Request for Proposal: Review existing learning materials against the CAPS, Mathematics, Grade 10 – 12 Context Mindset Learn has developed and produced over 250 learning resources for Grades 10, 11 and 12 Mathematics. The resources were developed between 2005 and 2011 and were aligned to the National Curriculum Statement. They include videos and supporting print documents. The Mathematics resources comprise videos and print notes for:
Grade 10: Linear Equations I (8), Algebraic Fractions 1 (12), Calculating with Data (8), Classification of Triangles (10), Co-ordinate and Transformation Geometry (10), Exponents (10), Introduction to Fractions (8), Investigating Geometry (6), Investigating Geometry 2 (8), Linear Functions (2), Linear Inequalities (3), Mathematical Modelling (8), Number Patterns (6), Properties of Quadrilaterals (10), Quadratic Equations (4), Representing Data (5), Simple, Compound and Exponential Growth (8), Simultaneous Equations (8), Study of Functions (8), Triangular Trigonometry 1 (8), Triangular Trigonometry 2 (6), Probability (6), Study of Functions 2(9), Surface Area (11), Volume (9), Manipulating Data (5). Grade 11: Co-ordinate and Transformation Geometry (4), Data Handling (6), Linear Programming (8), Simple Compound and Growth Decay (4), Trigonometry (5). Grade 12: Consolidating Algebra (8), Euclidian Geometry (12), Data Handling Applications (6). Please see full details of the lengths of these video series in the attached annexure. These Mindset Learn learning resources are available on our website, www.mindset.co.za/learn; follow the link to Mathematics and the relevant grade. Mindset will provide all video resources on DVD, once a contractor has been appointed.
Project Description Project objective Review all Mindset Learn’s Mathematics materials, listed above, against the final CAPS, to provide a report, in the form of a matrix provided by Mindset Learn, on the: a. Resources or portions of resources that can be retained as they are, because they currently satisfy CAPS requirements b. Resources that can or must be split or shortened, so that only a portion is used in one grade and another portion is discarded or utilised for another grade, for example. c. Resources or portions of resources that need updating because they are outdated and/or incomplete, in terms of today’s understanding and resources. 1 Mindset Network RFP: Mathematics CAPS Review
d. Resources or portions of resources that must be developed again and re-produced, to ensure alignment with and suitability for the CAPS e. Portions of the CAPS for which there is no suitable Mindset Learn resource; in this case, give a short, clear description of the content and treatment required in a new learning resource
Project Outputs Add detail to the provided matrix to reflect the following outputs: 1. Show the media and/or portions of existing Mindset Learn’s Mathematics media that can be used for specific sections of the CAPS, using media name(s), lesson number(s) and relevant time/position portions, where relevant and covering all the requirements in a – e above 2. Give detailed descriptions of changes that are required in the portions identified in c, d and e above. tutorials 3. List a minimum of 2 online or other accessible resources or references for each sub-topic, to serve as input for content developers and reviewers and to provide additional learning resources for learners and teachers.
Project details Mindset Learn will provide a comprehensive matrix of all curriculum requirements. The matrix is designed along the lines of the final Mathematics CAPS, with requirements per grade also indicated.
Time frames Completion dates include: A scope of work will be drawn up to indicate milestones for sections of the review and matrix, through March and part of April. Mindset Learn must review each section of the matrix in draft form, before a final version is submitted. The final version of the review matrix must be received by 16 April 2012
Available budget It is expected that the CAPS review for Mathematics, Grade 10 – 12, will cost between R65, 000 and R80, 000. Budgets outside this range will be considered but explicit details of all costs should be provided as justification.
Submission Requirements
Description of team members and their Mathematics education and curriculum skills and experience, including any previous content development experience
Proposed project plan
Detailed/itemised budget
Proposal Submission Submit proposals to:
Fleurette Maluleke (fleurette@mindset.co.za); for clarification of project requirements, phone Fleurette on 086 100 6463.
Submissions close on: 12h00; 9 March 2012 2 Mindset Network RFP: Mathematics CAPS Review
No late submissions will be accepted.
