Curriculum



PROVINCE OF THE

EASTERN CAPE

EDUCATION

DIRECTORATE: CURRICULUM FET PROGRAMMES

LESSON PLANS

TERM 2

MATHEMATICS

FOREWORD

The following Grade 10, 11 and 12 Lesson Plans were developed by Subject Advisors from 09 March – 13 March 2009. Teachers are requested to look at them, modify them where necessary to suit their contexts and resources. It must be remembered that Lesson Plans are working documents, and any comments to improve the lesson plans in this document will be appreciated. Teachers are urged to use this document with the following departmental policy documents: Subject Statement; LPG 2008; SAG 2008; Examination Guidelines 2009 and Provincial CASS Policy/ Guidelines.

Lesson planning is the duty of each and every individual teacher but it helps when teachers sometimes plan together as a group. This interaction not only helps teachers to understand how to apply the Learning Outcomes (LOs) and Assessment Standards (ASs) but also builds up the confidence of the teachers in handling the content using new teaching strategies.

It must please be noted that in order to help teachers who teach across grades and subjects, an attempt has been made to standardise lesson plan templates and thus the new template might not resemble the templates used in each subject during the NCS training. However, all the essential elements of a lesson plan have been retained. This change has been made to assist teachers and lighten their administrative load.

Please note that these lesson plans are to be used only as a guide to complete the requirements of the Curriculum Statements and the work schedules and teachers are encouraged to develop their own learner activities to supplement and/or substitute some of the activities given here (depending on the school environment, number and type of learners in your class, the resources available to your learners, etc).

Do not forget to build in the tasks for the Programme of Assessment into your Lesson Plans.

Strengthen your efforts by supporting each other in clusters and share ideas. Good Luck with your endeavors to improve Teaching, Learning and Assessment.

LESSON PLAN: 1 for Term 2

|Subject: Mathematics Grade 11 |

|Lesson Plan: Trigonometry : special angles and identities Number of Activities 3 Duration: |

|4H 30 Min Week 11-12/ Date |

|Context: Mathematical - Trigonometry : special angles and identities |

|Link with previous lesson: Grade 10 Trigonometry |

|KNOWLEDGE (K): Functions and trigonometry graphs SKILLS (S): Drawing, identification, VALUES (V): appreciation |

|Learning Outcome 1: |Learning Outcome 2: |Learning Outcome 3: Space, Shape and Measurement|Learning Outcome 4: Data |

|Number and Number Relationships |Functions and Algebra |The learner is able to describe, represent, |Handling and Probability |

|When solving problems, the learner is able to recognise, |The learner is able to investigate, analyse,describe and |analyse and explain properties of shapes in |The learner is able to collect,|

|describe, represent and work confidently with numbers and|represent a wide range of functions and solve related |2-dimensional and 3-dimensional space with |organise, analyse and interpret|

|their relationships to estimate, calculate and check |problems. |justification. |data to establish statistical |

|solutions. | | |and probability models to solve|

| | | |related problems. |

|11.1.1 Understand that not all numbers are | |11.2.1 (a) Demonstrate the ability to work with various| |11.3.1 Use the formulae for surface area | |11.4.1 | |

|real. | |types of functions | |and volume of right pyramids, right | |Calculate and represent| |

| | |(b) Recognise relationships between variables in terms | |cones, spheres and combinations of these | |measures of central | |

| | |of numerical, graphical, verbal and symbolic | |geometric objects. | |tendency and dispersion| |

| | |representations and convert flexibly between these | | | | | |

| | |representations ( | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | |Represent bivariate | |

|11.1.2 | |11.2.2 Generate as many graphs as necessary, initially | |11.3.3 Use a Cartesian co-ordinate system| |numerical data as a | |

|(a) Simplify expressions using the laws of | |by means of point-by-point plotting, supported by | |to derive and apply: | |scatter plot and | |

|exponents for rational exponents.(b) Add, | |available technology, to make and test conjectures | | | |suggest intuitively | |

|subtract, multiply and divide simple surds | |about the effect of the parameters k, p, a and q for | | | |whether a linear, | |

