# Year 6 Mathematics - Student Portfolio Summary

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1 Year 6 - Student Portfolio Summary WORK SAMPLE PORTFOLIOS These work sample portfolios have been designed to illustrate satisfactory achievement in the relevant aspects of the achievement standard. The work sample portfolios are a resource to support planning and implementation of the Foundation to Year 10 Australian Curriculum in English,, Science and History during They comprise collections of different students work annotated to highlight evidence of student learning of different aspects of the achievement standard. The work samples vary in terms of how much time was available to complete the task or the degree of scaffolding provided by the teacher. There is no pre-determined number of samples required in a portfolio nor are the work samples sequenced in any particular order. These initial work sample portfolios do not constitute a complete set of work samples - they provide evidence of most (but not necessarily all) aspects of the achievement standard. As the Australian Curriculum in English,, Science and History is implemented by schools in 2012, the work sample portfolios will be reviewed and enhanced by drawing on classroom practice and will reflect a more systematic collection of evidence from teaching and learning programs. THIS PORTFOLIO YEAR 6 MATHEMATICS This portfolio comprises a number of work samples drawn from a range of assessment tasks, namely: Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Fraction Poster Chance Spinners Maths investigation Numbers Mixed operations Measurements and geometry Rectangular prisms Financial mathematics Designing meal options Numbers and place value Everyday integers Plotting points on the Cartesian plane Map of the run course Fractions investigation Year 6 Page 1 of 31

2 Year 6 - Student Portfolio Summary This portfolio of student work shows understanding of fractions as representations of a decimal and a percentage (WS1, WS10) and ability to order fractions on a number line (WS7). The student writes correct number sentences using a variety of skills and demonstrates the use of integers in real situations (WS7). The student undertakes activities to describe the position of points on the Cartesian plane (WS8), uses scaled instruments to measure lengths and constructs rectangular prisms to establish methods of calculating volume (WS5, WS9). The student determines strategies for comparing theoretical and experimental probability (WS 2) and evaluates results to draw conclusions. The student undertakes an authentic investigation based on experience to demonstrate their understanding of timetables, graphical representations (WS3) and surveys and uses knowledge of percentages and decimals in an investigation into purchasing and discounts (WS6). The following aspects of the achievement standard are not evident in this portfolio: recognise the properties of prime, composite, square and triangular numbers make connections between the powers of 10 and the multiplication and division of decimals make connections between capacity and volume solve problems involving length and area describe combinations of transformations solve problems using the properties of angles evaluate secondary data displayed in the media. Year 6 Page 2 of 31

3 Year 6 - Work sample 1 Work sample 1: Fraction poster Relevant parts of the 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. Summary of task Students were asked to select a fraction and create a poster of their findings which they presented in class. They were asked to represent the fraction both as a decimal and percentage. Year 6 Page 3 of 31

4 Year 6 - Work sample 1 Work sample 1: Fraction poster Represents an equivalent fraction, decimal and percentage in various forms. Acknowledgment ACARA acknowledges the contribution of the NSW Department of Education and Communities for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 4 of 31

5 Year 6 - Work sample 2 Work sample 2: Chance Spinners Relevant parts of the 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. Summary of task In this activity students took turns in a game involving a spinner and completed a set worksheet. Students worked in pairs and recorded the differences between their scores after spinning a number on the spinner. They recorded the relative frequency of the results and they ordered their results from most likely to least likely. They made comparisons between theoretical and experimental probabilities and drew conclusions about the fairness of the game. Year 6 Page 5 of 31

6 Year 6 - Work sample 2 Work sample 2: Chance Spinners Records relative frequency. Communicates relative frequency as fractions. Year 6 Page 6 of 31

7 Year 6 - Work sample 2 Work sample 2: Chance Spinners Compares expected likelihood of outcomes with actual (experimental) outcomes. Records their findings in a display. Year 6 Page 7 of 31

8 Year 6 - Work sample 2 Work sample 2: Chance Spinners Calculates the likelihood of a number occurring. Acknowledgment ACARA acknowledges the contribution of the Queensland Studies Authority for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 8 of 31

9 Year 6 - Work sample 3 Work sample 3: Maths investigation Relevant parts of the 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. 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. Summary of task Students had spent time reviewing the following concepts: 12hr/24hr time/timetables Constructing bar/sector graphs Comparative bar graphs Surveying (conducting survey) Students were going on a camp and were required to undertake the task below while they were on camp. Year 6 Page 9 of 31

10 Year 6 - Work sample 3 Work sample 3: Maths investigation Year 6 Page 10 of 31

11 Year 6 - Work sample 3 Work sample 3: Maths investigation Calculates time durations. Uses 24 hour time. Year 6 Page 11 of 31

12 Year 6 - Work sample 3 Work sample 3: Maths investigation Creates pie chart of hours spent on activities. Creates a side by side column graph using categorical data from data collected. Year 6 Page 12 of 31

13 Year 6 - Work sample 3 Work sample 3: Maths investigation Provides an explanation for the time allocated to various activities. Acknowledgment ACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 13 of 31

