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4. Linear Inequalities Mathematics Grade 0 Teacher Guide Linear Inequalities ? Series overview ! In this series, we build an understanding of the steps involved in solving linear inequalities, especially R when multiplying or dividing by a negative amount. Then we solve a contextual problem. We represent the solutions graphically on number lines and using set builder notation and interval notation. E 2+2=4 Curriculum links G The lessons in this series link to the following Learning Outcomes and Assessment Standards of the ? National Curriculum Statement: ! Learning Outcome : Functions and Algebra 10.2.5(d) Solve linear inequalities in one variable and illustrate the solution graphically. R E Educational approach 2+2=4 There are three lessons in this series. The first lesson focuses on different ways to represent linear G inequalities. The second lesson shows the principles and mathematical skills needed to solve linear inequalities. We investigate how the inequality sign changes when both sides of the inequality are multiplied or divided by negative real numbers. In the third lesson we recap what was learnt in the first two lessons and then extend the learners’ knowledge by solving inequalities which contain fractions. The series begins with examples of how inequalities are used in the workplace and in real-life situations. In the past, many teachers have taught learners to solve inequalities as a skill where the numbers and variables are manipulated according to rules which are followed. Learners find it difficult to see how these inequalities are used in real life. So we have included many real world examples so that learners can realise how useful and relevant inequalities are to solve real problems. In this rich context, we introduce the different representations of inequalities, namely on number lines, in set builder notation and interval notation. An important educational approach is to provide the opportunity for learners to work together in small groups where they can discuss the concept of linear inequalities and the principles of solving linear inequalities and by doing this they construct their own understandings and meanings. The mathematical language and terminology used to describe set builder notation and interval notation can become a barrier to learning. This approach also ensures that the learners have enough opportunities to verbalise and write the terminology required. It is important to remember that mathematics involves conceptual understanding and the development of mathematical skills. No skill is achieved from one example! The lessons include many examples for learners to practise the necessary skills. We suggest that you use more examples from your classroom textbook to consolidate this work. The tasks set for each lesson can be used as an assessment tool. The learners can complete the tasks and these can be used to ? ! assess whether or not they have achieved the intended outcomes. R To get the full benefit of the lessons, your learners need to engage actively with the concepts presented. So, when you preview the videos, think about how to introduce each lesson and what E 2+2=4 follow up activities will be useful. Also watch out for places in the video where you can pause to have G a class discussion, or ask learners to complete an activity or solve a problem posed in the video. We have used this pause icon to suggest some of these places to you. ?Mathematics Grade 0 Teacher Guide ! Linear Inequalities R E 2+2=4 G Series at a Glance Lesson title Lesson Outcomes By the end of this lesson, the learner should be able to: . Linear Inequalities on the • use a number line to represent a linear inequality Number Line • use set builder notation and interval notation to represent a linear inequality . Solving a Linear Inequality • solve a simple linear inequality • solve a linear inequality that involves multiplying or dividing by a negative number • calculate the values for a linear inequality . More Linear Inequalities • solve linear inequalities that have a denominator • represent solutions on a number line. Mathematics Grade 0 Teacher Guide Linear Inequalities ? ! R E 2+2=4 G Teaching Guidelines Lesson : Linear Inequalities on the Number Line The video introduces inequalities in a real world context. Discuss further examples with the learners of where and how inequalities can be used to solve problems in real-life situations. The lesson guides learners to understand the concept of an inequality as opposed to an equation and to write an inequality using the appropriate inequality signs. You may want to stop the video after the problem on the two mountain climbers climbing Mount Everest is presented. Let the learners work together in small groups to discuss the problem with each other and then write the inequality and represent it on a number line and in set builder and interval notation. They can then check their answers with those on the video. Give the learners the opportunity to practise drawing number lines of closed and open intervals where x∈ ;x∈ and x ∈ . Many learners are not sure why and when they should draw a dot or a line, an open dot at the end of an interval or a closed dot. Learners also forget when to use a round bracket and a square bracket when writing in interval notation. Lots of practice will help clear up any confusion. Task Using the principles established in this lesson, learners can represent the inequality in the three different ways. Let them do this individually, as you have given them the opportunity to work together during the lesson. Lesson : Solving a Linear Inequality This lesson carefully works through the concept of keeping an inequality true when we add or subtract, or multiply and divide both sides of the inequality by positive and