New stage 1 New stage 2

Transcription

1 iv 1 New stage 1 New stage 2 Integers four rules, rounding and ordering 1.1 Face value and place value 1 Using place value diagrams NA2a 1.2 Reading, writing and 2 3 Using place value to read, write NA2a ordering numbers and order whole numbers 1.3 Number lines 3 4 Representing numbers, additions NA2a and subtractions on a number line 1.4 Adding and subtracting 4 5 Mental and written column NA3a/g/i/ methods j/4a/b/c 1.5 Multiplying and dividing 5 6 Mental and written methods NA3a/g/i/ including short division k/4b/c 1.6 Brackets and the order of 7 Order of operations, not NA3b/i operations including powers 1.7 Rounding numbers 8 9 Rounding to powers of 10 NA2a/3h 1.8 Factors, multiples and 9 10 Identifying factors and multiples NA2a common factors of numbers 1.9 LCM, HCF and prime Writing numbers in prime factor NA2a/3a factor decomposition form and using this to identify HCF; finding LCM by writing lists of multiples 1.10 Negative numbers Using a number line to calculate NA2a with negative numbers 1.11 Calculations with negative Using the four rules with NA3a numbers negative numbers Mixed exercise Summary of key points Fractions, decimals and percentages 2.1 Improper fractions and Converting improper fractions to NA2c mixed numbers mixed numbers and vice versa 2.2 Equivalent fractions Finding equivalent fractions; NA2c writing fractions in their simplest form 2.3 Ordering fractions Ordering fractions by converting NA2c them to equivalent fractions with the same denominator 2.4 Decimal place value Using a place value table for NA2d decimal numbers 2.5 Ordering decimals Using place value to order NA2d decimal numbers 2.6 Adding and subtracting Written column methods NA3j decimals

2 v 2.7 Multiplying and dividing Moving the digits a number of NA3a/i decimals by 10, 100 or places to right or left Multiplying and Multiplying whole numbers and NA3a/i/k dividing decimal numbers using place value adjustment; changing calculations involving decimals to calculations with whole numbers by multiplying by powers of Converting between Fraction to decimal conversion NA2d/3g/i fractions and decimals and vice versa; terminating and recurring decimals 2.10 Rounding to one Rounding whole numbers and NA3h significant figure decimals to 1 s.f Using significant figures Estimating by rounding all NA3h/o/p to estimate answers numbers in a calculation to 1 s.f Giving a sensible answer Rounding up or down in the NA3q/4a/d context of the problem; using an appropriate level of accuracy 2.13 Using trial and Trial and improvement where NA4b improvement to solve there is no obvious simple problems method 2.14 Understanding percentages Percentage as parts per hundred Na2e 2.15 Comparing different Ordering fractions by converting NA2e proportions using to percentages percentages 2.16 Working out a percentage Percentages of quantities NA2e of an amount Mixed exercise Summary of key points Powers, indices and calculations 3.1 Squares, cubes, square and Definitions; using a calculator NA2b/3o cube roots 3.2 Power facts you need to 47 Squares, cubes and roots to NA3g/i know memorise 3.3 Indices and powers Using index notation; solving NA2b simple equations involving indices 3.4 BIDMAS The order of operations NA3b 3.5 Calculations using a Using a calculator for complex NA3h/o/p/q calculator calculations 3.6 Index laws The rules for multiplying and NA2b dividing powers of the same number 3.7 Writing numbers in Using standard form in written NA2b standard form calculations and on a calculator Mixed exercise Summary of key points 56 57

3 vi 4 Coordinates and essential algebra 4.1 Coordinates in the first 58 Reading and plotting coordinates NA6b quadrant 4.2 Coordinates in all four 59 Reading and plotting positive and NA6b/SSM3e quadrants negative coordinates 4.3 Coordinates to complete Finding the coordinates of the SSM3e shapes final point to make a given shape (parallelogram, square, etc.) 4.4 Mid-points of line Using the formula to find the SSM3e segments coordinates of the mid-point D, 2-D or 3-D? Identifying 2-D and 3-D shapes; SSM3e using 3-D coordinates 4.6 Writing expressions Using letters to represent NA5a unknown numbers 4.7 Collecting like terms Simplifying expressions by NA5b collecting like terms 4.8 Simplifying products 68 Multiplying expressions and NA5a simplifying the result 4.9 Using brackets 69 Order of operations in NA5b calculations with brackets 4.10 Expanding brackets 70 Multiplying a single term over a NA5b bracket 4.11 Simplifying expressions Expressions where more than NA5b with brackets one term contains brackets 4.12 Factorising Writing a common factor outside NA5b the bracket 4.13 Multiplying expressions The product of two brackets: NA5b with brackets (e + f)(g + h) 4.14 Dividing algebraic 74 Cancelling common factors in NA5b expressions algebraic fractions Mixed exercise Summary of key points Sequences 5.1 Term to term rules Generating sequences and finding NA6a rules 5.2 Position to term rules Generating sequences NA6a 5.3 Sequences of shapes Number sequences from shapes; NA6a working out the number of matchsticks in different shapes in the sequence 5.4 The nth term Generating sequences and finding NA6a the nth term 5.5 nth term for shape Finding the number of matchsticks NA6a sequences in pattern number n Mixed exercise Summary of key points 89

