describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

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Learning Area: Mathematics Phase: Senior Phase (Grades 7-9) Overview of the Learning Outcomes Learning Outcome 1: Numbers, Operations and Relationships The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Learning Outcome focus Learning Outcome 1 builds the learners number sense, which is the foundation of further study in Mathematics. It also develops the learners understanding of: what different kinds of numbers mean; how different kinds of numbers relate to one another; the relative size of different numbers; how different numbers can be thought about and represented in various ways; and the effect of operating with numbers. Essential to the development of number sense is knowledge of basic number facts, the use of efficient and accurate methods for calculation and measurement, and a range of strategies for estimating and checking results. Learning Outcome 1 also provides opportunities for the learner to use appropriate technology and to engage with the historical and cultural developments of numerical counting and writing systems. Learners with a good sense of number and operations have the mathematical confidence to make sense of problems and results in various contexts. Contexts should be selected in which the learner has to count, estimate and calculate in a way that builds awareness of other Learning Areas, as well as human rights, social, economic, cultural, political and environmental issues. For example, the learner should be able to: compare counting in different African languages and relate this to the geographical locations of the language groups; count animals in the environment with an awareness of animals at risk of becoming extinct; compare national health statistics with an awareness of how learners own regions are affected; calculate and compare the ratios of elements in a chemical compound; interpret climatic conditions (e.g. read temperature and rainfall information); and calculate within financial contexts found in the Economic and Management Sciences Learning Area. Senior Phase focus The range of numbers developed by the end of Grade 9 is the set of rational numbers. In this phase, the learner should: expand the capacity to represent numbers in a variety of ways and move flexibly between representations; be given ample opportunity to solve a variety of problems, using an increased range of numbers and the ability to perform multiple operations correctly and fluently; be able to recognise irrational numbers such as p and the square roots of non-perfect squares that arise in the context of measurement; and be able to use rational approximations (determined by calculator) of p, square and cube roots. Contexts for solving problems should be expanded to contexts involving negative numbers and percentages (e.g. calculate simple and compound interest). The learner should be encouraged to: sharpen the ability to estimate and judge the reasonableness of solutions, using a variety of strategies (including mental calculations, calculators and proportional reasoning); and use number knowledge to develop algebraic skills. Learning Outcome 2: Patterns, Functions and Algebra The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. Learning Outcome focus Algebra is the language for investigating and communicating most of Mathematics. Algebra can be seen as generalised arithmetic, and can be extended to the study of functions and other relationships between variables. A central part of this outcome is for the learner to achieve efficient manipulative skills in the use of algebra. Learning Outcome 2 focuses on: describing patterns and relationships through…; Learning Area: Mathematics Phase: Senior Phase (Grades 7-9) Overview of the Learning Outcomes Learning Outcome 1: Numbers, Operations and Relationships The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Learning Outcome focus Learning Outcome 1 builds the learners number sense, which is the foundation of further study in Mathematics. It also develops the learners understanding of: what different kinds of numbers mean; how different kinds of numbers relate to one another; the relative size of different numbers; how different numbers can be thought about and represented in various ways; and the effect of operating with numbers. Essential to the development of number sense is knowledge of basic number facts, the use of efficient and accurate methods for calculation and measurement, and a range of strategies for estimating and checking results. Learning Outcome 1 also provides opportunities for the learner to use appropriate technology and to engage with the historical and cultural developments of numerical counting and writing systems. Learners with a good sense of number and operations have the mathematical confidence to make sense of problems and results in various contexts. Contexts should be selected in which the learner has to count, estimate and calculate in a way that builds awareness of other Learning Areas, as well as human rights, social, economic, cultural, political and environmental issues. For example, the learner should be able to: compare counting in different African languages and relate this to the geographical locations of the language groups; count animals in the environment with an awareness of animals at risk of becoming extinct; compare national health statistics with an awareness of how learners own regions are affected; calculate and compare the ratios of elements in a chemical compound; interpret climatic conditions (e.g. read temperature and rainfall information); and calculate within financial contexts found in the Economic and Management Sciences Learning Area. Senior Phase focus The range of numbers developed by the end of Grade 9 is the set of rational numbers. In this phase, the learner should: expand the capacity to represent numbers in a variety of ways and move flexibly between representations; be given ample opportunity to solve a variety of problems, using an increased range of numbers and the ability to perform multiple operations correctly and fluently; be able to recognise irrational numbers such as p and the square roots of non-perfect squares that arise in the context of measurement; and be able to use rational approximations (determined by calculator) of p, square and cube roots. Contexts for solving problems should be expanded to contexts involving negative numbers and percentages (e.g. calculate simple and compound interest). The learner should be encouraged to: sharpen the ability to estimate and judge the reasonableness of solutions, using a variety of strategies (including mental calculations, calculators and proportional reasoning); and use number knowledge to develop algebraic skills. Learning Outcome 2: Patterns, Functions and Algebra The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. Learning Outcome focus Algebra is the language for investigating and communicating most of Mathematics. Algebra can be seen as generalised arithmetic, and can be extended to the study of functions and other relationships between variables. A central part of this outcome is for the learner to achieve efficient manipulative skills in the use of algebra. Learning Outcome 2 focuses on: describing patterns and relationships through…

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