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Exploring mathematics: Tier 3 NC levels 4ab and 5cb Autumn 36 lessons S3.2 Probability 1 Language of probability Probability scale Equally likely outcomes 3 lessons Spring 31 lessons S3.3 Enquiry 1 Collecting, representing and interpreting data in bar line graphs, frequency diagrams for grouped discrete data, pie charts Mean, median, mode, range 4/5 lessons Summer 33 lessons S3.4 Enquiry 2 Collecting, representing and interpreting data in frequency diagrams; pie charts; simple statistics; comparing data sets Writing report 4/5 lessons S3.5 Probability 2 Probability scale; comparing experimental and theoretical probability in simple cases 3 lessons N3.3 Fractions and percentages Equivalent fractions, cancelling, ordering Adding/subtracting; multiplying fraction by integer; fraction of a number or quantity Equivalence of fractions, decimals and percentages; percentages of quantities 7 lessons A3.1 Patterns and sequences Generating integer sequences Term-to-term and position-to-term rules Describing a rule in words then symbols 5 lessons N3.4 Decimals and measures Measures/estimates of length, area, mass, capacity and time; conversions of units Mental and written calculations, including with measurements Problem solving with a calculator 5/6 lessons N3.5 Percentages, ratio and proportion Equivalence of fractions, decimals and percentages; percentages of quantities Using percentages for comparisons Ratio of two parts; direct proportion in simple contexts, currency conversions 4/5 lessons G3.2 Angles Labelling conventions for lines, angles, shapes Estimating/measuring acute, obtuse and reflex angles; angles on a straight line; angles at a point; vertically opposite angles; finding unknown angles 3 lessons A3.2 Equations and formulae Using letters; substituting in simple expressions, equations and formulae Using algebra to solve problems 5 lessons A3.3 Sequences, functions, graphs Sequences and rules Finding the general term in simple cases Coordinates in all four quadrants; simple linear functions, mappings and graphs 4/5 lessons R3.1 Revision/support Number, algebra, geometry and measures, statistics 5 lessons R3.2 Revision/support Number, algebra, geometry and measures, statistics 5 lessons A3.4 Functions, equations and graphs Simplification of and substitution in linear expressions and formulae Linear equations with integer coefficients (unknown on one side ) Graphs of simple linear functions Simple graphs of real situations 7/8 lessons N3.6 Solving number problems Equivalent fractions, decimals, percentages Mental and written calculations with whole numbers and decimals Comparing fractions; adding/subtracting fractions; multiplying a fraction by an integer Fractions and percentages of quantities 4/5 lessons 100 lessons 1 | Exploring mathematics | Tier 3 (green) G3.1 Area and perimeter Formulae for perimeter and area of rectangle; perimeter and area of shapes made from rectangles; word problems Visualising 3-D shapes from 2-D representations Surface area of cuboids 4 lessons G3.3 Transformations Line and rotation symmetry Reflection; rotation; translation Exploring symmetry and transformations with ICT 4/5 lessons G3.4 Properties of shapes Recognising parallel and perpendicular lines Angle, side and symmetry properties of triangles and quadrilaterals; angle sum of triangle and quadrilateral; finding unknown angles 5/6 lessons G3.5 Constructions Measuring and drawing lines to nearest mm Using ruler, set square, protractor to construct parallel/perpendicular lines; rectangles/squares; triangles (SAS, ASA); nets of 3-D shapes Exploring constructions with ICT 5/6 lessons Mathematical processes and applications are integrated into each unit S3.1 Grouped data and simple statistics Bar charts, including grouped discrete data, and pie charts 3 lessons N3.1 Properties of numbers Adding/subtracting integers Order of operations, brackets Squares and roots to 12 × 12; multiples, divisibility, factors, primes, prime factors, simple HCF/LCM 5 lessons N3.2 Whole numbers and decimals Decimal place value, ordering, rounding Mental calculations; adding/subtracting decimals; multiplying/dividing 3-digit by 2-digit whole numbers and decimals by 1-digit number; using a calculator 6 lessons Units SUPPORT Number 1: Properties of numbers (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • calculate a temperature rise and fall across 0C • identify the necessary information to understand or simplify a context or • recognise multiples up to 10 10, and larger multiples of 2, 5 and 10 Integers, powers and roots (48–59) CORE • identify factors of 2-digit numbers. problem • represent problems making correct use of numbers, words or diagrams • classify and visualise number properties and patterns • calculate accurately, selecting mental methods or a calculator as appropriate • generalise in simple cases by working logically • understand the significance of a counter-example • draw simple conclusions and explain reasoning • communicate own findings effectively, orally and in writing and to: • understand negative numbers as positions on a number line • order, add and subtract positive and negative integers in context • use the order of operations, including brackets. • recognise square numbers to at least 12 12, and corresponding roots, and use the square and square root keys of a calculator • recognise and use multiples, factors, primes (less than 100), common factors, highest common factors and lowest common multiples in simple cases • use simple tests of divisibility • use the bracket, square, square root and sign change keys of a calculator. 