Annexure MINDSET’S MATHEMATICS LEARNING RESOURCES – for CAPS review MATHS GRADE 10 FET
DURATION
Approx 48 hours Linear Equations1 Introduction to linear equations 2_Balancing equations 3_Equations with decimal fractions 4_Fractions in linear equations 5_Fractions with unknowns in the denominator 6_Fractions and factorising 7_Factorising denominators 8_Changing the subject of a formula
00:15:34:15 00:14:59:20 00:14:01:08 00:13:53:03 00:11:40:05 00:12:47:23 00:13:59:00 00:10:41:13
Algebraic Fractions 1 Revision of factorisation 2_Simplification of fractions I 3_Simplification of fractions II 4_Simplification of more advanced fractions I 5 Simplification of more advanced fractions II 6_Fractions including trinomials 7_Multiplication of fractions I 8_Multiplication of fractions II 9_Division of fractions 10_Finding the lowest common multiple 11_Addition and subtraction of fractions 12_Algebraic fractions
00:14:04:05 00:13:28:15 00:12:30:10 00:11:51:15 00:11:05:05 00:15:55:10 00:12:35:00 00:14:19:21 00:14:08:05 00:11:28:18 00:12:34:08 00:13:49:20
Calculating with Data 1_Collecting data 2_Collecting data - who and how? 3_Organising data 4_Representing data on a bar graph 5_Drawing pie charts 6_Mean, median and mode 7_Range and other measures of dispersion 8_Grouping data
00:16:44:18 00:16:36:18 00:13:04:08 00:14:59:13 00:14:14:23 00:17:19:23 00:15:09:10 00:14:59:05
Classification of triangles 1_Triangle inequalities 2_Naming triangles & constructions in the scalene triangle 3_Isosceles triangles 4_Equilateral triangles 5_Concurrency 6_Triangle theorems 7_Triangles and other geometric properties 8_Similarity in triangles 9_Application of similarity
00:12:52:20 00:15:54:00 00:11:47:18 00:14:55:23 00:11:14:08 00:11:40:05 00:11:11:15 00:11:48:08 00:15:01:00 3
Mindset Network RFP: Mathematics CAPS Review
10_Classification of triangles revisited
00:08:40:05
Co-ordinate and Transformation Geometry 1_Working in the cartesian plane 2_The distance formula 3_Using the distance formula 4_The midpoint of a line segment 5_The gradient of a line 6_Translating points and shapes 7_Reflections in the X and Y axes 8_Reflections about the line y = x 9_Parallel and perpendicular lines 10_Using your geometry toolkit
00:10:27:00 00:12:15:03 00:13:44:00 00:14:32:03 00:12:06:13 00:12:37:03 00:10:16:15 00:14:17:15 00:14:56:05 00:11:07:03
Exponents 1_Introduction to exponents 2_Multiplying and dividing with exponents I 3_Multiplying and dividing with exponents II 4_Negative and zero exponents 5_Raising of a power to a power 6_Applying the laws of exponents 7_Working with prime numbers 8_Fractions with exponents 9_Simplifying expressions 10_Using all the laws of exponents
00:13:41:15 00:11:28:17 00:12:45:15 00:13:57:17 00:14:19:10 00:09:00:20 00:13:26:10 00:13:05:22 00:11:52:05 00:11:59:05
Introduction to functions 1_Can you do it? 2_Dependent or independent? 3_Patterns 4_Precisely! 5_Using Functions 6_Graphs and Formulae 7_Boundaries and restrictions 8_Translations
00:14:26:20 00:14:22:00 00:14:27:08 00:14:07:23 00:15:04:18 00:12:10:13 00:15:40:03 00:13:36:15
Investigating Geometry 1 1_Geometry around the world 2_Geometric tool kit 1 3_Geometric tool kit 2 4_Inductive and deductive reasoning 5_Conjectures, proofs and triangles 6_Conjectures, proofs and polygons
