Y6 Long-term objectives

Transcription

1 Y6 Long-term objectives Cambridge Primary Mathematics Stage 6 Framework 6Nn1 Number and the number system Count on and back in fractions and decimals, e.g.⅓s, 0.1s, and repeated steps of whole numbers (and through zero) 6Nn2 Know what each digit represents in whole numbers up to a million 6Nn3 Know what each digit represents in one- and two-place decimal numbers 6Nn4 Multiply and divide any whole number from 1 to by 10, 100 or 1000 and explain the effect 6Nn5 Multiply and divide decimals by 10 or 100 (answers up to two decimal places for division) 6Nn6 Find factors of two-digit numbers 6Nn7 Find some common multiples, e.g. for 4 and 5 6Nn8 Round whole numbers to the nearest 10, 100 or Nn9 6Nn10 6Nn11 6Nn12 6Nn13 Round a number with two decimal places to the nearest tenth or to the nearest whole number Make and justify estimates and approximations of large numbers Order and compare positive numbers to one million, and negative integers to an appropriate level Use the >, < and = signs correctly Estimate where four-digit numbers lie on an empty line 6Nn14 6Nn15 Order numbers with up to two decimal places (including different numbers of places) Recognise and extend number sequences

2 Cambridge Primary Mathematics Stage 6 Framework 6Nn16 Recognise and use decimals with up to three places in the context of measurement Number and the number system (Continued) 6Nn17 Recognise odd and even numbers and multiples of 5, 10, 25, 50 and 100 up to Nn18 Make general statements about sums, differences and multiples of odd and even numbers 6Nn19 Recognise prime numbers up to 20 and find all prime numbers less than 100 6Nn20 Recognise the historical origins of our number system and begin to understand how it developed 6Nn21 Compare fractions with the same denominator and related denominators, e.g. ¾ with 6Nn22 Recognise equivalence between fractions, e.g. between s, s and ½s 6Nn23 Recognise and use the equivalence between decimal and fraction forms 6Nn24 Order mixed numbers and place between whole numbers on a number line 6Nn25 Change an improper fraction to a mixed number 6Nn26 Reduce fractions to their simplest form, where this is ¼, ½, ¾ or a number of fifths or tenths 6Nn27 Begin to convert a vulgar fraction to a decimal fraction using division 6Nn28 Understand percentage as parts in every 100 and express ½, ¼, ⅓,, as percentages 6Nn29 6Nn30 Find simple percentages of shapes and whole numbers Solve simple problems involving ratio and direct proportion Number/Calculation/Mental strategies 6Nc1 Recall addition and subtraction facts for numbers to 20 and pairs of v2 1Y08 2

3 Cambridge Primary Mathematics Stage 6 Framework one-place decimals with a total of 1, e.g Number/Calculation/Mental strategies (Continued) 6Nc2 Derive quickly pairs of one-place decimals totalling 10, e.g. 7.8 and 2.2 and two-place decimals totalling 1, e.g Nc3 Know and apply tests of divisibility by 2, 4, 5, 10, 25 and 100 6Nc4 6Nc5 6Nc6 6Nc7 6Nc8 6Nc9 6Nc10 Use place value and number facts to add or subtract two-digit whole numbers and to add or subtract three-digit multiples of 10 and pairs of decimals, e.g ; ; Add/subtract near multiples of one when adding numbers with one decimal place, e.g ; Add/subtract a near multiple of 10, 100 or 1000, or a near whole unit of money, and adjust, e.g ; Use place value and multiplication facts to multiply/divide mentally, e.g. 0.8 x 7; Multiply pairs of multiples of 10, e.g 30 x 40, or multiples of 10 and 100, e.g. 600 x 40 Double quickly any two-digit number, e.g. 78, 7.8, 0.78 and derive the corresponding halves Divide two-digit numbers by single-digit numbers, including leaving a remainder Number/Calculation/Addition and subtraction 6Nc11 6Nc12 6Nc13 Add two- and three-digit numbers with the same or different numbers of digits/decimal places Add or subtract numbers with the same and different numbers of decimal places, including amounts of money Find the difference between a positive and negative integer, and between two negative integers in a context such as temperature or on a number line Number/Calculation/Multiplication and division v2 1Y08 3

