These assessment pointers are for judging standards of student performance in Year 6 Mathematics. They are examples of what students may demonstrate rather than being a checklist of everything they should do. For reporting, they are used to make on-balance judgements about achievement, based on what has been taught and assessed during the reporting period. They can also be used to guide the pitch of assessment tasks, develop marking keys and inform assessment feedback. JUDGING STANDARDS IN YEAR 6 MATHEMATICS Reporting against the Achievement Standard YEAR 6 MATHEMATICS ACHIEVEMENT STANDARD By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media. Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages. YEAR 6 MATHEMATICS ASSESSMENT POINTERS Number and Algebra A B C D E Excellent achievement High achievement Satisfactory achievement Limited achievement Very low achievement Investigates and describes the relationships between prime, composite, square and triangular numbers. 2013/37234v7 [PDF 2013/37706] Published: 20 July, 2015 Applies properties of prime, composite, square and triangular numbers to solve problems, e.g. represents composites as a product of their primes, for instance 24 = 2 x 2 x 2 x 3. Identifies the properties of prime, composite, square and triangular numbers, e.g. factor trees. Identifies some key features of prime and composite numbers, e.g. that all prime numbers except 2 are odd numbers. Recalls multiples up to 10 x 10. Number and Algebra A B C D E Excellent achievement High achievement Satisfactory achievement Limited achievement Very low achievement Evaluates and applies efficient strategies to solve problems involving any of the four operations, with whole numbers, and justifies the use of the chosen strategies. Selects and applies appropriate strategies to solve problems involving any of the four operations, with whole numbers. Uses mental and written strategies to solve problems involving any of the four operations, with whole numbers, e.g. completes a sequence, creates an ordered list. Uses given strategies to solve problems involving any of the four operations, with small numbers, e.g. guess and check. Calculates addition and subtraction to solve problems. Investigates everyday situations that involve integers and solves related problems, using a number line, e.g. changes in temperature. Solves everyday additive problems involving integers, using a number line. Describes the use of integers in everyday situations, and locates integers on a number line, e.g. temperatures above and below zero. Completes number lines involving zero and positive integers. Completes number lines involving whole numbers. Compares related fractions by demonstrating their equivalence using a number line. Solves multi-step addition and/or subtraction word problems involving related fractions, e.g. If 2 3 of a group wore red and 5 10 wore green, what fraction wore another colour? Compares fraction families on a number line. Estimates before solving problems involving the addition and/or subtraction of related fractions. Locates fractions on a number line. Solves problems involving the addition and/or subtraction of related fractions, e.g. 1 5 5 3 8 + = + = . Represents fractions by drawing diagrams. Adds fractions with a common denominator, e.g. 4 2 6 + = . Completes arrangements or drawings to represent a unit fraction. Adds unit fractions with common denominators, e.g. 1 1 2 + = . Solves problems by identifying and applying simple fractions of a quantity, e.g. finds two-thirds of a cake cut into nine pieces: 2 2 9 of 9 = x = 6. Calculates simple fractions of a quantity and finds equivalent fractions of the same quantity, 1 1 9 e.g. of 9 = x = 3. Calculates simple fractions of a quantity, where the result is a whole number, e.g. one third of nine is the same as 9 ÷ 3 = 3. Models and calculates fractions with drawings and diagrams. Models and calculates unit fractions with drawings and diagrams. Solves problems involving decimals by recognising the operation to be performed, where results are rational. Uses estimation and rounding to check the reasonableness of answers. Adds, subtracts, multiplies and divides decimals, where results are terminating. Applies rounding to estimate a result before calculating. Adds and subtracts decimals and makes connections between the powers of 10 and the multiplication and division of decimals, where the results are rational, e.g. 2.05 x 100 = 205. Adds and subtracts decimals. Adds and subtracts whole numbers. 3 3 3 3 1 3 9 9 9 7 7 7 9 7 7 7 1 Number and Algebra Measurement and Geometry A B C D E Excellent achievement High achievement Satisfactory achievement Limited achievement Very low achievement Solves problems by selecting and applying appropriate equivalent decimals, fractions and percentages. Converts between equivalent decimals, fractions and percentages. Connects fractions, decimals and percentages as different representations of the same number. Connects unit fractions, decimals and simple percentages. Connects unit fractions and decimals. Solves problems involving the calculation and comparison of percentage discounts on items. Finds the total cost of given quantities and prices per item, after application of percentage discounts. Calculates common percentage discounts, e.g. calculates discounts of 10%, 25% and 50%. Calculates discounts of 10% and 50%. Calculates discounts of 10% and 50% only with digital technologies. Solves problems involving an additive or multiplicative pattern, to predict a given term in a sequence, e.g. finds a specific missing term such as the 18th house in the street from house number 43. Identifies sequence/s involving whole numbers, fractions and/or decimals represented in a pattern, and describes the rule used to create the sequence. Describes