END OF PRIMARY BENCHMARK MATHEMATICS 2012

END OF PRIMARY BENCHMARK MATHEMATICS

2012an analysis

The End of Primary Benchmark Mathematics 2012

Mental Paper Written Paper• 80% of the global mark• 1 hour 15 minutes long• 16 questions:

▫ 4 questions – 4 marks each▫ 8 questions – 5 marks each▫ 4 questions – 6 marks each

• questions cover all the four strands of the Mathematics Syllabus (Number and Algebra, Measures, Shape and Space, Data Handling and Problem Solving)

• 20% of the global mark• 15 minutes long• 20 short questions read

twice in succession by the class teacher

• questions are read out in English exactly as written (adherence to set intervals)

• code-switching is permitted only for giving out instructions

Global Mark – 100 marks

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Developing a strong number sense is a general goal for Mathematics at Primary Level, thus in both papers, the candidates had the opportunity to apply any strategies, methods or procedures which they were comfortable with to answer questions.

•Question 1

The Written paper also gave credit to those students who were able to reason mathematically and to solve routine problems, non routine problems and puzzles within the parametres of the syllabus.

•Question 16

Questions in both the Mental and the Written papers also assessed understanding of mathematical vocabulary. Mathematical vocabulary plays an integral role in the understanding and learning of mathematics at Secondary Level.

•Question 3

End of Primary Benchmark Mathematics 2012

As in normal practice, the examiners used a specification grid in order to ensure: the validity and reliability of the

paper; that all the questions in the paper

formed part of the mathematics syllabus;

that the questions covered as wide a cross-section of the year 6 syllabus as possible.


The Mathematics paper was graded and the level of difficulty of the questions catered for a wide range of abilities.


The choice of pictures and diagrams and the use of the words in questions was considered carefully in the planning and designing phase of both papers. The aim of these papers was to assess mathematical, not linguistic skills and abilities or other.

Common Difficulties in Mental Paper

• Rounding to the nearest hundred. (Q. 7)

• Choosing the fraction with largest denominator as the largest fraction. (Q. 15)

• Confusing clockwise with anticlockwise. (Q. 19)

• Working out the area of a square of sides 6cm. (Q. 14)

• Multiplying exactly (11 x 19) instead of giving an estimate. (Q. 16)

Common Difficulties

The most common mistake was noted in Question (1 c) where candidates gave the answer of 490 instead of 4900 for 70 x 70.

An error frequently occured in part (1 d) where many candidates gave 6•53 for an answer instead of 653.

Common Difficulties

l

Unfortunately a few other candidates ticked more than one box (measure).

The length of the pencil was read as 10•4cm or 10•8cm instead of 14cm by some candidates.

Quite a Positive Response

Common Difficulties

A substantial number of candidates did not give the answer in Question (4 b) in its simplest form.Converting a fraction into a percentage seemed to be the main difficulty and the most common answers given were 10% and 25% . The lack of working shown was also noted by the markers.

Common Difficulties

Question (5 aii) proved to be the hardest part of this question. Most common mistake was stating that 42 × 18 is equal to 42 × 10 × 8.

In Question (5) some candidates found it difficult to explain what 1/3 of 27 = 9 means and wrote down confusing explanations or incorrect expressions such as 3 ÷ 27. However a significant number of candidates gave a very good explanation of the statement given and a few even presented a situation (a story sum) to explain the statement.

Common DifficultiesSome candidates ignored the ‘Use all the digits in each question only once’ and gave answers like 52/10= 5.2 in Question (6 b). In Question (6 c) most candidates placed 6 and 7 in the correct place value, that representing the tens, however many gave 73 × 62 as an answer and did not actually work it out to check whether it really gave the largest possible answer.



Common Difficulties

Wrong answers were given mainly due to errors in converting the weights of the books to the same unit before calculating the total weight.

A good number of candidates equated 1030g to 1 kg 30 g.

Some candidates encountered difficulty in converting 4 ¾ kg to 4kg 750 g or to 4750g.


Candidates performed well especially in parts (a) and (b). Some candidates encountered difficulty in obtaining the rule for the sequence.

Common Difficulties

The most common mistake in this question was made in part (a) in working out the cost of 1 book.

Most of the candidates understood that they had to divide €15 by 6. However, since 15 divided by 6 leaves 3 as a remainder, common answers in part (a) was €2•30 and €2•03.


In part (a) many candidates drew the correct triangles, however some did not place the vertices of the triangles on the dots provided and other candidates did not use a ruler to draw the triangles.