2 | Exploring mathematics | Tier 3 (green) Number 2: Whole numbers and decimals (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • read and write whole numbers in figures and • identify the necessary information to understand or simplify a context or words • use decimal notation for tenths and hundredths, Place value understanding what each digit represents (36–47) • add and subtract mentally pairs of 2-digit numbers Calculations • use written methods to: problem • break calculations or problems into simpler steps • manipulate numbers and apply routine algorithms • calculate accurately, selecting mental methods or a calculator as appropriate (88–91, 102–105) – add and subtract whole numbers • check the accuracy of solutions, relating them to the original context Calculator methods – multiply TU × TU • communicate own findings effectively, orally and in writing (108–109) • use a basic calculator effectively. • discuss and compare approaches and results with others Solving problems (2–11) and to: • understand and use decimal notation and place value • compare and order decimals in different contexts • round whole numbers to the nearest 10, 100 or 1000 and decimals to the nearest whole number or one decimal place • consolidate recall of multiplication to 10 × 10 and quickly derive division facts • use mental methods to multiply and divide simple decimals by one-digit whole numbers, e.g. 0.8 × 6, 2.4 ÷ 3, using jottings as appropriate • use efficient written methods to: – add and subtract whole numbers and decimals – multiply 3-digit by 2-digit whole numbers • make and justify estimates and approximations of calculations. 3 | Exploring mathematics | Tier 3 (green) Number 3: Fractions and percentages (7 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • use fraction notation and the terms ‘numerator’ • identify the necessary information to understand or simplify a context or and ‘denominator’ • recognise simple equivalent fractions, including Fractions, decimals, percentages (60–77) Calculations (92–101, 110–111) Solving problems (28–31) relating hundredths to tenths • change an improper fraction to a mixed number, and vice versa • find simple fractions of shapes and small whole numbers. problem • recognise equivalent approaches • represent problems making correct use of numbers, words and diagrams • use accurate notation • calculate accurately, selecting mental methods or a calculator as appropriate • check the accuracy of solutions, relating them to the original context • communicate own findings effectively, orally and in writing and to: • use fractions and percentages to describe parts of shapes • use diagrams to compare two or more simple fractions • simplify fractions by cancelling and identify equivalent fractions • understand percentage as the ‘number of parts per 100’ and recognise equivalent percentages, fractions and decimals • calculate mentally, on paper and with a calculator, as appropriate, to: – add and subtract simple fractions and those with common denominators – multiply a fraction by an integer – calculate simple fractions and percentage of quantities and measurements. 4 | Exploring mathematics | Tier 3 (green) Number 4: Whole numbers, decimals and measures (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • suggest suitable metric units and measuring • identify the necessary information to understand or simplify a context or equipment to estimate or measure length, mass or capacity problem • represent problems making correct use of numbers, words and diagrams • read and interpret simple measuring scales • manipulate numbers and apply routine algorithms Calculations • divide a 2- or 3-digit number by a 1-digit number • calculate accurately, selecting mental methods or a calculator as (82–87, 92–103, 104–107, • round up or down after division, depending on the 110–111) Calculator methods (108–109) Measures (228–231) Solving problems (28–31) context • use a basic calculator effectively • use all four operations to solve simple word problems, including time. appropriate • check results by considering whether they are of the right order of magnitude and by working the problem backwards • discuss and compare approaches and results with others • communicate own findings effectively, orally and in writing and to: • choose and use units of measurement to measure, estimate, calculate and solve problems in everyday contexts • convert one metric unit to another (e.g. grams to kilograms) • read and interpret scales on a range of measuring instruments • use efficient written methods to: – add and subtract whole numbers and decimals – multiply and divide 3-digit by 2-digit whole numbers – multiply and divide decimals with up to two places by single-digit whole numbers • make and justify estimates and approximations of calculations • use inverse operations in the context of integers and decimals • use the memory of a calculator and interpret the display in different contexts. 