Internationella Engelska Gymnasiet Södermalm Math ... - IEGSmath

Internationella Engelska Gymnasiet Södermalm
Math Department Handbook
2012–2013
Version: 0.8.3
Friday 17 th May, 2013

Contents
I Assessment 3
1 Course Grading 4
1.1 How final grades are awarded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.1 Distribution of summative assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Assessment and grades – Skolverket [Tur13, 13] . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Test Design 6
2.1 Cover Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Student assessment policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Test design procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 National Tests 8
3.1 National tests and support for assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.1 The aim of the national tests is primarily to . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.2 The national tests also contribute to . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Invigilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.1 Invigilation FAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.2 Invigilation Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.3 Circulation of the Swedish version of the national test . . . . . . . . . . . . . . . . . . 10
3.2.4 Distribution of extra paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.5 Collection of tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.6 Calculators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Previous National Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.1 Math 1b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.2 Math 1c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.3 Math 2b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.4 Math 2c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.5 Math 3b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3.6 Math 3c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 Formula Sheets: National Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5 Frequently Asked Questions: National Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Special Examinations 15
4.1 Deadlines: special examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Procedure: special examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
II Math Support & Resources 16
5 Math Help 17
5.1 Math support times & locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.2 Matte Centrum - Free Math help beyond us . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1

III References 18
IV Appendix/Appendix 20
A GY2011 Local Knowledge Requirement Summaries 21
B GY2011- Knowledge Requirements 22
2

Part I
Assessment
3

1. Course Grading
Our department strives to ensure that all students are graded in a holistic, fair and equal manner. Our department
assessment procedures are based based on Skolverket’s Curriculum for the Upper Secondary School
[Tur13] and Upper Secondary School 2011 [Sko12].
Before setting a final course grade, the teacher will make use of all available information on a student’s knowledge
in relation to the national knowledge requirements of the course 1 , account for such knowledge that the
student has acquired outside the course and comprehensively evaluate each student knowledge outside the
national knowledge requirements.
We have developed a means of assessing students on the knowledge requirements locally, which aims to
1. be easy for students, parents, and teachers to understand,
2. align our local results with the national test results and
3. collect flexible, consistent and transparent results for each course.
1.1 How final grades are awarded
Ultimately, a decision needs to be taken by the teacher when setting a student’s final course grade, which
needs to be set based on evidence provided by summative assessment and at the same time be done in a
holistic context.
Our grading system is a framework for collecting evidence of each student’s attainment of knowledge requirements
over the course’s core content. It’s meant to give teachers of the same course a common overview of
each student’s summative assessment performance in addition to a calculated suggested final course grade.
A teacher can choose to override the suggested course grade if there are grounds to justify the decision.
1.1.1 Distribution of summative assessments
There are four major summative assessments for each GY2011 course and each contributing approximately
25% towards the students suggested final grade. The distribution of weight for each summative assessment
has been chosen to emphasise equality of assessment throughout the course.
• National test common for all students taking
the same course and helps to provide calibration
at the national level.
• Test 1 and Test 2 designed by all teachers
teaching the course concurrently, common for
all students taking the same course and helps
to provide calibration at the local level.
• In Class the number and type of assessment
will vary from teacher to to teacher. Allows the
teacher to use alternative forms of summative
assessment that reflect either the interest of the
teacher or the students of the group.
1 including the student’s national test result
4

1.2 Assessment and grades – Skolverket [Tur13, 13]
1.2.1 Goals
The goals of the school are that all students
individually:
• take responsibility for their learning and study
results, and
• can assess their study results and need for development
in relation to the requirements of the
education.
1.2.2 Guidelines
Teachers should:
• regularly provide each student with information
about their progress and the need for development
in their studies,
• work together with parents and guardians, and
provide information about the students’ school
situation and acquisition of knowledge, and
• inform students the basis on which grades are
awarded.
Teachers when awarding grades should:
• use all the information available about the student’s knowledge in relation to the national knowledge
requirements for each course,
• also take into account the knowledge that a student has acquired outside actual teaching, and
• on the basis of the national knowledge requirements for each course make an all round assessment of
each student’s knowledge.
5

