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END OF PRIMARY BENCHMARK MATHEMATICS 2012

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END OF PRIMARY BENCHMARK MATHEMATICS 2012

an analysis

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

- Question 1

Developing a strongnumber sense is a generalgoal forMathematics at Primary Level, thusin both papers, the candidates had the opportunity to apply any strategies, methodsor procedures which they were comfortable with to answer questions.

- Question 16

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 3

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

- 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.

- 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)
- Workingout the area of a square of sides 6cm.(Q. 14)
- Multiplying exactly (11 x 19) instead of giving an estimate. (Q. 16)

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

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

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

l

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

Quite a Positive Response

Common Difficulties

Asubstantial 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

In Question (5) some candidates found it difficult to explain what 1/3of 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.

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.

Common Difficulties

Somecandidates 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.

Quite a Positive Response

Quite a Positive Response

Common Difficulties

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.

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

Quite a Positive Response

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 3as a remainder, common answers in part (a) was €2•30 and €2•03.

Quite a Positive Response

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.

Quite a Positive Response

Common Difficulties

000000

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.

While most candidates obtained the value for the area of the black square, many failed to work out the Areaof 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

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.

Difficulty in giving a reason to justify answer.

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.

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.

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 minuteintervals rather than 15 minute intervals.

Quite a Positive Response

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.

Mathematics is greatly facilitated if students are engaged in purposeful experiences with concrete objects and number patterns. Weshould make sure that the mathematics weask students to learn is connected in meaningfulways 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.

Classroom 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.

Students 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.

Undoubtelysuch 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.

Opportunities 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 facedwith the demand to justify their answer in writing or orally.

Students 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.

Using 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 relatedto time throughout the whole school day (not necessarily in the Mathematics lesson).

Students 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.

Conversions 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.