|(c) Demonstrate an understanding of error | |functions including: | | | |quadratic or | |

|margins. | | | | | |exponential function | |

| | | | | | |would best fit the data| |

| | | | | | |(problems should | |

| | | | | | |include issues related | |

| | | | | | |to health | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.3 Investigate number patterns (including | |11.2.3 Identify characteristics as listed below and | |11.3.4 Investigate, generalise and apply | | | |

|but not limited to those where there is a | |hence use applicable characteristics to sketch graphs | |the effect on the co-ordinates | | | |

|constant second difference between consecutive | |of functions | | | | | |

|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. | | | | | | | |

| | | | | | | | |

| | | | | |√ | | |

|11.1.4 Use simple and compound decay formulae | |11.2.4 Manipulate algebraic expressions: | |11.3.5 Derive and use the values of the | | | |

|to solve problems (including straight line | |(a) by completing the square; | |trigonometric functions | | | |

|depreciation and depreciation on a reducing | |(b) simplifying algebraic fractions with binomial | | | | | |

|balance) (link to Learning Outcome 2). | |denominators. | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.5 Demonstrate an understanding of | |11.2.5 Solve: a) quadratic equations | |11.3.6 Solve problems in two dimensions | | | |

|different periods of compounding growth and | |(b) equations in two unknowns | | | | | |

|decay | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.6 Solve non-routine, unseen problems. | |11.2.6 Use mathematical models to investigate problems | | | | | |

| | |that arise in real-life contexts: | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.7 Investigate numerically the average gradient | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.8 Solve linear programming problems | | | | | |

| | | | | | | | |

| | | | | | | | |

| |Teachers Activities |Learners Activities |Teaching Methods |Assessment |Resources |Date Completed |

|Activity 1 |1. Teacher revises the | Once the learners have |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Special angles |trig. definitions by asking|grasped the concept of |answer, |memo rubric |worksheet | |

| |questions. |special angles, explain how| |Educator, peer | | |

| |2.Teacher gives learners a |they can use the special | | | | |

| |worksheet that will assist |angles in reduction | | | | |

| |them to discover special |formulae , a worksheet can | | | | |

| |angles |be given to learners. | | | | |

| |2.1 for 300 and 600 use an |Give learners more | | | | |

| |equilateral triangle |expression for learners to | | | | |

| |2.2 for 450 use a right- |simplify without using a | | | | |

| |angled isosceles triangle |calculator. | | | | |

| |3. Once the learners have | | | | | |

| |grasped the concept of | | | | | |

| |special angles, explain how| | | | | |

| |they can use the special | | | | | |

| |angles in reduction | | | | | |

| |formulae , a worksheet can | | | | | |

| |be given to learners. | | | | | |

|Activity 2 |Revise basic trig. Ratios, |Revise basic trig. Ratios, |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Basic Trig ratios |factorization, manipulation|factorization, manipulation|answer, |memo rubric |worksheet | |

| |of fractions, squaring of a|of fractions, squaring of a| |Educator, peer | | |

| |binomial, to ensure that |binomial, to ensure that | | | | |

| |the learners have an |the learners have an | | | | |

| |understanding and adequate |understanding and adequate | | | | |

| |skills for the concepts |skills for the concepts | | | | |

| |mentioned above a worksheet|mentioned above a worksheet| | | | |

| |can be used for this task. |can be used for this task. | | | | |

|Activity 3 |Deriving trig. |Deriving trig. |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Identities |Identities-the basic trig |Identities-the basic trig |answer, |memo rubric |worksheet | |

| |ratios can be expressed in |ratios can be expressed in | |Educator, peer | | |

