AQA



Tech-level in IT – Scheme of WorkAQA Level 3 Technical Level IT: Cyber Security and Security AdministrationUnit: Maths for computingUnit type: Internally assessedGuided learning hours: 90Guidance notesThis Scheme of Work (SoW) illustrates how the unit content could be delivered using a three term, 10 weeks per term, approach. Consideration should be given to the content in other units within this qualification when planning your unit and lessons – the content in some units for example would benefit from being covered prior to others – especially the knowledge and theory elements contained within the externally assessed units.The following units are synoptically linked. This means that learning from the units listed can contribute to assessment of this unit:? Unit 1 – Fundamental principles of computing? Unit 2 – Communication technologies? Unit 3 – Developing and maintaining computer networks? Unit 6 – Network and cyber security administration management? Unit 7 – Managing identity and access to systems? Unit 8 – Programming for networking and securityThe learners will be able to draw on their previous learning experience and transfer their technical knowledge, skills and understanding whilst working through the following activities and unit assignments. Appropriate assessment activities can be used to holistically assess the unit at the end of the course as opposed to ongoing assessment.Note: performance evidence can be videoed but the quality of sound and image must be sufficiently clear to confirm competent performanceAssessments will naturally occur as follows:Week 6 – Centre devised Assignment 1 (Performance outcome 1 - covering P1, P2, P3, P4, M1, M2, D1 and D2). Week 13 – Centre devised Assignment 2 (Performance outcome 2 - covering P5, P6, P7, M3, M4 and D3).Week 16 – Centre devised Assignment 3 or AQA devised Assignment (Performance outcome 3 - covering P8, P9, P10, P11, M5, M6 and D4). Week 21 – Centre devised Assignment 4 (Performance outcome 4 - covering P12, P13, M7, M8 and D5).Week 25 – Centre devised Assignment 5 (Performance outcome 5 - covering P8, P9, P10, P11, M5, M6 and D4).Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site? Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Autumn term1Performance outcome 1 – Work withnumber systems. (P1, P2, M1)Number systems fundamentals and base conversion.1. Understand positional numeralsystems and their origins, eg decimal/denary systems such as the Hindu–Arabic numeral system.2. Demonstrate correct use and interpretation of numbers using their positional values in denary and binary.3. Understand base and radix terms and the use of correctTutor led:Introduction to number systems and their history, using decimal/denary as a shared referenced point.Learner led:Problem solving, interpretingdecimal/denary numbers correctly based on their positional values.Tutor led:Demonstration of common base conversions methods for:Learner led: Topic review covering majorthemes.Encouragement of learners to test peers with simple problems representative of those covered in class.Positional numeral system, positional weights.Base or radix terms and correct notational mon number bases, eg denary, binary.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.notation.4. Convert values accurately between binary and denary and vice versa.? denary/decimal to binary (Base 2 weights or “repeated division-by-2”/modulus method)? binary to denary/decimal.Exercise sheets or interactive/online practical activities to test conversion skills. Calculators should not be permitted for this as techniques should be learnt and tuned through repetition.Resources:? Binary to decimal conversionelectronics-tutorials.ws/binary/bin_2.html? Converting from binary to decimal non-decimal- bases/convert-binary-to-decimal.php? Number bases conversion index.php/numberbases/Tutor led:Nominated question and answer.Conversion of number systems, eg binary to denary, denary to binary.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Activities to provide stretch and challenge could include:Identification of common tips and tricks when working with binary numbers (eg how odd/even binary numbers end) etc. Identification of common binary weights and where (and how they occur in computing), eg 64-bit processor, 512 megabytes of RAM etc.Activities to provide stretch and challenge could include: Representation of other world number systems could be considered for comparison, eg ancient Egyptian numerals using hieroglyphics.2Performance outcome 1 – Work withNumber systems fundamentals and base conversion.1. Demonstrate correct use andTutor led:Introduction to octal and hexadecimal number systems.Learner led: Topic reviewcovering majorPositional numeral system, positionalWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.number systems(P1, P2, M1)interpretation of numbers using their positional values in octaland hexadecimal.2. Convert values accurately between denary and hexadecimal, denary and octal and vice versa.3. Convert binary values accurately to octal and hexadecimal and vice versa.4. Discover larger number systems and their role in computing, eg Base 64.Tutor led:Rationale for using letters in numbers, eg A- F in Hexadecimal.Tutor led:Discussion on correct counting, eg “20” in hex is not pronounced “twenty” it is “two- zero”; “twenty” is a denary valueLearner led problem solving, interpreting octal and hexadecimal numbers correctly based on their positional values.Tutor led:Demonstration of common base conversions methods for:? decimal/denary to hexadecimal? hexadecimal to decimal/denary? decimal/denary to octalthemes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.weights.Base or radix terms and correct notational mon number bases, eg octal, hexadecimal.Conversion of number systems, eg denary to octal, denary to hexadecimal.Correct pronunciation of numbers inWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? octal to decimal/denary? hexadecimal to binary (4 bit method)? binary to hexadecimal (4 bit method).Learner led:Exploration of larger number bases, egBase 64.Exercise sheets or interactive/online practical activities to test conversion skills. Calculators should not be permitted for this as techniques should be learnt and tuned through repetition.Resources:? Binary to decimal conversionelectronics-tutorials.ws/binary/bin_2.html? Converting from binary to decimal non-decimal-specific bases.