School Based Assessment (Sba)

GAUTENG DEPARTMENT OF EDUCATION

SCHOOL BASED ASSESSMENT (SBA)

MATHEMATICS

GRADE 11

2017

CONTENTS Page

1.  Introduction 3

2.  Informal or daily assessment 4

3.  Formal assessment 5

4.  Programme of assessment 6

5.  Moderation Form 7

6.  Assessment tasks 9

Test 1

Test 2

Test 3

Test 4

Assignment 1

Project

Investigation

1.  INTRODUCTION

Assessment is a continuous planned process of identifying, gathering and interpreting information about the performance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence of achievement; evaluating this evidence; recording the findings and using this information to understand and assist in the learner’s development to improve the process of learning and teaching. Assessment should be both informal (Assessment for Learning) and formal (Assessment of Learning). In both cases regular feedback should be provided to learners to enhance the learning experience.

Although assessment guidelines are included in the Annual Teaching Plan at the end of each term, the following general principles apply:

·  Tests and examinations are assessed using a marking memorandum.

·  Assignments are generally extended pieces of work completed at home.

Assignments can be collections of past examination questions, but should focus on the more demanding aspects as any resource material can be used, which is not the case when a task is done in class under strict supervision. At most one project or investigation and an assignment if this is the preferred option should be set in a year. The assessment criteria need to be clearly indicated on the project specification. The focus should be on the mathematics involved and not on duplicated pictures and regurgitation of facts from reference material. The collection and display of real data, followed by deductions that can be substantiated from the data, constitute good projects. A project, in the context of Mathematics, is an extended task where the learner is expected to select appropriate Mathematical content to solve a context-based problem.

Investigations are set to develop the skills of systematic investigation into special cases with a view to observing general trends, making conjectures and proving them. To avoid having to assess work which is copied without understanding, it is recommended that while the initial investigation can be done at home, the final write up should be done in class, under supervision, without access to any notes. Investigations are marked using rubrics which can be specific to the task, or generic, listing the number of marks awarded for each skill:

·  40% for communicating individual ideas and discoveries, assuming the reader has not come across the task before. The appropriate use of diagrams and tables will enhance the investigation.

·  35% for the effective consideration of special cases;

·  20% for generalising, making conjectures and proving or disproving these conjectures; and

·  5% for presentation: neatness and visual impact.

2.  INFORMAL OR DAILY ASSESSMENT

The aim of assessment for learning is to collect continually information on a learner’s achievement that can be used to improve individual learning. Informal assessment involves daily monitoring of a learner’s progress. This can be done through observations, discussions, practical demonstrations, learner-teacher conferences, informal classroom interactions, etc., Informal assessment may be as simple as stopping during the lesson to observe learners or to discuss with learners how learning is progressing. Informal assessment should be used to provide feedback to the learners and to inform planning for teaching, it need not be recorded. This should not be seen as separate from learning activities taking place in the classroom. Learners or teachers can evaluate these tasks. Self-assessment and peer assessment actively involve learners in assessment. Both are important as these allow learners to learn from and reflect on their own performance. Results of the informal daily assessment activities are not formally recorded, unless the teacher wishes to do so. The results of daily assessment tasks are not taken into account for promotion and/or certification purposes.

3.  FORMAL ASSESSMENT

All assessment tasks that make up a formal programme of assessment for the year are regarded as Formal Assessment. Formal assessment tasks are marked and formally recorded by the teacher for progress and certification purposes. All Formal Assessment tasks are subject to moderation for the purpose of quality assurance. Formal assessments provide teachers with a systematic way of evaluating how well learners are progressing in a grade and/or in a particular subject. Examples of formal assessments include tests, examinations, practical tasks, projects, oral presentations, demonstrations, performances, etc. Formal assessment tasks form part of a year-long formal Programme of Assessment in each grade and subject.

Formal assessment tasks in Mathematics include tests, a June examination, a trial examination (for Grade 12), a project or an investigation. The forms of assessment used should be age- and developmental- level appropriate. The design of these tasks should cover the content of the subject and include a variety of activities designed to achieve the objectives of the subject. Formal assessment tasks need to accommodate a range of cognitive levels and abilities of learners as indicated in the CAPS document.