| |terms of a point on the |terms of a point on the | | | | |

| |terminal side of an angle, |terminal side of an angle, | | | | |

| |use this information to |use this information to | | | | |

| |help learners discover the |help learners discover the | | | | |

| |identities |identities | | | | |

| |Quotient identities: |Quotient identities: | | | | |

| |Tan ө= sin ө |Tan ө= sin ө | | | | |

| |Cos ө |Cos ө | | | | |

| | | | | | | |

| |Quadratic identities: |Quadratic identities: | | | | |

| |Sin2ө + cos2ө=1 |Sin2ө + cos2ө=1 | | | | |

| |Discuss the steps required | | | | | |

| |to solve identities and |Discuss the steps required | | | | |

| |give exercise to learners |to solve identities and | | | | |

| |to prove and simplify |give exercise to learners | | | | |

| | |to prove and simplify | | | | |

|Expanded Opportunities |

|Additional question papers given |

LESSON PLAN: 2 for Term 2

|Subject: Mathematics Grade 11 Lesson Plan: |

|Functions and trigonometry graphs Number of Activities 3 Duration: 4H 30 Min |

|Week 13- 14/ Date |

|Context: Mathematical - Trigonometry graphs |

|Link with previous lesson: Trigonometry : special angles and identities |

|KNOWLEDGE (K): Functions and trigonometry graphs SKILLS (S): Drawing, identification, VALUES (V): appreciation |

|Learning Outcome 1: |Learning Outcome 2: |Learning Outcome 3: Space, Shape and Measurement|Learning Outcome 4: Data |

|Number and Number Relationships |Functions and Algebra |The learner is able to describe, represent, |Handling and Probability |

|When solving problems, the learner is able to recognise, |The learner is able to investigate, analyse,describe and |analyse and explain properties of shapes in |The learner is able to collect,|

|describe, represent and work confidently with numbers and|represent a wide range of functions and solve related |2-dimensional and 3-dimensional space with |organise, analyse and interpret|

|their relationships to estimate, calculate and check |problems. |justification. |data to establish statistical |

|solutions. | | |and probability models to solve|

| | | |related problems. |

|11.1.1 Understand that not all numbers are | |11.2.1 (a) Demonstrate the ability to work with various|√ |11.3.1 Use the formulae for surface area | | |11.4.1 |

|real. | |types of functions | |and volume of right pyramids, right | | |Calcula|

| | |(b) Recognise relationships between variables in terms | |cones, spheres and combinations of these | | |te and |

| | |of numerical, graphical, verbal and symbolic | |geometric objects. | | |represe|

| | |representations and convert flexibly between these | | | | |nt |

| | |representations ( | | | | |measure|

| | | | | | | |s of |

| | | | | | | |central|

| | | | | | | |tendenc|

| | | | | | | |y and |

| | | | | | | |dispers|

| | | | | | | |ion |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | |Represent bivariate | |

|11.1.2 | |11.2.2 Generate as many graphs as necessary, initially | |11.3.3 Use a Cartesian co-ordinate system| |numerical data as a | |

|(a) Simplify expressions using the laws of | |by means of point-by-point plotting, supported by | |to derive and apply: | |scatter plot and | |

|exponents for rational exponents.(b) Add, | |available technology, to make and test conjectures | | | |suggest intuitively | |

|subtract, multiply and divide simple surds | |about the effect of the parameters k, p, a and q for | | | |whether a linear, | |

|(c) Demonstrate an understanding of error | |functions including: | | | |quadratic or | |

|margins. | | | | | |exponential function | |

| | | | | | |would best fit the data| |

| | | | | | |(problems should | |

| | | | | | |include issues related | |

| | | | | | |to health | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.3 Investigate number patterns (including | |11.2.3 Identify characteristics as listed below and | |11.3.4 Investigate, generalise and apply | | | |

|but not limited to those where there is a | |hence use applicable characteristics to sketch graphs | |the effect on the co-ordinates | | | |

|constant second difference between consecutive | |of functions | | | | | |

|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. | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.4 Use simple and compound decay formulae | |11.2.4 Manipulate algebraic expressions: | |11.3.5 Derive and use the values of the | | | |

|to solve problems (including straight line | |(a) by completing the square; | |trigonometric functions | | | |

|depreciation and depreciation on a reducing | |(b) simplifying algebraic fractions with binomial | | | | | |

|balance) (link to Learning Outcome 2). | |denominators. | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.5 Demonstrate an understanding of | |11.2.5 Solve: a) quadratic equations | |11.3.6 Solve problems in two dimensions | | | |