5 | Exploring mathematics | Tier 3 (green) Number 5: Percentages, ratio and proportion (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • find simple fractions and percentages of quantities • identify the necessary information to understand or simplify a context or and measurements. • solve simple problems using ideas of ratio and Fractions, decimals, percentages, proportion (‘one for every …’ or ‘one to every …’ ratio and proportion and ‘one in every …’). (70–81) problem • represent problems making correct use of numbers, words and diagrams • use accurate notation • calculate accurately, selecting mental methods or a calculator as appropriate Calculations (110–111) • check the accuracy of solutions, relating them to the original context • communicate own findings effectively, orally and in writing • discuss, compare and evaluate approaches and results with others • recognise equivalent approaches and to: • find equivalent percentages, fractions and decimals • express a smaller number as a fraction or percentage of a larger one • use percentages to compare simple proportions • calculate simple fractions and percentages of quantities and measurements • understand the relationship between ratio and proportion • use direct proportion in simple contexts • use ratio notation, simplify ratios and divide a quantity into two parts in a given ratio • solve simple problems involving ratio and direct proportion using informal strategies. 6 | Exploring mathematics | Tier 3 (green) Number 6: Solving number problems (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • add and subtract mentally pairs of 2-digit numbers • identify the necessary information to understand or simplify a problem • recall multiplication facts to 10 × 10and derive • represent problems mathematically quickly corresponding division facts Calculations (88–107, 110–111) Calculator methods (108–109) Fractions and percentages (66–77) • multiply pairs of 2-digit whole numbers and divide a 3-digit by 1-digit whole number • find simple fractions and percentages of quantities and measurements • round up or down after division, depending on the context. • interpret information from a mathematical representation or context • use accurate notation • use appropriate procedures and tools, including ICT • calculate accurately, selecting mental methods or a calculator as appropriate • make and justify estimates and approximations of calculations • generalise in simple cases by working logically Solving problems • explain and justify methods and conclusions (28–29) • discuss, compare and evaluate approaches and results with others • recognise equivalent approaches and to: • find equivalent percentages, fractions and decimals • calculate with whole numbers, decimals, fractions and percentages • carry out calculations with more than one step. Algebra 1: Patterns and sequences (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • recognise and extend number sequences formed • represent problems making correct use of symbols, words and diagrams by counting in steps of constant size • recognise simple number patterns. Sequences and functions (144–163) Formulae and identities (112–113) Solving problems (32–35) • classify and visualise properties and patterns • understand the significance of a counter-example • generalise in simple cases by working logically • draw simple conclusions and explain reasoning • communicate own findings effectively, orally and in writing and to: • describe integer sequences • generate the terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence) • generate sequences from patterns or practical contexts and describe the general term in simple cases. 7 | Exploring mathematics | Tier 3 (green) Algebra 2: Equations and formulae (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • understand and use relationships between • represent problems making correct use of symbols and words addition, subtraction, multiplication and division • use brackets in arithmetical expressions. Equations, formulae and identities • interpret information from a mathematical representation or context • manipulate algebraic expressions and equations • communicate own findings effectively, orally and in writing (112–119, 138–143) and to: Solving problems • use letter symbols to represent unknown numbers or variables (26–27) • simplify linear algebraic expressions by collecting like terms • understand that algebraic operations follow the rules of arithmetic • multiply a constant over a bracket (integer coefficients) • substitute positive integers into linear expressions and formulae • use simple formulae from mathematics and other subjects. Algebra 3: Sequences, functions and graphs (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • recognise and extend number sequences by • generalise