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.bases/convert-binary-to-decimal.php? Number bases conversion index.php/numberbases/3Performance outcome 1 – Work withnumber systems. (D1)Number systems fundamentals and base conversion:1. Identify instances where binarynumbers are required for a particular processing aspect.2. Identify instances where octal numbers are required for a particular processing aspect.3. Identify instances where hexadecimal numbers arerequired for a particularprocessing aspect.Tutor led:Introduction to the use of non-denary numbers in modern computing.Learner led:Discovery of common non-denary number occurrences.Tutor led:Practical activities for calculating non- denary numbers for use in common applications in modern computing. This is often supplemented with practical activities to place these in context and, as such, offer many opportunities for contextualisation in other technical units and disciplines.Learner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.Positional numeral system,positional weightsBase or radix terms and correct notational mon number bases, eg octal, hexadecimal.Conversion of number systems, eg denary to octal, denary to hexadecimal.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Suitable worked examples could include(but should not be limited to):1. BinaryCharacter representation, eg 7 or 8 bit American Standard Code for Information Interchange (ASCII) characters etc.eg Storing the characters of a learner’s forename as ASCII codes in RAM using binary or hex.Resources:? ASCII table ? Conversion tool Correct pronunciation ofnumbers in specific bases.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.2. OctalUnix/Linux CHMOD file permissions which control user access to a file or folder. Considering:Read (4)Write (2) Execute (1)What permissions would a command CHMOD 744 provide for OWNER, GROUP and OTHER.Resources:? CHMOD tutorial teachmod/? CHMOD html_chmod_calc ulator.htmWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.3. HexadecimalA business wants to use a specific colour, “Medium Orchid”, for its website. The colour is made from Red, Green and Blue (RGB) values of 186, 85, 211 as expressed in denary.What hexadecimal value would this be converted to in order to create a HEX code suitable for HTML and CSS?(Answer: #BA55D3 and note the contextualprefix.)Resources:? HTML colour names html/html_colornames.asp? HTML colour picker tags/ref_colorpicker.aspWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.4. Gray code, rationale and useAn example of using Gray code to perform basic error correction in cable TV systemsResources:? Gray code to binary conversion pc-control.co.uk/gray_code.htmStretch and challenge:The learners will carry out activities that will require them to consider how different number systems are intrinsically used in modern computing.Practical activities may be selected specifically for the chosen group and more complex activities (focusing on other uses, eg creating subnets using binary) may be added to the mix andWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.assigned to learners requiring more challenge and stimulation.4Performance outcome 1 – Work withnumber systems.(P3)Fractional and negative integers in binary:1. Identification of common binaryinteger signing techniques.2. Creation and interpretation of unsigned binary numbers.3. Creation and interpretation of signed binary numbers using different methods.Tutor led:Introduction to the use of signed and unsigned notation when using binary numbers.Tutor led:Demonstration of coding sample denary integers in binary using the following methods:? unsigned? sign and magnitude? one’s complement? two’s complement.Note. Common shortcut methods can be used (or discovered by learners) for converting a positive number into its two’sLearner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question& answer.Positional numeral system, positional weights.Base or radix terms and correct notational mon number bases, eg octal, hexadecimal.Conversion of number systems, eg denary to binary.Starting from the right-most bit, find the first “1”.00101001Invert all of the bits to its left.11010111Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills pliment equivalent, eg +41 becoming -41. Eg.Method 1+41 = 00101001-41 = 11010111.Method 2+41 = 00101001.Correct pronunciation ofnumbers in specific bases.Invert all the bits through the number.11010110Add 1 to the number.11010111Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.-41 = 11010111.Resources:? Signed and unsigned binary watch?v=0MSmwdX5jl w? Signed and unsigned numbers electronics.dit.ie/staff/tscarff/signed_n umbers/signed_numbers.htm? Decimal/Two’s complement converter twos-complement-converter/Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? Two’s complement representation for signed integersacademic.evergreen.edu/projects/bio physics/technotes/program/2s_comp. htmExercise sheets or interactive/online practical activities to test learner skills at representing signed and unsigned denary integer in binary using the various techniques covered.Calculators should not be permitted for this as techniques should be learnt and tuned through repetition.Learner led:Exploration of other signed binary notations, eg Base -2.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.5Performance outcome 1 – Work withnumber systems. (P3, D2)Fractional and negative integers in binary:1. Identification of techniques tostored fractional values in denary and binary.2. Creation and interpretation of fixed numbers in binary.3. Creation and interpretation of floating point numbers in binary.4. Evaluate the impact on magnitude and accuracy ofsingle and double precision numbers.Tutor led:Introduction to the use of fixed and floating point notation when using binary to store denary fractional valuesTutor led:Demonstration of coding sample denary fractional values using:? fixed point binary storage? floating point binary storage.Learners should be able to identify the following parts of a floating point number: the exponent and significance (also known as the mantissa).Exercise sheets or interactive/online practical activities to test learner skills at representing fractional denary values inLearner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.Positional numeral system,positional weights.Base or radix terms and correct notational mon number bases, eg octal, hexadecimal.Conversion of number systems, eg denary to binary.Floating and fixed point numbers.