KS3 Maths Progress Delta 2-year Scheme of Work

Transcription

1 KS3 Maths Progress Delta 2-year Schee of Work See the spreadsheet for the detail. Essentially this is an express route through our higher-ability KS3 Maths Progress student books Delta 1, 2 and 3 as follows: Year 1 (ostly Delta 2) Several units fro Delta 1 serve as required knowledge for units fro Delta 2 and are included in the teaching hours. So we recoend that these Delta 1 units are dipped into to confir / reinforce the required knowledge. Two Delta 3 units are taught in this year. Delta 1 Delta 2 Delta 3 Unit 4 Fractions Unit 6 Fractions, decials and percentages Unit 4 Collecting and analysing data Unit 6 Decials Unit 1 Factors and powers Unit 5 Multiplicative reasoning Unit 2 Nuber skills Unit 2 Working with powers Unit 3 Equations, functions and forulae Unit 3 2D shapes and 3D solids Unit 7 Equations Unit 7 Constructions and loci Unit 9 Perieter, area and volue Unit 8 Probability Unit 1 Analysing and displaying data Unit 4 Real-life graphs Unit 10 Sequences and graphs [part] Unit 5 Transforations Unit 8 Multiplicative reasoning Year 2 (ostly Delta 3) Delta 1 units and Delta 2 units serve as required knowledge for Delta 3 units and are included in the teaching hours. Delta 1 Delta 2 Delta 3 Unit 5 Angles and shapes Unit 9 Scale drawings and easureents Unit 1 Powers and roots Unit 10 Sequences and graphs [part] Unit 10 Graphs Unit 2 Quadratics Unit 3 Inequalities, equations and forulae Unit 6 Non-linear graphs Unit 7 Accuracy and easures

2 Unit 8 Graphical solutions Unit 9 Trigonoetry Unit 10 Matheatical reasoning

3 Ter Unit Teaching hours Required knowledge: Fractions (Delta 1 Unit 4) Delta Year 1 Schee of Work 2014 Prograe of Study Unit description Pre-2014 sub-levels 10 order decials and fractions use the four operations, including foral written ethods, with positive and negative fractions use the four operations, including foral written ethods, with positive and negative iproper fractions and ixed nubers define percentage as nuber of parts per hundred interpret percentages and percentage changes as a fraction or a decial express one quantity as a fraction of another, where the fraction is less than 1 express one quantity as a fraction of another, where the fraction is greater than 1 Use a diagra to copare two or ore siple fractions 5c Use < and > to copare fractions with sae denoinator, or unit fractions with different denoinators Siplify fractions by cancelling all coon factors Express one nuber as a fraction of another. The nubers should be very siple (halves, quarters, thirds) Use fraction notation to express a saller whole nuber as a fraction of a larger one Begin to add and subtract siple fractions and those with siple 5c coon denoinators Add fractions by writing with a coon denoinator, where the denoinators are 12 or less, where the answer is less than 1 Understand that when two positive fractions are added the answer is larger than either of the original two fractions Subtract fractions by writing with a coon denoinator, where the denoinators are less than 12 and the first fraction is larger than the second Understand that when two positive fractions are subtracted the answer is less than the first fraction but ay still be larger than the second Add and subtract siple fractions with denoinators of any size Check addition or subtraction of fractions with an inverse calculation Add and subtract up to 3 fractions ixing both addition and subtraction into the calculation, with denoinators less than or equal to 12 and the using the LCM denoinator in the calculation the answer can be a ixed nuber Extend the possible fractions that can be used in ental calculations by 5c using halving and doubling strategies Calculate siple fractions of quantities and easureents (whole nuber answers) Calculate fractions of quantities and easureents (fraction answers) Multiply a fraction by an integer Multiply an integer by a fraction Understand the effect of ultiplying a positive nuber by a fraction less than 1 Recall known facts including fraction to decial conversions Recall of equivalent fractions and decials and percentage including for fractions that are greater than 1 Use division to convert a fraction to a decial Use halving and doubling strategies on fractions to find decial equivalents of other fractions Interpret division as a ultiplicative inverse. Know that 1 divided by 1/4 is the sae as 1 4 Divide an integer by a fraction Understand the effect of dividing a positive nuber by a fraction less than 1 Multiply a fraction by a fraction (without cancelling) Cancel coon factors before ultiplying fractions Divide a fraction by a fraction Add ixed nuber fractions without coon denoinators, where the fraction parts add up to ore than 1 Be able to enter tie as a ixed nuber into a calculator Subtract ixed nuber fractions when the fractional part of the first fraction is all that is required for the calculation to take place Subtract ixed nuber fractions where the whole nuber part of the first fraction needs to be broken down to coplete the calculation Multiply a fraction by a ixed nuber Divide a ixed nuber by a fraction