2. Test Design
2.1 Cover Page
The cover page is formatted by the L ATEX test template
file. The cover page is to include at least the
following information:
• Name of the school and department
• test I or test II indicator - test name is optional.
• permitted materials
• test duration in minutes
• test date
• test version - date the test was created
• number of E, C and A points available
• course name
• student assessment policy
2.1.1 Student assessment policy
1. Mobile Devices are to be switched off and left in your lockers or placed at the front of the room. Mobile
devices cannot be used as a calculator.
2. All jackets and bags are to be left at the front of the room; however, it is preferred that they are left
in your lockers.
3. Students are not permitted to borrow items from other students during the assessment. This includes,
but is not limited to, pencils, erasers and calculators.
4. All solutions are to be neatly written as illegible work will not be graded. If square paper is provided,
solutions should be presented in the same order as they appear on the assessment and clearly numbered.
5. When the teacher indicates that the test is over, all students must stop writing immediately.
6. Students are not permitted to initiate nor engage in communication with other students.
7. Students cannot receive help with questions from the teacher nor the supervisor during the assessment.
8. Failure to follow the assessment policy could result in your test being void.
6

2.2 Test design procedure
1. individual teachers create questions to possibly
include on the test
2. decide which questions will included on the test
3. map the knowledge requirements to the solution
of the question in terms of E, C and A points
4. decide wether or not the solutions will be included
on the test or be presented on squared
paper
5. submit the finished test to the head of department
one week in advance
6. the head of department will typeset the test and
send it to the course teachers
7. any errors, omissions or changes are to be sent
to the head of department
8. course teachers print the test
7

3. National Tests
3.1 National tests and support for assessment
National tests in Mathematics are used to support teachers’ assessment and grading. National tests are
currently available for Math 1, 2, 3 and 4.
3.1.1 The aim of the national tests is primarily to
• support an equivalent and fair assessment and award of grades
• provide a basis for an analysis of the extent to which knowledge requirements are fulfilled at the school
level, at the level of the organiser, and at the national level.
3.1.2 The national tests also contribute to
• making the syllabi specific
• increasing student goal attainment.
Figure 3.1: Skolverket [Sko12, 57–59].
8

3.2 Invigilation
3.2.1 Invigilation FAQ
Why have I been asked to invigilate?
A teacher may be asked to help invigilate a Math national test because they have a regularly scheduled class,
cover duty or study hall during during the testing time. It is possible that a teacher could be assigned an
invigilation time that conflicts with their schedule, so it is recommended that all teachers asked to invigilate
check the invigilation schedule and notify the head of department of any issues so that the appropriate
changes can be made.
All members of the Math department will be scheduled to help invigilate Math national tests such that it
minimizes class disruptions.
How long will I be asked to invigilate?
In most cases, you will be asked to invigilate for 30 minutes at a time. If you have been assigned more than
one 30 minute block, you can request the head of department to consolidate your invigilation time.
What is my roll as an invigilator?
Your primary role as an invigilator is to ensure that students are doing their own work by circulating
throughout the Aula. At any time there should be at least three invigilators in the Aula who will be
responsible for:
1. granting students permission to use the toilet,
2. circulating the Swedish version of the national test,
3. distributing extra paper and
4. collecting tests from students.
You are kindly asked not to bring grading nor to work from your computers while invigilating. It is also
recommended that conversations between invigilators are kept to a minimum.
What if a student asks me for help?
During the information presentation at the start of the national test, students will be informed that invigilators
are not to provide help during the test. As an invigilator, you can always offer the student a copy of
the Swedish version of the test.
In the rare event that a student discovers an error in the test, simply forward this information to a member
of the Math department who will then decide on the appropriate action to take.
What if a student is found using a calculator on the non-calculator part of the test.
If a student is found to be in possession of a calculator during the non-calculator part of the test, then the
invigilator will take the following actions:
1. ensure that the student has their full name on the non-calculator part of the test
2. inform the student that their non-calculator part of the test is being collected because they were in
possession of a calculator and ask them to continue with the calculator part(s) of the test
3. place the test in the void tests folder, which will be located on the stage at the front of the aula
If you are unsure if a student should be in possession of a calculator, please ask a member of the Math
department for help.
9

