# Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.

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3 Work sample 1 Number and measurement: Food pyramids Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given this task to consolidate previously studied units on rates, ratios and percentages Edition Page 3 of 51

4 Work sample 1 Mathematics Year 8 Number and measurement: Food pyramids Measures and records only the lengths required to facilitate calculation of necessary areas. Shows each step in the solution process. Demonstrates fluency by selecting and applying the appropriate area formulas to calculate the areas of the necessary sections. Demonstrates fluency with percentage calculations. Uses appropriate units for area. Interprets the calculated answer in the context of the problem. Food Pyramids used by kind permission of NSW Department of Education and Communities. Note: For the purpose of the work sample portfolio, the image has been reduced in size Edition Page 4 of 51

5 Work sample 2 Number: Feed the family Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time relating to the unit of work they had completed on ratios and scales Edition Page 5 of 51

6 Work sample 2 Number: Feed the family Simplifies ratios using given quantities in both a simple and more complex question. Identifies that the original recipe needs to be scaled by a factor of 5. Puts correct answers in table and converts to larger units of measure Edition Page 6 of 51

7 Work sample 2 Number: Feed the family Calculates number of packets of each ingredient and cost based on answer to question 2 showing some working. Uses calculated cost to feed 20 people to reasonably estimate number of people who could be fed with \$50. Simplifies and applies ratios to scale quantities up and down Edition Page 7 of 51

8 Work sample 3 Statistics: Books, cricket and pets Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time relating to the unit of work they had completed on statistical analysis of data and the effects of outliers on the interpretation of data Edition Page 8 of 51

9 Work sample 3 Statistics: Books, cricket and pets Calculates mean, median and mode from a list of discrete data. Recognises that the outlier would increase the mean but have little effect on the median and mode Edition Page 9 of 51

10 Work sample 3 Statistics: Books, cricket and pets Calculates the mean showing working. Demonstrates understanding that the sum of the data values does not provide information about individual data values. Creates an appropriate data set with the correct median, number of values and sum. Interprets data presented in a graph to find the number of students surveyed and the total number of pets and calculates the mean using these numbers. Recognises 14 as the outlier and calculates the decrease in the number of pets and the mean without the outlier included Edition Page 10 of 51

11 Work sample 4 Algebra: Linear relationships in the real world Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were asked to research the peak rates for taxi hire in the ACT and NSW. The rates at the time are shown in the table below. ACT NSW Flag fall \$4.70 \$3.50 Price/km \$1.90 \$2.14 Students were asked to use their knowledge of graphing and equations to make comparisons between the two sets of information and to use mathematical reasoning to draw conclusions from the investigation Edition Page 11 of 51

12 Work sample 4 Algebra: Linear relationships in the real world Graphs linear relationships, labelling the axes and giving units, a key and a title Edition Page 12 of 51

13 Work sample 4 Algebra: Linear relationships in the real world Defines variables and derives correct linear equations from the information given. Links the equation created with the real-life problem and explains why the equation works to model the situation. Compares the graphs of two linear relationships, demonstrating understanding of the meaning of their point of intersection. Understands the variables used in the equation and solves the equation for a given situation Edition Page 13 of 51

14 Work sample 4 Algebra: Linear relationships in the real world Explains why the graph is a not valid representation and relates it to the context Edition Page 14 of 51

15 Work sample 5 Geometry: Sorting quadrilaterals Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time relating to the unit of work they had completed on quadrilaterals. They were required to show their reasoning when drawing conclusions Edition Page 15 of 51

16 Work sample 5 Geometry: Sorting quadrilaterals Demonstrates an understanding of the features of quadrilaterals. Demonstrates geometric reasoning when combining the constraints of the number of right angles and parallel sides in the construction of quadrilaterals Edition Page 16 of 51

17 Work sample 6 Number: Ratios Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time relating to the unit of work they had completed on reasoning using problem-solving strategies Edition Page 17 of 51

