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Exploring mathematics: Tier 5 NC levels 5 to 6 (level 5A/6CBA) Autumn 33 lessons N5.1 Powers and roots Prime factor decomposition Using ICT to estimate squares and roots Simple cases of index laws 3 lessons Spring 34 lessons S5.2 Probability 1 Mutually exclusive events Sum of probabilities Estimating probabilities from experimental data; comparing with theoretical probability 3/4 lessons N5.2 Proportional reasoning Fractions four operations and brackets Percentage change Ratio and proportion Mental and calculator calculations Solving problems 6 lessons N5.3 Calculations and calculators Multiplying and dividing by powers of 10; rounding and estimating calculations Mental and written calculations with decimals, all four operations Use of calculator Solving problems, including with measures 5/6 lessons R5.1 Revision/support Number, algebra, geometry and measures, statistics 5 lessons Summer 33 lessons S5.3 Enquiry 2 Collecting, representing and interpreting data on paper and using ICT frequency tables and diagrams for grouped continuous data Comparing two distributions Communicating findings, using ICT 6/7 lessons S5.4 Probability 2 Identifying outcomes of an experiment Comparing experimental with theoretical probability 4/5 lessons A5.2 Equations and formulae Single-term common factors; adding simple algebraic fractions; substitution in and changing subject of simple formulae Constructing and solving linear equations with integer coefficients Approximate solutions of equations using ICT 6 lessons A5.3 Functions and graphs Linear graphs, gradient and intercepts Simple properties of quadratic functions Deriving formulae 5/6 lessons A5.4 Using algebra Constructing, plotting and interpreting real-life functions Solving direct proportion problems 3 lessons R5.2 Revision/support Number, algebra, geometry and measures, statistics 5 lessons N5.4 Solving problems Investigating problems using number and algebra Proof; finding a counter-example History of mathematics 4/5 lessons A5.5 Equations, formulae and graphs Adding/subtracting algebraic fractions; removing/cancelling common factors; changing subject of simple formulae Constructing and solving equations by exact and approximate methods Graphs of linear functions; direct proportion and distance-time graphs 7/8 lessons 100 lessons 1 | Exploring mathematics | Tier 5 (blue) G5.1 Measures and mensuration Using measures to estimate, measure and calculate; converting measures Circumference and area of circle Volume and surface area of simple prisms 5/6 lessons G5.2 Angles and constructions Angle sum and exterior angle of polygons Finding unknown angles; geometrical reasoning Straight edge and compass constructions Simple loci 9 lessons G5.3 Transformations Plane symmetry of 3-D shapes Simple combinations of rotations, reflections and translations, on paper and using ICT Enlargement; scale drawings Exploring transformations with ICT 5/6 lessons G5.4 2-D and 3-D shapes Visualising 3-D shapes; plans and elevations Geometrical reasoning angles and shapes Surface area and volume of prisms 7/8 lessons Mathematical processes and applications are integrated into each unit S5.1 Enquiry 1 Designing survey to collect data, including data collection sheet Representing and interpreting data, on paper and using ICT line graphs for time series, scatter graphs Calculating statistics, including with a calculator; comparing distributions Communicating findings, using ICT 6 lessons A5.1 Sequences and graphs Generating sequences on paper and with ICT; finding the nth term of an arithmetic sequence Graphs of linear functions; gradient and intercepts; interpreting graphs of real-life functions, including distance-time 6 lessons Units SUPPORT Number 1: Powers and roots (3 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • recognise and use multiples, factors (divisors), • identify problems and the methods needed to tackle them common factor, highest common factor, lowest common multiple and primes. Integers, powers and roots (52–59) Calculations CORE • use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers. (86–101, 108–109) Equations, formulae and identities (114–115) • select and apply mathematics to find solutions • represent problems and synthesise information in different forms • use accurate notation • calculate accurately, selecting mental methods or a calculator as appropriate • use appropriate checking procedures • record methods, solutions and conclusions • make convincing arguments to justify generalisations or solutions • interpret and communicate solutions to problems and to: • use index notation for integer powers • know and use the index laws for multiplication and division of positive integer powers • extend mental methods of calculation with factors, powers and roots • use the power and root keys of a calculator • use ICT to estimate square roots and cube roots • use the prime factor decomposition of a number. Objectives in colour lay the groundwork for Functional Skills. 