in simple cases by working logically counting in steps of constant size • read and plot coordinates in the first quadrant • represent and interpret data in a line graph (e.g. Coordinates (218–219) Sequences, functions and graphs (148–167) Solving problems (2–13, 26–27) for a multiplication table). • describe and explain a simple number pattern. • represent problems making correct use of words, symbols, tables and graphs • classify and visualise properties and patterns • manipulate algebraic expressions and equations • draw accurate graphs, on paper and on screen • use appropriate procedures and tools, including ICT • use accurate notation • communicate own findings effectively, orally and in writing • explain and justify methods and conclusions and to: • generate the terms of a simple sequence, given a rule • generate sequences from patterns and describe the general term in simple cases • represent simple functions using words, symbols and mappings • use coordinates in all four quadrants and identify coordinates of points determined by geometric information • generate coordinate pairs that satisfy a simple rule • plot graphs of simple linear functions (y given explicitly in terms of x), on paper and using ICT. 8 | Exploring mathematics | Tier 3 (green) Algebra 4: Using algebra (8 hours) Equations, formulae and identities Before they start, pupils should be able to: In this unit, pupils learn to: • understand and use relationships between • represent problems making correct use of words, symbols, tables and addition, subtraction, multiplication and division graphs • use brackets in arithmetical expressions • classify and visualise properties and patterns • read and plot coordinates in all four quadrants. • use appropriate procedures and tools, including ICT (112–143) • draw accurate graphs, on paper and on screen Sequences, functions and graphs • use appropriate procedures and tools, including ICT (154–177) Solving problems (32–35) • manipulate algebraic expressions and equations • communicate own findings effectively, orally and in writing and to: • simplify linear expressions by collecting like terms • multiply a constant over a bracket (integer coefficients) • substitute positive integers into linear expressions and formulae and, in simple cases, derive a formula • construct and solve simple linear equations with integer coefficients (unknown on one side only) • generate sequences from patterns or practical contexts and describe the general term in simple cases • recognise the first few triangular numbers • generate coordinate pairs that satisfy a simple rule • plot graphs of simple linear functions (y given explicitly in terms of x), on paper and using ICT • plot and interpret the graphs of simple linear functions arising from real life situations. 9 | Exploring mathematics | Tier 3 (green) Geometry and measures 1: Area and perimeter (4 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • measure and draw lines to the nearest millimetre. • identify the necessary information to understand or simplify a context or • understand that area is measured in square centimetres (cm2) Mensuration (198–201, 228–231, 234–241) Solving problems • understand, measure and calculate perimeters of simple shapes • calculate areas of rectangles. (18–21) problem • represent problems making correct use of symbols, words and diagrams • classify and visualise properties of shapes • draw accurate mathematical diagrams and constructions • use appropriate procedures and tools • check the accuracy of solutions, relating them to the original context • discuss and compare approaches and results with others • communicate own findings effectively, orally and in writing and to: • know and use the formula for the area of a rectangle • calculate perimeters and areas of shapes made from rectangles • visualise 3D shapes and deduce some of their properties • calculate the surface areas of cubes and cuboids • choose and use units of measurement to measure, estimate, calculate and solve problems in everyday contexts. Geometry and measures 2: Angles (3 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • measure and draw acute and obtuse angles to • identify the necessary information to understand or simplify a context or the nearest degree. • calculate angles on a straight line. problem • represent problems making correct use of diagrams Geometrical reasoning: lines, angles • draw accurate diagrams and constructions and shapes • use accurate notation (178–183) Measures and mensuration (232–233) • use appropriate procedures and tools • generalise in simple cases by working logically • draw simple conclusions and explain reasoning • communicate own findings effectively, orally and in writing and to: • use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes • distinguish between and estimate acute, obtuse and reflex angles and measure and draw them to the nearest degree • know and calculate the sum of angles at a point and on a straight line, and recognise vertically opposite angles. 