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Resource Details

Resource Name:

snells law (Lesson Plan)

Resource Description:

learners must be able to draw venn diagram

Resource Status:

Unchecked / Unapproved Resources

Resource Tags:

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Resource Type:

Lesson Plan

Resource Media Type:

PDF

Resource Licencing Condition:

Creative Commons: Attribution- Share Alike

Resource Language:

English

Teacher Context:

N/A

Curriculum Links

Learning Level / Learning Area

South African Education Sectors

SA Schools

Further Education and Training

Grade 10

Grade 11

Curriculum Topics

Thutong

Data Handling and Probability

Venn Diagrams

Outcomes / Assessments

Outcomes

MAT.LO1 (FET)

Recognise, describe, represent and work confidently with numbers and their relationships to estimate, calculate and check solutions.

AS11.1.1

Understand that not all numbers are real. (This requires the recognition but not the study of non-real numbers.)

AS11.1.2

a. Simplify expressions using the laws of exponents for rational exponents.
b. Add, subtract, multiply and divide simple surds eg.

c. Demonstrate an understanding of error margins.

AS11.1.3

Investigate number patterns (including but not limited to those where there is a constant second difference between consecutive terms in a number pattern, and the general term is therefore quadratic) and hence:
a. make conjectures and generalisations
b. provide explanations and justifications and attempt to prove conjectures.

AS11.1.4

Use simple and compound decay formulae

to solve problems (including straight line depreciation and depreciation on a reducing balance) (link to Learning Outcome 2).

AS11.1.5

Demonstrate an understanding of different periods of compounding growth and decay (including effective compounding growth and decay and including effective and nominal interest rates.

AS11.1.6

Solve non-routine, unseen problems.

MAT.LO2 (FET)

Investigate, analyse, describe and represent a wide range of functions and solve related problems.

AS11.2.1

a. Demonstrate the ability to work with various types of functions including those listed in the following Assessment Standard.
b. Recognise relationships between variables in terms of numerical, graphical, verbal and symbolic representations and convert flexibly between these representations (tables, graphs, words and formulae).

AS11.2.2

Generate as many graphs as necessary, initially by means of point-by-point plotting, supported by available technology, to make and test conjectures about the effect of the parameters k, p, a and q for functions including:

AS11.2.3

Identify characteristics as listed below and hence use applicable characteristics to sketch graphs of functions including those listed above:
a. domain and range;
b. intercepts with the axes;
c. turning points, minima and maxima;
d. asymptotes;
e. shape and symmetry;
f. periodicity and amplitude;
g. average gradient (average rate of change);
h. intervals on which the function increases/decreases;
i. the discrete or continuous nature of the graph.

AS11.2.7

Investigate numerically the average gradient between two points on a curve and develop an intuitive understanding of the concept of the gradient of a curve at a point.

AS11.2.8

q. Solve linear programming problems by optimising a function in two variables, subject to one or more linear constraints, by numerical search along the boundary of the feasible region.
b. Solve a system of linear equations to find the co-ordinates of the vertices of the feasible region.

AS11.2.4

Manipulate algebraic expressions:
a. by completing the square;
b. simplifying algebraic fractions with binomial denominators.

AS11.2.5

Solve:
a. quadratic equations (by factorisation, by completing the square, and by using the quadratic formula) and quadratic inequalities in one variable and interpret the solution graphically;
b. equations in two unknowns, one of which is linear and one of which is quadratic, algebraically or graphically.

AS11.2.6

Use mathematical models to investigate problems that arise in real-life contexts:
a. making conjectures, demonstrating and explaining their validity;
b. expressing and justifying mathematical generalisations of situations;
c. using various representations to interpolate and extrapolate;
d. describing a situation by interpreting graphs, or drawing graphs from a description of a situation, with special focus on trends and pertinent features.
(Examples should include issues related to health, social, economic, cultural, political and envirionmental matters.)

MAT.LO3 (FET)

Describe, represent, analyse and explain properties of shapes in 2-dimensional and 3-dimensional space with justification.

AS11.3.1

Use the formulae for surface area and volume of right pyramids, right cones, spheres and combinations of these geometric objects.

AS11.3.2

a. Investigate necessary and sufficient conditions for polygons to be similar.
b. Prove and use (accepting results established in earlier grades):
> that a line drawn parallel to one side of a triangle divides the other two sides proportionally (the Mid-point Theorem as a special case of this theorem);
> that equiangular triangles are similar;
> that triangles with sides in proportion are similar;
> the Pythagorean Theorem by similar triangles.

AS11.3.3

Use a Cartesian co-ordinate system to derive and apply:
a. the equation of a line through two given points
b. the equation of a line through one point and parallel or perpendicular to a given line
c. the inclination of a line.

AS11.3.4

Investigate, generalise and apply the effect on the co-ordinates of:
a. the point (x ; y) after rotation around the origin through an angle of 90º or 180º;
b. the vertices (x₁ ; y₁), (x₂ ; y₂),..;(x_n ; y_n) of a polygon after enlargement through the origin, by a constant factor k.

AS11.3.5

a. Derive and use the values of the trigonometric functions (in surd form where applicable) of 30º, 45ºand 60º.
b. Derive and use the following identities:

c. Derive the reduction formulae for

d. Determine the general solution of trigonometric equations
e. Establish and apply the sine, cosine and area rules.

AS11.3.6

Solve problems in two dimensions by using the sine, cosine and area rules; and by constructing and interpreting geometric and trigonometric models.

AS11.3.7

Demonstrate an appreciation of the contributions to the history of the development and use of geometry and trigonometry by various cultures through educative forms of assessment (e.g. an investigative project).

MAT.LO4 (FET)

Collect, organise, analyse and interpret data to establish statistical and probability models to solve related problems.

AS11.4.1

a. Calculate and represent measures of central tendency and dispersion in univariate numerical data by:
> five number summary (maximum, minimum and quartiles);
> box and whisker diagrams;
> ogives;
> calculating the variance and standard deviation of sets of data manually (for small sets of data) and using available technology (for larger sets of data), and representing results graphically using histograms and frequency polygons.
b. Represent bivariate numerical data as a scatter plot and suggest intuitively whether a linear, quadratic or exponential function would best fit the data (problems should include issues related to health, social, economic, cultural, political and environmental issues).

AS11.4.4

Differentiate between symmetric and skewed data and make relevant deductions.

AS11.4.5

Use theory learned in this grade in an authentic integrated form of assessment (e.g. in an investigative project).

AS11.4.3

(a) Identify potential sources of bias, error in measurement, potential uses and misuses of statistics and charts and their effects (critical analysis of misleading graphs and claims made by persons or groups trying to influence the public is implied here).
(b) Effectively communicate conclusions and predictions that can be made from the analysis of data.