4 Required knowledge: Decials (Delta 1 Unit 6) understand and use place value for decials understand and use place value for integers order decials and fractions use the sybols =,, <, >,, work interchangeably with terinating decials and their corresponding fractions (such as 3.5 and 7/2 or and 3/8) interpret percentages and percentage changes as a fraction or a decial interpret percentages ultiplicatively express one quantity as a percentage of another copare two quantities using percentages work with percentages greater than 100% interpret fractions and percentages as operators use standard units of ass, length, tie, oney and other easures, including with decial quantities use approxiation through rounding to estiate answers solve probles involving percentage change: percentage increase solve probles involving percentage change: decrease solve probles involving percentage change: original value probles solve probles involving percentage change: siple interest in financial atheatics Order positive decials as a list with the sallest on the left. Decials should be to 4 or 5 significant figures Order negative decials as a list with the sallest on the left Order positive decials with the largest on the left. Decials should be to 4 or 5 significant figures Order negative decials as a list with the sallest on the left. Decials should be to 2 or 3 significant figures Order negative decials with the largest on the left. Decials should be to 2 or 3 significant figures Use > or < correctly between two positive decials. Decials should be to 4 or 5 significant figures. Use > or < correctly between two negative decials. Decials should be to 2 or 3 significant figures Round nubers to two or three decial places, Write nubers as a decial nuber of illions or thousands e.g as 23.6 illion Round to an appropriate nuber of decial places after calculations, e.g. oney probles after division, perieter when using the pi key and a radius in c etc. Work with nubers rounded to whole nubers or to 1 or two decial places to estiate solutions, e.g. average populations of cities under certain effects. Add and subtract ore than two integers or decials with up to two decial places, but with varying nubers of significant figures and using a ixture of operations within the calculation Use standard colun procedures to add and subtract integers and decials of any size, including a ixture of large and sall nubers with differing nubers of decial places Subtract integers and decials with up to two decial places, but with varying nubers of significant figures Extend written ethods to U.t U Multiply and divide decials with one or two places by single-digit whole nubers Use ental strategies for ultiplication - partitioning two 2 digit nubers where one nuber includes a decial (both nubers have two significant figures) Multiply integers and decials including by decials such as 0.6 and 0.06, 0.t 0.t or 0.t 0.0h, 0.0h 0.t and 0.0h 0.0h Multiply and divide by decials, dividing by transforing to division by an integer Understand the effect of ultiplying a positive nuber by a decial less than 1 Use ental strategies for ultiplication of decials - doubling and halving strategies Understand where to position the decial point by considering equivalent calculations which are given Use knowledge of place value to calculate the product of two decials / where one or both are less than 1 and at least one has two digits other than zero Multiply any nuber by 0.1 and 0.01 Know there are different ways of finding an approxiate answer Divide integers and decials including by decials such as 0.6 and 0.06 divisions related to 0.t 0.t or 0.t 0.0h, 0.0h 0.t and 0.0h 0.0h Use knowledge of place value to calculate the division of two decials where both are less than 1 and at least the first has two digits other than zero Multiply and divide by decials, dividing by transforing to division by an integer Divide.p by a two digit nuber to give.p Multiply and divide decials with one or two places by single-digit whole nubers Divide decials with one or two places by single-digit whole nubers

5 A u t u n t e r Fractions, decials and percentages (Delta 2 Unit 6) Required knowledge: Nuber skills (Delta 1 Unit 2) interpret percentages and percentage changes as a fraction or a decial interpret percentages ultiplicatively express one quantity as a percentage of another copare two quantities using percentages work with percentages greater than 100% 9 order positive and negative integers use the concepts and vocabulary of prie nubers use the concepts and vocabulary of factors (or divisors) use the concepts and vocabulary of ultiples use the concepts and vocabulary of coon factors use the concepts and vocabulary of coon ultiples use the concepts and vocabulary of highest coon factor use the concepts and vocabulary of lowest coon ultiple use the four operations, including foral written ethods, with positive and negative integers use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals use integer powers and associated real roots (square, cube and higher) recognise powers of 2, 3, 4, 5 Understand that dividing by 0.1 or 0.01 are equivalent to dividing by 1/10th or 1/100th or ultiplying by 10 or 100 Divide any nuber by 0.1 and 0.01 Know there are different ways of finding an approxiate answer Recall of equivalent fractions, decials and percentage including for fractions that are greater than 1. Match across all 3 types, and need to be siple fractions (1/2, 1/4, 1/5, 1/10) Use the equivalence of fractions, decials and percentages to copare proportions Find equivalent fractions, decials and percentages where percentages end in 0.5 Use strategies for finding equivalent fractions, decials and percentages involving decial percentages and decials greater 0 Order fractions by converting the to decials or otherwise Siplify converted terinating decial to fraction convert a terinating decial to a fraction and siplify the fraction Write terinating decials as fractions Interpret rounded off recurring decials displayed on a calculator as fractions 2/3, 1/6, 1 2/3, 1 1/6 Convert terinating decials to fractions really eans like = 745/ 1000, not 0.5 = 1/2 Extend the percentage calculation strategies with jottings to find any percentage Express one given nuber as a percentage of another Find the outcoe of a given percentage increase Find the outcoe of a given percentage decrease Use a unitary ethod Have strategies for calculating fractions and decials of a given nuber Know fractional equivalents to key recurring decials e.g , , Know the denoinators of siple fractions that produce recurring decials, and those that do not Convert a recurring decial to a fraction Use an inverse operation Use the unitary ethod for an inverse operation Calculate percentage change, using the forula 'actual change/original aount x 100' where forula is given Calculate percentage change, using the forula 'actual change/original aount x 100' where forula is recalled Calculate copound interest and repeated percentage change Find factor pairs using any whole nuber Find the HCF or LCM of 2 nubers less than 20 Multiply and divide negative integers by a positive integer Add and subtract integers positive and negative integers Add and subtract negative integers fro positive and negative integers Multiply and divide integers positive and negative integers Multiply and divide negative integers by a negative integer Use index notation for squares and cubes and for positive integer powers of 10 Know all the squares of nubers less than 16 and be able to find the square root given the square nuber Give the positive and negative square root of a square nuber Extend ental calculations to squares and square roots Be able to estiate square roots of non square nubers less than 100 Mentally be able to calculate the squares of nubers less than 16 ultiplied by a ultiple of ten (e.g. 0.2, 300, 0.400) Divide three-digit by two-digit whole nubers Using rounding to the nearest 10 or a nice nuber (e.g. 62 to 63 when dividing by 9 etc.) 5c