4 Cambridge Primary Mathematics Stage 6 Framework 6Nc14 Multiply pairs of multiples of 10, e.g. 30 x 40, or multiples of 10 and 100, e.g. 600 x 40 6Nc15 Multiply near multiples of 10 by multiplying by the multiple of 10 and adjusting 6Nc16 Multiply by halving one number and doubling the other, e.g. calculate with Nc17 Use number facts to generate new multiplication facts, e.g. the 17 table from tables 6Nc18 6Nc19 6Nc20 6Nc21 6Nc22 Multiply two-, three- or four-digit numbers (including sums of money) by a single-digit number and two- or three-digit numbers by two-digit numbers Divide three-digit numbers by single-digit numbers, including those leaving a remainder and divide three-digit numbers by two-digit numbers (no remainder) including sums of money Give an answer to division as a mixed number, and a decimal (with divisors of 2, 4, 5, 10 or 100) Relate finding fractions to division and use them as operators to find fractions including several tenths and hundredths of quantities Know and apply the arithmetic laws as they apply to multiplication (without necessarily using the terms commutative, associative or distributive) Geometry/Shape and geometric reasoning 6Gs1 6Gs2 6Gs3 6Gs4 Classify different polygons and understand whether a 2D shape is a polygon or not Visualise and describe the properties of 3D shapes, e.g. faces, edges and vertices Identify and describe properties of quadrilaterals (including the parallelogram, rhombus and trapezium), and classify using parallel sides, equal sides, equal angles Recognise and make 2D representations of 3D shapes including nets Geometry/Shape and geometric reasoning (Continued) v2 1Y08 4

5 Cambridge Primary Mathematics Stage 6 Framework 6Gs5 Estimate, recognise and draw acute and obtuse angles and use a protractor to measure to the nearest degree 6Gs6 Check that the sum of the angles in a triangle is 180, for example, by measuring or paper folding; calculate angles in a triangle or around a point Geometry/Position and movement 6Gp1 Read and plot co-ordinates in all four quadrants 6Gp2 Predict where a polygon will be after one reflection, where the sides of the shape are not parallel or perpendicular to the mirror line, after one translation or after a rotation through 90 about one of its vertices Measure/Length, mass and capacity 6Ml1 Select and use standard units of measure. Read and write to two or three decimal places 6Ml2 Convert between units of measurement (kg and g, l and ml, km, m, cm and mm), using decimals to three places, e.g. recognising that m is 1 m 24.5 cm 6Ml3 Interpret readings on different scales, using a range of measuring instruments 6Ml4 Draw and measure lines to the nearest centimetre and millimetre 6Ml5 Know imperial units still in common use, e.g. the mile, and approximate metric equivalents Measure/Time 6Mt1 Recognise and understand the units for measuring time (seconds, minutes, hours, days, weeks, months, years, decades and centuries); convert one unit of time into another 6Mt2 Tell the time using digital and analogue clocks using the 24-hour clock Measure/Time (Continued) 6Mt3 Compare times on digital and analogue clocks, e.g. realise quarter to four is later than 3:40 6Mt4 Read and use timetables using the 24-hour clock v2 1Y08 5

6 Cambridge Primary Mathematics Stage 6 Framework 6Mt5 Calculate time intervals using digital and analogue times 6Mt6 Use a calendar to calculate time intervals in days, weeks or months 6Mt7 Calculate time intervals in days, months or years 6Mt8 Appreciate how the time is different in different time zones around the world Measure/Area and perimeter 6Ma1 Measure and calculate the perimeter and area of rectilinear shapes 6Ma2 Estimate the area of an irregular shape by counting squares 6Ma3 Calculate perimeter and area of simple compound shapes that can be split into rectangles Handling data/organising, categorising and representing data 6Dh1 Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams, e.g. line graphs for distance and time; a price ready-reckoner for currency conversion; frequency tables and bar charts with grouped discrete data 6Dh2 Find the mode and range of a set of data from relevant situations, e.g. scientific experiments 6Dh3 Begin to find the median and mean of a set of data 6Dh4 Explore how statistics are used in everyday life Handling data/probability 6Db1 Use the language associated with probability to discuss events, to assess likelihood and risk, including those with equally likely outcomes Problem solving/using techniques and skills in solving mathematical problems v2 1Y08 6

7 Cambridge Primary Mathematics Stage 6 Framework 6Pt1 Choose appropriate and efficient mental or written strategies to carry out a calculation involving addition, subtraction, multiplication or division 6Pt2 Understand everyday systems of measurement in length, weight, capacity, temperature and time and use these to perform simple calculations 6Pt3 Check addition with a different order when adding a long list of numbers; check when subtracting by using the inverse 6Pt4 Recognise 2D and 3D shapes and their relationships, e.g. a cuboid has a rectangular cross-section 6Pt5 Estimate and approximate when calculating, e.g. use rounding, and check working Problem solving/using understanding and strategy in solving mathematical problems 6Ps1 Explain why they chose a particular method to perform a calculation and show working 6Ps2 Deduce new information from existing information and realise the effect that one piece of information has on another 6Ps3 Use logical reasoning to explore and solve number problems and mathematical puzzles 6Ps4 Use ordered lists or tables to help solve problems systematically 6Ps5 Identify relationships between numbers and make generalised statements using words, then symbols and letters, e.g. the second number is twice the first number plus 5 (n, 2n + 5); all the numbers are multiples of 3 minus 1 (3n 1); the sum of angles in a triangle is 180 Problem solving/using understanding and strategy in solving mathematical problems (Continued) 6Ps6 Make sense of and solve word problems, single and multi-step (all four operations), and represent them, e.g. with diagrams or on a number line; use brackets to show the series of calculations necessary 6Ps7 Solve simple word problems involving ratio and direct proportion v2 1Y08 7

