Maths Level 2 (Generic) - Sample Scheme of Work (word ...
Course delivery information: Functional Skills Level 1 (Construction)
Duration: 36 weeks
Aims:
Performance - Learners can:
• Understand routine practical problems in a wide range of familiar and unfamiliar contexts and situations
• Identify the situation or problem and the mathematical methods to tackle it
• Select and apply a range of mathematics to find solutions
• Use appropriate checking procedures and evaluate their effectiveness at each stage
• Interpret results, consider the accuracy and appropriateness of results and solutions, and communicate solutions to practical problems in familiar, unfamiliar, routine and un-routine contexts and situations
• Draw conclusions in light of situations and provide mathematical justifications
Regular resources/textbooks:
Smartboard, WB & Pens, Power Point, paper & pens for group work, textbook, internet and LRC resources.
|Week/ |Content |Learning Objectives: students will be able to|Assessment of Learning |Teaching and Learning Activities |Resources |Functional Skills Standards (including ECM |
|Session | | | | | |theme) |
|2 |Initial assessment|Complete the Profiler assessment |Profiler Assessment |Continue paper/computer-based diagnostic |Assessments | |
| |1:1 feedback |Complete autumn term progress sheets | |assessments |Computers | |
|3 |Language of Maths | Read, write order and compare large numbers |Observation of ordering activity |Activity - Order a set of monthly trading |Matching cards |Read, write, order and compare positive and |
| |Place value | | |figures for a year, including losses. |Thermometers |negative numbers of any size. |
| | |Discuss negative numbers in practical |Q&A |Worksheet – write the value of a digit in a |Worksheets | |
| | |contexts | |number |Computer |Understand the meaning of negative numbers in a |
| | | | |Cards activity - Order a set of +ve and –ve |Smartboard |practical context, for example temperature below|
| | |Read temperatures on a thermometer |Peer checking: Correctly read and record |numbers (smartboard) | |zero, loss in trading. |
| | | |temperature – feedback to learners |Paired activity - Describe a set of numbers | | |
| | |Use negative numbers in a practical context, | |(more than, less than, equal to) (smartboard) | | |
| | |e.g. temperature below zero, loss in trading |Discussion on government spending figures|Paired activity – measure and record body | | |
| | | |on public services |temperatures | | |
|4 |Relationship |Use mental and written methods of calculation|Successful completion of problem solving |Discuss different methods that can be used for |Activity cards |Understand multiple and factor, and relate them |
| |between multiples,|to generate results when solving problems |worksheet & mental maths game |mental and written calculations and share short |Worksheets |to multiplication and division facts. |
| |factors and prime |using whole numbers of any size | |cuts and 'tricks', with explanations, factors. |Follow on game cards|Understand primes and know prime numbers up to |
| |numbers | | |Use a number square and cross off multiples of |Dominoes |20. |
| | | |Observation of activity |numbers in turn to find prime numbers. Practise |Smartboard |Give the level of accuracy of results |
| | |Complete calculations using the words | |breaking down numbers into prime factors. |Computer | |
| | |multiple, prime number and factor and relate | | |Number square | |
| | |them to multiplication and division facts | | | | |
|5 |Ratio and | Solve problems involving the number of parts| Checking/Marking of progress/completion |Discussion – ratio in everyday situation |Activity cards |Understand ratio written in the form 3:2, |
| |Proportion |in a given ratio, and the value of one part |of problem solving worksheet |(smartboard) |Worksheets |sharing £60 in the ratio 3:2. |
| |(Context of | | |Worksheets – problem solving |Scale drawing | |
| |sharing according |Discus examples of inverse proportion |Peer checking: Scale quantities up (or |Group activity – calculation of inverse |Smartboard |Understand how to work out the number of parts |
| |to input – direct |(e.g. more people on a job means less time to|down), using direct proportion, e.g. |proportion |Computer |in a given ratio, and the value of 1 part. |
| |or inverse) |complete the job) |recipes, etc. – | | | |
| | | | | | | |
| | | |Observation and accurate calculation of | | | |
| | | |inverse proportion. | | | |
|6 |Simple Algebra |Use formula to calculate cost of gas bills | Observation of Smartboard activity |Discussion – examples of practical applications |Whiteboard |Understand that words and symbols in expressions|
| | | |-Matching expressions |of algebra. |Worksheets |and formulae represent variable quantities |