00:16:17:01 00:14:31:07 00:14:18:13 00:19:57:01 00:17:52:03 00:17:45:01
Investigating Geometry 2 1_Classifying quadrilaterals 2_Making definitions 3_Writing a good definition 4_Plans and paragraph proofs 5_Flowchart proofs 6_Proofs in co-ordinate geometry 7_Conjectures about area
00:14:52:05 00:13:45:10 00:14:39:16 00:11:08:00 00:12:40:13 00:14:10:18 00:11:06:02 4
Mindset Network RFP: Mathematics CAPS Review
8_Area theorems
00:14:57:08
Linear Functions 1_Introduction to linear functions 2_Graphs 3_Formulae and Graphs 4_More Formulae 5_Analysing the gradient 6_Translation 7_More about the Gradient 8_Linear functions
00:14:55:05 00:14:52:15 00:15:23:05 00:14:00:13 00:13:30:10 00:13:58:10 00:15:15:15 00:14:05:03
Linear Inequalities 1_Linear Inequalities on a number line 2_Solving a linear inequality 3_More linear inequalities
00:13:17:13 00:14:13:05 00:14:44:08
Mathematical Modelling 1_What is mathematical modelling? 2_Modelling – pregnancy testing 3_Modelling – sports drug testing 4_Modelling – cell phone contracts 5_Modelling – changing the values of the assumptions 6_Modelling – comparing cell phone contracts 7_Modelling – Traffic lights 8_Strengthening the traffic light model
00:12:34:20 00:14:57:05 00:16:49:00 00:12:49:00 00:10:56:15 00:11:29:23 00:14:18:10 00:15:14:00
Number Patterns 1_Investigating real patterns 2_Completing number patterns 3_Geometric number patterns 4_Finding the nth term 5_From patterns to algebra 6_From patterns to introducing functions
00:14:56:20 00:19:29:10 00:15:24:15 00:16:32:08 00:14:07:23 00:13:11:08
Properties of Quadrilaterals 1 Polygons 2_More about polygons 3_The square 4_The rhombus 5_The convex kite 6_The concave kite 7_The rectangle 8_The parallelogram 9_The trapezium 10_All the quadrilaterals
00:11:36:20 00:08:16:20 00:14:08:05 00:12:48:07 00:13:45:10 00:10:47:15 00:14:19:12 00:14:51:22 00:13:34:10 00:12:49:22
Quadratic Equations 1_Graphs and quadratic equations 2_Identify and solve quadratic equations 3_Finding the number of roots 4_Solving more challenging quadratic equations
00:10:48:03 00:14:52:05 00:14:53:08 00:14:50:05 5
Mindset Network RFP: Mathematics CAPS Review
Representing Data 1_Naming and reading graphs 2_Continuous data and drawing line graphs 3_Drawing histograms 4_Frequency polygons 5_Mean, median and mode
00:15:25:00 00:14:12:15 00:10:55:10 00:15:57:23 00:11:13:20
Simple, compound and exponential growth 1 Exponential growth 2_An exponential function 3_Solving equations by trial and error 4_Making the bases the same 5_Simple interest 6_Comparing simple and compound interest 7_Compound interest and inflation 8_Simple interest and hire purchase
00:12:33:00 00:09:25:02 00:11:37:00 00:13:02:15 00:14:45:00 00:15:28:20 00:11:44:20 00:12:38:05
Simultaneous Equations 1_What are simultaneous equations? 2_Graphical solutions 3_The substitution method 4_The elimination method 5_The elimination method 6_Problem solving 7_A money problem 8_A digit problem
00:14:02:18 00:13:48:10 00:14:30:08 00:13:32:13 00:13:14:20 00:14:03:00 00:09:12:05 00:10:51:15
Study of Functions 1 1_The linear function 2_Gradient of a Linear Function 3_The effect of q 4_The quadratic function 5_Shifting the quadratic function 6_The hyperbolic function 7_Changing the hyperbolic function 8_Comparing functions
00:19:38:05 00:18:31:20 00:13:38:10 00:15:58:15 00:14:30:13 00:16:39:15 00:16:27:00 00:14:14:10