3.2.2 Invigilation Procedures
Toilets
The only toilet to be used by students taking the Math national test in the Aula is found to the left of the
Aula’s stage. If for some reason this toilet is out of service, then the toilet found in the study area outside
the Aula’s main entrance can be used.
The toilet is considered available when there is no student student waiting at the door to the left of the Aula
stage. No more than one student can stand at the door waiting to use the toilet at any given time. If a
student wishes to use the toilet, then the student will raise their hand to call an invigilator when the toilet
is available. It is the invigilator who grants the student permission to use the toilet.
3.2.3 Circulation of the Swedish version of the national test
It is the responsibility of the student to raise their hand to signal to an invigilator that they wish to view or
return the Swedish version of the national test. Each invigilator should always have at least one copy of the
Swedish version ready for distribution. Invigilators may collect the Swedish version from a student who has
been in possession of the Swedish copy for an extended period of time.
3.2.4 Distribution of extra paper
If a student wishes for more paper, then they must raise their hand and request paper from the closest
available invigilator. Invigilators can find both the squared and blank paper on the Aula’s stage.
3.2.5 Collection of tests
All written work is to be placed into the appropriate folder located on the Aula’s stage. Folders are labelled
by both class and test part. Only invigilators are permitted to place a student’s paper into a folder. When
a student wishes to submit a part of the test, then they must raise their hand to have an invigilator collect
their test.
An announcement will be made 15 minutes before the lunch break and the end of the test to remind students
that no tests will be collected during the last 10 minutes of testing. During the last ten minutes, students
must remained seated and wait to have their test collected by an invigilator at the end of the test.
3.2.6 Calculators
Calculators are to be initially placed in the designated calculator area, located on the Aula’s stage, for the
non-calculator part of the test. Students are not to collect their calculator until they have submitted all
non-calculator parts of the test to an invigilator. It is the invigilator who will grant the student permission
to retrieve their calculator. Students have been instructed in advance to ensure that their full name is on
the calculator.
It should be noted that students are not permitted to share calculators nor can they use their mobile devices
as calculators.
10

3.3 Previous National Tests
3.3.1 Math 1b
Version Part I Part II Part III Oral Solutions
Spring 2012 – EN £ £ £ £ £
Spring 2012 – SV £ £ £ £ £
3.3.2 Math 1c
Year Part I Part II Part III Oral Solutions
Spring 2012 – EN £ £ £ £ £
Spring 2012 – SV £ £ £ £ £
3.3.3 Math 2b
Year Parts I-III Oral
Spring 2012 – EN £ £
Spring 2012 – SV £ £
3.3.5 Math 3b
Year Parts D-B Oral
Fall 2012 – EN £ £
Fall 2012 – SV £ £
3.4 Formula Sheets: National Tests
Courses English Swedish
1b & 1c £ £
2b & 2c £ £
3b & 3c £ £
4 £ £
11
3.3.4 Math 2c
Year Parts I-III Oral
Spring 2012 – EN £ £
Spring 2012 – SV £ £
3.3.6 Math 3c
Year Parts D-B Oral
Fall 2012 – EN £ £
Fall 2012 – SV £ £

3.5 Frequently Asked Questions: National Tests
The Link: Skolverket National Tests frequently asked questions (in Swedish)are available from Skolverket’s
website.
Will the National Test result affect a student’s final grade?
Probably not. Sometimes a student’s performance is better than their course results and sometimes worse.
The most common is that the test’s result corresponds to the teacher’s course grade. If there is a discrepancy,
then the teacher must assess whether the course grade or the national test grade is the most accurate. Thus,
the national test can result can be used to raise or lower grade.
Can the National Test only raise a student’s final grade?
No. It is false to assume the national test can only raise your grade.
Who grades the National Test?
The Math department is responsible for grading the National Test. No teacher within the Department is
permitted to grade their own students.
Is taking a national test compulsory?
Yes. Teachers are required to use the national test and thus students are required to take the national test.
From a student’s perspective, there is no difference between the national test and any other course test.
Is it compulsory to do all parts of the national test?
Yes.
Is it compulsory to participate in the oral part of the national test?
Yes. The oral part is a part of the national test. If the student does not participate in the oral part or any
other part of the test, then the test is deemed incomplete.
Is it possible to take the national test on a day that has not been designated by Skolverket?
Yes. If there are extenuating circumstances, the principal can decide on a later test date than assigned by
Skolverket. The alternative test date can never precede the first date assigned by Skolverket.
Can a student do a national test after the test date?
If a student does not take the national test on the assigned test date, then the student can apply to take a
test, a variation of the test, or a portion of the test at a later date convenient to the subject teacher. The
decision of whether or not the student can take the test will be decided by the school’s principal. Students
will only be approved under extenuating circumstances. The subject teacher decides which topics will be
necessary to support the student’s previous assessments and to set the course’s final grade.
What happens if a student is late for the written part of the National Test?
There are no official regulations by Skolverket regarding lateness. The Internationella Engelska Gymnasiet’s
Math department has agreed that students who are more than 1 hour late will not be permitted to take the
test - unless there are extenuating circumstances communicated by the school’s administration.
What happens if a student does not do the national test?
If a student does not participate in the national test, then the student does not get the opportunity to show
their knowledge and consequently the teacher will have less
12