2 | Exploring mathematics | Tier 5 (blue) Number 2: Proportional reasoning (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • order and round decimals • identify problems and the methods needed to tackle them • recognise fraction, decimal and percentage • select and apply mathematics to find solutions equivalents Fractions, decimals, percentages, ratio and proportion • add and subtract simple fractions, and multiply and divide a fraction by an integer • break down substantial tasks to make them more manageable • use connections with related contexts • move from one form of representation to another to gain a different (66–81) • find fractions and percentages of quantities Calculations • express one number as a percentage of another • use accurate notation • simplify rations and divide a quantity in a given • calculate accurately, selecting mental methods or a calculator as (82–103, 110–111) ratio • solve problems involving direct proportion using the unitary method. perspective on a problem appropriate • use appropriate checking procedures • review and refine own approaches on the basis of discussions with others • record and communicate methods, solutions and conclusions and to: • extend mental methods of calculation with fractions, percentages and ratios • use efficient written methods to add and subtract fractions, and to multiply or divide fractions, interpreting division as a multiplicative inverse, and cancelling common factors before multiplying • recognise when fractions or percentages are needed to compare proportions • solve problems involving percentage changes • use proportional reasoning to solve problems, choosing the correct numbers to take as 100%, or as a whole • compare two ratios and calculate ratios in a range of contexts. 3 | Exploring mathematics | Tier 5 (blue) Number 3: Calculations and calculators (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • read and write positive integer powers of 10 • select and apply mathematics to find solutions to problems • multiply and divide by 0.1 and 0.01 • break down substantial tasks to make them more manageable • use mental and efficient written methods to: • build on previous experience of similar situations and outcomes Place value – add and subtract integers and decimals (36–47) – multiply and divide integers and decimals, Fractions, decimals, percentages, including by decimals such as 0.6 or 0.06, ratio and proportion understanding where to position the decimal (60–65) point by considering equivalent calculations. Calculations (82–85, 104–107, 110–111) Calculator methods (108–109) Solving problems (28–29) • manipulate numbers and apply routine algorithms, selecting mental methods or a calculator as appropriate • recognise the impact of constraints or assumptions • record and communicate methods, solutions and conclusions and to: • understand and use equivalences between 0.1, 1⁄10 and 10–1, and multiply and divide by any integer power of 10 • understand the effects of multiplying or dividing by numbers between 0 and 1 • use positive and negative numbers of any size, the laws of arithmetic and inverse operations • understand the order of operations, including powers • use known facts to derive unknown facts and extend mental methods of calculation with decimals, including solving problems mentally • use efficient written methods to add and subtract decimals of any size, to multiply by decimals, and to divide by decimals by transforming to division by an integer • use a calculator efficiently and appropriately for complex calculations, knowing not to round during intermediate steps • use rounding to make estimates and to give solutions to an appropriate degree of accuracy • know that a recurring decimal is an exact fraction. 4 | Exploring mathematics | Tier 5 (blue) Number 4: Before they start, pupils should be able to: In this unit, pupils learn to: Solving problems • identify the mathematical features of a context or • solve routine and non-routine problems in familiar and unfamiliar contexts (5 hours) problem • try out and compare mathematical Solving problems (2–35) Percentages and proportion (75–81) Sequences, functions and graphs (148–153) representations • 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 • evaluate the efficiency of alternative strategies and approaches. • identify the situation or problem and the mathematical methods needed to tackle it • build on previous experience of similar situations and outcomes • break down substantial tasks to make them more manageable • select and apply mathematics to find solutions • represent problems and synthesise information in different forms • move from one form of representation to another to gain a different perspective on a problem • use connections with related contexts • generate fuller solutions by presenting a concise, reasoned argument • draw conclusions, identifying special cases and counter examples, and provide mathematical justifications • look for and reflect on other approaches and review and refine own findings and approaches on the basis of discussions with others • interpret and communicate solutions to problems and to: • appreciate the rich historical and cultural roots of mathematics. 