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.binary using the various techniques covered.Resources:? Floating point/fixed-point numbers en.wiki/Floating_Point/ Fixed-Point_Numbers? Decimal/Binary convert (also does fractional values)binary- converter/? Binary fractions to Decimal (and vice versa)watch?v=KMcUWgIAu1 cTutor led:Discussion of numbers stored using singleSignificant, mantissa andexponent.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.and double precision, noting the impact on magnitude and accuracy and the trade-offs which is involved when assigning binary digits to each part of a floating point number.Learners investigate ranges for floating point numbers using single and double precision and present to their peers.Resources:? Tutorial: Floating-Point Binary asm/workbook/floating_tut. htm? Mantissa and Exponent: Explained watch?v=Zzx7HN4wo3ALearner led:Exploration of single and doubleWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.precision data types in common programming languages such as C++,C#, Java etc and their effective ranges of values.6Performance outcome 1 – Work withnumber systems.(P4)Base arithmetic:1. Performing addition operationon binary and hex values to find their sums.2. Performing subtraction operation on binary and hex values to find their differences.3. Performing multiplication operation on binary and hexvalues to find their products.4. Performing division operation on binary and hex values to find their quotients.Tutor led:Introduction to the practicalities ofperforming basic arithmetic operations using non decimal/denary numbers, ie binary, hex etc.Tutor led:Demonstration of performing simple arithmetic operations on simple binary and hex values.Exercise sheets or interactive/online practical activities to test learner skills at performing these operations using theLearner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Positional numeral system, positional weightsBase or radixterms and correct notational mon number bases, eg octal, hexadecimal.Conversion of number systems,Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.various techniques covered.Calculators should not be permitted for this as techniques should be learnt and tuned through repetition.Resources:? Assignment brief? Add binary numbers Add-Binary-Numbers? Adding and subtracting binary numbers watch?v=CqU9Z3PSb6s? Adding and subtracting in Hexadecimal watch?v=UGK8VyV1gLEIssue of centre devised Assignment 1 covering performance criteria: P1, P2, P3, P4, M1, M2, D1 and D2.Tutor led:Nominated question and answer.eg denary to binary.Addition, subtraction, multiplication and division in different bases.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.7Performance outcome 1 – Work withnumber systems.Performance outcome review.8Performance outcome 2 – Understand and applying Boolean logic.(P5)Foundation of computer logic. Basic logical operators.1. Identify and interpret basicBoolean operations.2. Apply basic Boolean operations to binary data.3. Use symbols and logic gates appropriately for basic logical operations.Tutor led:Introduction to the work of English mathematician, philosopher and logician George Boole through the examination of Boolean logic and algebra.Tutor led:Description or demonstration of logic revolving around true/false 1/0 comparison and its mapping to the electronic nature of a modern computer.Processing and outputs of basic logical operations:Learner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated questionPositional numeral system,positional weights.Base or radix terms and correct notational mon number bases, eg octal, hexadecimal, Boolean logic, binary.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Learner led:Investigation and discussion of the followingBoolean terms:? conjunction? disjunction? negation.Tutor led:Demonstration of the basic AND, OR and NOT logical operations, introducing its mechanics, operator symbol and common logic gate symbol.Practical matching activity between logical operator, its mechanics and common symbol.and answer.Propositional logic, declarativesentences, compound sentences etc.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Basic gates and functions ee.surrey.ac.uk/Projects/CAL/digital-logic/gatesfunc/index.html? GCSE Bitesize: Electronic logic bbc.co.uk/schools/gcsebitesize/design/el ectronics/logicrev1.shtml? Boolean algebra and logic gates tech.plym.ac.uk/maths/resources/pdflate x/boolean_alg2.pdfEnrichment activities can include common use of basic Boolean logical operators, eg programming, networking, database searches eg:Boolean Operators: Pirates vs. Ninjas watch?v=sdx9dACkvyIWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Further reading and homework for stretch and challenge.Forerunning logic systems, eg Chinese, Greek etc. – propositional logic.9Performance outcome 2 – Understand and applying Boolean logic.(M3)Composition and derived operators.1. Identify and interpret derivedBoolean operations.2. Apply derived Boolean operations to binary data.3. Use symbols and logic gates appropriately for derived logical operations.Tutor led:Introduction to derived Boolean logical operations:? exclusive or (EOR or XOR)? negative or (NOR)? negative and (NAND)? exclusive negative or (XNOR).Learner led:Investigation and discussion of these operations, identifying for each - its mechanics, operator symbol and common logic gate symbol.Learner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Boolean logic, binary.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Exclusive-OR Gate Tutorialelectronics-tutorials.ws/logic/logic_7.html? Logic NOR Gate Tutorialelectronics-tutorials.ws/logic/logic_6.htmlXOR may also be studied in terms ofXOR encryption techniques as this gives a practical use of the logic operation.Tutor led:Nominated question& answer.10Performance outcome 2 – Understand and applying Boolean logic.