OCR Nationals
Sample Scheme of Work
GCSE Applications of Mathematics
OCR GCSE in Applications of Mathematics: J925
Unit: A381/01
This support material booklet is designed to accompany the OCR GCSE Applications of Mathematics specification for teaching from September 2010.
Contents
Contents 2
Introduction 3
Sample Scheme of Work: OCR GCSE Applications of Mathematics J925 Unit: A381/01 4
Introduction
In order to help you plan effectively for the implementation of the new specification we have produced sample schemes of work and lesson plans for Applications of Mathematics. These support materials are designed for guidance only and play a secondary role to the specification.
Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon and amend the content to suit your teaching style and learners’ needs.
This booklet provides examples of how to structure the teaching of this unit; the teaching hours are suggestions only.
The specification is the document on which assessment is based and specifies what content and skills need to be covered in delivering the course. At all times, therefore, this support material booklet should be read in conjunction with the specification. If clarification on a particular point is sought then that clarification should be sought in the specification itself.
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |N/A |Topic |F1A - General problem solving skills |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Solve problems using mathematical skills |These skills should be integrated within the other content| | |
|select and use suitable problem solving strategies |areas in the context of different areas of maths within | | |
|and efficient techniques to solve numerical problems |both more open ended and closed questions/problems | | |
|identify what further information may be required in | | | |
|order to pursue a particular line of enquiry and give| | | |
|reasons for following or rejecting particular | | | |
|approaches | | | |
|break down a complex calculation into simpler steps | | | |
|before attempting to solve it and justify their | | | |
|choice of methods | | | |
|use notation and symbols correctly and consistently | | | |
|within a problem | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |N/A |Topic |F1A - General problem solving skills |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|use a range of strategies to create numerical | | | |
|representations of a problem and its solution; move | | | |
|from one form of representation to another in order | | | |
|to get different perspectives on the problem | | | |
|interpret and discuss numerical information presented| | | |
|in a variety of forms | | | |
|present and interpret solutions in the context of the| | | |
|original problem | | | |
|review and justify their choice of mathematical | | | |
|presentation | | | |
|identify exceptional cases when solving problems | | | |
|show deduction in solving a problem | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |N/A |Topic |F1A - General problem solving skills |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|recognise the importance of assumptions when deducing| | | |
|results; recognise the limitations of any assumptions| | | |
|that are made and the effect that varying those | | | |
|assumptions may have on the solution to a problem | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |9-12 hours |Topic |F1B - Number |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Add, subtract, multiply and divide any number |Best to introduce in real life contexts eg temperature and| | |
|understand and use positive numbers and negative |have a number line visible | | |
|integers, both as positions and translations on a |Negative number puzzle |Number Line Bounce - NLVM | |
|number line |MyMaths.co.uk - negatives1 | | |
|add, subtract, multiply and divide integers and then | |Tarsia – negative numbers at SmartBoard Notepad files for | |
|any number |BODMAS: Positive and negative numbers |teaching mathematics | |
|multiply or divide any number by powers of 10 |MyMaths.co.uk - negatives2 | | |
|multiply or divide any positive number by a number | | | |
|between 0 and 1 |Multiplying and dividing by powers of 10. | | |
|multiply and divide by a negative number | | | |
|derive positive integer complements to 100 |Use My maths to deliver Tp’s and activities MyMaths.co.uk | | |
|recall all multiplication facts to 10 ( 10, and use |- decimalx10x100 |Waldomaths - operations with negative numbers |Incorporate reasoning questions eg explain why [pic] =|