|different periods of compounding growth and | |(b) equations in two unknowns | | | | | |

|decay | | | | | | | |

| | | | | | | | |

| | | |√ | | | | |

|11.1.6 Solve non-routine, unseen problems. | |11.2.6 Use mathematical models to investigate problems | | | | | |

| | |that arise in real-life contexts: | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.7 Investigate numerically the average gradient | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.8 Solve linear programming problems | | | | | |

| | | | | | | | |

| | | | | | | | |

| |Teachers Activities |Learners Activities |Teaching Methods |Assessment |Resources |Date Completed |

|Activity 1 |Learners are given |Learners are given |Group work, question and |Class work |Calculator, exemplars, | |

|Drawing of trig graphs |worksheets to generate as |worksheets to generate as |answer, |Memo |worksheet | |

| |many graphs as necessary, |many graphs as necessary, | |Educator, Peer | | |

| |initially by means of |initially by means of | | | | |

| |point-by-point plotting, |point-by-point plotting, | | | | |

| |supported by available |supported by available | | | | |

| |technology, to make and |technology, to make and | | | | |

| |test conjectures about the |test conjectures about the | | | | |

| |effect of the parameters k,|effect of the parameters k,| | | | |

| |p, a and q for functions |p, a and q for functions | | | | |

| |including: |including: | | | | |

| |[pic] |[pic] | | | | |

| |[pic] |[pic] | | | | |

| |[pic] |[pic] | | | | |

|Activity 2 |Learners are given |Learners are given |Group work, question and |Class work |Calculator, exemplars, | |

|Drawing of trig graphs |worksheets to generate as |worksheets to generate as |answer, |Memo |worksheet | |

| |many graphs as necessary, |many graphs as necessary, | |Educator, Peer | | |

| |initially by means of |initially by means of | | | | |

| |point-by-point plotting, |point-by-point plotting, | | | | |

| |supported by available |supported by available | | | | |

| |technology, to make and |technology, to make and | | | | |

| |test conjectures about the |test conjectures about the | | | | |

| |effect of the parameters k,|effect of the parameters k,| | | | |

| |p, a and q for functions |p, a and q for functions | | | | |

| |including: |including: | | | | |

| |[pic] |[pic] | | | | |

| |[pic] |[pic] | | | | |

| |[pic] |[pic] | | | | |

|Activity 3 |Learners are given |Learners are given |Group work, question and |Class work |Calculator, exemplars, | |

|Characteristics of trig |worksheets where they |worksheets where they |answer, |Memo |worksheet | |

|graphs |identify characteristics as|identify characteristics as| |Educator, Peer | | |

| |listed below and hence use |listed below and hence use | | | | |

| |applicable characteristics |applicable characteristics | | | | |

| |to sketch graphs of |to sketch graphs of | | | | |

| |functions including those |functions including those | | | | |

| |listed above: |listed above: | | | | |

| |domain and range; |domain and range; | | | | |

| |intercepts with the axes; |intercepts with the axes; | | | | |

| |turning points, minima and |turning points, minima and | | | | |

| |maxima; |maxima; | | | | |

| |asymptotes; |asymptotes; | | | | |

| |shape and symmetry; |shape and symmetry; | | | | |

| |periodicity and amplitude; |periodicity and amplitude; | | | | |

|Expanded Opportunities Additional question papers given |

LESSON PLAN: 3 for Term 2

|Subject: Mathematics Grade 11 Lesson Plan: |

|Data Handling Number of Activities 3 Duration: 4H |

|30 Min x2 Week 15-16 / Date |

|Context: Data Handling |

|Link with previous lesson: Revision of grade 10 Data Handling |

| KNOWLEDGE (K): Measures of central tendency and dispersion in univariate numerical data and bivariate numerical data SKILLS (S): Measuring, calculating, drawing, interpretation VALUES (V): appreciation |

|Learning Outcome 1: |Learning Outcome 2: |Learning Outcome 3: Space, Shape and Measurement|Learning Outcome 4: Data |

|Number and Number Relationships |Functions and Algebra |The learner is able to describe, represent, |Handling and Probability |