| |Representing |Evaluate expressions and make substitutions | |Board work - match expressions in words and |Calculators |(numbers) not things, so 2a + 2b cannot be |
| |variables and |in given formulae in words and symbols to |Peer checking – |symbols. |Smartboard |explained as 2 apples and 2 bananas. |
| |constant factors) |produce results. | |Convert expressions from words to symbols, and |Computer | |
| | | |Discussion |vice versa. (smartboard). | |Understand that the contents of brackets must be|
| | | | |Worksheets – calculate gas bills, commission on | |worked out first. |
| | | | |sales using formulae. | | |
| | | | |Paired activity - changing temperature from | | |
| | | | |Fahrenheit to Celsius, using formula. | | |
|7 |Recap of first |Complete mini project. |Direct questioning |Learners to complete mini project (work out |Mini project |Use efficient methods to carry out calculations |
| |half term topics |Q & A session | |profit & loss in a business) and answer oral | |involving two or more steps, including efficient|
| |and completion of | |Mark the assignment and give feedback |questions (e.g. House hold or small business | |use of a calculator. |
| |mini project. | | |budgeting) | | |
| | | | |Set homework | |Understand that when there is no operator |
| | | | | | |between a number and a variable, two variables, |
| | | | | | |or a bracket, multiplication is implied. |
| | | | | | | |
| | | | | | |Make substitutions in given formulae in words |
| | | | | | |and symbols. |
| | | | | | |ECM5 |
|HALF TERM |
|Week/ |Content |Learning Objectives: students will be able to|Assessment of Learning |Teaching and Learning Activities |Resources |Functional Skills Standards (including ECM |
|Session | | | | | |theme) |
|9 |Equivalent |Match equivalent fractions |Observation of matching cards game |Discussion – examples of fractions and its |Leaflets |Know how to change fractions to equivalent |
| |fractions | | |equivalencies in everyday life (use leaflets, |Whiteboard |fractions with a common denominator |
| | | |Q & A |adverts and headlines). Understand that |Matching cards | |
| | | | |fractions add up to one whole |Worksheets |Evaluate one number as a fraction or percentage |
| | | |Accurate completion of worksheet |Activity – use fraction to work out increase in |Drag and drop |of another. |
| | | | |wages or VAT (Smartboard) |exercise. | |
| | | | |Card activity – matching equivalent fractions, | | |
| | | | |decimal and percentages | | |
|10 |Decimals |Add, subtract, multiply and divide decimals |Successful completion of task |Discussion - rounding answers on a calculator |Whiteboard |Add, subtract, multiply and divide decimals up |
| | |up to three places |Checking/marking of progress/completion |and the degree of accuracy that might be |Ordering cards |to three places and check answers in the context|
| | | |of worksheet |appropriate, e.g. calculations with money- |Smartboard |of measurements and money |
| | |Use exchange rate to calculate the amount of | |Activity calculate gross pay/week and net pay) |computers | |
| | |foreign currency required | |Search for goods on European online shopping | | |
| | | | |sites and convert the prices from € to £ | | |
| | | | |sterling | | |
|11 |Percentage of |Calculate cost of credit |Q&A |Discuss quick ways of finding VAT |Worksheets |Use fractions, decimals and percentages to order|
| |quantities | | |Use interest rates to compare the cost of a loan|Interest rates from |and compare amounts or quantities and to solve |
| | |Solve problems involving percentages |Checking/marking the progress/completed | |banks. |practical problems. Choose to use a fraction, |
| | | |task |Paired Activity - Practise examples in context, |Internet |decimal or percentage to work out VAT. |
| | |Order and compare percentages and demonstrate| |e.g. percentage increase or decrease of | | |
| | |understanding of percentage increase and |Peer-checking |household bill, fuel. | | |
| | |decrease. | |Discus impact of a change in interest rates on | | |
| | | | |mortgages, savings etc. | | |
| | |Calculate VAT of given amounts. | |Adding 30% to prices as a profit margin in a | | |
| | | | |business. Use any methods. | | |
|12 |Evaluation of one |Calculate one number as percentage of |Direct questioning |Discussion – percentages using the attributes of|Whiteboard |Evaluate one number as a fraction or percentage |
| |number as a |another. | |the group, e.g. what percentage of the group is |Matching cards |of another. |
| |percentage of | |Peer checking – feedback to learners |male, |Smartboard | |
| |another |Know and use strategies to check answers | |Activity – match calculations to answers |Computers |Understand that quantities must be in the same |
| | |obtained with a calculator | |Smartboard / skillswise) |Calculators |units to evaluate and compare. |
| | | | |Activity – Use a calculator to check the answers| | |