|them to derive quickly the corresponding division | | |40 cannot be correct |
|facts |Multiply positive and negative numbers |VTC - KS4 - Maths - Number | |
|derive unknown facts from those they know | | | |
|add and subtract numbers with up to two decimal | |SmartBoard Notepad files for teaching mathematics – | |
|places | |multiplication puzzle, mental mathematics | |
|multiply and divide numbers with no more than one |MyMaths.co.uk - Sky Solver - Add 100 | | |
|decimal place, using place value adjustments, | | | |
|factorisation and the commutative, associative, and |MyMaths.co.uk - Introducing Multiplication | | |
|distributive laws, where possible | | | |
|add and subtract integers and decimals understanding | | | |
|where to position the decimal point | | | |
|perform a calculation involving division by a decimal|MyMaths.co.uk - DecimalAdding | | |
|(up to two decimal places) | | | |
| | | | |
| | |Base Blocks Decimals - NLVM | |
| | | | |
| |MyMaths.co.uk - Decimal multiplying1 |nrich. :: Mathematics Enrichment :: Forgot the | |
| | |Numbers | |
| |MyMaths.co.uk - Decimal multiplying2 | | |
| | |nrich. :: Mathematics Enrichment :: Route Product | |
| |MyMaths.co.uk - DecimalDividing | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |9-12 hours |Topic |F1B - Number |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|2 - Approximate to a specified or appropriate degree | | | |
|of accuracy |MyMaths.co.uk - rounding10 | |(1) Write 13 066 using words and to the nearest 100|
|use previous understanding of integers and place | |Approximation |(2) Write 345.46 to the nearest integer, 1 decimal |
|value to deal with arbitrarily large positive numbers|Rounding and estimation hangman | |place and 2 significant figures |
|estimate answers to problems involving decimals | |Rounding and estimation hangman |(3) Know that 3.5 on a calculator means 3.40 in |
|use a variety of checking procedures, including |MyMaths.co.uk - roundingDecimal | |money context and that 3.66666667 on a calculator is |
|working the problem backwards, and considering | |VTC - KS4 - Maths - Number |a recurring decimal |
|whether a result is of the right order of magnitude |MyMaths.co.uk - Decimal Places | | |
|round to the nearest integer, to a given power of |MyMaths.co.uk - Significant Figures | | |
|10(1), to any number of decimal places, specified or | | | |
|appropriate, and to any number of significant |MyMaths.co.uk - Estimatingintro | | |
|figures(2) | | | |
| |MyMaths.co.uk - Estimating | | |
| | | | |
| | | | |
|give solutions in the context of the problem to an | | | |
|appropriate degree of accuracy, interpreting the | | | |
|solution shown on a calculator display, and | | | |
|recognising limitations on the accuracy of data and | | | |
|measurements | | | |
|understand the calculator display, knowing when to | | | |
|interpret the display(3), when the display has been | | | |
|rounded by the calculator, and not to round during | | | |
|the intermediate steps of a calculation | | | |
| | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |9-12 hours |Topic |F1B - Number |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|3 - Use calculators effectively and efficiently | | |(1) [pic],[pic] |
|use calculators effectively and efficiently(1) | | |(2) [pic], [pic] |
|know how to enter complex calculations and use | | |(3) When using money interpret a calculator display|
|function keys for reciprocals, squares and powers(2) | | |of 2.6 as £2.60 |
|enter a range of calculations, including those | | | |
|involving measures(3) | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |1-2 hours |Topic |F1C - Hierarchy of operations |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Hierarchy of operations |MyMaths.co.uk - Operations Order | |Calculate [pic] |
|use brackets and the hierarchy of operations | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |2-3 hours |Topic |F1D - Factors, multiples and primes |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Factors, multiples and primes |Happy numbers activity – find numbers where sum of factors|Tarsia puzzle – factors and multiples at SmartBoard Notepad |Write down a number between 25 and 30 that is |
|use the concepts and vocabulary of factor (divisor), |is equal to number |files for teaching mathematics |(i) a multiple of 7 |
|multiple, common factor and prime number |Use factor tree software to illustrate use of prime | |(ii) a prime number |
