Mathematical Literacy Level 2 Module 13

Mathematical Literacy NQF 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Identify and complete patterns to solve problems Module 13 Downloaded from hlayiso.com Maths Lit NQF Level 2

Overview 13.1 Number patterns with a constant difference 13.2 Constant ratio patterns 13.3 Direct proportion and inverse proportion Downloaded from hlayiso.com Maths Lit NQF Level 2

Number patterns with a constant difference Unit 13.1 Definition ” A number pattern is a list of numbers that follow a rule. Even numbers Downloaded from hlayiso.com Maths Lit NQF Level 2

Describing number patterns Unit 13.1 Thabiso is an events planner who needs to work out how many people he can seat around a given number of tables. Each table can have five chairs around it. The total number of chairs forms the pattern: 5; 10; 15; 20; ... Downloaded from hlayiso.com Maths Lit NQF Level 2

Describing number patterns continued ... Unit 13.1 We can write this in a table of values: Number of tables 1 2 3 4 ... Total number of chairs 5 10 15 20 ... Now we can describe the number pattern. Downloaded from hlayiso.com Maths Lit NQF Level 2

Describing number patterns continued ... Unit 13.1 Number of tables 1 2 3 4 ... Total number of chairs 5 10 15 20 ... Step 1 Is the pattern increasing or decreasing? Increasing Step 2 Describe how the pattern is formed. Each number is 5 more than the number before it. Step 3 Identify the rule for the pattern Start at 5 and increase by 5 each time. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 13.1 page 241 Unit 13.1 a) i) Describe the number pattern 1; 4; 7; 10; 13; ... ii) Write down the next three numbers in the pattern. b) i) Describe the number pattern 18; 15; 12; 9; ... ii) Write down the next three numbers in the pattern. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 13.1 page 241 continued ... Unit 13.1 a) i) There are equal gaps between the numbers. Each gap is equal to 3. 1 4 7 10 13 The pattern is increasing. Each number is 3 more than the number before it. Rule: Start at 1 and increase by 3 each time. ii) 13 + 3 = 16 16 + 3 = 19 19 + 3 = 22 The next three numbers in the pattern are 16; 19; 22. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 13.1 page 241 continued ... Unit 13.1 b) i) There are equal gaps between the numbers. Each gap is equal to 3. 9 12 15 18 The pattern is decreasing. Each number is 3 less than the number before it. Rule: Start at 18 and decrease by 3 each time. ii) 9 - 3 = 6 6-3=3 3-3=0 The next three numbers in the pattern are 6; 3; 0. Downloaded from hlayiso.com Maths Lit NQF Level 2

Constant difference patterns Unit 13.1 • Look at this number pattern: • Each number in the pattern is called a term. • The pattern follows a rule. • The terms are multiples of 3. • The constant difference is also 3. Downloaded from hlayiso.com Maths Lit NQF Level 2

Constant difference patterns Unit 13.1 • We can add to the pattern by adding 3 to each term to get the next term. • We can show the pattern in a table: Term 1 2 3 4 5 6 7 Pattern 3 6 9 12 15 18 21 • To find a term without working out all the terms before it, link the value of a term to its position. • In this pattern, each term's value is 3 times the position of the term. • So the 10th term will be 3 × 10 = 30 • And the 15th term will be 3 × 15 = 45 Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 13.1 Unit 13.1 Complete Exercise 13.1 on page 243 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

A formula for a number pattern Unit 13.1 • Thabiso, the events planner, worked out this formula for the number of people he can seat at an event: p = 5t • The letters p and t are called variables. The number of tables and the number of people can change (or vary). • Now Thabiso can apply the formula to other situations. • If he has an event with 15 tables, he can use the formula to work out the number of people he can seat. • p = 5 × 15 = 75 So he can seat 75 people at 15 tables. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 13.2 Unit 13.1 Complete Exercise 13.2 on page 244 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

More number patterns -Unitadding 13.1 a constant value Thabiso, our event planner, is working on a wedding. The round tables are bigger and can seat 10 people. There is a head table of 6 people for the wedding couple and their closest family. Downloaded from hlayiso.com Maths Lit NQF Level 2