| | | | |to calculations done by other methods (manual or| | |
| | | | |by another person). | | |
|13 |Equivalent |Complete a table of equivalent fractions, |Observation of activity. |Boardwork – show learners how to convert between|Whiteboard |Understand that fractions, decimals and |
| |fractions, |decimals and percentages | |fractions, decimals and percentages. |Matching cards |percentages are different ways of expressing the|
| |decimals and | |Q&A |Paired activity – complete a table of |Worksheets |same thing. |
| |percentages |Convert percentage savings and profit to | |equivalencies |Computers | |
| | |fraction and decimals | |Matching game (Skillswise) | |Use fractions, decimals and percentages to order|
| | | | | | |and compare amounts or quantities and to solve |
| | | | | | |practical problems |
|14 |Completion of |Complete problem solving paper / mini project|Formative assessment of student’s work |Learners to complete mini project (e.g. planning|Mini project |Carry out calculations with numbers of any size |
| |project involving |covering work completed during second half | |a Xmas party for a youth club) | |in practical contexts |
| |Fraction, decimal |term |Directed questioning |Set homework according to ability | | |
| |and percentages | | | | |Understand and use equivalencies between |
| | | | | | |fractions, decimals and percentages |
| | | | | | |ECM5 |
|XMAS BREAK |
|Week/ |Content |Learning Objectives: students will be able to|Assessment of Learning |Teaching and Learning Activities |Resources |Functional Skills Standards (including ECM |
|Session | | | | | |theme) |
|16 |Metric & Imperial|Categorise metric and imperial units of |Observation of activity |Discuss the appropriate units of measure for |Whiteboard |Calculate, measure and record dates and times in|
| |measurement |length, distance, weight, capacity | |length, distance, weight, capacity, and the use |Quiz questions |different formats and know the relationship |
| | | |Observation of measuring tasks to varying|of metric and imperial units |Worksheets |between units of time, for example second, |
| | |Read scales to different levels of accuracy, |degree of accuracy with the appropriate |Activity – estimate, measure and record length |Measuring tape |minute, hour, day, week, month and year. |
| | |including reading between marked divisions |instrument. |and weights and capacities of supplied items |Bathroom and kitchen| |
| | | | |Paired activity – read both metric and imperial |scales | |
| | | | |amounts for lengths, weights and capacities. |Flip charts | |
| | | | | |Smartboard | |
|17 |Conversion of |Calculate with units of measure within the | Observation of activity. Q&A. |Discussion – metric and imperial units |Whiteboard |Calculate with units of measure between systems,|
| |metric and |same system | |Work out the best value of products of different|Worksheets |using conversion tables and scales, and know how|
| |imperial units | |Observation of measuring activity |weights or capacities. |Liquids and |to use approximate conversion factors |
| | |Use a measuring instrument accurately | |Board work – How to convert between different |containers | |
| | | |Checking/marking the progress/completed |units (review x & ÷ by 10, 100 and 1000) |Smartboard |Estimate, measure and compare length, distance, |
| | |Convert metric units to imperial units and |worksheet |Worksheets - Converting between different units | |weight, capacity and temperature, including |
| | |vice versa | |(calculate cost of petrol per gallon | |reading Celsius and Fahrenheit scales and |
| | | | |Activity –match metric and imperial amounts with| |conversion tables. |
| | | | |different units (smartboard) | | |
|18 |Area and perimeter|Use given formulae to find areas of composite|Observation of activity. |Discussion – finding the perimeter of composite |Whiteboard |Know what is meant by perimeter, circumference, |
| |of composite |shapes (e.g. non-rectangular rooms or plots | |shapes, such as rooms, which are not drawn to |Worksheets |diameter and radius. |
| |shapes |of land) |Q&A. |scale and do not have all the measurements |Matching cards | |
| | | | |included, and devise ways of finding the lengths|Measuring |Understand and use given formulae for finding |
| | |Break down a composite shape into regular |Checking/marking the progress/completed |of all the edges |instruments |perimeters and areas of common and composite |
| | |shapes |worksheet |Activity – Calculate how much tiles required for|Smartboard |shapes, circumference and area of circular |
| | | | |the floor, ceiling tiles and wallpaper border | |surfaces |
| | | | |needed. | | |
| | | | |Calculate the cost of both the floor and ceiling| | |
| | | | |tiles. | | |