| |factors in finding LCM/HCF after definitions have been |Sieve of Eratosthenes - NLVM |a factor of 104 |
| |established | |Write 96 as a product of prime factors using indices |
| | |Factors of Numbers - Waldomaths |Counter example problems could be bought in here |
| |Class activity: Identify a number from a description of | |eg Are all primes odd? |
| |its properties, for example, which number less than 50 has|Finding prime numbers - The Sieve of Eratosthenes 1 - | |
| |3 and 5 as factors and is a multiple of 9? Students make |Waldomaths | |
| |up their own descriptions and test one another. | | |
| | |Factor Tree - NLVM | |
| |Multiples prison cell game | | |
| | |Factor Tree - NLVM |Emphasise 1 not a prime and factor trees should not |
| |Use factor trees/factor staircase | |contain 1s |
| |Goldbach’s conjecture (counter example search) | | |
•
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |6-8 hours |Topic |F1E - Fractions, decimals and percentages |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Calculate with fractions | | |(1) Multiplication by [pic]is equivalent |
|calculate a given fraction of a given quantity, |MyMaths.co.uk - Fractions1 |SmartBoard Notepad files for teaching mathematics – lots of|to division by 5 |
|expressing the answer as a fraction | |tarsia puzzles to download on fractions and processes | |
|express a given number as a fraction of another |MyMaths.co.uk - Adding fractions |Fractions - Adding - NLVM | |
|add and subtract fractions by writing them with a | |Fractions review | |
|common denominator |MyMaths.co.uk - FractoDec |Adding and subtracting fractions | |
|convert a simple fraction to a decimal | |Worksheet: Fraction addition | |
|multiply and divide a fraction by an integer and by |MyMaths.co.uk - Mult Div Fractions |nrich. :: Mathematics Enrichment :: The Greedy | |
|a unit fraction | |Algorithm – unit fraction investigation | |
|understand and use unit fractions as multiplicative |MyMaths.co.uk - Multiplying Fractions |Mixed numbers and improper fractions | |
|inverses(1) | | | |
| |MyMaths.co.uk - Dividing Fractions |Follow me cards: Calculating fractions | |
| | | | |
| |MyMaths.co.uk - Calculations with Mixed Numbers |nrich. :: Mathematics Enrichment :: Peaches Today,| |
| | |Peaches Tomorrow.... | |
| |MyMaths.co.uk - Reciprocal | | |
| | |nrich. :: Mathematics Enrichment :: Fractions in a| |
| | |Box | |
| | |VTC - KS4 - Maths - Number | |
|2 - Order rational numbers |MyMaths.co.uk - Comparing Fractions |Ordering fractions | |
|order integers | | | |
|order fractions | |Ordering decimals | |
|order decimals |MyMaths.co.uk - DecimalOrdering | | |
|3 - Understand equivalent fractions |MyMaths.co.uk - Equivalent fractions |SmartBoard Notepad files for teaching mathematics – |nrich. :: Mathematics Enrichment |
|understand equivalent fractions and simplify a | |fractions activities |:: Fractions Jigsaw |
|fraction |MatchingFractions |Simplifying fractions | |
| | |Matching equivalent fractions | |
| |FractionPairs |Fractions - Equivalent - NLVM | |
|4 - Understand percentage | |Percentages puzzle | |
|understand that ‘percentage’ means ‘number of parts | | | |
|per 100’ and use this to compare proportions |MyMaths.co.uk - Fdp Intro |SmartBoard Notepad files for teaching mathematics – | |
|know the fraction-to-percentage (or decimal) | |fracts/dec/% tarsia puzzles and % puzzles | |
|conversion of familiar simple fractions | | | |
| | |Match fractions decimals and percentages | |
| | | | |
| | |nrich. :: Mathematics Enrichment :: Matching | |
| | |Fractions Decimals Percentages | |
|5 - Interpret fractions, decimals and percentages as | | |(1) A 15% decrease in Y is calculated as |
|operators | |nrich. :: Mathematics Enrichment :: 100 Percent |0·85 × Y |
|interpret percentage as the operator ‘so many |VTC - KS4 - Maths - Number | |eg Know that to increase an amount by 15%,|
|hundredths of’ | |MyMaths.co.uk - Fruit Machine |a multiplier of 1·15 can be used and that |
|convert between fractions, decimals and percentages |MyMaths.co.uk - Fdp Intro | |to increase an amount by 15% and then 10%,|
|understand the multiplicative nature of percentages | |Percentages - NLVM |amount × 1·15 × 1·10 is the equivalent |
|as operators(1) |MyMaths.co.uk - Fdp Harder | | |
| | |nrich. :: Mathematics Enrichment :: Are You a | |
| |MyMaths.co.uk - Percentagesamounts |Smart Shopper? | |
| | | | |
| | |nrich. :: Mathematics Enrichment :: Put Out the | |
| | |Flags | |
|6 - Proportional change |MyMaths.co.uk - SimpleProp |eg foreign currency and money problems |(1) eg 5 books cost £23·50, find the cost |