Triangular Trigonometry 1 1_What is trigonometry all about? 2_Using an astrolabe 3_Discovering the tangent ratio 4_Using the tan ratio 5_Using the sine ratio 6_Using the cosine ratio 7_Which ratio? 8_Choosing a ratio
00:14:44:15 00:15:14:03 00:15:08:05 00:15:06:23 00:15:05:03 00:14:57:08 00:14:30:23 00:15:02:03
Triangular Trigonometry 2 1_Solving trig equations with a calculator 2_What about the angle? 3_Going up - angles of elevation
00:14:40:18 00:14:43:13 00:14:37:13 6
Mindset Network RFP: Mathematics CAPS Review
4_Going down - angles of depression 5_Solving trig problems 6_Trig on the Cartesian plane
00:14:19:18 00:14:21:18 00:14:54:18
Probability 1_What`s the chance? 2_Calculating probabilities 3_Relative frequency 4_Venn diagrams and probability 5_Complementary events 6_Inclusive and exclusive events
00:13:35:02 00:13:40:15 00:16:00:12 00:14:28:10 00:12:47:12 00:21:56:07
Study of Functions 2 1_The sine rule 2_Sine and cosine graphs 3_Changing the sine and cosine functions 4_Shifting the sine and cosine functions 5_The tan function 6_The effect of a and q on the tan function 7_The exponential function 8_Changing a and q in the exponential function 9_Comparing changes to functions
00:19:24:22 00:18:57:15 00:17:50:05 00:00:00:00 00:16:56:15 00:17:04:07 00:20:26:22 00:19:57:22 00:19:10:20
Surface Area 1_Defining Area 2_Formulae for Surface Area 3_More Formulae for Surface Area 4_Different viewpoints 5_Rectangular Prisms 6_Triangular Prisms 7_Hexagonal Prisms 8_The Area Formula for a circle 9_The Cylinder 10_Increasing Surface Area 11_Decreasing Surface Area
00:13:11:20 00:11:17:07 00:11:33:05 00:09:41:10 00:09:26:17 00:11:50:15 00:08:38:20 00:11:11:07 00:10:45:07 00:13:11:02 00:00:00:00
Volume 1_Right rectangular prisms 2_Right rectangular prisms in 2-D 3_The concept of volume 4_The formula for volume 5_Calculating volume 6_Volume of different right prisms 7_Volume of cylinders 8_Doubling the dimensions 9_Changing the dimensions by k
00:12:03:00 00:10:43:02 00:14:34:22 00:11:36:10 00:10:09:12 00:14:05:12 00:15:21:07 00:12:29:15 00:14:50:17
Manipulating Data Data Teacher Guide 1 Avoiding bias in sample selection 2 Avoiding Bias in survey questionaires 3 Graphs that misrepresent data
00:15:30:05 00:16:00:22 00:10:18:10 00:12:39:22 7
Mindset Network RFP: Mathematics CAPS Review
4 Statistics in the media and politics 5 Using statistics to present opposing views
00:18:19:00 00:13:42:05
MATHS GRADE 11 FET Approx 8 hours Co-ordinate and Transformation Geometry 1_The Straight Line in the Cartesian Plane 2_Parallel and Perpendicular Lines 3_Rotation in the Cartesian Plane 4_The Enlargement of a Polygon in the Cartesian Plane
DURATIONS
Data Handling 1_Box and Whisker Plot 2_Ways to Represent Data 3_Drawing Cumulative Frequency Graphs 4_Variance and Standard Deviation 5_Drawing and Intepreting Scatter Plots 6_Linear, Quadratic and Exponential Functions on Scatter Plots
00:17:40:10 00:15:21:22 00:19:02:05 00:17:28:07
00:20:18:20 00:19:22:10 00:18:24:02 00:23:33:02 00:19:00:15 00:20:43:20
Linear Programming 1_Linear Programming and making choices 2_The feasible region 3_Plotting the feasible region 4_Linear inequalities 5_Graphing the feasible region 6_Using a search line 7_Solving a linear programming problem 8_More work with linear programming