negative real numbers. After Busi’s problem has been presented, stop the video and let the learners discuss with each other and use their common sense to solve the problem. You may want to guide them to write an inequality to solve the problem. They can then check their thinking and their answers from the video. The critical learning point in this lesson is the changing of the direction of the inequality sign when multiplying or dividing both sides of the inequality by a negative real number. Very few learners understand this concept. They simply learn this ‘rule’ and apply it as best as they can remember it. We lead the learners through an investigation of why the sign changes direction. Give the learners the opportunity to discuss this concept. Let them work in pairs and demonstrate their understanding of this to each other. There are two examples of inequalities to solve. You may want to stop the video and let the learners solve these in small groups and then check their answers. If the learners are very unsure, let them watch the first inequality being solved on the video. Then they could redo this example and then try the second one on their own. Give them more examples to practise. Task The learners are expected to solve inequalities which include changing the direction of the sign. Some learners may need more practice and further explanation to achieve the outcomes of this lesson confidently. 4 Mathematics Grade 0 Teacher Guide Linear Inequalities Lesson : More Linear Inequalities In this lesson we recap the previous two lessons and then use clear steps to solve an inequality that contains fractions. If your learners have never been to Gold Reef City, discuss this theme park with them and the different rides they could have there. Also discuss why there is a maximum number of people that can go on the Big Wheel at a time. This discussion can lead to other examples of maximum and minimum amounts, which are the limits that can be applied to linear inequalities. After the problem on the Big Wheel has been presented, stop the video and allow the learners to work in groups and solve the problem on their own first. The second problem, where the learners must calculate the maximum total mass of the loaded Big Wheel, is an extension activity which the competent and confident learners will enjoy. You can pair up confident learners with less confident ones. Task The learners need to use their knowledge and understanding of all three lessons to complete this task. The rubric below can be used to assess the learners’ ability to solve linear inequalities. Name of Learner: Criteria : 4 6 7 The learner Not Achieved Elementary Moderate Adequate Substantial Excellent Outstanding can: achievement achievement achievement achievement Achievement achievement Use a Number line Number line Number line Number line Number line Number line Number line number line incorrect; correctly correctly correctly correctly correctly correctly drawn, to represent interval drawn; drawn; interval drawn; interval drawn; interval drawn; interval interval marked a linear marked interval marked marked marked marked correctly, inequality. incorrectly; marked correctly; open/ correctly; correctly; open/ correctly; open/closed dot open/closed incorrectly; closed dot not open/closed closed dot open/closed correct, sure of dot not open/closed correct and/or dot correct correct; sure of dot correct; real or natural correct; dot not unsure of real but unsure of real or natural sure of real numbers and unsure of real correct and/or or natural real or natural numbers. or natural can explain or natural unsure of real numbers. numbers. numbers. principles to numbers. or natural peers. numbers. Use set All Most Some One Most All All components builder components components components component components components of notation notation of notation of notation of notation of notation of notation of notation correctly written; and interval incorrectly incorrectly incorrectly incorrectly correctly correctly uses correct notation. written. written. written. written. written. written. terminology. Solve a linear Does not Mostly does Sometimes Mostly Always Always Always changes inequality change the not change does not changes the changes changes the the direction of that involves direction of the direction change the direction of the the direction direction of the sign and multiplying or the sign and of the sign direction of sign but cannot of the sign, the sign and clearly explains dividing by cannot solve and cannot the sign and explain why but cannot can give some why this a negative the inequality. explain why cannot explain this happens. give a clear explanation happens with numberr. this happens. why this explanation of why this examples happens. of why this happens. happens. Solve a linear Cannot identify Sometimes Mostly Identifies Identifies Multiplies Multiplies inequality common identifies identifies common common by common by common that has a denominator; common common denominator, denominator denominator denominator and denominator. cannot solve denominator denominator sometimes and usually and solves solves the linear the linear but cannot but cannot solves solves the the linear inequality with inequality. solve the solve the linear the linear linear inequality inequality confidence and linear inequality. inequality. correctly. correctly. ease. inequality .

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Linear Inequalities, rational expressions, Linear equations, Intermediate Algebra, Radical Expressions, Real Numbers, linear inequality, Equations and Inequalities, Chapter 6, Linear Equations in Two Variables

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posted: | 3/29/2011 |

language: | English |

pages: | 5 |

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