unit 11.1 • Direct proportion between two variables: “The variables both increase or both decrease in the same proportion.” Number of manuals printed 1 2 3 4 5 Cost of printing R75 R150 R225 R300 R375 • Compare ratios 2 : 3 = 150 : 225 • This is also a linear pattern, with a constant difference of 75. Downloaded from hlayiso.com Maths Lit NQF Level 4

Inverse proportion Unit 11.1 • Inverse proportion between two variables: “As one value increases, the other decreases.” • The time taken to travel a distance and the speed are inversely proportional. Speed (km/h) 40 60 80 100 120 140 Time taken (h) 1,5 1 0,75 0,6 0,5 0,43 time × speed = distance 60 km The two values multiplied together give the same constant value. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 11.4 page 224 Unit 11.1 Downloaded from hlayiso.com Maths Lit NQF Level 4

Different ways of describing number Unit 11.1 patterns • This flow diagram shows you how you can describe patterns: Is the pattern increasing, decreasing or does it not change? it does not change it is increasing or decreasing Is there a constant difference or constant ratio between the terms? neither constant difference constant ratio Is there an indirect proportion Is there a direct proportion between the terms? between the terms? Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 11.3 Unit 11.1 Complete Exercise 11.3 on page 225 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Using written information and formulae Unit 11.2 to generate patterns • Generating patterns from a formula: If you have a formula, you can find the value of any term in the pattern without writing down the whole pattern. > Example 11.5 page 226 no 1 A zoo charges groups of school children accompanied by an adult a flat fee of R50 and R5 per child. Set up a table to show the costs for up to 100 children. Number of 0 20 40 60 80 100 children Entry fee (R) 50 150 250 350 450 550 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 11.4 Unit 11.1 Complete Exercise 11.4 on page 227 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Writing formulae for linear number Unit 11.2 patterns 1 Make a table of input and output values for the pattern. Calculate the difference between terms. 2 The difference times the input number is part of the formula. Example: If the difference is 2, then 2n is part of the formula. Use this as a starting point. Write a formula to link the input number to the output number. 3 Try it out on a few terms and test if you need to add or subtract a constant number. Downloaded from hlayiso.com Maths Lit NQF Level 4

Writing formulae for linear number Unit 11.2 patterns continued… • You are given a simple sequence: 1; 3; 5; 7; 9; 11 • Use this information in a table. Use 1, 2, 3, 4, 5, 6 as input numbers. Input value (n) 1 2 3 4 5 6 Output value 1 3 5 7 9 11 • Difference between terms is 2 • Start the formula with 2n. • Try this on the 1st term: 2n = 2(1) = 2, which is not the output value. • Subtract 1 from 2n to get 2n - 1. • Test this on the other terms e.g. 2(2) - 1 = 3; 2(3) - 1 = 5. • For an input number of 100, the output is 2(100) - 1 = 199. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 11.6 page 228 Unit 11.2 1. Complete the patterns and write down the general formula for the sequences. Use n to represent the position of the term in the sequence. b) 15; 28; 41; 54; … 1. Difference between terms is 13 13n must be in the formula. First term is 13(1) + 2 = 15 13n + 2 = 15 Second term is 13(2) + 2 = 28 13n + 2 = 28 So the formula is 13n + 2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 11.5 Unit 11.2 Complete Exercise 11.5 on page 229 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

VIDEO: Application in the Workplace Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 11 Complete Module assessment on page 231 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

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