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ASSESSING MATHS LITERACY IN GRADE 11 Jackie Scheiber

RADMASTE Centre, Wits University jackie.scheiber@wits.ac.za

Mathematical Literacy was introduced in Grade 10 in 2006. In 2007 teachers will have to assess Grade 11 Maths Literacy learners for the first time. During this workshop participants will • Answer a typical Grade 11 Maths Literacy question • Study the requirements for the Grade 11 Maths Literacy examination as listed in

the Subject Assessment Guidelines MATHEMATICAL LITERACY (January 2007).

• Study the Description of the Levels in the Mathematical Literacy Assessment Taxonomy

• Analyse the Maths Literacy question in terms of the requirements and the taxonomy

• Study the Assessment Frameworks for Papers 1 and 2 and complete a similar framework for the given question.

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A TYPICAL GRADE 11 MATHS LITERACY QUESTION QUESTION 1 Mrs Phumzile owns a taxi business. The table below shows a list of Mrs Phumzile's income and expenditure for her business, for the month of February 2007.

INCOME EXPENDITUREPetrol R 1 065,70 Washing of taxi R 60,00 Servicing of taxi ( oil change, spark plugs et cetera)

R 546,09

Fares paid by taxi commuters R7 842,00 Insurance for the taxi (in case of an accident) R 305, 45 Taxi-driver salary R 3 500,00 Taxi association fee R 200,00

1.1 Determine, for February 2007:

1.1.1 The total income 1.1.2 The total expenditure

(1) (2)

1.2 Did Mrs Phumzile’s taxi business make a profit or a loss for the month

of February? (1) 1.3 Calculate the profit or loss for this month (2) 1.4 Hence determine the profit margin for the month

Use the formula: Profit Margin = −Income ExpensesExpenses

× 100% (3) 1.5 Mandla works as a taxi driver for Mrs Phumzile. His basic salary is

R35,00 per hour. On Monday 18 February he worked from 06:00 to 15:30 and had 1 hour off for lunch. 1.5.1 How many hours did he work on that day? 1.5.2 How much money did he earn on that day?

(2) (2)

Mrs Phumzile asks Mandla to transport passengers to a wedding 170 km away. Mandla drives the taxi at an average speed of 90 km/h. How many hours will the journey take? (Use the formula: Distance = Speed x Time to calculate your answer.) Write your answer correct to two decimal places. (4)

[17]

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The requirements for the grade 11 mathematics literacy examination as listed in the subject assessment guidelines mathematical literacy (January 2007). According to the Subject Assessment Guidelines, the following the time allocations and number of papers is recommended for the final examinations for Grades 10, 11 and 12: GRADE 10 – one 3-hour paper of 150 marks GRADE 11 – two 2 ½ hour papers of 100 marks each GRADE 12 – two 3-hour papers of 150 marks According to the Subject Assessment Guidelines, an examination should • Give equal weighting to the four Learning Outcomes and should attempt to

examine all of the Assessment Standards determined for the grade • Consist of questions which all focus on a context • Consist of questions which integrate Assessment Standards from more than one

Learning Outcome • Be differentiated according to the Mathematics Literacy taxonomy with the

following proportion of marks allocated to each of the levels: o 30% of the marks at the knowing level o 30% of the marks at the applying routine procedures in a variety of contexts level o 20% of the marks at the applying multi-step procedures in a variety of contexts

level o 20% of the marks at the reasoning and reflecting level.

TABLE 1 – REQUIREMENTS FOR GRADE 11 LEVEL 1

(30%) Knowing

LEVEL 2 (30%) Applying routine procedures in familiar contexts

LEVEL 3 (20%) Applying multi-step procedures in a variety of contexts

LEVEL 4 (20%) Reasoning and reflecting

LO1 25%

PAPER 1 (2 ½ hours - 100 marks)

Paper 2 (2 ½ hours – 100 marks)

LO2 25%

Paper 1 is intended to be a basic knowing and routine application paper

Paper 2 is intended to be an applications and reasoning and reflecting paper

LO3 25%

Consists of between 5 and 8 shorter questions

Consists of between 4 and 6 longer questions. These questions will require more

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interpretation and application of the information provided

Questions focus on a context

Questions focus on a context LO4

25% 60% on Level 1 and 40% on Level 2

20% on Level 2, 40% on Level 3 and 40% on Level 4

TABLE 2 – DESCRIPTION OF THE LEVELS IN THE MATHEMATICAL LITERACY ASSESSMENT TAXONOMY

LEVEL 1 (30%) LEVEL 2 (30%) LEVEL 3 (20%) LEVEL 4 (20%) Knowing Applying Routine

Procedures In Familiar Contexts

Applying multi-step procedures in a

variety of contexts

Reasoning and reflecting

• Calculate using the basic operations, including:

-Algorithms for +, –, x and ÷ -Appropriate rounding of numbers - Estimation - Calculating a percentage of a given amount - measurement