8 Cambridge Primary Mathematics Stage 6 Framework 6Ps8 Solve simple word problems involving percentages, e.g. find discounted prices 6Ps9 Make, test and refine hypotheses, explain and justify methods, reasoning, strategies, results or conclusions orally v2 1Y08 8

9 7Ni1 7Ni2 7Ni3 7Np1 7Np2 7Np3 7Nf1 7Nf2 7Nf3 7Nf4 7Nf5 7Nf6 7Nf7 7Nf8 7Nf9 Cambridge Secondary 1 Mathematics Stage 7 Number/Integers, powers and root Recognise negative numbers as positions on a number line, and order, add and subtract positive and negative integers in context Recognise multiples, factors, common factors, primes (all less than 100), making use of simple tests of divisibility; find the lowest common multiple in simple cases; use the sieve for generating primes developed by Eratosthenes Recognise squares of whole numbers to at least and the corresponding square roots; use the notation 7² and 49 Number/Place value, ordering and rounding Interpret decimal notation and place value; multiply and divide whole numbers and decimals by 10, 100 or 1000 Order decimals including measurements, changing these to the same units Round whole numbers to the nearest 10, 100 or 1000 and decimals, including measurements, to the nearest whole number or one decimal place Number/Fractions, decimals, percentages, ratio and proportion Recognise the equivalence of simple fractions, decimals and percentages Simplify fractions by cancelling common factors and identify equivalent fractions; change an improper fraction to a mixed number, and vice versa; convert terminating decimals to fractions, e.g = 23 hundredths Compare two fractions by using diagrams, or by using a calculator to convert the fractions to decimals Add and subtract two simple fractions; find fractions of quantities (whole number answers); multiply a fraction by an integer Understand percentage as the number of parts in every 100; use fractions and percentages to describe parts of shapes, quantities and measures Calculate simple percentages of quantities (whole number answers) and express a smaller quantity as a fraction or percentage of a larger one Use percentages to represent and compare different quantities Use ratio notation, simplify ratios and divide a quantity into two parts in a given ratio Recognise the relationship between ratio and proportion Number/Fractions, decimals, percentages, ratio v2 1Y08 9

10 Cambridge Secondary 1 Mathematics Stage 7 7Nf10 7Nc1 7Nc2 and proportion (Continued) Use direct proportion in context; solve simple problems involving ratio and direct proportion Number/Calculation/Mental strategies Consolidate the rapid recall of number facts, including positive integer complements to 100, multiplication facts to and associated division facts Use known facts and place value to multiply and divide two-digit numbers by a single-digit number, e.g. 45 6, Nc3 Know and apply tests of divisibility by 2, 3, 5, 6, 8, 9, 10 and 100 7Nc4 7Nc5 7Nc6 7Nc7 7Nc8 7Nc9 7Nc10 7Nc11 7Ae1 7Ae2 7Ae3 7Ae4 7Ae5 7Ae6 7Ae7 7As1 Use known facts and place value to multiply simple decimals by onedigit numbers, e.g. 0.8 x 6 Calculate simple fractions and percentages of quantities, e.g. one quarter of 64, 20% of 50 kg Use the laws of arithmetic and inverse operations to simplify calculations with whole numbers and decimals Use the order of operations, including brackets, to work out simple calculations Add and subtract integers and decimals, including numbers with different numbers of decimal places Multiply and divide decimals with one and/or two places by single-digit numbers, e.g x 8, Know that in any division where the dividend is not a multiple of the divisor there will be a remainder, e.g = 6 remainder 7. The remainder can be expressed as a fraction of the divisor Know when to round up or down after division when the context requires a whole-number answer Algebra/Expressions, equations and formulae Use letters to represent unknown numbers or variables; know the meanings of the words term, expression and equation Know that algebraic operations follow the same order as arithmetic operations Construct simple algebraic expressions by using letters to represent numbers Simplify linear expressions, e.g. collect like terms; multiply a constant over a bracket Derive and use simple formulae, e.g. to change hours to minutes Substitute positive integers into simple linear expressions/formulae Construct and solve simple linear equations with integer coefficients (unknown on one side only), e.g. 2x = 8, 3x + 5 = 14, 9-2x = 7 Algebra/Sequences, functions and graphs Generate terms of an integer sequence and find a term given its v2 1Y08 10