|When solving problems, the learner is able to recognise, |The learner is able to investigate, analyse,describe and |analyse and explain properties of shapes in |The learner is able to collect,|

|describe, represent and work confidently with numbers and|represent a wide range of functions and solve related |2-dimensional and 3-dimensional space with |organise, analyse and interpret|

|their relationships to estimate, calculate and check |problems. |justification. |data to establish statistical |

|solutions. | | |and probability models to solve|

| | | |related problems. |

|11.1.1 Understand that not all numbers are | |11.2.1 (a) Demonstrate the ability to work with various| |11.3.1 Use the formulae for surface area | |11.4.1 |√ |

|real. | |types of functions | |and volume of right pyramids, right | |Calculate and represent| |

| | |(b) Recognise relationships between variables in terms | |cones, spheres and combinations of these | |measures of central | |

| | |of numerical, graphical, verbal and symbolic | |geometric objects. | |tendency and dispersion| |

| | |representations and convert flexibly between these | | | | | |

| | |representations ( | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | |Represent bivariate |√ |

|11.1.2 | |11.2.2 Generate as many graphs as necessary, initially | |11.3.3 Use a Cartesian co-ordinate system| |numerical data as a | |

|(a) Simplify expressions using the laws of | |by means of point-by-point plotting, supported by | |to derive and apply: | |scatter plot and | |

|exponents for rational exponents.(b) Add, | |available technology, to make and test conjectures | | | |suggest intuitively | |

|subtract, multiply and divide simple surds | |about the effect of the parameters k, p, a and q for | | | |whether a linear, | |

|(c) Demonstrate an understanding of error | |functions including: | | | |quadratic or | |

|margins. | | | | | |exponential function | |

| | | | | | |would best fit the data| |

| | | | | | |(problems should | |

| | | | | | |include issues related | |

| | | | | | |to health | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.3 Investigate number patterns (including | |11.2.3 Identify characteristics as listed below and | |11.3.4 Investigate, generalise and apply | | | |

|but not limited to those where there is a | |hence use applicable characteristics to sketch graphs | |the effect on the co-ordinates | | | |

|constant second difference between consecutive | |of functions | | | | | |

|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. | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.4 Use simple and compound decay formulae | |11.2.4 Manipulate algebraic expressions: | |11.3.5 Derive and use the values of the | | | |

|to solve problems (including straight line | |(a) by completing the square; | |trigonometric functions | | | |

|depreciation and depreciation on a reducing | |(b) simplifying algebraic fractions with binomial | | | | | |

|balance) (link to Learning Outcome 2). | |denominators. | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.5 Demonstrate an understanding of | |11.2.5 Solve: a) quadratic equations | |11.3.6 Solve problems in two dimensions | | | |

|different periods of compounding growth and | |(b) equations in two unknowns | | | | | |

|decay | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.6 Solve non-routine, unseen problems. | |11.2.6 Use mathematical models to investigate problems | | | | | |

| | |that arise in real-life contexts: | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.7 Investigate numerically the average gradient | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.8 Solve linear programming problems | | | | | |

| | | | | | | | |

| | | | | | | | |

| |Teachers Activities |Learners Activities |Teaching Methods |Assessment |Resources |Date Completed |

|Activity 1 |Educator give learners worksheets |Learners given worksheets to |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Measures of central |to calculate and represent |calculate and represent measures of |answer, |memo rubric |worksheet | |

|tendency and dispersion in |measures of central tendency and |central tendency and dispersion in | |Educator, peer | | |

|univariate numerical data |dispersion in univariate |univariate numerical data by: | | | | |

| | |five number summary (maximum, minimum| | | | |

| | |and quartiles); | | | | |

| | |box and whisker diagrams; | | | | |

|Activity 2 |Educator demonstrate to learners |Learners to draw and interpret |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Measures of central |how to draw and interpret ogives |ogives and also to calculate variance|answer, |memo rubric |worksheet | |

|tendency and dispersion in |and also to calculate variance and|and standard deviation (use of the | |Educator, peer | | |

|univariate numerical data |standard deviation (use of the |calculator is advised). Interpret | | | | |

