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- Mathematics grade 10 teachers'
- Mathematics grade 10 teachers'
- Overview
Outcomes
Summary of topics, outcomes and their relevance:
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1. Functions – linear, quadratic, exponential, rational |
|
Outcome |
Relevance |
| 10.1.1 |
Relationships between variables in terms of graphical, verbal and symbolic representations of functions (tables, graphs, words and formulae). |
Functions form a core part of learners’ mathematical understanding and reasoning processes in algebra. This is also an excellent opportunity for contextual mathematical modelling questions. |
| 10.1.2 |
Generating graphs and generalising effects of parameters of vertical shifts and stretches and reflections about the x-axis. |
| 10.1.3 |
Problem solving and graph work involving prescribed functions. |
|
2. Number Patterns, Sequences and Series |
|
Outcome |
Relevance |
| 10.2.1 |
Number patterns with constant difference. |
Much of mathematics revolves around the identification of patterns. |
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3. Finance, Growth and Decay |
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Outcome |
Relevance |
| 10.3.1 |
Use simple and compound growth formulae. |
The mathematics of finance is very relevant to daily and long-term financial decisions learners will need to make in terms of investing, taking loans, saving and understanding exchange rates and their influence more globally. |
| 10.3.2 |
Implications of fluctuating exchange rates. |
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4. Algebra |
|
Outcome |
Relevance |
| 10.4.1 |
Identifying and converting forms of rational numbers.Working with simple surds that are not rational. |
Algebra provides the basis for mathematics learners to move from numerical calculations to generalising operations, simplifying expressions, solving equations and using graphs and inequalities in solving contextual problems. |
| 10.4.2 |
Working with laws of integral exponents.Establish between which two integers a simple surd lies.Appropriately rounding off real numbers. |
| 10.4.3 |
Manipulating and simplifying algebraic expressions (including multiplication and factorisation). |
| 10.4.4 |
Solving linear, quadratic and exponential equations.Solving linear inequalities in one and two variables algebraically and graphically. |
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5. Differential Calculus |
|
Outcome |
Relevance |
| 10.5.1 |
Investigate average rate of change between two independent values of a function. |
The central aspect of rate of change to differential calculus is a basis to further understanding of limits, gradients and calculations and formulae necessary for work in engineering fields, e.g. designing roads, bridges etc. |
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6. Probability |
|
Outcome |
Relevance |
| 10.6.1 |
Compare relative frequency and theoretical probability.Use Venn diagrams to solve probability problems.Mutually exclusive and complementary events.Identity for any two events A and B. |
This topic is helpful in developing good logical reasoning in learners and for educating them in terms of real-life issues such as gambling and the possible pitfalls thereof. |
|
7. Euclidean Geometry and Measurement |
|
Outcome |
Relevance |
| 10.7.1 |
Investigate, form and try to prove conjectures about properties of special triangles, quadrilaterals and other polygons.Disprove false conjectures using counter-examples.Investigate alternative definitions of various polygons. |
The thinking processes and mathematical skills of proving conjectures and identifying false conjectures is more the relevance here than the actual content studied. The surface area and volume content studied in real-life contexts of designing kitchens, tiling and painting rooms, designing packages, etc. is relevant to the current and future lives of learners. |
| 10.7.2 |
Solve problems involving surface area and volumes of solids and combinations thereof. |
|
8. Trigonometry |
|
Outcome |
Relevance |
| 10.8.1 |
Definitions of trig functions.Derive values for special angles.Take note of names for reciprocal functions. |
Trigonometry has several uses within society, including within navigation, music, geographical locations and building design and construction. |
| 10.8.2 |
Solve problems in 2 dimensions. |
| 10.8.3 |
Extend definition of basic trig functions to all four quadrants and know graphs of these functions. |
| 10.8.4 |
Investigate and know the effects of a and q on the graphs of basic trig functions. |
|
9. Analytical Geometry |
|
Outcome |
Relevance |
| 10.9.1 |
Represent geometric figures on a Cartesian coordinate system.For any two points, derive and apply formula for calculating distance, gradient of line segment and coordinates of mid-point. |
This section provides a further application point for learners’ algebraic and trigonometric interaction with the Cartesian plane. Artists and design and layout industries often draw on the content and thought processes of this mathematical topic. |
|
10. Statistics |
|
Outcome |
Relevance |
| 10.10.1 |
Collect, organise and interpret univariate numerical data to determine mean, median, mode, percentiles, quartiles, deciles, interquartile and semi-interquartile range. |
Citizens are daily confronted with interpreting data presented from the media. Often this data may be biased or misrepresented within a certain context. In any type of research, data collection and handling is a core feature. This topic also educates learners to become more socially and politically educated with regards to the media. |
| 10.10.2 |
Identify possible sources of bias and errors in measurements. |
Mathematics educators also need to ensure that the following important specific aims and general principles are applied in mathematics activities across all grades:
- Calculators should only be used to perform standard numerical computations and verify calculations done by hand.
- Real-life problems should be incorporated into all sections to keep mathematical modelling as an important focal point of the curriculum.
- Investigations give learners the opportunity to develop their ability to be more methodical, to generalise and to make and justify and/or prove conjectures.
- Appropriate approximation and rounding skills should be taught and continuously included and encouraged in activities.
- The history of mathematics should be incorporated into projects and tasks where possible, to illustrate the human aspect and developing nature of mathematics.
- Contextual problems should include issues relating to health, social, economic, cultural, scientific, political and environmental issues where possible.
- Conceptual understanding of when and why should also feature in problem types.
- Mixed ability teaching requires educators to challenge able learners and provide remedial support where necessary.
- Misconceptions exposed by assessment need to be dealt with and rectified by questions designed by educators.
- Problem solving and cognitive development should be central to all mathematics teaching and learning so that learners can apply the knowledge effectively.
Source:
OpenStax, Mathematics grade 10 teachers' guide - siyavula webbooks. OpenStax CNX. Aug 10, 2011 Download for free at http://cnx.org/content/col11341/1.1
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