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WS06 - Reclaim the void

Mathematics, Year 8

By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students solve problems involving the 4 operations with integers and positive rational numbers. They use mathematical modelling to solve practical problems involving ratios, percentages and rates in measurement and financial contexts. Students apply algebraic properties to rearrange, expand and factorise linear expressions. They graph linear relations and solve linear equations with rational solutions and one-variable inequalities, graphically and algebraically. Students use mathematical modelling to solve problems using linear relations, interpreting and reviewing the model in context. They make and test conjectures involving linear relations using digital tools. 

 

Students use appropriate metric units when solving measurement problems involving the perimeter and area of composite shapes, and volume of right prisms. They use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angle triangles. Students use formulas to solve problems involving the area and circumference of circles. They solve problems of duration involving 12- and 24-hour cycles across multiple time zones. Students use 3 dimensions to locate and describe position. They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity. Students apply the properties of quadrilaterals to solve problems.    

 

They conduct statistical investigations and explain the implications of obtaining data through sampling. Students analyse and describe the distribution of data. They compare the variation in distributions of random samples of the same and different size from a given population with respect to shape, measures of central tendency and range. Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems. They conduct experiments and simulations using digital tools to determine related probabilities of compound events.

Number

AC9M8N04

use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate

Measurement

AC9M8M01

solve problems involving the area and perimeter of irregular and composite shapes using appropriate units

Measurement

AC9M8M03

solve problems involving the circumference and area of a circle using formulas and appropriate units

Measurement

AC9M8M05

recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure

Measurement

AC9M8M07

use mathematical modelling to solve practical problems involving ratios and rates, including financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

Disclaimer: This artefact is an authentic sample of student work and contains some calculation errors and other inaccuracies, The annotations indicate how the student has demonstrated evidence of the achievement standard.

Annotations

 

1. Provides an overview of the situation to be modelled, including context and a proposed plan for solving the problem.

2.  Formulates the problem by identifying the components that need to be considered to provide a solution to the problem.

3. Identifies the measurements needed to establish how much fabric is required to make a rug.

 

4. Explains how the use of a digital tool will help to determine the area of the mines.

5. Identifies and displays the measurements involved in determining the area of composite shapes and circles.

6. Uses an appropriate method to calculate the areas of composite shapes.

7. Formulates and calculates the size (area) of each of the circular rugs and the amount of fabric used to make the rugs.

8. Uses a visual to communicate the difference between rug A and rug B as referenced further in the report.

9. Uses a digital tool to estimate key measurements of the mine site, explaining how limitations of the tool were addressed.

10. Establishes the scale on the digital map by calculating a ratio using actual measurements of the mine and corresponding measurements of distance on the map.

11. Uses the shape of trapeziums to approximate sections of the mine area.

12. Applies the scale factor to the measurements for each side when calculating area.

13. Reviews and compares the methods used for calculating the area of the mines and discusses the appropriateness of each method.

 

14. Explains the method and assumptions for calculating the number of rugs needed to cover the mine holes.

15. Uses an appropriate conversion factor to express the areas of the mine and the rugs with the same area units (square metres).

 

16. Uses previous results of relevant calculations to determine the number of rugs required to cover each mine area.

17. Identifies an appropriate level of accuracy based on the context of the situation.

18. Summarises previous results of calculations and describes how these results will be used to determine the amount of fabric required to make enough rugs to cover the mine sites.

19. Uses ratio calculations and appropriate metric area conversions to determine the amount of fabric required to make rugs to cover the area of one of the mine sites.

20. Uses time spent making one rug to establish a rate and explains the process for determining the total amount of time expressed in days.

21. Explains how a time conversion to 5.5 hours was used to assist in calculations and refers to days as an appropriate time unit when communicating a solution in terms of the situation.

22. Describes the process used to determine the most accurate method to measure the mass of each rug. 

23. Applies ratios and appropriate metric conversions to determine the mass of fabric that would be used to make all of the rugs. 

24. Provides a summary of findings for questions that were considered to contribute to a solution to the problem.

25. Provides a concluding statement about the findings of the modelling task.

26. Considers the results and proposes increasing the number of people involved.