rules used in sequences involving whole numbers, fractions and/or decimals. Completes sequences involving whole numbers, unit fractions or decimals. Follows given sequences. Applies order of operations to solve problems involving more than two operations. Applies order of operations to solve problems involving up to two operations. Writes number sentences using brackets and order of operations, e.g. (20 x 6) + 15 = 135. Writes number sentences with any combination of addition, subtraction, multiplication and division. Writes number sentences with combinations of addition and subtraction. Converts and calculates to solve problems involving the comparison of length, mass, area, volume and capacity, using the correct operations. Converts units and calculates measurements of length, mass, area, volume and capacity. Compares lengths and areas to solve problems, e.g. given the area, finds possible lengths of sides. Connects decimals to the metric system, e.g. 1.5 m = 150 cm. Chooses appropriate units of measurement to perform calculations. Makes connections between capacity and volume. Solves problems involving length and area. Converts between standard metric units for length and mass. Applies standard metric units to measure length. Interprets timetables and uses timetables for planning, e.g. plans a day trip involving a bus and a train. Interprets timetables and uses a timetable to schedule events. Interprets timetables. Identifies events and their start and finish times. Identifies the starting time of a given event. Creates nets to construct prisms and pyramids, satisfying given criteria. Creates nets to construct prisms and pyramids, comparing features. Constructs simple prisms and pyramids, e.g. from given nets. Models simple prisms and pyramids, e.g. using play dough. Distinguishes between prisms and pyramids. Measurement and Geometry Statistics and Probability A B C D E Excellent achievement High achievement Satisfactory achievement Limited achievement Very low achievement Applies combinations of translations, reflections and rotations to change the position and orientation of shapes, e.g. designs a logo. Draws and describes the transformation of one shape, i.e. reflects, translates or rotates, and identifies the new position. Describes combinations of transformations, e.g. uses terms such as flip/reflect, slide/translate, turn/rotate. Describes one transformation of a regular shape, e.g. identifies a triangle was flipped. Identifies line and rotational symmetry. Applies and explains combinations of transformations of shapes on the Cartesian plane, maintaining shape and size. Provides instructions to locate and draw a shape on the Cartesian plane. Locates an ordered pair in any one of the four quadrants on the Cartesian plane. Identifies 𝑥 and 𝑦 axes on the Cartesian plane and plots coordinates. Misplaces 𝑥 and 𝑦 values. Solves problems involving unknown angles. Measures angles of two-dimensional regular shapes and writes a relationship, e.g. the three angles of a triangle add to 180°. Compares angles and classifies them according to size, i.e. as acute, right, obtuse, straight or reflex angles. Solves problems using the properties of angles, e.g. finds a missing angle. Measures angles using a protractor. Identifies angles in relation to a right angle, i.e. as greater than, less than or the same as. Designs and conducts a chance experiment to investigate probabilities of changed conditions, such as a 50% increase in the proportion of a spinner that is red, and lists the probabilities. Matches statements of probability and numerical expressions in fractions, decimals and percentages. Lists the probabilities of all possible outcomes using simple fractions, decimals and percentages, e.g. assesses the various probabilities with an unequally coloured spinner. Lists probabilities of outcomes using a range from 0 to 1 in simple fractions. States the probability of outcomes as likely or unlikely. Interprets the similarities and differences between expected outcomes and actual results of both small and large numbers of trials. Compares observed results in trials with expected outcomes, using an appropriate expression, e.g. in 30 rolls of a six-sided die, a two was rolled 7/30, when it was expected to be rolled 5/30. Compares observed and expected frequencies, e.g. when rolling a six-sided die 12 times, a one was expected to come up two times but it was rolled four times. Conducts trials and records results. Records the results of a trial. Statistics and Probability A B C D E Excellent achievement High achievement Satisfactory achievement Limited achievement Very low achievement Evaluates data in complex displays with multi-layered information. Evaluates secondary data displayed in the media by validating its accuracy, identifying potentially misleading representations and explaining possible reasons for specific representations, e.g. to emphasise a point of view. Interprets data in complex displays with multi-layered information. Evaluates secondary data displayed in the media by validating its accuracy and identifying potentially misleading representations, e.g. graphics not drawn to scale. Interprets and compares data displayed in a variety of ways, including displays for two categorical variables, e.g. identifies the value of the symbol in a graph to display the populations of different cities. Evaluates secondary data displayed in the media by assessing its usefulness, e.g. consults web-based rainfall data to decide the best month for an overseas holiday. Identifies information from a range of data displays. Makes literal statements about secondary data displayed in the media, e.g. there was 4 mm of rain overnight. Identifies information from simple data displays, e.g. displays for one categorical variable.