6 Factors and powers (Delta 2 Unit 1) Required knowledge: Equations, functions and forulae (Delta 1 Unit 3) use the concepts and vocabulary of prie factorisation use product notation and the unique factorisation property round nubers and easures to an appropriate degree of accuracy [for exaple, to a nuber of decial places or significant figures] calculate possible errors resulting fro estiating, expressed using inequality notation a < x b Use ental strategies for ultiplication doubling and halving strategies Checking by an inverse operation (questions other than four rules, e.g. square roots checked with squaring) Be able to estiate answers to calculations involving 2 or ore operations and BIDMAS Use index notation for sall integer powers (e.g. 3 2³ = 24) Extend ental calculations to cubes and cube roots Extend calculations to cubes and cube roots using ental ethods and a calculator when appropriate Be able to find square roots by factorising Be able to find cube roots by factorising Be able to use ental strategies to solve word probles set in context using square roots and cubes roots entally Be able to work with calculations where the brackets are squared or square rooted Cobine laws of arithetic for brackets with ental calculations of cubes and squares Cobine laws of arithetic for brackets with ental calculations of square roots Cobine laws of arithetic for brackets with ental calculations of cube roots and square roots Understand which part of an expression is raised to a power by knowing the difference between 3 (7 + 8) 2 and 3 2 (7 + 8) and (3 (7 + 8)) 2 Find the prie factor decoposition of a nuber / Know the prie factorisation of nubers up to 30, giving answers as powers Use prie factor decoposition to find the HCF or LCM of 2 nubers Establish index laws for positive powers where the answer is a positive power Apply the index laws for ultiplication and division of positive integer / powers Show that any nuber to the power of zero is 1 Understand that each of the headings in the place value syste, to the right of the tens colun, can be written as a power of ten Know the prefixes associated with 10 9, 10 6, 10 3 (giga, ega and kilo) Understand the effect of ultiplying or dividing by any integer power of 10 / // Understand the order in which to calculate expressions that contain powers and brackets in both the nuerator and denoinator of a fraction Round nubers to a given nuber of significant figures Use nubers of any size rounded to 1 significant figure to ake standardized estiates for calculations with 1 step Half ter 11 use and interpret algebraic notation: ab in place of a b Siplify siple expressions by collecting like ters use and interpret algebraic notation: 3y in place of y + y + y and 3 y Understand the difference between 2n and n² use and interpret algebraic notation: a 2 in place of a a Know that expressions involving repeated ultiplication can be written as use and interpret algebraic notation: a 3 in place of a a a n, n 2, n 3 use and interpret algebraic notation: a 2 b in place of a a b Siplify siple expressions involving powers but not brackets, by use and interpret algebraic notation: b/a in place of a b collecting like ters use and interpret algebraic notation: brackets Construct expressions fro worded description, using addition, substitute nuerical values into forulae and expressions, including scientific forulae subtraction and ultiplication understand and use the concepts and vocabulary of expressions, equations, inequalities, ters Construct expressions fro worded description, using all 4 basic and factors operations siplify and anipulate algebraic expressions to aintain equivalence: collecting like ters Express siple functions in sybols siplify and anipulate algebraic expressions to aintain equivalence: ultiplying a single ter over a bracket Know that the contents of brackets are evaluated first when using algebra siplify and anipulate algebraic expressions to aintain equivalence: taking out coon Know that ultiplication and division are carried out before addition and factors subtraction odel situations or procedures by translating the into algebraic expressions or forulae Substitute positive integers into expressions involving sall powers

7 Required knowledge: Equations (Delta 1 Unit 7) Working with powers (Delta 2 Unit 2) Required knowledge: Perieter, area and volue (Delta 1 Unit 9) rearrange forulae to change the subject use algebraic ethods to solve linear equations in one variable (including all fors that require rearrangeent) Evaluate an expression by substituting a positive value into the expression x 2 Use the distributive law to take out nuerical coon factors Multiply a single ter over a bracket Add, subtract, ultiply and divide integers extend to the distributive law a(b + c) Substitute positive integers into siple forulae expressed in words 4a Substitute integers into ore coplex forulae expressed in letter sybols Substitute positive integers into siple forulae expressed in letter sybols Substitute integers into ore coplex forulae (involving brackets and ore than one operation) expressed in letter sybols Substitute positive and negative integers into siple forulae Identify the unknowns in a forula and a function Derive forulae expressed in letter sybols / Understand the different role of letter sybols in forulae and functions Derive coplex algebraic expressions and forulae Solve siple linear equations with integer coefficients, of the for ax = b or x +/ b = c e.g. 2x = 18, x + 7 = 12 or x 3 = 15 Solve siple two-step linear equations with integer coefficients, of the for ax + b = c e.g. 3x + 7 = 25 Substitute integers into forulae to give equations and solve Solve linear equations of the for ax +/ b = cx +/ d Solve equations of the for a(x +/ b) = c(x +/ d) [a or c can be 1] Find a positive and negative square root as a solution of an equation involving x² Construct and solve equations of the for a(x +/ b) = c(x +/ d) [a or c can be 1] Use systeatic trial and iproveent to find the approxiate solution to one decial place of equations such as x³ + x = 50 use and interpret algebraic notation: coefficients written as fractions rather than as decials Siplify siple expressions involving powers, but not brackets, by use and interpret algebraic notation: brackets collecting like ters understand and use the concepts and vocabulary of expressions, equations, inequalities, ters Siplify siple expressions involving index notation, i.e. x² + 2x², p p², r and factors 5 r² siplify and anipulate algebraic expressions to aintain equivalence: collecting like ters siplify and anipulate algebraic expressions to aintain equivalence: ultiplying a single Know and understand the eaning of an identity and use the identity sign ter over a bracket Siplify expressions involving brackets and powers e.g. x(x 2 + x + 4), 3(a use algebraic ethods to solve linear equations in one variable (including all fors that require + 2b) 2(a + b) rearrangeent) Establish index laws for positive powers of variables where the answer is a positive power Apply the index laws for ultiplication and division of sall integer / powers, e.g. a³ a², x³ x² Know and use the general fors of the index laws for ultiplication and division of positive integer powers. (e.g. pa pb, pa pb, (pa)b) Multiply a single ter over a bracket e.g. x(x + 4), 3x(2x 3) Use the distributive law to take out single ter algebraic factors, e.g. x³ + x² + x = x(x² + x + 1) Substitute positive and negative integers into linear expressions and expressions involving powers Construct and solve equations that involve ultiplying out brackets by a negative nuber and collecting like ters (e.g. 4(2a 1) = 32 3(2a 2)) 12 understand and use place value for easures use standard units of ass, length, tie, oney and other easures, including with decial quantities round nubers and easures to an appropriate degree of accuracy [for exaple, to a nuber of decial places or significant figures] understand and use standard atheatical forulae change freely between related standard units [for exaple tie, length, area, volue/capacity, Find the area of triangles by counting i.e. adding full and partial squares Use a forula to calculate the area of triangles Deduce a forula for the area of a triangle Use a forula to calculate the area of parallelogras Deduce and use the forula for the area of a parallelogra 5c