|19 |Scale Drawing | Draw an accurate scale plan of the new |Observation of activity |Discuss scales and how they are used. Work from |Tracing paper |Work out dimensions from scale drawings. |
| | |beauty salon using a scale expressed as a | |several examples such as If the scale is 1:100 |Whiteboard |Estimate amounts using proportions, for example |
| | |ratio |Successful completion of task. Q&A |on a plan, what would a centimetre represent? |Internet |the length of the room is about three times its |
| | | | |What would 10 cm represent? |Smartborad |width, and the stockroom is about two-thirds |
| | |Accurately work out distances from the scale | |Activity - Produce a scale drawing of the salon | |full. |
| | |on a map. | |showing furniture layout. Use different scales, | | |
| | | | |e.g. 1:20, 1:10, and 1:50. | | |
|20 |Measurements and |Measure a room and present the dimensions in |Observation of set task. Check marked |Learners to measure the café and plan a |Measuring tape |Know that measurements must be in the same units|
| |scale drawings |form of scale drawing. |work. |redecoration |Rulers |when calculating perimeters, areas or volumes. |
| | | | |Produce a scale drawing of café |Whiteboard | |
| | |Calculate the area and perimeter of the room.| |Set homework | |Understand the symbol for pi and know its |
| | | | | | |approximate value |
| | | | | | | |
| | | | | | |Understand and use given formulae for finding |
| | | | | | |volumes of common shapes |
|HALF TERM |
|Week/ |Content |Learning Objectives: students will be able to|Assessment of Learning |Teaching and Learning Activities |Resources |Functional Skills Standards (including ECM |
|Session | | | | | |theme) |
|22 |Extracting Data |Extract and interpret information from lists,|Observation of activity. |Discuss the difference between continuous and | Whiteboard |Know how to extract discrete and continuous data|
| | |tables, charts and graphs | |discrete data. A useful example is that the size|Holiday brochure |from tables, spreadsheets, bar charts, pie |
| | | |Q&A |of shoe someone wears is discrete, but the |Graph paper |charts and line graphs with more than one line. |
| | | | |length of their foot is continuous. |Smartboard | |
| | | | |Board work – Look at the use of different scales|Internet | |
| | | | |and their effect on the graph. Comment on trends| | |
| | | | |from the slope of the graph. | | |
| | | | |Activity – Online game, Extract information from| | |
| | | | |tables in catalogues, brochures, web sites. | | |
|23 |Organising and |Measure the height of everyone in the class |Check correct information included on |Discussion - Use given sets of data and discuss | Whiteboard |Draw conclusions from scatter diagrams, |
| |representing data.|and present information as a chart / graph. |chart |the most suitable form of representation. |Internet |understanding that correlation does not imply |
| | | | |Activity – Measure and record classmates’ |Tape rule |causality. |
| | |Collect and record data from exchange rates |Observation of activity and correct |height; present the data in a suitable form. | | |
| | |or a particular share issue over a period of |completion of chart or graph |Worksheets – Plot a graph showing exchange rates| |Understand how to use scales in diagrams, charts|
| | |time. Display the data on a chart or graph | |over a period. | |and graphs. |
|24 |Present findings | Present outcome of investigation using a pie|Check correct information included on |Activity – investigate the menu offered in the |Canteen Menu |Know how to extract discrete and continuous data|
| |in a suitable way |chart and bar chart. |chart |canteen on Tuesday and find out the most and |Graph paper |from tables, spreadsheets, bar charts, pie |
| | | | |least popular. | |charts and line graphs with more than one line. |
| | | |Observation of activity Correct |Present findings using pie chart. | | |
| | | |completion of chart | | | |
|25 |Collecting and |Carry out an investigation and present the |Check result of investigation. |Activity – collecting and presenting data – e.g.|Quiz questions |Know how to extract discrete and continuous data|
| |presenting data |outcome in a suitable form | |Investigate the most popular music genre in the |Worksheets |from tables, spreadsheets, bar charts, pie |
| | | |Directed questioning |college to prepare for the end of year |Square Paper |charts and line graphs with more than one line. |
| | | | |performance |Smartboard | |
| | | | | | |Know how to choose a suitable format and scale |
| | | | | | |to fit the data and ensure all charts, graphs |
| | | | | | |and diagrams are labelled. |
|26 |Averages & range |Calculate mean, median and mode. |Observation of activity |Discuss the use of mean, median and mode. |Graph papers |Find the mean, median and mode and understand |
| | | |Listen to discussion points |Discussion - the use of range in everyday |Whiteboard |that each average is useful for different |