Can a student re-take a national test?
It is not the intention that the national test be done several times. It is not unusual for a student to think he
or she has not passed a national test and want to redo it. It is important to emphasize that a national test
is a tool among others to help ensure fair grading practices and is not an examination. The subject teacher
decides which pieces of assessment he or she needs to assign a final grade in the course.
Can a student diagnosed with dyslexia use a calculator on the non-calculator part of the test?
No. Even if a student as been diagnosed with dyslexia, they may not use a calculator to solve problems on the
non-calculator part of the test. However, the teacher can subsequently give the student another opportunity
to use a calculator to solve the same problems and then together with the student discuss the solutions.
Is the test in English or Swedish?
All students will take the test in English, which is a decision made by the principle of the school. Swedish
versions of the test will be made available to those students who raise their hand during the test. Once the
student is finished with the Swedish version, it is the student’s responsibility to raise their hand to signal to
an invigilator that they are done so that the Swedish version can be collected and redistributed.
Can students ask questions during the test?
Invigilators are not to answer any student questions during the test. It is therefore advised that students ask
to see the Swedish translation for question clarification. At the discretion of a Math teacher, an explanation
of difficult words can be given to help all students understand the context of the question without revealing
the procedure for answering the question.
Can food and drinks be brought into the testing room?
Yes. It is recommended that students bring something to drink and eat during the test provided that the
food is non-aromatic, nut free and that it’s in the original packing or a transparent bag.
Will calculators be provided?
No. Each student is responsible for having their own functional calculator and knowing how to operate it.
Batteries and extra calculators will not be provided.
What does a student do with their calculator during the non-calculator part of the test?
Each student should place their calculator at the front of the room during the non-calculator part of the test.
The student can only use their calculator once the non-calculator part of the test has been handed-in.
What happens if a calculator is used for a non-calculator section of the test?
The invigilator will mark the non-calculator section as void and then take it from the student. It is expected
that the student will continue with the calculator section(s) of the test.
Are CAS calculators permitted for the calculator parts of the test?
Yes, calculators that feature a computer algebra system (CAS) are permitted.
Is using a dictionary permitted?
Students are permitted language support throughout the Math national test. Dictionaries are permitted if
they have been submitted to the Head of Mathematics for inspection at least two days prior to the national
test date. The student’s dictionary can be collected at the test location.
Can students have a mobile phone, mp3 players or similar electronic devices during the test?
No. Mobile phones, mp3 players, or similar electronic devices are not permitted during the test. A student
in possession of such a device will have their test voided and asked to leave the testing room immediately.
13

Can two or more students share a calculator?
No. The sharing of any materials during the test is prohibited and doing so could result in your test being
void.
How long do we store students’ National Tests?
IEGS archives all Math National Tests after they are graded and retained for a period of five years.
14

4. Special Examinations
4.1 Deadlines: special examinations
Date Information
2013-March-08 Deadline for submission of all special examination contracts
2013-March-13 All special examination test papers to be submitted with cover sheet
2013-April-10 Test Date
2013-April-11 Completed special examination tests to be collected
2013-April-29 All special examination results to be submitted
4.2 Procedure: special examinations
1. Subject teacher completes the teacher section
and gives it to the student.
2. Student completes the student section
3. Student signs the signature section and gives
the form to their parent(s)/guardian(s)
4. Parent(s)/guardian(s) signs the signature section
and then submits it to Mr. Thedning
5. Students will be informed of the examination
dates and times by Mr. Thedning.
15