8 2D shapes and 3D solids (Delta 2 Unit 3) Constructions and loci (Delta 2 Unit 7) change freely between related standard units [for exaple tie, length, area, volue/capacity, ass] Deduce a forula for the area of a trapeziu derive forulae to calculate and solve probles involving perieter of triangles, parallelogras, Calculate the area of ore coplex shapes ade fro rectangles trapezia Calculate the perieter and area of shapes ade fro rectangles derive and apply forulae to calculate and solve probles involving area of triangles, parallelogras, trapezia Calculate areas of copound shapes ade fro rectangles and triangles derive and apply forulae to calculate and solve probles involving volue of cuboids (including Know and use geoetric properties of cuboids cubes) Identify ore coplex nets of 3D shapes including irregular polyhedra calculate and solve probles involving coposite shapes derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for Know and use geoetric properties of shapes ade fro cuboids exaple, equal lengths and angles] using appropriate language and technologies Know and use the forula for the volue of a cuboid / Calculate volues of shapes ade fro cuboids, for lengths given as whole nubers Calculate the surface area of cubes, without a net Use nets to calculate the surface area of siple cuboids Calculate the surface area of siple cuboids (without use of nets) Calculate surface areas of shapes ade fro cuboids, for lengths given as whole nubers Convert c 3 to l and litres and vice versa Convert between area easures (e.g. ² to c², c² to ², and vice versa) Convert between volue easures (e.g. ³ to c³, c³ to ³, and vice versa) Know rough etric equivalents of iperial easures in daily use (feet, iles, pounds, pints, gallons) understand and use standard atheatical forulae Begin to use plans and elevations derive and apply forulae to calculate and solve probles involving volue of priss (including Visualise and use a wide range of 2-D representations of 3-D objects cylinders) Analyse 3-D shapes inforally and through cross-sections, plans and / calculate and solve probles involving perieters of circles elevations calculate and solve probles involving areas of circles Calculate the volue and surface area of right priss / use Pythagoras Theore to solve probles involving right-angled triangles Calculate the lengths, areas and volues in cylinders Convert between larger volue easures to saller ones (e.g. ³ to c³) Calculate the lengths and areas given the volues in right priss Use the forula for the circuference of a circle Know the naes of parts of a circle Use the forulae to find area of a circle, given the radius or diaeter Use the forulae for the area of a circle, given area, to calculate the radius or diaeter Be able to correctly identify the hypotenuse Know the forula for Pythagoras' theore and how to substitute in values fro a diagra Use and apply Pythagoras' theore to solve probles Given the coordinates of points A and B, calculate the length of AB End of ter 10 draw and easure line segents and angles in geoetric figures Construct a triangle given two sides and included angle (SAS) derive and use the standard ruler and copass constructions: perpendicular bisector of a line Construct a triangle given two angles and the included side (ASA) segent Use straight edge and copass to construct a triangle, given three sides derive and use the standard ruler and copass constructions: constructing a perpendicular to a (SSS) given line fro/at a given point Use ruler and protractor to draw accurate nets of 3-D shapes, using derive and use the standard ruler and copass constructions: bisecting a given angle squares, rectangles and triangles e.g. regular tetrahedron, square-based recognise and use the perpendicular distance fro a point to a line as the shortest distance to pyraid, triangular pris the line Use straight edge and copass to construct the id-point and describe, sketch and draw using conventional ters and notations: points, lines, parallel lines, perpendicular bisector of a line segent perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and Use straight edge and copass to construct the bisector of an angle rotationally syetric Use straight edge and copass to construct the perpendicular fro a use the standard conventions for labelling the sides and angles of triangle ABC point on a line segent Use straight edge and copass to construct a triangle, given right angle, hypotenuse and side (RHS) Use straight edge and copass to construct the perpendicular fro a point to a line segent