| |calculator is advised). Interpret|standard deviations for normal | | | | |

| |standard deviations for normal |distributions. | | | | |

| |distributions | | | | | |

|Activity 3 |Work sheets given to learners to |Work sheets given to learners to |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Represent bivariate |represent bivariate numerical data|represent bivariate numerical data as|answer, |memo rubric |worksheet | |

|numerical data |as a scatter plot and suggest |a scatter plot and suggest | |Educator, peer | | |

| |intuitively whether a linear, |intuitively whether a linear, | | | | |

| |quadratic or exponential function |quadratic or exponential function | | | | |

| |would best fit the data (problems |would best fit the data (problems | | | | |

| |should include issues related to |should include issues related to | | | | |

| |health, social, economic, |health, social, economic, cultural, | | | | |

| |cultural, political and |political and environmental issues). | | | | |

| |environmental issues). | | | | | |

|Expanded Opportunities |

|Additional question papers given |

LESSON PLAN: 4 for Term 2

|Subject: Mathematics Grade 11 Lesson Plan:|

|Quadratic Equations Number of Activities 3 Duration: 4h30 |

|Week 17/ Date |

|Context: Mathematical, Real life situation |

|Link with previous lesson: Completing the square |

|KNOWLEDGE (K): Quadratic Equations |

|SKILLS (S): Problem solving, demonstrate, drawing |

|VALUES (V): appreciation |

|Learning Outcome 1: |Learning Outcome 2: |Learning Outcome 3: Space, Shape and Measurement|Learning Outcome 4: Data |

|Number and Number Relationships |Functions and Algebra |The learner is able to describe, represent, |Handling and Probability |

|When solving problems, the learner is able to recognise, |The learner is able to investigate, analyse,describe and |analyse and explain properties of shapes in |The learner is able to collect,|

|describe, represent and work confidently with numbers and|represent a wide range of functions and solve related |2-dimensional and 3-dimensional space with |organise, analyse and interpret|

|their relationships to estimate, calculate and check |problems. |justification. |data to establish statistical |

|solutions. | | |and probability models to solve|

| | | |related problems. |

|11.1.1 Understand that not all numbers are | |11.2.1 (a) Demonstrate the ability to work with various| |11.3.1 Use the formulae for surface area | |11.4.1 | |

|real. | |types of functions | |and volume of right pyramids, right | |Calculate and represent| |

| | |(b) Recognise relationships between variables in terms | |cones, spheres and combinations of these | |measures of central | |

| | |of numerical, graphical, verbal and symbolic | |geometric objects. | |tendency and dispersion| |

| | |representations and convert flexibly between these | | | | | |

| | |representations ( | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | |Represent bivariate | |

|11.1.2 | |11.2.2 Generate as many graphs as necessary, initially | |11.3.3 Use a Cartesian co-ordinate system| |numerical data as a | |

|(a) Simplify expressions using the laws of | |by means of point-by-point plotting, supported by | |to derive and apply: | |scatter plot and | |

|exponents for rational exponents.(b) Add, | |available technology, to make and test conjectures | | | |suggest intuitively | |

|subtract, multiply and divide simple surds | |about the effect of the parameters k, p, a and q for | | | |whether a linear, | |

|(c) Demonstrate an understanding of error | |functions including: | | | |quadratic or | |

|margins. | | | | | |exponential function | |

| | | | | | |would best fit the data| |

| | | | | | |(problems should | |

| | | | | | |include issues related | |

| | | | | | |to health | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.3 Investigate number patterns (including | |11.2.3 Identify characteristics as listed below and | |11.3.4 Investigate, generalise and apply | | | |

|but not limited to those where there is a | |hence use applicable characteristics to sketch graphs | |the effect on the co-ordinates | | | |

|constant second difference between consecutive | |of functions | | | | | |

|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. | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.4 Use simple and compound decay formulae | |11.2.4 Manipulate algebraic expressions: | |11.3.5 Derive and use the values of the | | | |

|to solve problems (including straight line | |(a) by completing the square; | |trigonometric functions | | | |