|find proportional change using fractions, decimals |MyMaths.co.uk - Six Boosters - Proportion | |of 3 books; foreign currency conversion; |
|and percentages |MyMaths.co.uk - Proportionlearn |eg best value for money situations with reasons |recipes; best value for money problems |
|understand and use direct proportion | | | |
| |Solve straightforward problems involving exchange rates. Up-to-date | | |
| |information from a daily newspaper or internet is useful to illustrate| | |
| |varying exchange rates. | | |
| | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |3-5 hours |Topic |F1F - Indices and surds |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Indices in common use |MyMaths.co.uk - SquareTriangle | | |
|use the terms ‘square’, ‘positive square root’, | |Concentration squares game | |
|‘negative square root’, ‘cube’ and ‘cube root’ |MyMaths.co.uk - SquareNumbers |Numbersearch: Powers of 2 and 3 | |
|recall integer squares from 11 ( 11 to 15 ( 15 and | |Square numbers starter | |
|the corresponding square roots |MyMaths.co.uk - SquarePairs |Opportunities for counter example work – are all squares | |
|recall the cubes of 2, 3, 4, 5 and 10 | |odd etc? | |
| |MyMaths.co.uk - Cubepairs | | |
| |Extension activity: 121 is a palindromic square number | | |
| |(when the digits are reversed it is the same number). | | |
| |Write down all the palindromic square numbers less than | | |
| |1000. | | |
|2 - Use index notation | |SmartBoard Notepad files for teaching mathematics – Tarsia | |
|use index notation for squares, cubes and powers of |MyMaths.co.uk - IndicesPart1 |– Index notation 1 and 2 | |
|10 | |Basic index notation worksheet | |
|use index notation for simple integer powers |MyMaths.co.uk - IndiciesPart2 |Indices rules | |
|use index laws for multiplication and division of |(not fractional indices) | | |
|integer powers | |nrich. :: Mathematics Enrichment :: Power Crazy | |
|use index laws to simplify, and calculate the value | | | |
|of, numerical expressions involving multiplication | | | |
|and division of integer powers | | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |2-3 hours |Topic |F1G - Measures |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Solve real-life problems involving measures | | |(1) Given a picture of a building and an adult man, |
|interpret scales on a range of measuring instruments,|Measurement: Reading scales | |estimate the height of the building in metres |
|and recognise the inaccuracy of measurements | | |(2) How far do you go travelling at 40 mph for 3 |
|convert measurements from one unit to another |Worksheet: Reading scales | |hours? |
|make sensible estimates of a range of measures in | | |(3) Use bearings to specify direction |
|everyday settings(1) |Scales: Is the statue of liberty's nose too long? | | |
|understand and use compound measures (including | |MyMaths.co.uk - Millionaire - Measures |A water barrel holds 10 gallons. Roughly how many |
|speed(2) and density) in familiar contexts |MyMaths.co.uk - Convert | |litres is this? |
|understand and use bearings(3) | |nrich. :: Mathematics Enrichment :: Sizewise |Include problems in selecting the most appropriate |
|measure and draw lines correct to the nearest |MyMaths.co.uk - Imperial Measures | |metric unit for a particular situation – provide the |
|millimetre and angles correct to the nearest degree | |MyMaths.co.uk - Millionaire |choices eg m/km/g/kg/l/ml/mm etc |
| |MyMaths.co.uk - Bearings teaching and learning activities | | |
| |Bearings |nrich. :: Mathematics Enrichment :: All in a Jumble|Independent research on internet - which is bigger? |
| |Bearings game | |- 1 kg or 1lb |
| |Bearings: Drawing and estimating | |- 1 tonne or 1 ton etc |
| |Maths 4 Real video: Bearings | |Give reasons - produce poster |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |2-3 hours |Topic |F1H - Coordinates |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Use the conventions for coordinates in the plane | | |(1) Plot (3, 6) and (2, -4) on the grid provided |
|use the conventions for coordinates in the plane; |Coordinates in one quadrant |Geoboard - Goordinate - NLVM | |
|plot points in all four quadrants | | | |
|understand that one coordinate identifies a point on |Plotting coordinates |MyMaths.co.uk - Flippyneck | |
|a number line and two coordinates identify a point in|Flash game: Plotting coordinates | | |
|a plane, using the terms ‘1D’ and ‘2D’ | |MyMaths.co.uk - Flippynecktwo | |