9 S p r i n g t e r Recognise and use the perpendicular distance fro a point to a line as the shortest distance to the line Draw the locus equidistant between 2 points or fro a point Draw the locus equidistant between 2 lines Know that all the points equidistant fro a single point in space for the surface of a sphere Draw the locus equidistant fro a line and around a rectangle Produce shapes and paths by using descriptions of loci Use construction to find the locus of a point that oves according to a rule Understand and use the probability scale fro 0 to 1 5c Identify all possible utually exclusive outcoes of a single event Find and justify probabilities based on equally likely outcoes in siple contexts Calculate the probability of a cobination of events or single issing events of a set of utually exclusive events using 'su of outcoes = 1' Calculate the probability of the final event of a set of utually exclusive events Know that if probability of event is p, probability of not occurring is 1 p Understand relative frequency as an estiate of probability and know when to add or ultiply probabilities Know how to calculate relative frequency 5c Use relative frequency to ake estiates Apply estiated probabilities to future data Estiate probabilities based on these data (collected fro a siple experient) Plot and use relative frequency diagras, and recognise that with repeated trials experiental probability tends to a liit Use experientation to coplete a data collection sheet, e.g. throwing a die or data-logging Identify all utually exclusive outcoes for two successive events with / two or three outcoes in each event Use the vocabulary of probability to assign probability to events. // Identify conditions for a fair gae / Draw and use tree diagras to represent outcoes of two independent events and calculate probabilities Calculate the probability of independent and dependent events Half ter 13 describe, interpret and copare observed distributions of a single variable through: appropriate Copare two siple distributions using appropriate easures 4c, 5c, easures of central tendency (ean, ode, edian) Calculate the ean fro a siple frequency table construct and interpret frequency tables Copare two distributions given suary statistics, construct and interpret bar charts Recognise when it is appropriate to use ean, edian or ode construct and interpret pie charts construct and interpret vertical line (or bar) charts for ungrouped data Use two way tables for discrete data., construct and interpret vertical line (or bar) charts for grouped nuerical data Make inferences about data through extracting inforation fro a two way describe siple atheatical relationships between two variables (bivariate data) in table observational and experiental contexts Construct and interpret pie charts and line graphs, illustrate siple atheatical relationships between two variables (bivariate data) using scatter Use questionnaire responses to coplete a data collection sheet graphs Construct and interpret copound and dual (coparative) bar charts Interpret and / or copare bar graphs and frequency diagras which are isleading Construct a siple frequency table with equal class intervals for continuous data Be able to use > or < correctly between two positive decials. Decials should be to 4 or 5 significant figures. Be able to use > or < correctly between two negative decials. Decials should be to 2 or 3 significant figures. Construct a frequency table with given equal class intervals for continuous data (boundary data given) Construct a frequency diagra fro a grouped frequency table Probability (Delta 2 Unit 8) 10 record, describe and analyse the frequency of outcoes of siple probability experients involving randoness, fairness, equally and unequally likely outcoes use appropriate language of probability use the 0 1 probability scale understand that probabilities of all possible outcoes su to 1 generate theoretical saple spaces for single and cobined events with equally likely and utually exclusive outcoes use saple spaces for single and cobined events to calculate theoretical probabilities. Required knowledge: Analysing and displaying data (Delta 1 Unit 1)

10 Collecting and analysing data (Delta 3 Unit 4) Required knowledge: Sequences and graphs (Delta 1 Unit 10 PART ONLY) Real-life graphs (Delta 2 Unit 4) Find the odal class of a set of continuous data Construct line graphs for tie series Construct and interpret scatter graphs Identify which graphs are the ost useful in the context of the proble Use correlation to describe relations between sets of data, Draw and use a line a best fit to estiate a issing value, use a calculator and other technologies to calculate results accurately and then interpret the Select appropriate level of accuracy of data / appropriately Select the range of possible ethods that could be used to collect this describe, interpret and copare observed distributions of a single variable through: appropriate data as priary data graphical representation involving discrete data Select and discuss the range of possible sources that could be used to describe, interpret and copare observed distributions of a single variable through: appropriate collect this data as secondary data graphical representation involving continuous and grouped data Fro a range of saple sizes identify the ost sensible answer describe, interpret and copare observed distributions of a single variable through: appropriate Deterine the saple size and degree of accuracy needed easures of spread (range, consideration of outliers) Fro a sall choice of options identify ways to reduce bias in a saple or questionnaire Identify a rando saple Use ste and leaf diagras to find ode, edian, ean, range Construct ste and leaf diagras Use back to back ste and leaf diagras to copare sets of data Construct a frequency diagra fro a grouped frequency table, and use it to draw a frequency polygon. Copare two distributions using the shape of the distributions frequency polygons. Construct and use frequency polygons to copare sets of data Estiate the range of a large set of grouped data Calculate an estiate of the ean of a large set of grouped data Estiate the ean fro a frequency polygon Identify the class that contains the edian of a set of grouped data fro a table Calculate possible values of the set of data given suary statistics Find quartiles fro raw data and present data in a box plot Find the lower and upper quartiles of a set of grouped data using a cuulative frequency chart and box and whisker diagra Draw a grouped frequency graph Estiate the edian of a set of grouped data using a cuulative frequency chart Find the interquartile range of a large set of grouped data using a cuulative frequency chart Interpret / construct histogras 8+ End of ter 9 Read x and y co-ordinates in all four quadrants 5c Plot a coordinate in all four quadrants Know how to find the idpoint of a line segent Recognise straight line graphs parallel to x or y axis Find the idpoint of a horizontal or vertical line segent AB, using coordinates of these points (no diagras) Find the idpoint of a diagonal line segent AB using the coordinate of these points (no diagras) Plot a graph of a siple linear function in the first quadrant. Copare graphs of siple functions Generate four quadrant coordinate pairs of siple linear functions In tables of functions copare changes in y with corresponding changes in x and how this relates to the function Plot and recognise graphs of y = x and y = x Plot the graphs of siple linear functions in the for y = x + c in four quadrants understand and use standard atheatical forulae Extend a proportion or relationship beyond known values (given proportion rearrange forulae to change the subject graphically or in words) odel situations or procedures by translating the into algebraic expressions or forulae Recognise graphs that show direct proportion find approxiate solutions to contextual probles fro given graphs of a variety of functions:,