|depreciation and depreciation on a reducing | |(b) simplifying algebraic fractions with binomial | | | | | |

|balance) (link to Learning Outcome 2). | |denominators. | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | |√ | | | | |

|11.1.5 Demonstrate an understanding of | |11.2.5 Solve: a) quadratic equations | |11.3.6 Solve problems in two dimensions | | | |

|different periods of compounding growth and | |(b) equations in two unknowns | | | | | |

|decay | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.6 Solve non-routine, unseen problems. | |11.2.6 Use mathematical models to investigate problems | | | | | |

| | |that arise in real-life contexts: | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.7 Investigate numerically the average gradient | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.8 Solve linear programming problems | | | | | |

| | | | | | | | |

| | | | | | | | |

| |Teachers Activities |Learners Activities |Teaching Methods |Assessment |Resources |Date Completed |

|Activity 1 |Educator gives worksheets |Learners given worksheet to|Group work, question and |Class work , home work |Calculator, exemplars, | |

|Quadratic equations |to solve: quadratic |solve: quadratic equations |answer, |memo rubric |worksheet | |

| |equations (by |(by factorisation, by | |Educator, peer | | |

| |factorisation, by |completing the square, and | | | | |

| |completing the square, and |by using the quadratic | | | | |

| |by using the quadratic |formula) and quadratic | | | | |

| |formula) and quadratic |inequalities in one | | | | |

| |inequalities in one |variable and interpret the | | | | |

| |variable and interpret the |solution graphically; | | | | |

| |solution graphically; | | | | | |

|Activity 2 |Educator demonstrates and |Learners given worksheet of|Group work, question and |Class work , home work |Calculator, exemplars, | |

|Quadratic equations |give learners a worksheet |equations in two unknowns, |answer, |memo rubric |worksheet | |

|algebraic |of equations in two |one of which is linear and | |Educator, peer | | |

| |unknowns, one of which is |one of which is quadratic, | | | | |

| |linear and one of which is |algebraically | | | | |

| |quadratic, algebraically | | | | | |

|Activity 3 |Educator gives learners a |Learners given a worksheet |Group work, question and |Class work , home work |Calculator, exemplars, | |

|Quadratic equations : |worksheet to work out the |to work out the equations |answer, |memo rubric |worksheet | |

|Graphically |equations in two unknowns, |in two unknowns, one of | |Educator, peer | | |

| |one of which is linear and |which is linear and one of | | | | |

| |one of which is quadratic, |which is quadratic, | | | | |

| |graphically. |graphically. | | | | |

|Expanded Opportunities Additional question papers given |

LESSON PLAN: 5 for Term 2

|Subject: Mathematics Grade 11 Lesson Plan: |

|Quadratic equations and inequalities Number of Activities 2 Duration: 4H 30 Min |

|Week 18 / Date |

|Context: Mathematical – quadratic inequalities |

|Link with previous lesson: Linear inequalities in one variable AS 10.2.5 and quadratic equations and functions 11.2.5 a |

|CORE CONTENT: (KSV) |

|KNOWLEDGE (K): Quadratic equations and inequalities |

|SKILLS (S): solving problems |

|VALUES (V): appreciation |

|Learning Outcome 1: |Learning Outcome 2: |Learning Outcome 3: Space, Shape and Measurement|Learning Outcome 4: Data |

|Number and Number Relationships |Functions and Algebra |The learner is able to describe, represent, |Handling and Probability |

|When solving problems, the learner is able to recognise, |The learner is able to investigate, analyse,describe and |analyse and explain properties of shapes in |The learner is able to collect,|

|describe, represent and work confidently with numbers and|represent a wide range of functions and solve related |2-dimensional and 3-dimensional space with |organise, analyse and interpret|

|their relationships to estimate, calculate and check |problems. |justification. |data to establish statistical |

|solutions. | | |and probability models to solve|

| | | |related problems. |

|11.1.1 Understand that not all numbers are | |11.2.1 (a) Demonstrate the ability to work with various| |11.3.1 Use the formulae for surface area | |11.4.1 | |

|real. | |types of functions | |and volume of right pyramids, right | |Calculate and represent| |