18 Work sample 6 Number: Ratios Explores both ratios to find an example that satisfies both of them. Multiplies one ratio by a factor of three to generate a solution. Synthesises the requirements of both ratios to analyse the composition of the group Edition Page 18 of 51

19 Work sample 7 Number: Halfway Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time relating to the unit of work they had completed on rational numbers. The task required students to demonstrate their reasoning and problem-solving skills to answer the questions Edition Page 19 of 51

20 Work sample 7 Number: Halfway Represents rational numbers on a number line on which the line segments are equally spaced. Compares the two rational numbers using equivalent fractions with the same denominator. Uses fraction bars of approximately equal length and area to show the relative sizes of the rational numbers being compared Edition Page 20 of 51

21 Work sample 8 Algebra: Solving linear equations Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time after a unit of work on algebraic expansions and solving equations Edition Page 21 of 51

22 Work sample 8 Algebra: Solving linear equations Expands each expression and then solves the equation. Expands the expression ensuring correct usage of negatives in the expansion and the solution of the equation Edition Page 22 of 51

23 Work sample 9 Probability: Venn diagrams and two-way tables Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students had been using Venn diagrams and two-way tables to model information and hence draw conclusions. Students were required to complete the activity involving Venn diagrams and a two-way table Edition Page 23 of 51

24 Work sample 9 Year 8 Mathematics Probability: Venn diagrams and two-way tables Synthesises information in Venn diagram to reason a solution to each question. Demonstrates understanding of the structure of the two-way table and how the totals of the vertical columns and horizontal rows align Edition Page 24 of 51

25 Work sample 10 Measurement: Circumference and area Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time after a unit of work on circles Edition Page 25 of 51

26 Work sample 10 Measurement: Circumference and area Calculates the circumference and area of the circle with correct usage of units. Uses the wrong radius for area but performs a correct calculation. Identifies and labels the required parts of the circle. Rounds answers and states the number of decimal places to which they were rounded Edition Page 26 of 51

27 Work sample 11 Measurement: Rain on the roof Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time after a unit of work on volume Edition Page 27 of 51

28 Work sample 11 Measurement: Rain on the roof Calculates to volume of water on the roof in litres. Draws a correct conclusion as to why the numerical answer in litres is the same as the numerical answer to the area of the roof Edition Page 28 of 51

29 Work sample 12 Number and measurement: Investigating circles Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students had been learning about the concept of irrational numbers, including π, and the relationship between the circumference of a circle and the radius. The students were asked to investigate the relationship between the circumference and the diameter of a circle by measuring a variety of circular objects. They were given one week to complete the task Edition Page 29 of 51

30 Work sample 12 Number and measurement: Investigating circles Names and indicates some parts of a circle. Measures the circumference and diameter of a variety of circular objects with reasonable accuracy. Determines the ratio of the circumference to the diameter and writes it in the form a:1. Obtains several reasonable approximations for the irrational number π Edition Page 30 of 51

31 Work sample 12 Number and measurement: Investigating circles Describes in detail how the circumference and diameter of each object was measured and identifies possible sources of error in the measurement processes used Edition Page 31 of 51

32 Work sample 12 Number and measurement: Investigating circles Obtains reasonable measurements for the diameter and circumference. Determines the ratio of the circumference to the diameter. Concludes that the drive is circular by observing that the ratio of the circumference to the diameter has a value close to those found for other circular objects Edition Page 32 of 51

33 Work sample 13 Geometry: Congruence Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students had completed a unit of work on congruence in which they used transformations to create congruent figures and investigated the conditions for the congruence of triangles. Students were asked to demonstrate and apply their knowledge of transformations and the conditions for the congruence of triangles. They completed the task in class under exam conditions Edition Page 33 of 51

34 Work sample 13 Geometry: Congruence Identifies and names corresponding sides and angles of congruent triangles in matching order. Reflects a figure in a vertical axis Edition Page 34 of 51