11 Required knowledge: Multiplicative reasoning (Delta 1 Unit 8) Multiplicative reasoning (Delta 3 Unit 5) find approxiate solutions to contextual probles fro given graphs of a variety of functions: including piece-wise linear graphs solve probles involving direct proportion solve proportion probles including graphical and algebraic representations use copound units such as speed, unit pricing and density to solve probles 11 use ratio notation reduce a ratio to siplest for divide a given quantity into two parts in a given part:part ratio divide a given quantity into two parts in a given part:whole ratio express the division of a quantity into two parts as a ratio understand that a ultiplicative relationship between two quantities can be expressed as a ratio or a fraction relate the language of ratios and the associated calculations to the arithetic of fractions relate the language of ratios and the associated calculations to linear functions solve probles involving direct proportion solve probles involving inverse proportion calculate and solve probles involving perieters of circles calculate and solve probles involving areas of circles Transforations (Delta 2 Unit 5) 10 identify properties of, and describe the results of: translations identify properties of, and describe the results of: rotations identify properties of, and describe the results of: reflections construct siilar shapes by enlargeent without coordinate grids construct siilar shapes by enlargeent coordinate grids Half ter Solve probles involving direct proportion with a graph Discuss and interpret real-life graphs Interpret inforation fro a coplex real life graph, read values and discuss trends Plot the graphs of a function derived fro a real life proble Discuss and interpret linear and non linear graphs fro a range of sources Recognise graphs showing constant rates of change, average rates of change and variable rates of change Plot a siple straight line graph (distance-tie) Draw and use graphs to solve distance-tie probles Identify isleading graphs and statistics choosing the appropriate reasons fro a sall choice of options Identify isleading graphs and statistics choosing the appropriate reasons fro a wide choice of options, or writing their own reasons. Reduce a ratio to its siplest for Reduce a ratio to its siplest for Reduce a three part ratio to its siplest for by cancelling Siplify a ratio expressed in fractions or decials Convert between larger area easures to saller ones (e.g. c² to ²) Increase the knowledge of standard etric units to include tonne, hectare Siplify a ratio expressed in different units Copare ratios by changing the to the for 1: or :1 Divide a quantity into two parts in a given ratio, where ratio given in ratio notation Divide a quantity into ore than 2 parts in a given ratio Write ratios as fractions, percentages Understand the relationship between ratio and proportion (convert proportions to ratios) Solve word probles involving direct proportion Use the unitary ethod to solve siple word probles involving ratio and direct proportion Relate the language of ratios and the associated calculations to the arithetic of fractions and to linear functions Given a relationship (as proportion) graphically or in words, extend beyond known values (e.g. off lines of chart, or above pairs of values given Check by drawing graphs whether two variables are in direct proportion Set up equations to show direct proportion Recognise sets of data that are proportional Understand direct proportion as equality of ratio Use algebraic ethods to solve probles involving variables in direct proportion Use expressions of the for y is proportional to x Use expressions of the for y is proportional to x 2 Identify data that is proportional to the inverse of a variable Understand / use inverse proportion 8+ Recognise the forulae for length of arcs in a circle Recognise the forulae for area of sectors in a circle Use the forulae for length of arcs and area of sectors of circles to solve probles Describe a reflection, giving the equation of the line of reflection Show reflection on a coordinate grid in y = x, y = x Describe and carry out translations using colun vectors Describe a rotation on a coordinate grid

12 construct siilar shapes by enlargeent coordinate grids apply angle facts, triangle congruence, siilarity and properties of quadrilaterals to derive results about angles and sides End of ter End of year Know that translations, rotations and reflections preserve length and angle Know that translations, rotations and reflections ap objects on to congruent iages Enlarge 2D shapes, given a centre of enlargeent and a positive whole / nuber scale factor Describe 2D enlargeents Enlarge 2D shapes, given a centre of enlargeent outside the shape and a negative whole-nuber scale factor Enlarge 2D shapes, given a fractional scale factor Recognise that enlargeents preserve angle but not length Enlarge 2D shapes and recognise the siilarity of resulting shapes Transfor 2D shapes by siple cobinations of rotations, reflections and translations, using ICT Transfor 2D shapes by ore coplex cobinations of rotations, reflections and translations Identify reflection syetry in 3D shapes Understand the iplications of enlargeent for perieter Identify the scale factor of an enlargeent as the ratio of the lengths of any two corresponding line segents Calculate areas and volues of shapes after enlargeent / Ter Unit Teaching hours Required knowledge: Angles and shapes (Delta 1 Unit 5) Delta Year 2 Schee of Work 2014 Prograe of Study Unit description Pre-2014 sub-levels 10 apply the properties of angles at a point apply the properties angles at a point on a straight line apply the properties vertically opposite angles understand and use the relationship between parallel lines and alternate and corresponding angles derive and use the su of angles in a triangle use the su of angles in a triangle to deduce the angle su in any polygon derive properties of regular polygons Solve siple geoetrical probles showing reasoning Recognise and use vertically opposite angles Identify alternate angles Identify corresponding angles Identify alternate and corresponding angles on the sae diagra Calculate angles in a triangle Solve geoetric probles using side and angle properties of equilateral and isosceles triangles, Scale drawings and easures (Delta 2 Unit 9) use scale factors use scale diagras use aps interpret scale drawings know and use the criteria for congruence of triangles identify and construct congruent triangles Understand a proof that the su of the angles of a triangle is 180 degrees Understand a proof that the exterior angle of a triangle is equal to the su of the two interior opposite angles Identify all the syetries of 2D shapes 5c Identify and begin to use angle, side and syetry properties of quadrilaterals Find co-ordinates of points deterined by geoetric inforation Classify quadrilaterals by their geoetric properties Understand a proof that the su of the angles of a quadrilateral is 360 degrees Explain how to find the sus of the interior and exterior angles of quadrilaterals, pentagons and hexagons Calculate the interior and exterior angles of regular polygons Use the interior and exterior angles of regular and irregular polygons Use scales in aps and plans Use and interpret aps, using proper ap scales (1:25 000) Draw diagras to scale Use and interpret scale drawings, where scales use ixed units, and drawings aren't done on squared paper, but have easureents arked on the. Solve siple geoetrical probles showing reasoning Distinguish between conventions, definitions and derived properties