11 Cambridge Secondary 1 Mathematics Stage 7 7As2 7As3 7As4 7Gs1 7Gs2 7Gs3 position in the sequence; find simple term-to-term rules Generate sequences from spatial patterns and describe the general term in simple cases Represent simple functions using words, symbols and mappings Generate coordinate pairs that satisfy a linear equation, where y is given explicitly in terms of x; plot the corresponding graphs; recognise straight-line graphs parallel to the x- or y-axis Geometry/Shapes and geometric reasoning Identify, describe, visualise and draw 2D shapes in different orientations Use the notation and labelling conventions for points, lines, angles and shapes Name and identify side, angle and symmetry properties of special quadrilaterals and triangles, and regular polygons with 5, 6 and 8 sides 7Gs4 Estimate the size of acute, obtuse and reflex angles to the nearest 10 7Gs5 7Gs6 7Gs7 7Gs8 7Gs9 7Gs10 7Gp1 7Gp2 Start to recognise the angular connections between parallel lines, perpendicular lines and transversals Calculate the sum of angles at a point, on a straight line and in a triangle, and prove that vertically opposite angles are equal; derive and use the property that the angle sum of a quadrilateral is 360 Solve simple geometrical problems by using side and angle properties to identify equal lengths or calculate unknown angles, and explain reasoning Recognise and describe common solids and some of their properties, e.g. the number of faces, edges and vertices Recognise line and rotation symmetry in 2D shapes and patterns; draw lines of symmetry and complete patterns with two lines of symmetry; identify the order of rotation symmetry Use a ruler, set square and protractor to: measure and draw straight lines to the nearest millimetre; measure and draw acute, obtuse and reflex angles to the nearest degree; draw parallel and perpendicular lines; construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA); construct squares and rectangles; construct regular polygons, given a side and the internal angle Geometry/Position and movement Read and plot coordinates of points determined by geometric information in all four quadrants Geometry/Position and movement (Continued) Transform 2D points and shapes by: reflection in a given line; rotation about a given point; v2 1Y08 11

12 7Ml1 7Ml2 7Ml2 7Mt1 7Mt2 7Ma1 7Ma2 7Ma3 7Ma4 7Dc1 7Dc2 7Dc3 7Dp1 7Dp2 7Dp3 Cambridge Secondary 1 Mathematics Stage 7 translation Know that shapes remain congruent after these transformations Measure/Length, mass and capacity Choose suitable units of measurement to estimate, measure, calculate and solve problems in everyday contexts Know abbreviations for and relationships between metric units; convert between: kilometres (km), metres (m), centimetres (cm), millimetres (mm) kilometres (km), metres (m), centimetres (cm), millimetres (mm); tonnes (t), kilograms (kg) and grams (g); litres (l) and millilitres (ml) Read the scales on a range of analogue and digital measuring instruments Measure/Time and rates of change Draw and interpret graphs in real life contexts involving more than one stage, e.g. travel graphs Know the relationships between units of time; understand and use the 12-hour and 24-hour clock systems; interpret timetables; calculate time intervals Measure/Area, perimeter and volume Know the abbreviations for and relationships between square metres (m²), square centimetres (cm²), square millimetres (mm²) Derive and use formulae for the area and perimeter of a rectangle; calculate the perimeter and area of compound shapes made from rectangles Derive and use the formula for the volume of a cuboid; calculate volumes of cuboids Calculate the surface area of cubes and cuboids from their nets Handling data/planning and collecting data Decide which data would be relevant to an enquiry and collect and organise the data Design and use a data collection sheet or questionnaire for a simple survey Construct and use frequency tables to gather discrete data, grouped where appropriate in equal class intervals Handling data/processing and presenting Find the mode (or modal class for grouped data), median and range Handling data/processing and presenting (Continued Calculate the mean, including from a simple frequency table Draw and interpret: bar-line graphs and bar charts; v2 1Y08 12

13 Cambridge Secondary 1 Mathematics Stage 7 7Di1 7Di2 7Db1 frequency diagrams for grouped discrete data; simple pie charts; pictograms Handling data/interpreting and discussing results Draw conclusions based on the shape of graphs and simple statistics Compare two simple distributions using the range and the mode, median or mean Handling data/probability Use the language of probability to describe and interpret results involving likelihood and chance 7Db2 Understand and use the probability scale from 0 to 1 7Db3 7Db4 7Db5 7Db6 7Pt1 7Pt2 7Pt3 7Pt4 7Pt5 7Pt6 7Pt7 7Pt8 Find probabilities based on equally likely outcomes in simple contexts Identify all the possible mutually exclusive outcomes of a single event Use experimental data to estimate probabilities Compare experimental and theoretical probabilities in simple contexts Problem solving/using techniques and skills in solving mathematical problems Use the laws of arithmetic and inverse operations to simplify calculations with whole numbers and decimals Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Understand everyday systems of measurement and use them to estimate, measure and calculate Recognise and use spatial relationships in two and three dimensions Draw accurate mathematical diagrams, graphs and constructions Check results of calculations by using inverse operations Estimate, approximate and check their working Solve word problems involving whole numbers, percentages, decimals, money or measures: choose operations and mental or written methods appropriate to the numbers and context, including problems with more than one step 7Ps1 7Ps2 Problem solving/using understanding and strategies in solving problems Identify and represent information or unknown numbers in problems, making correct use of numbers, symbols, words, diagrams, tables and graphs Recognise mathematical properties, patterns and relationships, generalising in simple cases v2 1Y08 13