5 | Exploring mathematics | Tier 5 (blue) Algebra 1: Sequences, functions and graphs (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • generate and describe integer sequences • identify situations or problems and the methods needed to tackle them • plot graphs of linear functions, where y is given • select and apply mathematics to find solutions explicitly in terms of x, on paper and using ICT • recognise that equations of the form y = mx + c Sequences, functions and graphs (148–159, 172–177) Solving problems (26–27) correspond to straight-line graphs • discuss and interpret simple linear graphs arising from real situations. • represent and interpret problems in algebraic or graphical form • move from one form to another to gain a different perspective on the problem • manipulate algebraic expressions and equations • draw accurate graphs on paper and on screen • draw conclusions and provide mathematical justifications • make convincing arguments to justify generalisations or solutions, considering special cases and to: • generate terms of a sequence using term-to-term and position-to-term rules, on paper and using ICT • generate sequences from practical contexts and write and justify an expression for the nth term of an arithmetic sequence • generate points and plot graphs of linear functions (y given implicitly in terms of x, e.g. ay + bx = 0, y + bx + c = 0), on paper and using ICT • find the gradient of lines given by equations of the form y = mx + c, given values for m and c • construct functions arising from real situations and plot and interpret graphs their corresponding graphs. 6 | Exploring mathematics | Tier 5 (blue) Algebra 2: Equations and formulae (6 hours) Equations, formulae and identities (112–113, 116–125, 132–135) Before they start, pupils should be able to: In this unit, pupils learn to: • simplify linear expressions by collecting like terms • represent and interpret problems in algebraic form • multiply a single term over a bracket • build on previous experience of similar situations and outcomes • construct and solve linear equations with integer • manipulate algebraic expressions and equations coefficients (unknown on either or both sides) • substitute integers into simple expressions and formulae • use appropriate checking procedures • generate fuller solutions by presenting a concise, reasoned argument using symbols and related explanations and to: • factorise algebraic expressions by taking out single-term common factors • add simple algebraic fractions • substitute numbers into expressions and formulae and, in simple cases, change the subject of a formula • construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution) • use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20. Algebra 3: Functions and graphs (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • plot graphs of linear functions, where y is given • break down substantial tasks to make them more manageable explicitly in terms of x, on paper and using ICT • represent and interpret problems in algebraic or graphical form • recognise that equations of the form y = mx + c Equations, formulae and identities (136–143) Sequences, functions and graphs (160–177) Solving problems (26–27) correspond to straight-line graphs • express simple functions in symbols. • draw accurate graphs on paper and on screen • move from one form to another to gain a different perspective on the problem • manipulate algebraic expressions and equations • use appropriate checking procedures • generate fuller solutions by presenting a concise, reasoned argument using symbols, diagrams, graphs and related explanations • make convincing arguments to justify generalisations or solutions, considering special cases • review and refine own findings and approaches on the basis of discussions with others and to: • find the inverse of a linear function • generate points and plot graphs of linear functions (y given implicitly in terms of x, e.g. ay + bx = 0, y + bx + c = 0) • find the gradient of lines given by equations of the form y = mx + c, given values for m and c. 7 | Exploring mathematics | Tier 5 (blue) Algebra 4: Using algebra (3 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • plot graphs of linear functions, where y is given • break down substantial tasks to make them more manageable explicitly in terms of x, on paper and using ICT • represent and interpret problems in algebraic or graphical form • given values for m and c, find the gradient of lines Equations, formulae and identities given by equations of the form y = mx + c (136–143) • substitute values in expressions of the form y kx Sequences, functions and graphs • express simple functions in symbols. (160–177) Solving problems (26–27) • draw accurate graphs on paper and on screen • move from one form to another to gain a different perspective on the problem • manipulate algebraic expressions and equations • use appropriate checking procedures • generate fuller solutions by presenting a concise, reasoned argument using symbols, diagrams, graphs and related explanations • make convincing arguments to justify generalisations or solutions, considering special cases • justify the mathematical features drawn from a context and the choice of approach and to: • use algebraic methods to solve problems involving direct proportion, relating solutions to graphs of the equations, using ICT as appropriate • use formulae from mathematics and other subjects, derive a formula and, in simple cases, change its subject • substitute numbers into expressions and formulae • construct functions arising from real-life problems and plot their corresponding graphs • interpret graphs arising from real situations • explore simple properties of quadratic functions. 