4.  Programme of Assessment:

Learners are expected to have eight (8) formal assessment tasks for their school-based assessment, including end of year examinations. The weighting and number of tasks are listed below:

TERM / TASK / WEIGHT / DATE
Term 1 / Project or Investigation
Test / 20
10
Term 2 / Test or Assignment
Mid-year examination / 10
30
Term 3 / Test
Test / 10
10
Term 4 / Test / 10
School-based Assessment / 100
School-based Assessment mark
(as % of promotion mark) / 25%
End-of-year Examinations / 75%
Promotion mark / 100%

NB: The school programme of assessment should indicate specific dates when tasks are to be administered during the year. In the event that teachers are not able to abide by the set dates due to unforeseen circumstances, minimal deviations are permissible. Although the project/investigation is indicated in the first term, it could be scheduled in terms 2 or 3. Only ONE project/investigation should be set per year. Tests should be at least ONE hour long and count at least 50 marks.

ANNEXURE A

PRE-MODERATION OF SBA ACTIVITIES SET AT SCHOOL LEVEL

MATHEMATICS

DISTRICT
SUBJECT
GRADE
NAME OF SCHOOL
NAME OF EDUCATOR (S)
NAME OF HOD
NAME OF MODERATOR
NAME OF SUBJECT ADVISOR
DATE
MODERATION
FRONT PAGE / YES / NO / COMMENT
Name of school
Names of moderator and examiner
Time allocation
Total mark
Subject, e.g. Mathematics or Mathematical Literacy
Grade, e.g. Grade 10 or Grade 11 or Grade 12
Assessment activity, e.g. Assignment or Investigation or Project
Date, e.g. June 2017
Are the instructions to candidates clearly specified and unambiguous?
REST OF THE ACTIVITY / YES / NO / COMMENTS
All pages numbered
Mark totals indicated correctly per subsections
Mark totals indicated correctly per question
Correlation between mark allocation, level of difficulty and time allocation
Is “please turn over” indicated?
Is the assessment activity complete with grid, memorandum, and diagram sheets?
LAYOUT OF THE ACTIVITY / YES / NO / COMMENTS
Is the appearance and typing consistent? e.g. font type and size
Are sketches clear?
Are sketches labelled and/or numbered?
STANDARD OF ASSESSMENT TASK / YES / NO / COMMENTS
Does the task correspond with the programme of assessment?
Is there a verbatim reproduction of questions from previous SBA activities?
Are questions ordered from easy to difficult, e.g. Level 1 to Level 4 (different cognitive levels)?
Are the subsections grouped by topics?
Are questions concise and to the point (not ambiguous)?
Are the assessment standards appropriately linked and integrated?
Are the questions compliant with CAPS?
Is the mark allocation/weighting for the task in accordance with CAPS?
ASSESSMENT TOOLS / YES / NO / COMMENTS
Are the assessment tools e.g. rubric, memoranda, checklists, etc. for the assessment task included?
Are the tools on standard?
AREAS OF GOOD PRACTICE
CHALLENGES
RECOMMENDATIONS/FOLLOW-UP
YES / NO
The SBA activity is approved.
The SBA activity is provisionally approved and requires some adjustments.
The SBA activity is not approved and must be resubmitted on the following date:

______

EDUCATOR SIGNATURE DATE

______

HOD/ SUBJECT HEAD SIGNATURE DATE

(MODERATOR)

______

DISTRICT FACILITATOR SIGNATURE DATE

ASSESSMENT TASKS

TEST 1

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.  This question paper consists of 3 questions.

2.  Answer ALL the questions.

3.  Number the answers correctly according to the numbering system used in this question paper.

4.  Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers.

5.  Answers only will not necessarily be awarded full marks.

6.  You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.

7.  If necessary, round off answers to TWO decimal places, unless stated otherwise.

8.  Diagrams are NOT necessary drawn to scale.

9.  Write neatly and legibly.

QUESTION 1

1.1  Solve for

1.1.1 (4)

1.1.2 (5)

1.1.3 (4)

1.2 Solve simultaneously for and in the following set of equations:

(5)

1.3  For which value(s) of will the expression be non-real? (3)

1.4 Simplify, without the use of a calculator:

(4)

[25]

QUESTION 2

The sequence 4; 9; 37; . . . is a quadratic sequence.

2.1 Calculate (3)

2.2 Hence, or otherwise, determine the term of the sequence. (4)

[7]

QUESTION 3

In the diagram, the points P (-3; 5), S (1; -2), Q (5; 1) and R (5; 6) are given.

M is the midpoint of RS.

3.1 Calculate the gradient on PQ. (3)

3.2 Determine the equation of the line RS in the form (4)

3.3 Calculate the length of PQ (leave answer in surd form). (3)

3.4 Calculate the coordinates of M, the midpoint of RS. (3)

3.5 What relationship is there between the line segments PQ and RS? (2)

Give a reason for your answer.