• Know and use appropriate vocabulary such as equation, formula, bar graph, pie chart, Cartesian plane, table of values, mean, median and mode • Know and use

formulae such as the area of a

c) Performs well-known procedures in familiar contexts. All the information required to solve the problem is immediately available to the student d) Solves equations by means of trial and error or algebraic processes e) Draw data graphs for provided data f) Draw algebraic graphs for given equationsg) Measure dimensions (e.g. length, weight and time) using appropriate

h) Solve problems using well-known procedures. This required procedure is, however, not immediately obvious from the way the problem is posed. Learners will have to decide on the most appropriate procedure to solve the solution to the question and may have to perform one or more preliminary calculations before determining a solution

i) Select the most appropriate

k) Pose and answer questions about what mathematics they require to solve a problem and then to select and use that mathematical content. k) Interpret the

solution they determine to a problem in the context of the problem and where necessary to adjust the mathematical solution to make sense in the context

l) Critique solutions to problems and statements about situations made by others

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rectangle, a triangle and a circle where each of the required dimensions is readily available

Read information directly from a table (e.g. the time a particular bus departs from the terminal)

measuring instruments sensitive to levels of accuracy

data from options in a table of values to solve a problem

j) Decide on the best way to represent data to create a particular impression

m) Generalize patterns observed in situations, make predictions based on these patterns and/or other evidence and determine conditions that will lead to desired outcomes

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TABLE 3 – EXAMPLE OF AN ASSESSMENT FRAMEWORK FOR PAPER 1

Learning Outcomes

Taxonomy Level Q Context

detail Item LO 1

LO 2

LO 3

LO 4 L1 60% L2 40%

Sub-total Total

1.1.1 1 1 1 1.1.2 2 2 2 1,2 1 1 1 1,3 2 2 2 1,4 3 3 3 1.5.1 2 2 2 1.5.2 2 2 2

1 Buying a cell phone

1,6 4 4 4

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2.1.1a 2 2 2 2.1.1b 2 2 2 2.1.2 4 2 2 4 2.1.3 2 2 2 2.1.4 2 2 2 2.1.5 4 2 2 4 2.1.6 2 2 2 2.1.7a 2 2 2 2.1.7b 3 3 3 2.2.1 1 1 1 2.2.2 1 1 1 2.2.3a 1 1 1 2.2.3b 1 1 1 2.2.3c 1 1 1

2 Building a house

2.2.4 1 1 1

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3.1.1a 1 1 1 3.1.1b 1 1 1 3.1.2a 1 1 1 3.1.2b 2 1 1 2 3,2 1 1 1 3,3 2 1 3 3 3,4 2 2 2 3.5.1 5 5 5 3.5.2 1 1 1

3 Buying a new car

3.5.3 4 3 1 4

21

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4.1.1 1 1 1 4.1.2 2 2 2 4.1.3 3 2 1 3 4.1.4 2 2 2 4.1.5 2 1 1 2 4.2.1a 3 3 3 4.2.1b 2 1 1 2 4.2.2 5 3 2 5 4.3.1 2 2 2

4 Global warming

4.3.2 3 3 3

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5.1.1 2 2 2 5.1.2 1 1 1 5.1.3 2 2 2

5 Consumer Price Index

5,2 3 2 1 3

8

22 29 26 23 56 44 100 100

TABLE 4 – EXAMPLE OF AN ASSESSMENT FRAMEWORK FOR PAPER 2

Learning Outcomes

Taxonomy Level Q Context

detail Item LO 1

LO 2

LO 3

LO 4

L2 20%

L3 40%

L4 40%

Sub-tot Total

1.1.1 1 1 1 1.1.2 1 1 1 1.2.1a 2 2 2 1.2.1b 2 2 2 1.2.1c 4 4 4 1.2.1d 5 5 5 1.2.1e 2 2 2 1.2.2 3 3 3 1.2.3 4 4 4 1.3.1 4 4 4 1.3.2a 2 1 1 2 1.3.2b 2 1 1 2 1.3.3 2 2 2 1.4.1 3 3 3 1.4.2 2 2 2 1.4.3a 2 2 2 1.4.3b 2 2 2

1 Buying a washing machine

1,5 3 1 2 3

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2 Plan of 2.1.2 1 1 1 22

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2.1.2 3 3 3 2.1.3 2 2 2 2.2.1 3 3 3 2.2.2 4 2 2 4 2.3.1 1 1 1 2.3.2 5 5 5 2.3.3a 1 1 1

the school building

2.3.3b 2 2 2 3,1 2 2 2 3,2 2 2 4 4 3.3.1 4 1 5 5 3.3.2a 2 2 2 3.3.2b 2 2 2 3.3.3a 2 2 2 3.3.3b 2 2 2

3 Global warming

3.3.4 2 2 2

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4,1 2 2 2 4,2 3 3 3 4.3.1 2 2 2 4 Crime

Statistics 4.3.2 4 4 4

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27 21 30 22 22 39 39 100 100