8 | Exploring mathematics | Tier 5 (blue) Algebra 5: Equations, formulae and graphs (8 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • simplify linear expressions by collecting like terms • break down substantial tasks to make them more manageable • multiply a single term over a bracket • represent and interpret problems in algebraic or graphical form • construct and solve linear equations with integer • draw accurate graphs on paper and on screen coefficients (unknown on either or both sides) Fractions using appropriate methods (e.g. inverse (62–63) operations, transforming both sides in the same Equations, formulae and identities way) (122–125, 132–143) • plot the graphs of linear functions, where y is Graphs given explicitly in terms of x, on paper and using (164–171) ICT. Solving problems (6–13) • move from one form to another to gain a different perspective on the problem • manipulate algebraic expressions and equations • use appropriate checking procedures • generate fuller solutions by presenting a concise, reasoned argument using symbols, diagrams, graphs and related explanations • make convincing arguments to justify generalisations or solutions, considering special cases and to: • factorise algebraic expressions by taking out single-term common factors • add and subtract simple algebraic fractions • substitute numbers into expressions and formulae and, in simple cases, change the subject of a formula • construct and solve linear equations with integer coefficients • use systematic trial and improvement methods and ICT tools to find approximate solutions of equations such as x3 + x = 20 • generate points and plot graphs of linear functions (y given implicitly in terms of x, e.g. ay + bx = 0, y + bx + c = 0) • find the gradient of lines given by equations of the form y = mx + c, given values for m and c. 9 | Exploring mathematics | Tier 5 (blue) Geometry and measures 1: Measures and mensuration (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • convert a metric unit of length, mass or capacity to • identify situations or problems and the methods needed to tackle them a related larger or smaller unit • make sensible estimates of a range of measures Coordinates (218–219) in relation to everyday situations • know and use the formulae for the area of a Measures and mensuration rectangle, the area of a triangle, trapezium and (228–231, 234–241) parallelogram, and the volume of a cuboid. • select and apply mathematics to find solutions • break down substantial tasks to make them more manageable • justify the mathematical features drawn from a context and the choice of approach • use accurate notation • manipulate numbers and apply routine algorithms, selecting mental methods or a calculator as appropriate • use appropriate checking procedures • recognise the impact of constraints or assumptions • record, interpret and communicate solutions to problems and to: • solve problems involving measurements in a variety of contexts • convert between area measures and between volume measures • know and use the formulae for the circumference and area of a circle, and use the key of a calculator • calculate the surface area and volume of right prisms. 10 | Exploring mathematics | Tier 5 (blue) SUPPORT CORE Geometry and measures 2: Angles and constructions (9 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • identify alternate angles and corresponding • identify situations or problems and the methods needed to tackle them Geometrical reasoning: lines, angles • understand a proof that: angles and shapes – the sum of the angles of a triangle is 180° (178–189, 194–197) – the exterior angle of a triangle is equal to the Construction and loci 220–227) Solving problems (14–17) sum of the two interior opposite angles • solve problems using side and angle properties of triangles and quadrilaterals • use ruler and compasses to construct: – the midpoint and perpendicular bisector of a • select and apply mathematics to find solutions • break down substantial tasks to make them more manageable • represent problems in geometric form, making accurate mathematical diagrams on paper and on screen • generate, explain and communicate fuller solutions using diagrams and related explanations • make convincing arguments to justify generalisations or solutions • review and refine own findings and approaches on the basis of discussions with others line segment – the bisector of an angle – a triangle, given three sides (SSS). and to: • explain how to find, calculate and use: – the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons – the interior and exterior angles of regular polygons • solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text • know the definition of a circle and the names of its parts, and inscribe regular polygons by constructing equal divisions of a circle • use straight-edge and compasses to construct:: – the perpendicular from a point to a line – the perpendicular to a line from a point on the line – triangles, given right angle, hypotenuse and side (RHS) • find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT • use ICT to explore constructions of triangles and other 2D shapes 11 | Exploring mathematics | Tier 5 (blue) Geometry and measures 