13 A u t u n t e r Solve geoetric probles using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals Solve probles using properties of angles, of parallel and intersecting // lines, and of triangles and other polygons Make siple drawings, deonstrating accurate easureent of length and angle Use bearings to specify direction Solve angle probles involving bearings Begin to use congruency to solve siple probles in triangles and quadrilaterals Know and use the criteria for congruence of triangles Identify 2-D shapes that are congruent or siilar by reference to sides and angles Use the inforation given about the length of sides and size of angles to deterine whether triangles are congruent, or siilar Know that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not. Find points that divide a line in a given ratio, using the properties of siilar triangles Use siilarity to solve probles in 2-D shapes Graphs (Delta 2 Unit 10) 11 recognise and use relationships between operations including inverse operations Plot the graphs of linear functions in the for y = x + c and recognise odel situations or procedures by using graphs and copare their features work with coordinates in all four quadrants Recognise that linear functions can be rearranged to give y explicitly in recognise, sketch and produce graphs of linear functions of one variable with appropriate ters if x e.g. rearrange y + 3x 2 = 0 in the for y = 2 3x scaling, using equations in x and y and the Cartesian plane interpret atheatical relationships both algebraically and graphically Recognise that straight line graphs can be written in the for y = x + c reduce a given linear equation in two variables to the standard for y = x + c Be able to work out when a point is on a line calculate and interpret gradients and intercepts of graphs of such linear equations nuerically Begin to consider the features of graphs of siple linear functions, where calculate and interpret gradients and intercepts of graphs of such linear equations graphically y is given explicitly in ters of x calculate and interpret gradients and intercepts of graphs of such linear equations algebraically Without drawing the graphs, copare and contrast features of graphs such as y = 4x, y = 4x + 6, y = x + 6, y = 4x, y= x 6 Know and use y = x + c for any straight line Know for a straight line y = x + c, is the gradient and = (change in y)/(change in x) Recognise that any line parallel to a given line will have the sae gradient. Know that a line perpendicular to the line y = x + c, will have a gradient of 1/ Recognise when lines are parallel or perpendicular fro their equations Recognise when lines are parallel and where a line crosses the y-axis fro the equation of the line Find the inverse of a linear function such as x 2x + 5, x 2(x 3), x (x + 2)/4, x 5x 4 Recognise the graph of the inverse of siple linear functions Recognise that when the linear and inverse of a linear function such as y = 2x, y = 3x are plotted, they are a reflection in the line y = x Recognise geoetric sequences and appreciate other sequences that arise Powers and roots (Delta 3 Unit 1) Find approxiate solutions to contextual probles fro given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs Solve probles involving direct and inverse proportion, including graphical and algebraic representations Half ter 11 distinguish between exact representations of roots and their decial approxiations Find the reciprocal of siple nubers /fractions entally, e.g. 10 and 1/ interpret nubers in standard for A 10n 1 A < 10, where n is a positive or negative integer 10, 1/3 and 3 etc. or zero Know that a nuber ultiplied by its reciprocal is 1 copare nubers in standard for A 10n 1 A < 10, where n is a positive or negative integer Know that the reciprocal of a reciprocal is the original nuber or zero