14 7Ps3 7Ps4 7Ps5 7Ps6 Cambridge Secondary 1 Mathematics Stage 7 Work logically and draw simple conclusions Relate results or findings to the original context and check that they are reasonable Record and explain methods, results and conclusions Discuss and communicate findings effectively, orally and in writing. v2 1Y08 14

15 Cambridge Secondary 1 Mathematics Stage 8 8Ni1 8Ni2 8Ni3 8Np1 Number/Integers, powers and root Add, subtract, multiply and divide integers Identify and use multiples, factors, common factors, highest common factors, lowest common multiples and primes; write a number in terms of its prime factors, e.g. 500 = 2² x 5³ Calculate squares, positive and negative square roots, cubes and cube roots; use notation and index notation for positive integer powers Number/Place value, ordering and rounding Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, Np2 Order decimals, including measurements, making use of the =,, > and < signs 8Np3 Round whole numbers to a positive integer power of 10, e.g. 10, 100, 1000 or decimals to the nearest whole number or one or two decimal places 8Nf1 8Nf2 8Nf3 8Nf4 8Nf5 8Nf6 8Nf7 8Nf8 8Nc1 Number/Fractions, decimals, percentages, ratio and proportion Find equivalent fractions, decimals and percentages by converting between them Convert a fraction to a decimal using division; know that a recurring decimal is a fraction Order fractions by writing with common denominators or dividing and converting to decimals Add and subtract fractions and mixed numbers; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction Calculate and solve problems involving percentages of quantities and percentage increases or decreases; express one given number as a fraction or percentage of another Use equivalent fractions, decimals and percentages to compare different quantities Simplify ratios, including those expressed in different units; divide a quantity into more than two parts in a given ratio Use the unitary method to solve simple problems involving ratio and direct proportion Number/Calculation/Mental strategies Use known facts to derive new facts, e.g. given 20 x 38 = 760, work out 21 x 38 Number/Calculation/Mental strategies (Continued) v2 1Y08 15

16 8Nc2 8Nc3 8Nc4 Cambridge Secondary 1 Mathematics Stage 8 Recall squares to 20 20, cubes to 5 5 5, and corresponding roots Recall simple equivalent fractions, decimals and percentages Use known facts and place value to multiply and divide simple fractions 8Nc5 8Nc6 8Nc7 8Nc8 8Nc9 8Nc10 8Nc11 8Nc12 8Nc13 8Ae1 8Ae2 8Ae3 8Ae4 8Ae5 8Ae6 Use known facts and place value to multiply and divide simple decimals, e.g x 9, Use known facts and place value to calculate simple fractions and percentages of quantities Recall relationships between units of measurement Solve simple word problems including direct proportion problems Use the laws of arithmetic and inverse operations to simplify calculations with integers and fractions Use the order of operations, including brackets, with more complex calculations Consolidate adding and subtracting integers and decimals, including numbers with differing numbers of decimal places Divide integers and decimals by a single-digit number, continuing the division to a specified number of decimal places, e.g Multiply and divide integers and decimals by decimals such as 0.6 or 0.06, understanding where to place the decimal point by considering equivalent calculations, e.g x 0.3 = (4.37 x 3) 10, = (92.4 x 100) 6 Algebra/Expressions, equations and formulae Know that letters play different roles in equations, formulae and functions; know the meanings of formula and function Know that algebraic operations, including brackets, follow the same order as arithmetic operations; use index notation for small positive integer powers Construct linear expressions Simplify or transform linear expressions with integer coefficients; collect like terms; multiply a single term over a bracket Derive and use simple formulae, e.g. to convert degrees Celsius ( C) to degrees Fahrenheit ( F) Substitute positive and negative integers into formulae, linear expressions and expressions involving small powers, e.g. 3x² + 4 or 2x³, including examples that lead to an equation to solve 8Ae7 Algebra/Expressions, equations and formulae (Continued) Construct and solve linear equations with integer coefficients (unknown on either or both sides, without or with brackets) v2 1Y08 16