(D3)Visual representation of logical operations.1. Create accurate truth table fordifferent logical operations.2. Design functioning logic gate diagrams for specified circuits.3. Represent logical operation in a visual manner using Venn diagrams.Tutor led:Introduction to representing Boolean logic concepts in various diagrammatic forms:? Truth tables for each using x and y as inputs.? Digital logic gate diagrams for circuits.? Venn diagrams.Exercise sheets or interactive/online practical activities to test learner skills atLearner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative ofBoolean logic, binary.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.recognising, completing and creating various Boolean logic problems using a combination of different visual tools.Learner led:Investigation and report on creating circuits using only one type of logic gate, eg using just NAND or NOR gates and why this can be beneficial.Resources:? Building other basic logic gate types with only NAND gates watch?v=NbBv8LmRtcU? OR gate from NAND gate id/OR-gate-from- NAND-gate/? NOR gate from NAND gate id/NOR-gate-from-those covered in class.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.NAND-gate/? How do NAND gate equivalents work?nand_logic.htmlSpring term11Performance outcome 2 – Understand and applying Boolean logic.(P6, P7, M4)Working with Boolean algebra.1. Recognise and identify terms in a Boolean algebraic equation.2. Interpret a Boolean algebraic equation correctly.3. Evaluate inputs to a Boolean algebraic equation correctly,both simple and complex.Tutor led:Recap of the notation used to represent Boolean logic operators using symbols only. These will already have been introduced in previous sessions.Tutor led:Interpretation of simple Boolean algebraic equations, eg: (x.y) + x.Exercise sheets or interactive/online practical activities to test learner skills at recognising and interpreting various simple Boolean algebraic equations. They may confirm their understanding through the useLearner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated questionBoolean logic, simple andcomplex Boolean algebra, simplification techniques such as De Morgan’sLaws andKarnaugh maps.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.of previously learnt visual tools such as logic gate diagrams and truth tables.Tutor led:Interpretation of complex Boolean algebraic equations, eg:Exercise sheets or interactive/online practical activities to test learner skills at recognising and interpreting various complex Boolean algebraic equations. They may confirm their understanding through the use of previously learnt visualtools such as logic gate diagrams and truth tables.and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Enrichment activities can include peers setting simple and complex Boolean algebraic equations for each other to interpret.Resources:? Boolean Algebra Part 1 watch?v=lEgyiudC-nkTutor led:Introduction to common techniques used to simplify complex Boolean expressions, in addition to truth tables (already seen), these must include:? Boolean identities? De Morgan’s laws? Karnaugh maps.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Exercise sheets or interactive/online practical activities to test learner skills at simplifying various complex Boolean algebraic equations. They may confirm their understanding through the use of previously learnt visual tools such as logic gate diagrams and truth tables.Resources:? Logic Simplification Examples Using Boolean Rules watch?v=59BbncMjL8I? DeMorgans Theorem watch?v=wTUO3_kYOMY? Karnaugh Maps watch?v=eGNdpwOrsTo12Performance outcome 2 – Understand andPerformance outcome review.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.applying Boolean logic.13Performance outcome 3 – Calculate with sequences, series, probability and recursion. (P8, M5)Sequence and series.1) Identify sequences by finding their rules.2) Differentiate between arithmetic and geometric sequences.3) Creation of a series and the use of sigma notation.Tutor led:Introduction and class-based discussion of number sequences.Themes covered include:? type, eg whether they are finite or infinite? notation, including the use of the ‘Nth’term? rules and finding rules? term and term number? difference between an arithmetic (eg. adding and subtracting forming acommon difference) and geometric sequence (multiplication).Learner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.Sequences, Series, Nth term, arithmetic vs geometric, sigmanotation.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Sequences algebra/sequences-series.html? Common number sequences – square, cube and Fibonacci numberpatterns.html? The method of common differences modules/nextnumb.htm? Arithmetic sequences math/precalculus/seq_induction/seq_and_series/v/arithmetic- sequencesEnrichment activities can include investigation into common sequences such as square, cube and, especially, Fibonacci and its relationship to the Golden Mean/Ratio.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Nature, The Golden Ratio and FibonacciNumbers numbers/nature-golden- ratio-fibonacci.htmlExercise sheets or interactive/online practical activities to test learner skills at identifying simple sequences of numbers. Peers may test each other using sequences they have created for the other to solve using discovered rules.Tutor led:Introduction to mathematical series, themes to include:? definition? their contrast to a sequence? use of sigma (Σ) notation (GreekWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.alphabet and other Greek symbols commonly used in mathematics).Resources:? Sigma notation algebra/sigma- notation.html? Series as sum of sequence math/precalculus/seq_induction/seq_and_series/v/series-as-sum-of-sequenceIssue of centre devised Assignment 2 covering performance criteria: P5, M3, D3, P6, M4 and P7.14Performance outcome 3 – Calculate with sequences,Probability:1. Define concept of probability.2. Identify sample space and point.3. Identify an event.Tutor led:Introduction and class-based discussion of probability and its associated termsLearner led: Topic review covering majorthemes.Week numberSpecification referenceseries, probability and recursion. (P9, P10)Key learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).4. Describe different types of event.5. Visualise probability through appropriate diagrams.Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).Themes covered include:? probability definitionProbability of an event happening =The Number Of Ways Event A Can OccurThe total number Of Possible Outcomes? probability line – a continuous linear scale between 0 (impossible) and 1 (certain)? experiment or trial – an action where the result is uncertain? sample space – all possible outcomes for an action? sample point – one possible outcome from an action in the sample space? events – one result from an experiment or trialPlenaryHow will learner progress be checked?Evidence requirements?Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? event types:? dependent – the probability of an event occurring is affected by aprevious event, eg drawing a particular type of card or suit from apack? independent – the probability of an event occurring is not connected to the outcome of a previous event, e.g. tossing a coin – the probability of the coin landing on either side is equal, irrespective of what happened on the previous coin toss? mutually exclusive – when events can’t occur at the same time, so one outcome will invalidate the probability of the other, eg a coin toss landing as “heads” means that it cannot also land “tails” at the same time.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Exercise sheets or interactive/online practical activities to test learner skills at calculating probability of events occurring whilst reinforcing their use of the correct specialist terms connected to the probability topic.The use of physical props such as coins, packs of cards etc. can be used to reinforce these skills through live and unpredictable performance. Encourage learners to discover other possible sample spaces and experiments that could be conducted in and outside the classroom.Learner led:Investigation and report on probabilityevents connected to the IT industry, eg hard disk failures, network data packets blockedWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.by a firewall etc.Resources:? Probability lessons/vol6/intro_pro bability.html? Probability data/probability.html? Probability event types data/probability-events- types.htmlTutor led:Introduction and class-based discussion on diagrams which can be used to represent probability using visual techniques.Examples should include, but are not limitedWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.to:? space diagrams eg “double” values when two dice are thrown? visualising events:? using Venn diagrams (mutually exclusive events)? using tree diagrams (dependent events).Resources:? Probability space diagrams ictedusrv.cumbria.ac.uk/maths/SecMath s/U3/page_13.htm? Probability advanced-level- maths-revision/statistics/probability? Venn diagrams and the addition rule math/precalculus/prob_comb/addition_rule_prob_precalc/v/addWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.ition-rule-for-probability? Probability: Drawing a Venn diagram maths- revision/statistics/probability/venn- diagrams/tutorial-1.php? Probability Tree diagrams data/probability-tree- diagrams.html15Performance outcome 3 – Calculate with sequences, series, probability and recursion. (P11)Recursion:1. Identify common series.2. Describe common series.3. Explain the mechanics involved in recursion.Tutor led:Introduction and class-based discussion of common series.These can include (but should not be limited to:? Fibonacci? Factorial.Learner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative of those covered inRecursion, Fibonacci, factorial etc.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Learner led:Research and peer presentation into the concept of recursionResources:? Introducing recursion watch?v=to7tAmiZ_Ic? How recursion works watch?v=ozmE8G6YKww? Recursive sequences modules/nextnumb3.htm? Recursive series and sequences tutorials/recursive-series-and- sequences--2Tutor led:Introduction to the rules, language andclass.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.concepts involved in recursion:? have a base case? state change toward base case? must call itself.16Performance outcome 3 – Calculate with sequences, series, probability and recursion (M6, D4)Recursion:1. Describe an algorithm.2. Explain how a recursive algorithm works.3. Implement a recursive algorithm.4. Evaluate recursive algorithms vs traditional iterations.Tutor led:Introduction and class-based discussion on creating algorithms used in computing which rely on recursive methods.What is an algorithm? (Learners to research the term and present findings to peers).These can include (but should not be limited to:? Fibonacci? factorial? quicksort? binary searchLearner led: Topic reviewcovering majorthemes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated questionRecursion, Fibonacci,factorial etc.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? directory traversal? Sierpinski triangle.Learner led:Research and peer presentation into a selection of the recursive algorithms sampled by the tutor.More able learners may be able to tackle more complex recursive problems such as the Towers of Hanoi.Tutor selects a recursive algorithm (e.g. Fibonacci) and uses a simple scripting tool to implement and demonstrate. Learnerscan replicate individually or in pilot-navigator fashion. More able learners can tackle more complex recursive problems.and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Assignment brief? Factorial calculator calculators/discretemathematics/factorials.php? Fibonacci calculator maths.surrey.ac.uk/hosted- sites/R.Knott/Fibonacci/fibCalcX.html? Recursive Fibonacci Example watch?v=urPVT1lymzU? Stepping Through Recursive watch?v=zg-ddPbzcKMNB - A scripting tool, such as that provided by PyScripter, a free and open- source Python Integrated Development Environment (IDE), can be used to good effect, offering both the tutor and theWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).learners a wonderfully practical and expressive method for designing and implementing simple recursive algorithms.pyscripter - An open-source Python Integrated Development Environment (IDE) will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.p/pyscripter/SamplePython code:def F(n):if n == 0: return 0 elif n == 1: return 1else: return F(n‐1)+F(n‐2)print F(10)Classdiscussion detailing where simple iterative techniques may be more efficient.