10 | Exploring mathematics | Tier 3 (green) Geometry and measures 3: Transformations (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • draw a line of symmetry in a 2D shape • identify the necessary information to understand or simplify a context or • complete a 2D shape given a line of symmetry • recognise where a shape will be after a translation Transformations parallel to an axis. problem • represent problems making correct use of diagrams • draw accurate diagrams and constructions on paper and on screen (202–212) • classify and visualise properties of shapes Solving problems • generalise in simple cases by working logically (14–17, 32–35) • use appropriate procedures and tools, including ICT • take account of feedback and learn from mistakes • communicate own findings effectively, orally and in writing and to: • understand and use the language and notation associated with reflections, translations and rotations • recognise and visualise the symmetries of a 2D shape • transform 2D shapes by: – reflecting in given mirror lines – rotating about a given point – translating • explore these transformations and symmetries using ICT. 11 | Exploring mathematics | Tier 3 (green) Geometry and measures 4: Properties of shapes (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • calculate angles in a triangle • identify the necessary information to understand or simplify a context or • recognise lines of symmetry in 2D shapes • recognise isosceles, equilateral and scalene Geometrical reasoning: lines, angles and shapes (180–189) triangles. problem • classify and visualise properties of shapes and patterns • represent problems using words and diagrams • generalise in simple cases by working logically • understand the significance of a counter-example • draw simple conclusions and explain reasoning • communicate own findings effectively, orally and in writing and to: • use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes • identify parallel and perpendicular lines • calculate the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles • identify and use angle, side and symmetry properties of triangles and quadrilaterals • explore geometrical problems, explaining reasoning orally, and using step-by-step deduction supported by diagrams. 12 | Exploring mathematics | Tier 3 (green) Geometry and measures 5: Constructions (6 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • measure and draw lines to the nearest millimetre • identify the necessary information to understand or simplify a context or • estimate, measure and draw acute and obtuse angles Geometrical reasoning: lines, angles and shapes • identify nets for closed and open cubes. problem • classify and visualise properties of shapes • represent problems by drawing accurate diagrams and constructions, on paper and on screen (184–212) • use appropriate procedures and tools, including ICT Construction • generalise in simple cases by working logically (220–223) • discuss and compare approaches and results with others • recognise equivalent approaches • communicate own findings effectively, orally and in writing and to: • use a ruler, set square and protractor to: – estimate, measure and draw lines to the nearest millimetre and acute, obtuse and reflex angles to the nearest degree – draw parallel and perpendicular lines – construct squares and rectangles – construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA) – draw simple nets of 3D shapes • use ICT to explore constructions. 13 | Exploring mathematics | Tier 3 (green) Statistics 1: Grouped data and simple statistics (3 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • solve a problem by collecting, organising and • represent problems, making correct use of tables, diagrams and graphs interpreting data from a simple survey or experiment • construct and interpret simple bar charts, line Statistics graphs and frequency tables. • interpret information from a mathematical representation or context • draw simple conclusions and explain reasoning • discuss and compare approaches and results with others • relate findings to the original context (256–265, 268–271) • communicate own findings effectively, orally and in writing and to: • construct frequency tables for gathering discrete data, grouped where appropriate in equal class intervals • find the mode, mean, median and range for a set of discrete data, and the modal class for grouped discrete data • construct and interpret graphs and diagrams to represent data, including: – bar-line graphs – frequency diagrams for grouped discrete data interpret simple pie charts. Statistics 2: Probability 1 (3 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • discuss events, including those with equally likely • interpret information from a mathematical representation or context outcomes, using the language of probability • place the likelihood of events on a scale from Probability (276–283) impossible to certain. • draw accurate tables, diagrams and graphs on paper and on screen • generalise in simple cases by working logically • discuss and compare approaches and results with others • explain and justify methods and conclusions • communicate own findings effectively, orally and in writing and to: • use the vocabulary and ideas of probability, drawing on experience • understand and use the probability scale from 0 to 1 • find and justify probabilities based on equally likely outcomes in simple contexts • identify all the possible mutually exclusive outcomes of a single event. 