17 8As1 8As2 8As3 8As4 8Gs1 8Gs2 8Gs3 8Gs4 8Gs5 8Gs6 8Gs7 8Gs8 8Gs9 Cambridge Secondary 1 Mathematics Stage 8 Algebra/Sequences, functions and graphs Generate terms of a linear sequence using term-to-term and positionto-term rules; find term-to-term and position-to-term rules of sequences, including spatial patterns Use a linear expression to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated Express simple functions algebraically and represent them in mappings Construct tables of values and use all four quadrants to plot the graphs of linear functions, where y is given explicitly in terms of x; recognise that equations of the form y = mx + c correspond to straightline graphs Geometry/Shapes and geometric reasoning Know that if two 2D shapes are congruent, corresponding sides and angles are equal Classify quadrilaterals according to their properties, including diagonal properties Know that the longest side of a right-angled triangle is called the hypotenuse Identify alternate angles and corresponding angles Understand a proof that: the angle sum of a triangle is 180 and that of a quadrilateral is 360 ; the exterior angle of a triangle is equal to the sum of the two interior opposite angles Solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and special quadrilaterals, explaining reasoning with diagrams and text Draw simple nets of solids, e.g. cuboid, regular tetrahedron, squarebased pyramid, triangular prism Identify all the symmetries of 2D shapes Use a straight edge and compasses to construct: the midpoint and perpendicular bisector of a line segment; the bisector of an angle 8Gs10 Geometry/Shapes and geometric reasoning (Continued) Use a ruler and compasses to construct circles and arcs a triangle, given three sides (SSS) a triangle, given a right angle, hypotenuse and one side (RHS) v2 1Y08 17

18 8Gp1 8Gp2 8Gp3 8Gp4 8Ml1 8Ml2 8Mt1 8Ma1 8Ma2 8Ma3 8Dc1 8Dc2 8Dc3 8Dp1 8Dp2 Cambridge Secondary 1 Mathematics Stage 8 Geometry/Position and movement Find the midpoint of the line segment AB, given the coordinates of points A and B Transform 2D shapes by rotation, reflection and translation, and simple combinations of these transformations Understand and use the language and notation associated with enlargement; enlarge 2D shapes, given a centre of enlargement and a positive integer scale factor Interpret and make simple scale drawings Measure/ Length, mass and capacity Choose suitable units of measurement to estimate, measure, calculate and solve problems in a range of contexts, including units of mass, length, area, volume or capacity Know that distances in the USA, the UK and some other countries are measured in miles, and that one kilometre is about of a mile Measure/Time and rates of change Draw and interpret graphs in real life contexts involving more than one component, e.g. travel graphs with more than one person Measure/Area, perimeter and volume Know the definition of a circle and the names of its parts; know and use formulae for the circumference and area of a circle Derive and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound 2D shapes, and lengths, surface areas and volumes of cuboids Use simple nets of solids to work out their surface areas Handling data/ Planning and collecting data Identify and collect data to answer a question; select the method of collection, sample size and degree of accuracy needed for measurements Know the difference between discrete and continuous data Construct and use: frequency tables with given equal class intervals to gather continuous data two-way tables to record discrete data Handling data/processing and presenting data Calculate statistics for sets of discrete and continuous data; recognise when to use the range, mean, median and mode and, for grouped data, the modal class Draw, and interpret: frequency diagrams for discrete and continuous data pie charts simple line graphs for time series v2 1Y08 18

19 8Di1 8Di2 8Di3 8Db1 8Db2 8Db3 8Db4 8Pt1 8Pt2 8Pt3 8Pt4 8Pt5 8Pt6 8Pt7 8Pt8 Cambridge Secondary 1 Mathematics Stage 8 stem-and-leaf diagrams Handling data/interpreting and discussing results Interpret tables, graphs and diagrams for discrete and continuous data, and draw conclusions, relating statistics and findings to the original question Compare two distributions, using the range and one or more of the mode, median and mean Compare proportions in two pie charts that represent different totals Handling data/probability Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 p Find probabilities based on equally likely outcomes in practical contexts Find and list systematically all possible mutually exclusive outcomes for single events and for two successive events Compare estimated experimental probabilities with theoretical probabilities, recognising that: when experiments are repeated different outcomes may result increasing the number of times an experiment is repeated generally leads to better estimates of probability Problem solving/using techniques and skills in solving mathematical problems Calculate accurately, choosing operations and mental or written methods appropriate to the numbers and context Use the order of operations, including brackets, with more complex calculations Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Understand everyday measurement systems, using them to estimate, measure and calculate Recognise and use spatial relationships in two and three dimensions Draw accurate mathematical diagrams, graphs and constructions Problem solving/using techniques and skills in solving mathematical problems (Continued) Estimate, approximate and check working Solve word problems involving calculations with whole numbers, fractions, percentages, decimals, money or measures, including multistep problems Problem solving/using understanding and strategies in solving problems v2 1Y08 19