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Issue of centre devised Assignment 3, or AQA Assignment covering performance criteria: P8, M5, P9, P10, P11, M6 andD4.17Performance outcome 3 – Calculate with sequences, series, probability and recursion.Performance outcome review.18Performance outcome 4 – Gather and interpret data in a meaningful manner.(P12, M7)Gathering data:1. Differentiate data from information.2. Recognise data sources and their relative advantages and disadvantages.3. Differentiate between qualitative and quantitative data and theirrelative advantages andTutor led:Introduction and class-based discussion on ics should include (but should not be limited to):? what is data?? difference between data and informationLearner led: Topic reviewcovering majorthemes.Encouragement of learners to test peers with simple problemsQuantitative data, real-worldmeasurements.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.disadvantages.4. Identify data gathering methods.5. Describe the limitations of gathered data.? primary vs. secondary data – the advantages and disadvantages of each? quantitative and qualitative data – the advantages and disadvantages of each.Resources:? Data vs. Information EinsteinX2/data-vs- information? Types of data ? Primary and secondary data iwh.on.ca/wrmb/primary-data-and-secondary-data? What is data?data/data.html? Qualitative vs Quantitative data probability- statistics/qualitative-quantitative-representative of those covered inclass.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.data.htmlExercise sheets or interactive/online practical activities to test learners’ ability to differentiate data from information using suitable samples, primary or secondary data and quantitative or qualitative data. This could be done as round-robin tasks, individually or in pairs depending on the ability of the learners.Learner led:Research and peer presentation into common methods of gathering data.Coverage should be complemented by the tutor where gaps occur, ensuring that (minimally) the following are detailed:Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? real world measurements? observation? questionnaires? surveys? web analytics.Learners should identify the strengths andweaknesses of using each method and the likely success rate (in terms of reaching a representative sample) of each.Resources:? 5 useful methods of collecting primary data in statistics 201104125345/met hods-of-collecting-primary-data-in- statistics.html? Data collection techniquesWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE. led:Introduction and class-based discussion on the extraction of required information from raw data.Tutor led:Introduction and class-based discussion on the limitations of gathered data, eg:? accuracy? sample size? need for cleaning invalid data points (eg extreme outliers).Learners should be given sample data sets to identify possible issues and shortcomings with them.Additional challenge can be provided byWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.conducting live observation or measurement-based data capture in the classroom to build live and unpredictable data sets, eg learner heights, distance travelled to institution, shoe size, free disk space on PCs etc. This data may then be used in successive sessions when representing the data and interpreting it.19Performance outcome 4 – Gather and interpret data in a meaningful manner.(P13)Representing data:1. Identify the range of a set of values.2. Identify different types of mean and calculate them.3. Describe the relationship between different types ofaverage.Tutor led:Introduction and class-based discussion on the concepts and techniques for comparing data ics should include (but should not be limited to):? range (difference between the lowest and highest values in a set of values)Learner led: Topic reviewcovering majorthemes.Encouragement of learners to test peers with simple problems representative ofWorking with ranges,calculating meanvalues (arithmetic, median and mode), distribution and skew.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? range limits (particularly when extreme values are in the set)? averages, eg arithmetic mean, median(middle value), mode (most frequent)? relationship between mean, median, mode, eg symmetrical (normal or no- skew) distribution, positive or negative skew.Resources:? Range (statistics)data/range.html? Arithmetic mean average mean.html? Mean, median, mode and range modules/meanmode.htm? Skewness data/skewness.htmlthose covered in class.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Exercise sheets or interactive/online practical activities to test learners’ ability to work with data sets to calculate all three averages and identify the range and skew. Data can be brought forward from previous practical tasks where real-world data has been collected.More able learners can work on larger and more complex data sets.20Performance outcome 4 – Gather and interpret data in a meaningful manner.(P13)Representing data:1. Create cumulative frequency tables and graphs.2. Calculate interquartile range.3. Identify statistical dispersion.Tutor led:Introduction and class-based discussion on cumulative frequency and statistical ics should include (but should not be limited to):? cumulative frequency tables andLearner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problemsCumulative frequency,interquartile range, lower, media (2nd) and upper quartiles.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.diagrams/graphs? statistical dispersion measures, eg interquartile (IQR) range and the difference between the upper and lower quartiles, median etc.Resources:? Cumulative Frequency definitions/cumulative-frequency.html? Cumulative Tables and Graphs data/cumulative-tables- graphs.html? Cumulative frequency – The Department for Education .uk/sta/professional/b00211213/numeracy/areas/cumulative- frequencyrepresentative of those covered inclass.