00:09:49:18 00:15:28:13 00:17:10:12 00:19:52:03 00:23:17:16 00:22:53:18 00:23:44:13 00:22:12:10
Simple compound and growth decay 1_Understanding simple and compound decay 2_Using the simple and compound decay formulae 3_Nominal and effective interest rates 4_Problem solving with simple compound decay
00:12:36:15 00:14:34:20 00:12:02:15 00:15:29:15
Trigonometry 1_Solving Triangles Using Trigonometry 2_The Area Rule 3_The Sine Rule 4_The Cosine Rule 5_Applying The Sine, Cosine and Area Rules
00:14:51:00 00:13:39:00 00:15:57:10 00:17:58:02 00:17:27:20
MATHS GRADE 12 FET Approx 16 hours Other Geometries
DURATIONS
Teacher Guide
00:12:25:22
1_Taxicab Geometry
00:20:54:12
2_Great Circles in Spherical Geometry
00:18:53:02
3_Triangles in Spherical Geometry
00:15:21:20 8
Mindset Network RFP: Mathematics CAPS Review
4_Fractals
00:20:43:15
Calculus Teacher Guide
00:14:48:17
1_Introduction to Calculus
00:15:09:20
2_Establishing what we need Calculus for
00:19:42:02
3_In search of the gradient of the tangent
00:16:18:00
4_The tangent search continued
00:16:39:15
5_The derivative function
00:20:15:20
6_Determining derivatives
00:25:38:20
7_Sketching the graph of a cubic function
00:22:37:07
8_Rate of Change
00:23:07:15
9_Solving a Problem
00:26:21:17
Sequences & Series Teacher Guide 1_Introduction to Sequences and Series 2_Sigma Notation 3_Arithmetic Progressions 4_Geometric Progressions 5_Sum to infinity of Geometric Progressions
00:15:55:15 00:19:02:19 00:20:58:12 00:23:02:13 00:25:06:22 00:19:50:06
Financial Maths 1_Saving for Future Studies
00:19:13:07
2_Evaluating Loan Options
00:21:22:05
3_Housing Loans
00:16:30:00
4_A Sinking Fund
00:13:42:10
Trigonometry & Geometry 1_Circles
00:19:02:00
2_Tangents
00:15:10:00
3_Identities and Equations
00:19:06:02
4_Using the Compound Angle Formulae
00:18:05:05
5_Transformation Geometry
00:16:36:17
6_Trigonometric Graphs
00:17:53:12
7_Sine Area and Cosine Rules
00:15:05:05
8_Problems in 3 Dimensions
00:16:07:15
Functions 1_Defining a Function
00:11:11:16
2_Vertical Translations of Functions
00:15:46:12
3_More Transformations of Functions
00:14:07:02
4_Stretching of Functions
00:13:58:24
5_Application of Transformation
00:15:34:09 9
Mindset Network RFP: Mathematics CAPS Review
6_Introducing Inverse Functions
00:16:03:07
7_The Inverse of Linear Functions
00:13:14:00
8_The Inverse of Exponential Functions
00:11:37:08
9_The Inverse of Quadratic Functions
00:07:56:22
Euclidian Geometry 1_Similarity and Proportion 2_Similarity and Proportion Theorems 3_Similarity and Pythagoras 4_Chord Theorems 5_Angles in the Same Segment 6_Cyclic Quadrilaterals 7_Tangent Chord Theorems 8_Converse of Tangent Chord Theorem 9_A Summary of the Geometry Theorems 10_Solving Geometry Problems I 11_Solving Geometry Problems II 12_Solving Geometry Problems III
196 minutes total
Consolidating Algebra 1_Quadratic Equations I 2_Quadratic Equations II 3_Quadratic Functions and Graphs 4_Quadratic Inequalities 5_Simultaneous Equations 6_Cubic Functions and Equations 7_Surds and Exponents 8_Why logs?
123 minutes total
Data Handling 1_Mean and Standard Deviation 2_Graphs of Normal Distribution and Mean 3_Bivariate Data 4_Correlation Co-efficients 5_The Use and Misuse of Statistics 6_The Bell Curve and Normal Distribution
78 minutes total
10 Mindset Network RFP: Mathematics CAPS Review