|use axes and coordinates to specify points in all | | | |
|four quadrants |Coordinate code breaking | | |
|locate points with given coordinates(1) |Points and lines | | |
| |Coordinate problems |nrich. :: Mathematics Enrichment :: Cops and | |
| | |Robbers | |
| |MyMaths.co.uk - Coord midpoint | | |
| | |nrich. :: Mathematics Enrichment :: Coordinate | |
| | |Patterns | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |2-3 hours |Topic |F1I - Formulae |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Derive a formula, substitute numbers into a |MyMaths.co.uk - Formulae | | |
|formula | | |Formulae for the area of a triangle, the area enclosed|
|use formulae from mathematics and other subjects |Formula Pairs game | |by a circle, wage earned = hours worked ( rate per |
|expressed initially in words and then using letters | |Happy planet index - functional |hour |
|and symbols |Class activity: Investigate the difference between simple |Happy planet index - data support sheets | |
|substitute numbers into a formula |algebraic expressions which are often confused, for | |Find r given that C =(r, find x given y |
|derive a formula |example, find the difference between 2x, 2 + x and x2 for | |= mx + c |
| |different values of x. | | |
| | |Fitness calculator |Link formulae/expression derivation to perimeter |
| |Spider diagram activities – different expressions on the |Fitness support sheets |problems of polygons with variables for lengths; |
| |legs with a value in the body | |costs; ages etc |
| | | | |
| |MyMaths.co.uk - Substituting |Reading age formulae | |
| | |Reading age formulae support | |
| |MyMaths.co.uk - Substituting Further |Reading age fomulae lesson plan | |
| | | | |
| |Maths 4 Real video: Rearranging formulae | | |
| | | | |
| |Starter problem: Substitution into BMI formula | | |
| | | | |
| |Rearranging formulae power point | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |6-8 hours |Topic |F1J - Linear equations |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Manipulate algebraic expressions |Try algebra pyramids for collecting like terms; matching |Tarsia puzzle – simplifying at SmartBoard Notepad files for |Collecting like terms |
|understand that the transformation of algebraic |games – expression with answer; odd ones out |teaching mathematics | |
|expressions obeys and generalises the rules of | | |Expanding brackets |
|generalised arithmetic(1) |MyMaths.co.uk - SimplifyingExpressions |MyMaths.co.uk - SimplifyPairs | |
|manipulate algebraic expressions by collecting like | | |Factorising by removing common factors |
|terms(2), by multiplying a single term over a |MyMaths.co.uk - FactoriseExpressions |MyMaths.co.uk - Simplify Pairs 2 | |
|bracket, and by taking out common factors(3) | | |(1) a(b + c) = ab + ac |
| |Expanding brackets |Algebra Tiles - NLVM |(2) x + 5 – 2x – 1 = 4 – x |
| | | |(3) 9x – 3 = 3(3x – 1) or x2 – 3x = x(x – 3) |
| |Tarsia and Easiteach resources: Algebra – select from |Tarsia – expanding brackets at SmartBoard Notepad files for | |
| |these resources |teaching mathematics | |
|2 - Set up and solve simple equations | |Algebra Balance Scales - NLVM |(1) Richard is x years, Julie is twice as old and |
|set up simple equations(1) |MyMaths.co.uk - Equations Simple | |their combined age is 24 years. Write an equation to |
|solve simple equations(2) by transforming both sides | |Solving simple linear equations - Waldomaths |show this information |
|in the same way |Flowchart method to begin to consolidate inverse | | |
| |operations leading to the balance method |Tarsia puzzle – solving equations at SmartBoard Notepad |(2) 11 – 4x = 2; 3(2x + 1) = 8; |
| | |files for teaching mathematics |2(1 – x) = 6(2 + x); 3x2 = 48; 3 =[pic] |
| |MyMaths.co.uk - solving Equations | | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |6-8 hours |Topic |F1J - Linear equations |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|solve linear equations, with integer coefficients, in| |Simple Equations 2 - Waldomaths | |
|which the unknown appears on either | | | |
|side or on both sides of the equation | |Algebra Balance Scales - Negatives - NLVM | |
|3 - Plot graphs of simple equations | | |Know that the lines represented by y = 5x and y |
|recognise and plot equations that correspond to |MyMaths.co.uk - PlottingGraphs |Drawing straight line graphs |= 3 + 5x are parallel, each having gradient 5 |
|straight line graphs in the coordinate plane | | | |
| | |nrich. :: Mathematics Enrichment :: Translating | |
| | |Lines | |
| | | | |