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? Statistics - Compute the Interquartile range watch?v=DGAXeX42eoE? Cumulative frequency curves : ExamSolutions watch?v=X9ajjBamRPc? Median, Quartiles and InterquartileRange : Exam Solutions watch?v=wNamjO-JzUgExercise sheets or interactive/online practical activities to test learners’ ability to work with data sets to calculate statistical dispersion. Data can be brought forward from previous practical tasks where real- world data has been collected.Where possible diagrams should be manually drawn to reinforce learning.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.More able learners can work on larger and more complex data sets.Summer term21Performance outcome 4 – Gather and interpret data in a meaningful manner.(P13)Representing data:1. Describe and calculate standard deviation.2. Describe and calculate variance.3. Create histograms from a data set.Tutor led:Introduction and class-based discussion on standard deviation and ics should include (but should not be limited to):? standard deviation (SD)? variance? histograms.Resources:? Histograms data/histograms.html? Standard Deviation and Variance data/standard-Learner led: Topic review covering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.Standard deviation, variance and histograms.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.deviation.html? Standard Deviation Calculator data/standard-deviation- calculator.html? Variance and standard deviation (ungrouped data) statstutor.ac.uk/resources/uploaded/vars tddev.pdf? Standard Deviation from frequency tables : Exam Solutions Maths Revision Tutorials watch?v=JvaJjjnOkRgExercise sheets or interactive/online practical activities to test learners’ ability to work with data sets to calculate standard deviation and variance. Data can be brought forward from previous practical tasks where real-world data has been collected.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Where possible diagrams should be manually drawn to reinforce learning.More able learners can work on larger and more complex data sets.Issue of centre devised Assignment 4 covering performance criteria: P12, M7, P13, M8 and D5.22Performance outcome 4 – Gather and interpret data in a meaningful manner.(M8, D5)Interpreting data:1. Analyse summary data using appropriate tools.2. Identify trends and recurring patterns in data.3. Prove a hypothesis.Tutor led:Introduction and class-based discussion on interpreting ics should include (but should not be limited to):? analysing summary data? identification of trends and recurring patternsLearner led: Topic reviewcovering majorthemes.Encouragement of learners to test peers with simple problems representative ofTrends and patterns in data.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? proving a hypothesis (late 16th century:via late Latin fromGreek hupothesis ‘foundation’,from hupo ‘under’ + thesis ‘placing’)Resources:? Trend line definitions/trend-line.html? How to Do Trend Analysis in Excel Do-Trend-Analysis-in-Excel? Understanding Hypotheses nrich.6178Exercise sheets or interactive/online practical activities to test learners’ ability to work with data sets in order to analyse them and identify trends and patterns. Data canbe brought forward from previous practicalthose covered in class.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.tasks where real-world data has been collected.Practical analysis of data can be performed through the use of spreadsheet software such as Microsoft Excel or Apache OpenOffice. Learners should be encouraged to use this type of software to assist their investigations.Resources:? Apache OpenOffice Where possible diagrams should be manually drawn to reinforce learning.More able learners can work on larger and more complex data sets.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.23Performance outcome 4 – Gather and interpret data in ameaningful manner.Performance outcome review.24Performance outcome 5 – Apply matrix methods to solve problems.(P14)Matrices:1. Describe how matrices store data.2. Identify and create different forms of matrix.3. Use matrix terminologyaccurately.Tutor led:Introduction and class-based discussion on ics should include (but should not be limited to:? matrices to represent ordered data? matrix terminology, eg rows, columns, elements or entries, subscripts, “m-by-n”size definitions? different forms of matrix;Learner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Matrices, vectors and subscripts; correct notation.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? row vector? column vector? square matrix.Resources:? Matrices algebra/matrix-introduction.html? Introduction to matrices watch?v=xyAuNHPsq-g? Introduction to the matrix math/precalculus/precalc- matrices/Basic_matrix_operations/v/intro duction-to-the-matrix? Introduction to Matrices/Matrix Size modules/matrices.htm? Matrix Notation/Types of Matrices modules/matrices2.htmTutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.? Matrix Equality modules/matrices3.htmExercise sheets or interactive/online practical activities to test learners’ ability to create and recognise different types of matrices.Learners can research and present the use of matrices in computing, e.g. computer graphics (3D geometry), data profile matching, equation solving etc. More able learners can compare and contrast matrices with implementation methods in common programming languages (ie one, two and multi- dimensional arrays of data).25Performance outcome 5 –Matrix operations:1. Identify basic matrix operations.Tutor led:Introduction and class-based discussion onLearner led: Topic reviewMatrices, matrix addition andWeek numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Apply matrix methods to solve problems.(M9)2. Perform matrix addition.3. Describe size limitations to entry-wise operations.basic matrix operations such as ics should include (but should not be limited to:? matrix addition.? limitations, i.e. matrices have to be of same dimensions as addition (andsubtraction) is performed in an entry- wise fashion.? matrix subtraction.Exercise sheets or interactive/online practical activities to test learners’ ability to perform basic matrix operations (such as addition) on sample data. Learners can set additional problems for each other and either check answers manually or confirm accuracy using online matrix calculators.covering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.subtraction.Subject terminology as specialist vocabulary, eg matrix, matrices, matrix addition.