14 Required knowledge: Sequences and graphs (Delta 1 Unit 10 PART ONLY) Quadratics (Delta 3 Unit 2) or zero substitute nuerical values into forulae and expressions, including scientific forulae 11 appreciate the infinite nature of the sets of integers, real and rational nubers generate ters of a sequence fro a ter-to-ter rule generate ters of a sequence fro a position-to-ter recognise arithetic sequences find the nth ter recognise geoetric sequences and appreciate other sequences that arise siplify and anipulate algebraic expressions to aintain equivalence: expanding products of two or ore binoials generate ters of a sequence fro a ter-to-ter rule generate ters of a sequence fro a position-to-ter recognise arithetic sequences find the nth ter recognise geoetric sequences and appreciate other sequences that arise Use the index laws to include negative power answers and understand that these answers are saller than 1 Evaluate powers of fractions Write nubers greater than 10 in standard for Write nuber less than 10 in standard for Order nubers written in standard for Coplete calculations using nubers written in standard for Use fractional indices and write a fractional power as a root Work out negative fractional powers of nubers Siplify expressions which include surds Present a concise and reasoned arguent using surds Understand / use rational / irrational nubers 8+ Distinguish between exact representations of roots and their decial 8+ approxiations Understand the infinite nature of a set of integers Know that an arithetic sequence is generated by a starting nuber a, 5c then adding a constant nuber d Generate ters of a linear sequence using ter to ter using positive or negative integers Find a ter given its position in a sequences like 10 th nuber in 4 table 5c is 40 (one operation on n) Recognise geoetric sequences and other sequences that arise. Begin to use a linear expression to describe the nth ter in a one-step arithetic sequence Generate ters of a linear sequence using position to ter with positive integers using the nth ter. Begin to use linear expressions to describe the nth ter in a two step arithetic sequence (e.g. nth ter is 3n + 1 or 2n 3) Generate ters of a linear sequence using position to ter with negative integers Begin to use foral algebra to describe the nth ter in an arithetic sequence Generate and describe integer sequences such as powers of 2 and 5c growing rectangles Generate ters fro a coplex practical context (e.g. axiu crossing for a given nuber of lines) Predict how the sequence will continue and test for several ore ters. Find the ter-to-ter rule for geoetric sequences and continue to the next few ters Generate any ter of a sequence when the nth ter is given. Generate the next ter in a quadratic sequence Find a ter of a quadratic sequence with T(n) = an 2 for a given value of n Find the nth ter of a quadratic sequence of the ter with T(n) = an 2 +/ b Find the nth ter of a quadratic sequence of the ter with T(n) = an 2 +/ bn +/ c Generate the sequence of triangle nubers by considering the arrangeent of dots and deduce that T(n) = n, the su of the series By looking at the spatial patterns of triangular nubers, deduce that the nth ter is n (n + 1)/2 Multiply out brackets involving positive ters such as (a + b)(c + d) and collect like ters Multiply out brackets involving positive and negative ters such as (a + b)(c d) or (a b)(c d) and collect like ters Square a linear expression and collect like ters Derive and use identities for the product of two linear expressions of the for (a + b)(a b) = a 2 b 2 and (x + 2)(x 2) = x 2 4 Factorise a quadratic expression / Factorise a perfect square

15 Inequalities, equations and forulae (Delta 3 Unit 3) Derive and use the difference of two squares Solve quadratics with first ter x squared (no ultiples of x squared) End of ter 11 understand and use the concepts and vocabulary of expressions, equations, inequalities, ters Solve linear inequalities and represent the solution on a nuber line and factors rearrange forulae to change the subject Multiply both sides of an inequality by a negative nuber use algebraic ethods to solve linear equations in one variable (including all fors that require Know that a 0 = 1 rearrangeent) Use the index laws to include negative power answers and establish that these answers are saller than 1 Explain the distinction between equations, forulae and functions Solve equations of the for (ax +/ b)/c = (dx +/ e)/f {One of c or f should be 1} Construct and solve equations of the for (ax +/ b)/c = (dx +/ e)/f {c and f are bigger than 1} Change the subject of a forula Use factorisation to ake a given letter the subject of a forula Change algebraic fractions to equivalent fractions Change the subject of a coplex forula that involves fractions, e.g. ake u or v the subject of the forula 1/v + 1/u =1/f Solve probles by finding a variable that is not the subject of a forula S p r i n g t e r Non-linear graphs (Delta 3 Unit 6) 10 recognise, sketch and produce graphs of quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane find approxiate solutions to contextual probles fro given graphs of a variety of functions: reciprocal graphs Siplify coplex algebraic expressions 8+ Construct a table of values, including negative values of x for a quadratic function such as y = ax 2 Recognise the graph of a quadratic function Construct a table of values, including negative values of x for a function such as y = ax 2 + b Find the line of syetry and write down the turning point of a quadratic graph Explain the effect on a quadratic graph of changing the paraeter Solve siple quadratic equations graphically, e.g. x 2 10 = 0, 2x 2 15 = 0 Construct a table of values, including negative values of x for a function such as y = ax 2 + bx and y = ax 2 + bx + c Solve quadratic equations such as ax 2 + bx = 0 graphically and relate the solutions to quadratic factorisation Solve quadratic equations such as x 2 + bx + c = 0 graphically and relate the solutions to quadratic factorisation Construct a table of values, including negative values of x for a function such as y = ax 3 Recognise the graphs of y = x 2, y = 3x 2 + 4, y = x 3 Recognise graphs of functions of the for y = ax 2 + b and y = ax 3 Identify axia, inia and lines of syetry on quadratic and cubic graphs Construct odels of real-life situations by drawing graphs and constructing algebraic equations Sketch / interpret graphs of reciprocal functions 8+ Recognise and use reciprocal graphs and graphs for inverse proportion 8 Accuracy and easures (Delta 3 Unit 7) Half ter 9 use copound units such as speed, unit pricing and density to solve probles round nubers and easures to an appropriate degree of accuracy [for exaple, to a nuber of decial places or significant figures] use approxiation through rounding to estiate answers calculate possible errors resulting fro estiating, expressed using inequality notation a < x b Solve probles using constant rates and related forulae. Extend to siple conversions of copound easures (e.g. convert 2 /s to k/hr) Solve probles using average rate of change and related forulae Identify the upper and lower bounds of a easureent by calculating +/ half of the unit used for rounding Identify upper and lower bounds for rounding of discrete and continuous data Calculate siple error intervals using inequality notation a < x <= b Calculate the lower and upper bounds of area easureent Calculate the upper and lower bounds of copound easures