3: Transformations (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • identify all the symmetries of 2D shapes • identify situations or problems and the methods needed to tackle them • understand that if two 2D shapes are congruent, • select and apply mathematics to find solutions corresponding sides and angles are equal Geometrical reasoning: lines, angles and shapes • transform 2D shapes by rotations, reflections and translations • break down substantial tasks to make them more manageable • represent problems in geometric form, making accurate mathematical diagrams on paper and on screen (178–179, 190–191) • simplify a ratio • generate, explain and communicate fuller solutions using diagrams Transformations • make simple scale drawings. • make convincing arguments to justify generalisations or solutions (202–217) Mensuration and to: (242–247) • identify reflection symmetry in 3D shapes Ratio and proportion • use a coordinate grid to solve problems involving translations, rotations, (78–81) reflections and enlargements • recognise that translations, rotations and reflections preserve length and angle, and map objects onto congruent images • explore and compare combinations of translations, reflections and rotations of 2D shapes, on paper and using ICT • enlarge 2D shapes, given a centre of enlargement and a positive integer scale factor, identifying the scale factor as the ratio of the lengths of any two corresponding line segments • recognise that enlargements preserve angle but not length • devise instructions for a computer to generate and transform shapes • use and interpret maps and scale drawings. 12 | Exploring mathematics | Tier 5 (blue) Geometry and measures 4: 2D and 3D shapes (8 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • solve problems using side and angle properties of • identify situations or problems and the methods needed to tackle them Geometrical reasoning: lines, angles • classify quadrilaterals • break down substantial tasks to make them more manageable and shapes • calculate volumes and surface areas of cuboids • represent problems in geometric form, making accurate mathematical (184–189, 198–201) Transformations (216–217) triangles and quadrilaterals and shapes made from cuboids. • select and apply mathematics to find solutions diagrams on paper and on screen • generate fuller solutions by presenting a concise, reasoned argument using accurate notation, diagrams and related explanations Mensuration (238–241) Solving problems (14–19, 30–31) • make convincing arguments to justify generalisations or solutions • interpret and communicate solutions to problems • review and refine own findings and approaches on the basis of discussions with others • look for and reflect on other approaches and to: • solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons • visualise and use 2D representations of 3D objects, and analyse 3D shapes through 2D projections, including plans and elevations • solve problems involving measurements in a variety of contexts • calculate the surface area and volume of right prisms. 13 | Exploring mathematics | Tier 5 (blue) SUPPORT Statistics 1: Enquiry 1 (6 hours) CORE Before they start, pupils should be able to: In this unit, pupils learn to: • identify possible sources of data • pose questions and use statistical methods to investigate situations • plan how to collect data • break down substantial tasks to make them more manageable • construct frequency tables with equal class • collect and represent discrete and continuous data, using ICT where Statistics intervals for continuous data and two-way tables (248–275) for discrete data • construct and interpret: – pie charts – bar charts and frequency diagrams for discrete data – simple scatter graphs • compare two simple distributions, using the range and one of the mode, median or mean. appropriate • use and interpret statistical measures, tables and diagrams, for discrete and continuous data, using ICT where appropriate • draw conclusions to support or cast doubt on initial conjectures and make convincing arguments to justify generalisations • recognise the impact of constraints or assumptions • review and refine own findings and approaches on the basis of discussions with others • justify the mathematical features drawn from a context and the approach • interpret and communicate fuller solutions to problems using selected tables, diagrams, graphs and related explanations and to: • identify the sample size and degree of accuracy needed, and possible primary or secondary sources of data, including the internet • design, trial and if necessary refine data collection sheets • construct frequency tables for gathering discrete or continuous data, choosing suitable class intervals • calculate statistics and select those which address the questions posed, constructing stem-and-leaf diagrams where appropriate • select, construct and modify, on paper and using ICT, suitable graphs and diagrams to progress an enquiry, e.g. frequency diagrams, pie charts • compare distributions and make inferences, using the shape of the distributions and appropriate statistics. 