35 Work sample 13 Geometry: Congruence Selects a pair of congruent triangles. States all appropriate tests that can be used to show that the triangles are congruent. Attempts to identify the correct test for congruency Edition Page 35 of 51

36 Work sample 13 Geometry: Congruence Rotates a figure by the desired angle but does not use the correct centre of rotation. Recognises the connection to Pythagoras Theorem and explains how this could be used to prove the triangles are congruent by a different test. Identifies the two congruent triangles and states a test that can be used to show that the triangles are congruent Edition Page 36 of 51

37 Work sample 14 Measurement: Perimeter and area Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students completed a unit of work on finding the perimeter and area of a range of two-dimensional shapes. The task required students to answer a number of questions related to the perimeter and area of a range of twodimensional shapes, including circles. Students were asked to apply their skills to some real-world problems. They completed the task under exam conditions in class time Edition Page 37 of 51

38 Work sample 14 Measurement: Perimeter and area Determines the perimeter of various plane shapes. Uses appropriate formulas to determine the areas of typical plane shapes. Uses Pythagoras Theorem to calculate the lengths of unknown sides in order to determine the perimeter Edition Page 38 of 51

39 Work sample 14 Measurement: Perimeter and area Draws and names almost all parts of a circle. Provides a reasonable explanation for why an area cannot be determined. Provides an estimate for the area of a shape by applying a known formula and reasoning about the relationship of this calculated area to the area that is to be estimated Edition Page 39 of 51

40 Work sample 14 Measurement: Perimeter and area Determines the area of the rectangle correctly and then estimates the area of the segment to be bigger than one square centimetre. Connects the concept of the circumference of a circle to solve a realworld problem in three dimensions Edition Page 40 of 51

41 Work sample 14 Measurement: Perimeter and area Explains why the triangles have the same area using appropriate mathematical terminology. Indicates that a triangle with a vertex that is opposite the centre of the base will result in the triangle of smallest perimeter Edition Page 41 of 51

42 Work sample 15 Number: Integers Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students had completed a unit of work on integers. Students were asked a series of questions that involved calculation and reasoning with integers. The use of calculators was not permitted and students were given 20 minutes of class time to complete the task Edition Page 42 of 51

43 Work sample 15 Number: Integers Adds and subtracts integers but makes an error. Multiplies integers. Divides integers. Applies the order of operations to correctly evaluate expressions involving integers Edition Page 43 of 51

44 Work sample 15 Number: Integers Determines the correct answer and explains their reasoning using appropriate mathematical terminology. Determines correct solutions to number sentences involving integers and including the order of operations. Determines the validity of a given statement, justifying their decision with an appropriate explanation and examples Edition Page 44 of 51

45 Work sample 16 Number: Percentages Year 8 Mathematics achievement standard The parts of the achievement standard targeted in the assessment task are highlighted. By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss. They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the effect of outliers on means and medians in that data. Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students determine complementary events and calculate the sum of probabilities. Summary of task Students were given a task to complete in class time after a unit of work on profit and loss Edition Page 45 of 51

46 Work sample 16 Number: Percentages Calculates required percentage. Solves simple profit and loss problems but with an error Edition Page 46 of 51

47 Work sample 16 Number: Percentages Calculates percentage profit and loss. Draws conclusions based on reason. Calculates and simplifies ratios and percentages, but with one error in interpretation Edition Page 47 of 51

48 Work sample 16 Number: Percentages Performs the required calculations Edition Page 48 of 51

49 Work sample 16 Number: Percentages A picture of a side table A picture of a side table A picture of a side table Reasons with explanations. Understands the difference between calculating correctly the solution in two stages and the method implied in the customer s comment Edition Page 49 of 51

50 Work sample 16 Number: Percentages Answers required questions to enable calculations Edition Page 50 of 51

51 Work sample 16 Number: Percentages Demonstrates logical reasoning. Selects items and calculates totals Edition Page 51 of 51

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