20 8Ps1 8Ps2 8Ps3 8Ps4 8Ps5 8Ps6 Cambridge Secondary 1 Mathematics Stage 8 Identify the mathematical features of a context or problem; try out and compare mathematical representations using accurate notation Conjecture and generalise, identifying exceptional cases or counterexamples Use logical argument to interpret the mathematics in a context or to establish the truth of a statement Give accurate solutions appropriate to the context or problem Record and compare reasoning, solutions and conclusions Refine approaches and findings on the basis of discussions with others v2 1Y08 20

21 Cambridge Secondary 1 Mathematics Stage 9 Number/Integers, powers and root 9Ni1 9Ni2 9Ni3 9Np1 9Np2 9Np3 9Nf1 9Nf2 9Nf3 9Nf4 9Nf5 9Nf6 9Nc1 9Nc2 9Nc3 9Nc4 9Nc5 Add, subtract, multiply and divide directed numbers Estimate square roots and cube roots Use positive, negative and zero indices and the index laws for multiplication and division of positive integer powers Number/Place value, ordering and rounding Recognise the equivalence of 0.1, and 10ˉ¹; multiply and divide whole numbers and decimals by 10 to the power of any positive or negative integer Round numbers to a given number of decimal places or significant figures; use to give solutions to problems with an appropriate degree of accuracy Use the order of operations, including brackets and powers Number/Fractions, decimals, percentages, ratio and proportion Consolidate writing a fraction in its simplest form by cancelling common factors Add, subtract, multiply and divide fractions, interpreting division as a multiplicative inverse, and cancelling common factors before multiplying or dividing Solve problems involving percentage changes, choosing the correct numbers to take as 100% or as a whole, including simple problems involving personal or household finance, e.g. simple interest, discount, profit, loss and tax Recognise when fractions or percentages are needed to compare different quantities Compare two ratios; interpret and use ratio in a range of contexts Recognise when two quantities are directly proportional; solve problems involving proportionality, e.g. converting between different currencies Number/Calculation Extend mental methods of calculation, working with decimals, fractions, percentages and factors, using jottings where appropriate Solve word problems mentally Consolidate use of the rules of arithmetic and inverse operations to simplify calculations Multiply by decimals, understanding where to position the decimal point by considering equivalent calculations; divide by decimals by transforming to division by an integer Number/Calculation (Continued) Recognise the effects of multiplying and dividing by numbers between 0 and 1 v2 1Y08 21

22 9Ae1 9Ae2 9Ae3 9Ae4 9Ae5 9Ae6 9Ae7 9Ae8 9Ae9 9Ae10 9Ae11 9As1 9As2 9As3 9As4 9As5 9As6 9As7 9As8 9Gs1 Cambridge Secondary 1 Mathematics Stage 9 Algebra/Expressions, equations and formulae Know the origins of the word algebra and its links to the work of the Arab mathematician Al Khwarizmi Use index notation for positive integer powers; apply the index laws for multiplication and division to simple algebraic expressions Construct algebraic expressions Simplify or transform algebraic expressions by taking out singleterm common factors Add and subtract simple algebraic fractions Derive formulae and, in simple cases, change the subject; use formulae from mathematics and other subjects Substitute positive and negative numbers into expressions and formulae Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution); solve a number problem by constructing and solving a linear equation Solve a simple pair of simultaneous linear equations by eliminating one variable Expand the product of two linear expressions of the form x ± n and simplify the corresponding quadratic expression Understand and use inequality signs; construct and solve linear inequalities in one variable; represent the solution set on a number line Algebra/Sequences, functions and graphs Generate terms of a sequence using term-to-term and position-toterm rules Derive an expression to describe the nth term of an arithmetic sequence Find the inverse of a linear function Construct tables of values and plot the graphs of linear functions, where y is given implicitly in terms of x, rearranging the equation into the form y = mx + c; know the significance of m and find the gradient of a straight line graph Find the approximate solutions of a simple pair of simultaneous linear equations by finding the point of intersection of their graphs Use systematic trial and improvement methods to find approximate solutions of equations such as x² + 2x = 20 (1, 2 and 7) Construct functions arising from real-life problems; draw and interpret their graphs Use algebraic methods to solve problems involving direct proportion, relating solutions to graphs of the equations Geometry/Shapes and geometric reasoning Calculate the interior or exterior angle of any regular polygon; prove and use the formula for the sum of the interior angles of any polygon; prove that the sum of the exterior angles of any polygon is 360 v2 1Y08 22