| | |(b) Recognise relationships between variables in terms | |cones, spheres and combinations of these | |measures of central | |

| | |of numerical, graphical, verbal and symbolic | |geometric objects. | |tendency and dispersion| |

| | |representations and convert flexibly between these | | | | | |

| | |representations ( | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | | | | |Represent bivariate | |

|11.1.2 | |11.2.2 Generate as many graphs as necessary, initially | |11.3.3 Use a Cartesian co-ordinate system| |numerical data as a | |

|(a) Simplify expressions using the laws of | |by means of point-by-point plotting, supported by | |to derive and apply: | |scatter plot and | |

|exponents for rational exponents.(b) Add, | |available technology, to make and test conjectures | | | |suggest intuitively | |

|subtract, multiply and divide simple surds | |about the effect of the parameters k, p, a and q for | | | |whether a linear, | |

|(c) Demonstrate an understanding of error | |functions including: | | | |quadratic or | |

|margins. | | | | | |exponential function | |

| | | | | | |would best fit the data| |

| | | | | | |(problems should | |

| | | | | | |include issues related | |

| | | | | | |to health | |

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.3 Investigate number patterns (including | |11.2.3 Identify characteristics as listed below and | |11.3.4 Investigate, generalise and apply | | | |

|but not limited to those where there is a | |hence use applicable characteristics to sketch graphs | |the effect on the co-ordinates | | | |

|constant second difference between consecutive | |of functions | | | | | |

|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. | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.4 Use simple and compound decay formulae | |11.2.4 Manipulate algebraic expressions: | |11.3.5 Derive and use the values of the | | | |

|to solve problems (including straight line | |(a) by completing the square; | |trigonometric functions | | | |

|depreciation and depreciation on a reducing | |(b) simplifying algebraic fractions with binomial | | | | | |

|balance) (link to Learning Outcome 2). | |denominators. | | | | | |

| | | | | | | | |

| | | | | | | | |

| | | |√ | | | | |

|11.1.5 Demonstrate an understanding of | |11.2.5 Solve: a) quadratic equations | |11.3.6 Solve problems in two dimensions | | | |

|different periods of compounding growth and | |(b) equations in two unknowns | | | | | |

|decay | | | | | | | |

| | | | | | | | |

| | | | | | | | |

|11.1.6 Solve non-routine, unseen problems. | |11.2.6 Use mathematical models to investigate problems | | | | | |

| | |that arise in real-life contexts: | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.7 Investigate numerically the average gradient | | | | | |

| | | | | | | | |

| | | | | | | | |

| | |11.2.8 Solve linear programming problems | | | | | |

| | | | | | | | |

| | | | | | | | |

| |Teachers Activities |Learners Activities |Teaching Methods |Assessment |Resources |Date Completed |

|Activity 1 |Teacher provides learners |Learners given worksheets|Discussion, question and |Class work home work |Work sheets, calculator | |

|Linear inequalities |with worksheets to revise |to revise linear |answer |Memo | | |

| |linear inequalities with |inequalities with emphasis | |Educator, individual, peer,| | |

| |emphasis on division and |on division and | | | | |

| |multiplication with a |multiplication with a | | | | |

| |negative number – including|negative number – including| | | | |

| |graphing on a number line.|graphing on a number line.| | | | |

|Activity 2 |Teacher introduces learners|Teacher introduces learners|Discussion, question and |Class work home work |Work sheets, calculator | |

|Quadratic inequalities |to quadratic inequalities |to quadratic inequalities |answer |Memo | | |

| |and shows them the various |and shows them the various | |Educator, individual, peer,| | |

| |methods of solving them |methods of solving them | | | | |

| |including sketch graphs. |including sketch graphs. | | | | |

| |ax2 ≥ c if a>0 and ax2 + c |ax2 ≥ c if a>0 and ax2 + c | | | | |

| |≤0 if a> 0 |≤0 if a> 0 | | | | |

| |a(x-p)2 + q ≥q if a>0 and |a(x-p)2 + q ≥q if a>0 and | | | | |

| |a(x-p) + q ≤q if a ................
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