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Adding and Subtracting Matrices modules/mtrxadd.htm? Adding matrices watch?v=x0IaGTzYogU? Matrix addition and subtraction math/precalculus/precalc- matrices/Basic_matrix_operations/v/matr ix-addition-and-subtraction-1? Matrix calculator algebra/matrix-calculator.htmlIssue of centre devised Assignment 5 covering performance criteria: P8, M5, P9, P10, P11, M6 and D4.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.26Performance outcome 5 – Apply matrix methods to solve problems.(M9)Matrix operations:1. Identify basic matrix operations.2. Perform scalar multiplication.3. Perform matrix transposition.Tutor led:Introduction and class-based discussion on basic matrix operations such as scalar multiplication and ics should include (but should not be limited to):? scalar multiplication (and purpose of a scalar)? matrix multiplication? transposition.Exercise sheets or interactive/online practical activities to test learners’ ability to perform basic matrix operations (such as scalar multiplication and transposition) on sample data. Similarly learners can practically perform simple matrix transposition, perhaps by using interactiveLearner led: Topic reviewcovering major themes.Encouragement of learners to test peers with simple problems representative of those covered in class.Tutor led:Nominated question and answer.Matrices, scalar multiplication, transposition.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.whiteboards or slates, sharing their answers with their peers.Matrix multiplication techniques may be researched and implemented by more able learners.Resources:? How to Multiply Matrices algebra/matrix- multiplying.html? Scalar and Matrix Multiplication modules/mtrxmult.htm? Matrices Lesson 3 - Scalar Multiplication algebra/24-matrices/03-scalar-multiplication-01.htm? Scalar multiplication math/precalculus/prec alc-Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.matrices/Basic_matrix_operations/v/scal ar-multiplication? Transpose of a Matrix t/transpose_of_a_matrix.htm? Transpose of a Matrix math/linear- algebra/matrix_transformations/matrix_tr anspose/v/linear-algebra-transpose-of-a- matrix27Performance outcome 5 – Apply matrix methods to solve problems.(P15)Common matrix applications and techniques:1. Identify the purpose of asimultaneous equation.2. Solve a simultaneous equation using common techniques.3. Solve a simultaneous equation using matrices.Tutor led:Introduction and class-based discussion on practical matrix applications and techniques which solve common problems.This session would focus on solving simultaneous ics should include (but should not beLearner led: Topic reviewcovering majorthemes.Encouragement of learners to test peers with simple problemsSolving simultaneousequations using avariety of different techniques.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.limited to:? what is a simultaneous equation?? solving simultaneous equations using common techniques:? substitution? elimination? straight line graphs? solving simultaneous equations using matrices.Exercise sheets or interactive/online practical activities to test learners’ ability to solve simultaneous equations using common techniques and matrices .Where possible, equations should be industry related to help contextualise the process for learners, this is very important in terms of assessment.representative of those covered inclass.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Simultaneous equations gcse-maths-revision/algebra/simultaneous-equations? Unit 5 Section 5: Simultaneous Equations cimt.plymouth.ac.uk/projects/mepres/boo k9/bk9i5/bk9_5i5.html? Using Matrices to Solve a System of Equations or Simultaneous Equations simultaneous- equations-matrices.html? Solving Simultaneous Equations Using Matrices watch?v=Y7lFQ9npBfI28Performance outcome 5 – Apply matrix methods to solveCommon matrix applications and techniques.1. Describe matrix transformationtechniques.Tutor led:Introduction and class-based discussion on practical matrix applications and techniques which solve common problems.Learner led: Topic review covering major themes.Transforming vectors including shear, flip, scale and rotate.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.problems. (P15)2. Perform matrix transformation on a vector.3. Visualise matrix transformation on a vector.This session would focus on ics should include (but should not be limited to):? transformation (T), point (P) and new (N)matrices? hear? flip? scale (eg to produce enlargement, reduction)? rotate.Exercise sheets or interactive/online practical activities to test learners’ ability to perform basic transformation on vectors. These can be visualised through plotting on graph paper or online systems.Encouragement of learners to testpeers with simple problems representative of those covered inclass.Tutor led:Nominated question and answer.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Resources:? Matrix Transformations people.bath.ac.uk/sej20/transform.html? 2D Transformations willamette.edu/~gorr/classes/GeneralGraphics/Transforms/transforms2d.htm? 3D geometric transformations cs.brandeis.edu/~cs155/Lecture_07_6.p dfMore able students may experiment with matrices and 3D transformations.29Performance outcome 5 – Apply matrix methods to solve problems.Performance outcome review.30Complete unit review.Individual learner performance review.Week numberSpecification referenceKey learning objectivesConsider inclusion and differentiation (as appropriate and relevant). Equality and Diversity in BLUE (to be enhanced by unit teacher as appropriate for learner group).Learning activities and resourcesWhat will be learner led? What will be tutor led? Topics for plenary? Homework?Classroom based or off-site?Employer engagement?Stretch and Challenge in RED (to be enhanced by unit teacher as appropriate for learner group).PlenaryHow will learner progress be checked?Evidence requirements?Embedding or contextualising(opportunities for skills development).Maths in PURPLE. English inGREEN. TransferableSkills inORANGE.Individual learner unit feedback for tutor. ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download