23 9Gs2 9Gs3 9Gs4 9Gs5 9Gs6 9Gs7 9Gp1 9Gp2 9Gp3 9Gp4 9Gp5 9Gp6 9Gp7 9Gp8 9Gp9 9Ml1 9Mt1 9Mt2 9Ma1 Cambridge Secondary 1 Mathematics Stage 9 Solve problems using properties of angles, of parallel and intersecting lines, and of triangles, other polygons and circles, justifying inferences and explaining reasoning with diagrams and text Draw 3D shapes on isometric paper Analyse 3D shapes through plans and elevations Identify reflection symmetry in 3D shapes Use a straight edge and compasses to: construct the perpendicular from a point to a line and the perpendicular from a point on a line inscribe squares, equilateral triangles, and regular hexagons and octagons by constructing equal divisions of a circle Know and use Pythagoras theorem to solve two-dimensional problems involving right-angled triangles Geometry/Position and movement Tessellate triangles and quadrilaterals and relate to angle sums and half-turn rotations; know which regular polygons tessellate, and explain why others will not Use the coordinate grid to solve problems involving translations, rotations, reflections and enlargements Transform 2D shapes by combinations of rotations, reflections and translations; describe the transformation that maps an object onto its image Enlarge 2D shapes, given a centre and positive integer scale factor; identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments Recognise that translations, rotations and reflections preserve length and angle, and map objects on to congruent images, and that enlargements preserve angle but not length Know what is needed to give a precise description of a reflection, rotation, translation or enlargement Use bearings (angles measured clockwise from the north) to solve problems involving distance and direction Make and use scale drawings and interpret maps Find by reasoning the locus of a point that moves at a given distance from a fixed point, or at a given distance from a fixed straight line Measure/Length, mass and capacity Solve problems involving measurements in a variety of contexts Measure/Time and rates of change Solve problems involving average speed Use compound measures to make comparisons in real-life contexts, e.g. travel graphs and value for money Measure/Area, perimeter and volume Convert between metric units of area, e.g. mm² and cm², cm² and m² and volume, e.g. mm³ and cm³, cm³ and m³; know and use the v2 1Y08 23

24 9Ma2 9Ma3 9Ma4 9Dc1 9Dc2 9Dc3 9Dc4 9Dp1 9Dp2 9Di1 9Di2 9Di3 9Db1 9Db2 9Db3 9Pt1 Cambridge Secondary 1 Mathematics Stage 9 relationship 1 cm³ = 1 ml Know that land area is measured in hectares (ha), and that 1 hectare = m²; convert between hectares and square metres Solve problems involving the circumference and area of circles, including by using the π key of a calculator Calculate lengths, surface areas and volumes in right-angled prisms and cylinders Handling data/planning and collecting data Suggest a question to explore using statistical methods; identify the sets of data needed, how to collect them, sample sizes and degree of accuracy Identify primary or secondary sources of suitable data Design, trial and refine data collection sheets Collect and tabulate discrete and continuous data, choosing suitable equal class intervals where appropriate Handling data/processing and presenting data Calculate statistics and select those most appropriate to the problem Select, draw, and interpret diagrams and graphs, including: frequency diagrams for discrete and continuous data line graphs for time series scatter graphs to develop understanding of correlation back to back stem-and-leaf diagrams Handling data/interpreting and discussing results Interpret tables, graphs and diagrams and make inferences to support or cast doubt on initial conjectures; have a basic understanding of correlation Compare two or more distributions; make inferences, using the shape of the distributions and appropriate statistics Relate results and conclusions to the original question Handling data/probability Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving probability problems Find and record all outcomes for two successive events in a sample space diagram Handling data/probability (Continued) Understand relative frequency as an estimate of probability and use this to compare outcomes of experiments in a range of contexts Problem solving/using techniques and skills in solving mathematical problems Calculate accurately, choosing operations and mental or written methods appropriate to the numbers and context v2 1Y08 24

25 9Pt2 9Pt3 9Pt4 9Pt5 9Pt6 9Pt7 9Ps1 9Ps2 9Ps3 9Ps4 9Ps5 9Ps6 9Ps7 Cambridge Secondary 1 Mathematics Stage 9 Manipulate numbers, algebraic expressions and equations, and apply routine algorithms Understand everyday systems of measurement and use them to estimate, measure and calculate Recognise and use spatial relationships in two dimensions and three dimensions Draw accurate mathematical diagrams, graphs and constructions Decide how to check results, by: using rounding to estimate numbers to one significant figure and calculating mentally then comparing with the estimate considering whether an answer is reasonable in the context of the problem using inverse operations Estimate, approximate and check their working. Solve a range of word problems involving single or multi-step calculations Problem solving/using understanding and strategies in solving problems Identify, organise, represent and interpret information accurately in written, tabular, graphical and diagrammatic forms Explore the effect of varying values in order to generalise Find a counter-example to show that a conjecture is not true Present concise, reasoned arguments to justify solutions or generalisations using symbols, diagrams or graphs and related explanations Recognise the impact of constraints or assumptions Recognise connections with similar situations and outcomes Consider and evaluate the efficiency of alternative strategies and approaches and refine solutions in the light of these v2 1Y08 25