14 | Exploring mathematics | Tier 5 (blue) Statistics 2: Probability 1 (4 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • recall that if the probability of an event occurring is • pose questions and use statistical methods to investigate situations p, then the probability of it not occurring is 1 – p • use diagrams and tables to record in a systematic Probability way all possible mutually exclusive outcomes for (276–285) single events and two successive events Fractions (66–69) • understand that: – if an experiment is repeated there may be different outcomes – increasing the number of times an experiment • break down substantial tasks to make them more manageable • draw accurate diagrams and graphs • look for patterns • draw conclusions and make convincing arguments to justify generalisations • review and refine own findings and approaches on the basis of discussions with others is repeated generally leads to better estimates • record methods, solutions and conclusions of probability. • interpret and communicate fuller solutions to problems using diagrams, graphs and related explanations and to: • identify all the mutually exclusive outcomes of an experiment • know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems • use a numerical scale from 0 to 1 to express and compare experimental and theoretical probabilities in a range of contexts. 15 | Exploring mathematics | Tier 5 (blue) Statistics 3: Enquiry 2 (7 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • design and use two-way tables for discrete data • pose questions and use statistical methods to investigate situations • construct and interpret: • break down substantial tasks to make them more manageable – pie charts Statistics (250–251, 254–275) Solving problems (28–29) – bar charts and frequency diagrams for discrete data – simple scatter graphs • construct and use stem-and-leaf diagrams • compare two simple distributions, using the range and one of the mode, median or mean. • collect and represent discrete and continuous data, using ICT where appropriate • use and interpret statistical measures, tables and diagrams, for discrete and continuous data, using ICT where appropriate • draw conclusions to support or cast doubt on initial conjectures and make convincing arguments to justify generalisations • recognise the impact of constraints or assumptions • review and refine own findings and approaches on the basis of discussions with others • justify the mathematical features drawn from a context and the approach • interpret and communicate fuller solutions to problems using selected tables, diagrams, graphs and related explanations and to: • design, trial and if necessary refine data collection sheets • select, construct and modify, on paper and using ICT, suitable graphs and charts to progress an enquiry, including: – line graphs for time series – scatter graphs to develop further understanding of correlation. 16 | Exploring mathematics | Tier 5 (blue) Statistics 4: Probability 2 (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • recall that if the probability of an event occurring is • pose questions and use statistical methods to investigate situations p, then the probability of it not occurring is 1 – p • use diagrams and tables to record in a systematic Probability way all possible mutually exclusive outcomes for (276–285) single events and two successive events • break down substantial tasks to make them more manageable • draw accurate diagrams and graphs • look for patterns • draw conclusions and make convincing arguments to justify • understand that: – if an experiment is repeated there may be different outcomes – increasing the number of times an experiment generalisations • review and refine own findings and approaches on the basis of discussions with others is repeated generally leads to better estimates • record methods, solutions and conclusions of probability. • interpret and communicate fuller solutions to problems using diagrams, graphs and related explanations and to: • identify all the mutually exclusive outcomes of an experiment • know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems • use a numerical scale from 0 to 1 to express and compare experimental and theoretical probabilities in a range of contexts. • appreciate the difference between mathematical explanation and experimental evidence. Revision 1 and 2 - here are the process objectives Previous learning Objectives based on NC levels 5 and 6 (mainly level 5) Pupils should already be able to apply and use In this unit, pupils consolidate their ability to: many of the skills shown on the right. This unit • build on previous experience of similar situations and outcomes offers is an opportunity to consolidate and refine these skills. • identify the methods needed to tackle problems • select and apply mathematics to find solutions • calculate accurately, using mental methods or a calculator as appropriate • manipulate numbers, algebraic expressions and equations, and apply routine algorithms • make accurate mathematical diagrams and graphs • use appropriate checking procedures, giving accurate solutions appropriate to the context • record and communicate solutions to problems • review and refine own findings and approaches on the basis of discussions with others and to: Number content objectives are as in the unit remind me to colour functional skills objectives 17 | Exploring mathematics | Tier 5 (blue) 18 | Exploring mathematics | Tier 5 (blue)