More number patterns -Unitadding 13.1 a constant value Thabiso writes a new formula for the number of people that can be seated. p = 10 t + 6 • The number 6 (at the head table) is a constant in the formula. • It does not change, even if the values of p and t change. • Thabiso has 6 tables of guests, so he works out: p = (10 × 6) + 6 = 66 people Downloaded from hlayiso.com Maths Lit NQF Level 2

Independent and dependent variables Unit 13.1 Definition The independent variable is the variable that makes the dependent ” variable change. So, in the formula Thabiso used, t, the number of tables is the independent variable. p = 10t + 6 We write the independent variable in the first row of a table and choose the values that we want to work with. Number of tables (t) independent variable Number of people (p) dependent variable Downloaded from hlayiso.com Maths Lit NQF Level 2

Independent and dependent variables continued ... Unit 13.1 Definition A dependent variable is the quantity that changes because the ” independent variable changes. The variable for the number of people, p, is the dependent variable. p = 10t + 6 Its value changes, depending on how many tables Thabiso is given. Number of tables (t) independent variable Number of people (p) dependent variable Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 13.3 Unit 13.1 Complete Exercise 13.3 on page 247 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Constant ratio patterns Unit 13.2 Definition In a constant ratio pattern, each term is multiplied by the same ” number to get the next term. For example, multiply by 2 each time in this number pattern: 4; 8; 16; 32; 64; 128; 256; ... Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 13.4 a) page 249 Unit 13.2 a) 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 is in the table: Number of steps 1 2 3 4 5 Number of people helped 3 9 27 81 243 i) Describe the pattern he has created. ii) Give the constant ratio, if there is one. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 13.4 a) page 249 Unit 13.2 Number of steps 1 2 3 4 5 Number of people helped 3 9 27 81 243 i) Step 1 Is the pattern increasing The pattern is increasing. or decreasing? Step 2 Describe how the Each term is 3× larger than the pattern is formed. previous term. Step 3 Identify the rule for the The pattern starts at 3, and pattern. each term is multiplied by 3 to get the next term. ii) The constant ratio is 3. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 13.4 Unit 13.2 Complete Exercise 13.4 on page 250 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Direct proportion and inverse proportion Unit 13.3 Direct proportion As one amount increases, the other amount increases at the same ” rate. Downloaded from hlayiso.com Maths Lit NQF Level 2

Direct proportion and inverse proportion Unit 13.3 Inverse proportion One value decreases at the same rate as the other value increases. Downloaded from hlayiso.com Maths Lit NQF Level 2 ”

Example 13.5 b) page 252 Unit 13.3 b) A machine in a factory produces 235 plastic cartons every hour. i) Write a formula that shows how many cartons are produced per hour by completing the formula: Number of cartons = _________ × ________ ii) Use your formula to work out how many cartons are produced in an eight-hour day. iii) Is this a direct proportion? Explain. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 13.5 b) page 252 continued Unit 13.3 b) A machine in a factory produces 235 plastic cartons every hour. i) Number of cartons = 235 x number of hours ii) Number of cartons = 235 x 8 = 1 880 cartons iii) Yes. The formula shows that each time the number of hours increases by 1, the number of cartons increases by 235. If the number of hours = 0, then the number of cartons = 0. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 13.5 Unit 13.3 Complete Exercise 13.5 on page 252 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 13.3 What happens if one quantity decreases as the other increases? 6cm 4cm Area = 6 cm × 4 cm = 24 cm2 3cm Area = 8 cm × 3 cm = 24 cm2 8cm The rectangles have the same area of 24 cm2 To keep the area the same, as one quantity increases, the other decreases. So the length and breadth are inversely proportional. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 13.3 Formula for area of a rectangle = length x breadth A=l×b 6cm For these rectangles, the area is a constant value of 24. 4cm l × b = 24 Length ( l ) 24 12 8 6 3cm Table of ( b Breadth some) possible 1 values 2 for l3and b: 4 8cm Note: It is not possible for one of these values to be zero. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 13.6 Unit 13.3 Complete Exercise 13.6 on page 254 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Applications in the Workplace Downloaded from hlayiso.com Maths Lit NQF Level 2

Module assessment Module 13 Complete Module assessment on page 255 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

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