| | |nrich. :: Mathematics Enrichment :: Diamond | |
| |MyMaths.co.uk - Equationofline |Collector | |
| | | | |
| | |y = mx + c | |
| | | | |
| | |nrich. :: Mathematics Enrichment :: Parallel Lines | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time |7-9 hours |Topic |F1K - Angles and properties of shapes |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Lines and angles | | | |
|recall and use properties of angles at a point, angles|Anglesums |Angles at a point | |
|at a point on a straight line (including right | | | |
|angles), perpendicular lines, and opposite angles at a|MyMaths.co.uk - Angler |Calculating missing angles | |
|vertex | | | |
|distinguish between acute, obtuse, reflex and right |MyMaths.co.uk - Parallel Lines |Categorising angles | |
|angles; estimate the size of an angle in degrees | | | |
|distinguish between lines and line segments |MyMaths.co.uk - Angle Proofs |Acute or Obtuse? | |
|use parallel lines, alternate angles and corresponding| | | |
|angles | |Angle properties | |
|understand the consequent properties of parallel and | | | |
|intersecting lines, triangles (including a proof that | |nrich. :: Mathematics Enrichment :: Right Time | |
|the angle sum of a triangle is 180°) and | | | |
|parallelograms | |Parallel lines and pairs of angles | |
| | | | |
| | |Angles on parallel lines | |
| | | | |
| | |Angles in parallelograms | |
|2 - Properties of shapes | | | |
|use angle properties of equilateral, isosceles and |anglesums |Angles in triangles | |
|right-angled triangles | | | |
|recall the essential properties and definitions of |MyMaths.co.uk - Angle Reasoning |Angles in quadrilaterals | |
|special types of quadrilateral, including square, | | | |
|rectangle, parallelogram, trapezium, kite and rhombus |Use diagonal from one vertex and angle of triangles to |Click on the shape to view its properties | |
|classify quadrilaterals by their geometric properties |demonstrate | | |
|distinguish between centre, radius, chord, diameter, |MyMaths.co.uk - Angle Proofs |Properties of quadrilaterals | |
|circumference, tangent, arc, sector and segment | | | |
|understand that inscribed regular polygons can be |MyMaths.co.uk - LinesQuads |True or False? – quiz on shape facts | |
|constructed by equal division of a circle | | | |
|recognise reflection and rotation symmetry of 2D |Practical activity – stick the labels on parts of the | | |
|shapes |circle | | |
| | | | |
| |Card sort game – terms with pictures | | |
| | | | |
| |Use compasses and protractor to construct regular | | |
| |pentagons; hexagons; octagons etc | | |
| | | | |
| |Simple angle related angle calcs involving angle at centre| | |
| |of polygon and isosceles triangles | | |
|3 - Congruence and similarity | |Similarity ratio | |
|understand congruence | | |Formal proofs of congruent triangles not required. |
|understand similarity and the relationship between |MyMaths.co.uk - Similar Triangles |Similar triangles: Starter problem | |
|lengths and angles in similar figures | | |Must be able to give clear geometric reasons why |
| | |nrich. :: Mathematics Enrichment :: Number the |triangles are similar |
| | |Sides | |
|OCR GCSE Applications of Mathematics Unit: A381/01 |
|Suggested teaching time | |Topic |F1L - Area and volume |
|Topic outline |Suggested teaching and homework activities |Suggested resources |Points to note |
|1 - Perimeter, area and volume | | |Could involve inverse calculations – find the length of|
|find areas of rectangles, recalling the formula, |MyMaths.co.uk - Area of a Rectangle |KS4 Shape – tarsia and puzzles on area/vol |an edge given the volume and two other edges |
|understanding the connection to counting squares and | |House design: Area and perimeter | |
|how it extends this approach | |Worksheet: Area, perimeter, volume |After skills work emphasise functional aspects eg |
|find the area of a parallelogram and a triangle | |Area and perimeter cross number |design patio with area 60 m² |
|calculate perimeters and areas of shapes made from |MyMaths.co.uk - Area of a Parallelogram |nrich. :: Mathematics Enrichment :: Tangram |– How many paving stones will you need? |
|triangles and rectangles | |nrich. :: Mathematics Enrichment :: Hidden | |
| |MyMaths.co.uk - Area of a Triangle |Dimensions |– What will be the cost? |
| | |nrich. :: Mathematics Enrichment :: Pick's | |
| | |Theorem |eg You have 100 m of fencing, what is the maximum area |
| | |Perimeter and area problem |that can be enclosed? |
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