14 | Exploring mathematics | Tier 3 (green) Statistics 3: Enquiry 1 (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • solve a problem by collecting, organising and • identify the necessary information to simplify a problem interpreting data from a simple survey or experiment Statistics (248–255, 262–265, 268–271) Solving problems (24–25) • construct and interpret simple bar charts, line graphs and frequency tables. • draw accurate tables, diagrams and graphs, on paper and on screen • interpret information from a mathematical representation • draw simple conclusions and explain reasoning • relate findings to the original context • communicate own findings effectively, orally and in writing • discuss, compare and evaluate approaches and results with others and to: • suggest possible answers, given a question that can be addressed by statistical methods • decide which data would be relevant to an enquiry and possible sources • design and use a data collection sheet or questionnaire • construct frequency tables for gathering discrete data, grouped where appropriate in equal class intervals • construct, on paper and using ICT, and interpret graphs and diagrams to represent data, including: – bar-line graphs – frequency diagrams for grouped discrete data – simple pie charts. 15 | Exploring mathematics | Tier 3 (green) Statistics 4: Enquiry 2 (5 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • solve a problem by collecting, organising and • identify the necessary information to simplify a problem interpreting data from a simple survey or experiment Statistics (250–273) Solving problems • construct and interpret simple bar charts, line graphs and frequency tables • find simple statistics for a set of data. • draw accurate tables, diagrams and graphs, on paper and on screen • interpret information from a mathematical representation • draw simple conclusions and explain reasoning • relate findings to the original context • communicate own findings effectively, orally and in writing (24–25) • discuss, compare and evaluate approaches and results with others and to: • suggest possible answers, given a question that can be addressed by statistical methods • design and use a data collection sheet or questionnaire • construct frequency tables for discrete data, grouped where appropriate in equal class intervals • construct and interpret bar-line graphs and frequency diagrams for grouped discrete data, on paper and using ICT • find the mode, median and range, and the modal class for grouped data, and calculate the mean, including from a simple frequency table • compare two simple distributions, using the range and one of the mode or modal class, median or mean • write a short report of a statistical enquiry, including appropriate diagrams, graphs and charts, using ICT as appropriate. Statistics 5: Probability 2 (3 hours) Before they start, pupils should be able to: In this unit, pupils learn to: • discuss events, including those with equally likely • interpret information from a mathematical representation or context outcomes, using the language of probability • find the probabilities of events based on equally Probability (278–285) likely outcomes in simple contexts. • draw accurate tables, diagrams and graphs on paper and on screen • generalise in simple cases by working logically • discuss and compare approaches and results with others • explain and justify methods and conclusions • communicate own findings effectively, orally and in writing and to: • identify all the possible mutually exclusive outcomes of a single event. • understand and use the probability scale from 0 to 1 • find and justify probabilities based on equally likely outcomes in simple contexts • estimate probabilities by collecting data from a simple experiment and recording in a frequency table • compare experimental and theoretical probabilities in simple contexts. 16 | Exploring mathematics | Tier 3 (green) Revision 1 and 2 - here are the process objectives Previous learning Objectives based on NC levels 4 and 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 • identify the necessary information to understand or simplify a context or problem offers is an opportunity to consolidate and refine these skills. • use appropriate procedures and tools • calculate accurately, selecting mental methods or a calculator as appropriate • manipulate numbers, algebraic expressions and equations, and apply routine algorithms • draw accurate mathematical diagrams and graphs • check the accuracy of solutions, relating them to the original context • communicate own findings effectively, orally and in writing • discuss, compare and evaluate approaches and results with others • recognise equivalent approaches • take account of feedback and learn from mistakes and to: Number content objectives are as in the unit 17 | Exploring mathematics | Tier 3 (green)