14 Year 6 - Work sample 4 Work sample 4: Numbers Mixed operations Relevant parts of the 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. 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. Summary of task Students have calculated solutions to problems involving mixed operations. Students practiced this activity and were then asked to show a real variety and sophistication of skills not just repeated standard number sentences. The following instructions were given: Select 15 numbers between 1 and 100 Express each of your numbers in different ways using mixed operations For example, 2 = For example, 2 = 4 x 1 2 Year 6 Page 14 of 31

15 Year 6 - Work sample 4 Work sample 4: Numbers Mixed operations Demonstrates an adequate level of competence in using the four operations to express numbers in different ways. Understanding of the order of operations is evident. Most calculations are accurate. Uses numbers up to 100. Acknowledgment ACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 15 of 31

16 Year 6 - Work sample 5 Work sample 5: Measurement and geometry Rectangular prisms Relevant parts of the 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. Summary of task Students had previously covered the following concepts: Relationship of two-dimensional (area) with three dimensional (volume) Choosing appropriate units of measure square cm for area, cubic cm for volume Constructing simple prisms Formula for volume right prism= L X B X H. Students were required to construct rectangular prisms using 24 interlocking cubes, record and describe their findings. They made a rectangular prism with a volume of 24 cubic units. They described their rectangular prism in terms of its length, breadth and height and recorded this information using diagrams and words. Students made other rectangular prisms with a volume of 24 cubic units, recording the results and describing what they noticed. Year 6 Page 16 of 31

17 Year 6 - Work sample 5 Work sample 5: Measurement and geometry Rectangular prisms Establishes the calculations to develop the formulae for the volume of a rectangular prism. Accurately carries out calculations. Acknowledgment ACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 17 of 31

18 Year 6 - Work sample 6 Work sample 6: Financial mathematics Designing meal options Relevant parts of the 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. Summary of task Students had been given opportunities to develop their ability to multiply decimals in the context of money. They have also investigated simple fraction and percentage discounts. In this activity students prepared a quote for providing meal options for a catering company. They calculated costs and outlined various price options including special bulk buying. Students were given information about discounts which were available for bulk purchases. The discounts were: 1/3 off vegetarian patties and sizzling sausages 25% off juicy steak. All calculations were completed using mental or written methods. Year 6 Page 18 of 31

19 Year 6 - Work sample 6 Work sample 6: Financial mathematics Designing meal options Year 6 Page 19 of 31

20 Year 6 - Work sample 6 Work sample 6: Financial mathematics Designing meal options Accurately adds decimals and carries out calculations involving the four operations. Year 6 Page 20 of 31

21 Year 6 - Work sample 6 Work sample 6: Financial mathematics Designing meal options Multiplies decimals by a single digit number. Demonstrates they can add decimals. Demonstrates they can subtract a decimal amount from 100. Year 6 Page 21 of 31

22 Year 6 - Work sample 6 Work sample 6: Financial mathematics Designing meal options Implies demonstration of a calculated fractional discount. Implies demonstration of a 25% discount. Demonstrates ability to subtract decimals. Acknowledgment ACARA acknowledges the contribution of the Queensland Studies Authority for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 22 of 31

23 Year 6 - Work sample 7 Work sample 7: Numbers and place value Everyday integers Relevant parts of the 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. Summary of task Students have investigated the use of positive and negative integers in authentic situations. Students completed the task to solve problems in everyday contexts using integers. Year 6 Page 23 of 31

24 Year 6 - Work sample 7 Work sample 7: Numbers and place value Everyday integers Reads positive and negative integers from a number line. Solves problems involving positive and negative integers. Acknowledgment ACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 24 of 31

25 Year 6 - Work sample 8 Work sample 8: Plotting points on the Cartesian plane Relevant parts of the 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. Summary of task Students have been building their understanding of grid references. Students designed and plotted coordinates on all four quadrants of the Cartesian plane. They worked in pairs. The first student drew a pattern on grid paper and described their diagram to their partner using coordinates on the Cartesian plane. The second student was required to reproduce the first student s patterns using the information provided. Year 6 Page 25 of 31

26 Year 6 - Work sample 8 Work sample 8: Plotting points on the Cartesian plane Accurately reproduces the partner s pattern by locating most coordinates in all four quadrants. Acknowledgment ACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 26 of 31

27 Year 6 - Work sample 9 Work sample 9: Map of the run course Relevant parts of the 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. Summary of task In pairs, students planned the course of a fun run within school grounds. Students measured using tapes and trundle wheels. Students were provided with a map of the school and discussed the scale they used to draw the diagram of their course. Students calculated the total length of their course. Year 6 Page 27 of 31

28 Year 6 - Work sample 9 Work sample 9: Map of the run course Uses appropriate scaled instruments to measure length. Acknowledgment ACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 28 of 31

29 Year 6 - Work sample 10 Work sample 10: Fractions investigation Relevant parts of the 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. Summary of task Students have completed work on equivalent fractions and performed simple calculations using fractions. Students were required to complete a task in class requiring them to demonstrate their understanding of equivalent fractions. Year 6 Page 29 of 31

30 Year 6 - Work sample 10 Work sample 10: Fractions investigation Demonstrates an understanding of unit fractions. Calculates differences to make 1 whole. Displays an understanding of equivalent fractions. Year 6 Page 30 of 31

31 Year 6 - Work sample 10 Work sample 10: Fractions investigation Orders fractions on a number line. Acknowledgment ACARA acknowledges the contribution of the trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards. Year 6 Page 31 of 31

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