Common Difficulties

In Question (12 a) many candidates attempted to work out 22 × 15 for the area but failed to obtain the correct answer for the product.

Other candidates worked out the Perimeter instead of the area.

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While most candidates obtained the value for the area of the black square, many failed to work out the Area of the net of the cube.

Working out the area of the remaining cardboard proved to be the most challenging part of this question. It was also noted here that a substantial number of students did not show any working in the question.

Quite a Positive Response Common Difficulties

The most challenging part in this question was definitely part (d). In fact only a few answered this part correctly.

Knowing a procedure does not necessarily mean knowing a concept.

Quite a Positive Response Common Difficulties

Difficulty in giving a reason to justify answer.

Most errors occured in the conversion of millilitres to litres or vice versa. Candidates working out their calculations in millilitres either got mixed up in the number of zeros obtained in the multiplication or did not convert their answer to litres correctly.

Common Difficulties

The most common error in Question (15 a) occured in the position of the hour hand. A significant number of candidates placed the hour hand of the clock pointing to the number nine.

A good number of candidates converted the 165 minutes in Question (15 c) to 2 h 45 min. However, converting 165 minutes to 1 hr 65 minutes was also common. Also some candidates interpreted the scale in the timeline as having 25 minute intervals rather than 15 minute intervals.

In the final part of Question 15, quite a few candidates did not take notice of the p.m. in the answer box and gave their answer in 24 hour clock format.

Although this was a challenging question, a considerable number of candidates obtained the correct value for A, B and C. Trial and error was the most common approach. There were many positive attempts to a solution in general. Most trials involved multiples of ten, but some used different values for B when substituting in A + B = 90 and B + C = 60. Some candidates used the elimination to find C, then A.


Implications for Teaching and LearningMathematics is greatly facilitated if students are engaged in purposeful experiences with concrete objects and number patterns. We should make sure that the mathematics we ask students to learn is connected in meaningful ways to their experiences: bridging school and out of school mathematics practices.

In this situation, the funds of knowledge of each student would become an integral aspect of the mathematics lesson. Inherent in this approach to pedagogy is the decentering of the source of knowledge from only the teacher or textbook to include student knowledge and skills.

Implication for Teaching and LearningClassroom activities should be rich and aimed towards building the confident aptitude required for approaching mathematical problems especially non routine ones, in a successful way.

Students should be guided to adopt the problem solving strategies they feel comfortable with and understand that there is not only one correct way to solve a problem and that a mathematical problem does not always necessarily has only one right answer.

Students should not be confronted with just routine problems which require only basic operations and calculations.

Implication for Teaching and LearningStudents need plenty of opportunity to engage in mental mathematics and estimation activities. Such opportunities should be provided daily.

Mental mathematics and estimation further enables students to judge the reasonableness of answers and to quickly recall basic number facts.

Undoubtely such opportunities will further enable students to be more efficient problem solvers. Frequent use of estimation and mental computation are also important ingredients in the development of a strong number sense.

Implication for Teaching and LearningOpportunities should be given for communication even in the mathematics lesson.

Discussion of their own invented strategies for problem solutions helps students strengthen their intuitive understanding of numbers and the relationships between numbers.

Such opportunities will in time help students feel more confident when they are faced with the demand to justify their answer in writing or orally.

Implication for Teaching and LearningStudents should be further encouraged to show the steps towards a solution in a complete and clear way which can be understood by anyone else who reads it.

Introduction to new technical mathematical terms should be done through suitable contexts and with the aid of relevant real objects, mathematical apparatus, pictures and/or diagrams, rather than through the use of everyday language.

Implication for Teaching and LearningUsing a timeline is recommended and may very often help students to solve problems related to time.

Of equal importance is asking the students to read the time using the classroom clock and to work out simple problems related to time throughout the whole school day (not necessarily in the Mathematics lesson).

Implication for Teaching and LearningStudents need more opportunities to construct and assimilate certain knowledge facts such as the multiplication tables. It is important that students understand and memorise the multiplcation tables. Also through the use of manipulatives and other activities, a student needs to understand what multiplication is - the grouping of sets, repeated addition, a faster way of adding.

Implication for Teaching and LearningConversions from one unit to another, say kilograms to grams, litre to millilitres, or kilometres to metres are also important knowledge facts which need to be stressed out mainly through a variety of opportunities, both on paper and hands on.

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END OF PRIMARY BENCHMARK MATHEMATICS 2012