4 vii 6 Linear graphs 6.1 Straight lines parallel to Graphs of x = c and y = c NA6b the axes 6.2 Straight lines passing Graphs of y = ax for positive and NA6b through the origin negative a 6.3 Graphs of linear functions Graphs of equations of the form NA6b y = mx + c 6.4 Straight line graphs in real Interpreting and drawing graphs NA6c life of linear functions from real-life situations Mixed exercise Summary of key points Properties of shapes 7.1 Polygons Definitions and names of SSM1f polygons with different numbers of sides 7.2 Parallel and perpendicular 105 Definitions and notation for SSM2a/c lines parallel and perpendicular lines 7.3 Properties of triangles Special triangles SSM2d 7.4 Properties of quadrilaterals Special quadrilaterals SSM2f 7.5 Angle properties of Finding angles in scalene, triangles equilateral and isosceles triangles. SSM2d 7.6 Properties of circles The parts of a circle SSM2i 7.7 Exploring cubes and Euler s relationship between SSM2j cuboids numbers of edges, faces and vertices 7.8 Drawing on isometric Drawing different grids representations of 3-D shapes SSM2j Mixed exercise Summary of key points Angles and bearings 8.1 Describing angles Acute, obtuse and reflex angles; SSM2b labelling conventions 8.2 Angles on a straight line Calculating angles on a straight SSM2a line 8.3 Angles meeting at a point Vertically opposite angles; SSM2a calculating angles at a point 8.4 Angles in parallel lines Alternate and corresponding SSM2c angles 8.5 Proofs Proofs of angle properties of SSM2c parallelogram and triangle 8.6 Bearings Three-figure bearings SSM4b Mixed exercise Summary of key points 131

5 viii 9 Measures 9.1 Time hour and 24-hour clock NA3p/SSM4a times, analogue and digital 9.2 Time calculations Distance between times and NA3p/4c/SSM4a adding times together 9.3 Reading scales Reading a variety of different SSM4a scales 9.4 Choosing suitable units Choosing appropriate units for SSM4a measuring different quantities 9.5 Estimating Estimating measurements by SSM4a comparing to a known measurement 9.6 Converting between metric Converting metric units of SSM4a units length, weight and capacity 9.7 Metric equivalents Using approximate metric to SSM4a imperial conversions 9.8 Accuracy 143 Accuracy and maximum NA4d/SSM4a possible error for continuous measurements 9.9 Speed Calculating speed using the SSM4c formula 9.10 Changing units Changing between km/h, m/s SSM4a and mph 9.11 Density Calculating density using the SSM4c formula 9.12 Comparing measurements Finding the better buy; SSM4a comparing measurements given in different units by converting to the same units Mixed exercise Summary of key points Perimeter, area and volume 10.1 Perimeter Working out perimeters on SSM4f grids and by calculation 10.2 Area Area by counting squares SSM4f 10.3 Area of rectangles Using the formula SSM4f 10.4 Area of triangles, Area formulae for triangles, SSM4f parallelograms, trapezia splitting parallelograms, and composite shapes trapezia; splitting composite shapes into simple shapes 10.5 Surface area of cuboids Calculating surface area by SSM4f working out areas of faces 10.6 Volume of cuboids Counting cubes and then SSM4g using the formula 10.7 Volume of prisms Using the formula for volume SSM4g of a prism 10.8 Fitting boxes into larger Working out how many small SSM4g boxes boxes will fit into a larger box

6 ix Mixed exercise Summary of key points 171 Examination practice paper Stage 1 (multiple choice) Practice questions Stage 1 (multiple choice) Formulae sheet 182 Answers