3.6 Prove that PSQR is a Kite? Motivate your answer. (3) [18]

TOTAL [50]

TOETS 1

INFORMASIE en INSTRUKSIES

Lees die volgende instruksie deeglik voordat jy die vrae beantwoord.

10.  Hierdie vraestel bestaan uit 3 vrae.

11.  Beantwoord ALLE vrae.

12.  Nommer alle antwoorde korrek en volgens die nommering gebruik in die vraestel

13.  Toon alle berekenings, diagramme, grafieke, ens. wat jy gebruik het om die vrae te beantwoord.

14.  Slegs ʼn antwoord sal nie noodwendig volpunte toegeken word nie.

15.  Jy mag slegs gebruik maak van ʼn goedgekeurde wetenskaplike sakrekenaar (nie-programmeerbaar en nie-grafies), tensy anders vermeld.

16.  Rond af tot TWEE desimale plekke indien nodig, tensy anders vermeld.

17.  Diagramme is nie noodwendig op skaal geskets nie.

18.  Skryf netjies en lessbaar.

VRAAG 1

1.2  Los op vir

1.1.1 (4)

1.1.2 (5)

1.1.3 (4)

1.2 Los x en y in die volgende gelyktydige vergelykings:

(5)

1.4  Vir watter waarde(s) van sal die volgende uitdrukking nie-reëel wees?

(3)

1.4 Vereenvoudig, sonder die gebruik van ʼn sakrekenaar:

(4)

[25]

VRAAG 2

Die ry 4; 9; 37; . . . is ʼn kwadratiese ry.

2.1 Bereken (3)

2.2 Vervolgens, of andersins, bepaal die term van ry. (4)

[7]

VRAAG 3

In die diagram, is die punte P (-3; 5), S (1; -2), Q (5; 1) en R (5; 6) gegee.

M is die middelpunt van RS.

3.1 Bereken die gradient/ helling van PQ. (3)

3.2 Bepaal die vergelyking van die lyn RS in die vorm (4)

3.3 Bereken die lengte van PQ (laat jou antwoord in wortelvorm). (3)

3.4 Bereken die koördinate van M, die middelpunt van RS. (3)

3.5 Wat is die verwantskap tussen die lynsegment PQ en RS? (2)

Gee ʼn rede vir jou antwoord.

3.6 Bewys dat die figuur PSQR ʼn Vlieër is. Motiveer jou antwoord. (3) [18]

TOTAAL [50]

TEST 1 MEMORANDUM

QUESTION 1

1.1.1 /

or / √ standard form
√ factors
√√ answers
(4)
1.1.2 /
or / √ standard form
√ substitution into formula
√ 265
√√ answers
(5)
1.1.3 /
CV: or
or / √ standard form
√ critical values
√√ answers
(4)
1.2 / Substitute in

or
or
OR


or
or / √ substitution
√ standard form
√ factors
√ both value
√ both value
(5)
√ substitution
√ standard form
√ factors
√ both values
√ both values
(5)
1.3 / will be non-real if:

However, the expression will be undefined if . Therefore, the expression will be non-real if where
/ √ non-real if
√
√
(3)
1.4 / / √
√
√ applying exponential laws
√ answer
(4)
[25]

QUESTION 2

2.1 / 4 9 37
5

First difference: 5;
Second difference:



OR




OR



/ √ first differences

√ second difference
√ answer
(3)
√ equating
√ manipulation
√ answer
(3)
√ first differences

√ equating
√ answer
(3)
3.2 / 4 9 20 37

5 11 17
6 6







/ √
√
√
√
(4)
[7]

QUESTION 3

3.1 / / √ gradient formula
√ substitution in gradient formula
√ answer
(3)
3.2 /
= 2

/ √ substitution in gradient formula
√
√ substituting gradient and R(5;6) or S(1;-2)
√ equation in correct form
(4)
3.3 /
=
=
= or 4 / √ formula
√ substitution
√ answer (3)
3.4 / /
√ correct formula
√ substitution in mid-point formula
√ answer
(3)
3.5 /
Thus PQ RS / √ PQ RS
√
(2)
3.6 / The diagonal PQ bisects diagonal RS at
NOTE: For adjacent sides are equal this must be shown by calculations that
PS=PR= √ and SQ=QR=5√ / √ Length PS and PR
√ PQ bisects RS
√
(3)
[18]

TEST TERM 3