Exemplar for Internal Assessment Resource Mathematics and Statistics Level 1. Resource title: Taxi Charges

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1 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Exemplar for Internal Assessment Resource Mathematics and Statistics Level 1 Resource title: Taxi Charges This exemplar supports assessment against: Achievement Standard Apply Linear Algebra in Solving Problems Grade boundary specific exemplar The exemplar has been developed from student material specific to an A or B assessment resource. Date version published by Ministry of Education December 2010 To support internal assessment from 2011 Crown 2010

2 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Grade Boundary: Low Excellence 1. The student has demonstrated extended abstract thinking which is the requirement for Excellence. In terms of correct mathematical statements dollar signs are missing from the initial costs and the use of up to is not completely accurate. However all aspects of the problem have been solved and mathematical insight is communicated with the formation, graphical presentation and discussion related to the cheaper pricing options for Fred. With the final $30 charge for distances over 60km the student has recognised the possibility of additional charges for distances over 60km for the Flatrate Company. Crown 2010

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5 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Grade Boundary: High Merit 2. The student has met the requirements for Merit because relational thinking has been demonstrated and communicated. Communicating thinking using appropriate mathematical statements is evident in the calculated costs for the chosen destinations for the three companies and the conclusion relating to the best company. 3. The models for Fred and P&G have been used to find the range of distances where P&G is cheaper but the up to 19km is not accurate. 4. The student has not demonstrated extended abstract thinking, which is the requirement for Excellence, because option 1 is not the cheapest for distances between 0 and 3.3km and option 2 is not the cheapest between 30 and 38km. More in the way of communication of why the options are cheaper is needed Crown 2010

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8 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Grade Boundary: Low Merit 5. There is evidence of relational thinking in the use of the models to find the costs for the city centre and the conclusion relating to the cheapest company. The price difference of $1 for the best company is incorrect and charges for at least two destinations are expected. It is for these reasons the appropriate classification is low Merit. 6. The models for Fred and P&G have been used to find the range of distances where P&G is cheaper and this demonstrates the quality of relational thinking which is expected for Merit Crown 2010

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11 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Grade Boundary: High Achieved. 7. Correctly forms a linear model. 8. Linear models are graphed. 9. Use of simultaneous equations is implied with the 20km distance. 10. Achieved has been met because a range (at least three) of methods has been demonstrated with forming a linear model, graphing, and using simultaneous equations. 11. Merit has not been met because evidence of relational thinking is missing from the recommendations relating to which company to use for journeys to the city centre and Bethlehem. The student would need to show how the models were used to make the recommendation Crown 2010

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14 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Grade Boundary: Low Achieved 12. Correctly forms a linear model. 13. Correctly uses formulae. 14. Linear models graphed. 15. Achieved has been met because a range (at least three) of methods has been demonstrated with forming a linear model, using formulae, and the graph. The graph and point of intersection lack sufficient accuracy to be used as evidence for relational thinking which is the requirement for Merit Crown 2010

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17 Exemplar for internal assessment resource Mathematics and Statistics 1.4A for Achievement Standard Grade Boundary: High Not Achieved 16. Correctly forms a linear model. 17. Correctly uses formulae. 18. The student graphs showing the charges for the different companies for the three destinations are not graphs of a linear model. 19. Applying linear algebra requires using a range of methods for Achieved and Explanatory Note 4 (EN4) of the standard indicates that a range of methods is at least three different methods. The student is Not Achieved because there is evidence of the use of only two methods. Crown 2010

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