| | |Discuss the distinctions that each average is| |language, e.g. price range, age range |Computers – Excel to|purposes. |
| | |useful for different purposes. |Peer checking – feedback to learners |Q&A – extracting information from different |produce charts and | |
| | | | |sources |graphs | |
| | |Find the range and use it to describe the | |Activity – Compare the distribution of pay | |Use the range to describe the spread within a |
| | |spread within sets of data | |scales in two organisations. | |set of data, for example sales results. |
| | | | |Paired Activity – Collect data of interest and | | |
| | | | |compare the range | |Use the average and range to compare two sets of|
| | | | | | |data |
|27 |Recap of data |Complete the revision questions on last |Checking/marking of worksheet |Worksheets – Investigate BMI of 20 people and |Worksheets |Collect and represent discrete and continuous |
| |handling |term’s topics | |calculation the percentage of each weight |Calculator |data, using ICT where appropriate |
| | | | |categories within your chosen sample |Progress Record Form|ECM3 |
| | |Review spring term progress sheet and | | | | |
| |Feedback to |complete targets for summer term | |Feedback with tutor – evaluate students progress| | |
| |students | | |with regard to their learning and their personal| | |
| | | | |development | | |
|EASTER BREAK |
|Week/ |Content |Learning Objectives: students will be able to|Assessment of Learning |Teaching and Learning Activities |Resources |Functional Skills Standards (including ECM |
|Session | | | | | |theme) |
|29 |Practice test |Complete practice FS assessments |Check answers on practice test. |Completing the questions and activities on FS |Assignments |Use and interpret discrete and continuous data, |
| | | | |assessment |Calculators |using ICT where appropriate, statistical |
| | | | | |Protractors |measures, tables and diagrams |
| | | | | |Pen / Paper |Use statistical methods to investigate |
| | | | | |Graph paper |situations |
| | | | | | |ECM 3 |
|30 |Feedback |Feedback on practice paper both as a class |Q & A |Discussion |Assignments | |
| | |and individuals | |Direct questioning |Calculators | |
| | | | | |Protractors | |
| | | | | |Pen / Paper | |
| | | | | |Graph paper | |
|31 |Summative |Start functional skills assessments |Mark work completed |Completing the questions and activities on FS |Assignments | |
| |assessment | | |assessment |Calculators | |
| | | | | |Protractors | |
| |Practice Test for | | | |Pen / Paper | |
| |some if needed | | | |Graph paper | |
|32 |Summative |Continue / complete functional skills |Mark work completed |Completing the questions and activities on FS |Assignments |ECM 3 |
| |assessment |assessment | |assessment |Calculators | |
| | | | | |Protractors | |
| | | | | |Pen / Paper | |
| | | | | |Graph paper | |
|33 |Summative |Continue / complete functional skills |Mark work completed |Completing the questions and activities on FS |Assignments |ECM 3 |
| |assessment |assignment | |assessment |Calculators | |
| | | | | |Protractors | |
| | | | | |Pen / Paper | |
| | | | | |Graph paper | |
|33 |Introduce Project |Discus the appropriate research method and |Observation of activity. |Gather as much information as possible from |Project |ECM 3 & 5 |
| |1-Redesigning the |resources required to complete the task. | |internet, brochures and flyers |Calculators | |
| |interior of a | |Q&A | |Pen | |
| |beauty salon | | |Select and cost the new furniture for the beauty|Ruler | |
| | | | |room. |Graph Paper | |
|34 |Presentation of |Present findings of their research using |Q&A. |Present their research findings to the whole |Project |ECM 3 & 5 |
| |Research findings |appropriate charts and diagrams | |class |Feedback sheets | |
| |and group feedback| |Observation of task |Explain the rationale behind their choice of |Computers | |
| | | | |holiday destination | | |
| | | | |Discuss issues encountered and receive feedback | | |
| | | | |from peers | | |
|35 |Introduce Project |Present personal monthly budget plan to the |Observation of presentation |Discuss ways of managing spending |Project |ECM 3 & 5 |
| |2-Financial |group | |Calculate monthly budget |Feedback sheets | |
| |management | |Q&A |Present their research findings to the whole |Computers | |
| | | | |class | | |
| | | | |Explain the rationale behind their spending | | |
| | | | |Discuss problem encountered and receive feedback| | |
| | | | |from peers | | |
|36 |Whole Class |Review individual student’s progress sheets |Q&A |Whole class evaluation of tasks |Progress sheets |ECM 3 & 5 |
| |Evaluation and | | |Discuss progression opportunities for the next |Questionnaire | |
| |Review Progress | | |academic year | | |
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