Part II
Math Support & Resources
16

5. Math Help
5.1 Math support times & locations
Our department has flexible Math help hours, which means that students can easily request help from any
Math teacher within the department by sending them an email to arrange a mutually convenient time to
meet. Math teachers are also available in the study hall at various times throughout the week.
This year, we launched Math Support by investing an additional 9 hours every week to providing a dedicated
& scheduled Math help location.
Day Time Location
Monday 14:40–17:40 5.2
Wednesday 14:40–17:40 5.2
Thursday 15:00–18:00 4.3
5.2 Matte Centrum - Free Math help beyond us
There is never too much Math support available. Mattecentrum is a dedicated organization of volunteers who
provide free Math support to students in Sweden. Here in Stockholm, we are super lucky to have multiple
locations where the Math Support is offered and our students have mentioned great things about the support
they received. They also offer online help at http://matteboken.se, which has a brilliant library of materials
(p˚a svenska) that support the Swedish Math curriculum - including videos!
1. Stockholm times & locations
2. MatteCentrum.se
3. Matteboken.se
17

Part III
References
18

Bibliography
[AS11a] Gunilla Viklund Daniel Duf˚aker Mikael Marklund Attila Szabo, Niclas Larson. Matematik Origo
1b. Number 9789152309247. Sanoma Utbildning, Replacement Cost: 290:-, 2011.
[AS11b] Gunilla Viklund Daniel Duf˚aker Mikael Marklund Attila Szabo, Niclas Larson. Matematik Origo
1c. Number 9789152309254. Sanoma Utbildning, Replacement Cost: 290:-, 2011.
[AS11c] Gunilla Viklund Daniel Duf˚aker Mikael Marklund Attila Szabo, Niclas Larson. Matematik Origo
3c. Number 9789152317228. Sanoma Utbildning, Replacement Cost: 290:-, 2011.
[AS12a] Gunilla Viklund Daniel Duf˚aker Mikael Marklund Attila Szabo, Niclas Larson. Matematik Origo
2b. Number 9789152317235. Sanoma Utbildning, Replacement Cost: 290:-, 2012.
[AS12b] Gunilla Viklund Daniel Duf˚aker Mikael Marklund Attila Szabo, Niclas Larson. Matematik Origo
2c. Number 9789152309704. Sanoma Utbildning, Replacement Cost: 290:-, 2012.
[AS13] Gunilla Viklund Daniel Duf˚aker Mikael Marklund Attila Szabo, Niclas Larson. Matematik Origo 4.
Number 9789152319017. Sanoma Utbildning, Replacement Cost: 290:-, 2013.
[Sko12] Skolverket. Upper Secondary School 2011. Number 978-91-87115-34-9. Skolverket,
http://www.skolverket.se/publikationer?id=2801, 2012.
[Tur13] Brian Turner. Curriculum for the Upper Secondary School. Number 978-91-7559-022-6. Skolverket,
http://www.skolverket.se/polopolyf s/1.191473!/Menu/article/attachment/Curriculum.pdf, 2013.
19

Part IV
Appendix/Appendix
20

21
A. GY2011 Local Knowledge Requirement Summaries
Category E Local Summary C Local Summary A Local Summary
Concept
Procedure
Problem Solving
Understands concepts, their purpose
and connections between them,
illustrated by some examples and
different representations
Carries out one-step procedures, some
alternative solution methods
Solves problems in familiar
situations, with simple
interpretations/formulations
Modeling Uses given models
Reasoning & Evaluation
Communication
Context & Relevance
Simple evaluation and reasoning,
differentiates between guesses and
well-founded statements
Can communicate with some
certainty. Uses symbols, terms and
conventions
Some contextualization through
examples
Thoroughly understands concepts,
their purpose and connections between
them, illustrated by some examples
and different representations
Carries out multi-step procedures
Solves, formulates and analyses
problems with advanced
interpretations/formulations
Chooses and applies appropriate
models
Well-founded reasoning with
nuanced judgement and evaluation
Can communicate with some
certainty. Uses symbols, terms and
conventions according to purpose
and context
Relevant contextualization through
examples
Thoroughly understands concepts,
their purpose and connections between
them, illustrated by several examples
and different representations
Fluently interchanges solution
methods
Solves, formulates and analyses
complex problems effectively
Adapts mathematical models and
provides alternative solution
strategies
Well-founded and nuanced
reasoning, judgement and evaluation.
Finds general rules and
relationships and expresses these
using algebra and symbols
Can communicate with certainty.
Symbols, terms and conventions are
well-suited to purpose and context
Well-founded and nuanced
contextualization through examples

B. GY2011- Knowledge Requirements
Grade E
Eleven kan översiktligt beskriva innebörden av centrala begrepp med hjälp av n˚agra representationer samt
översiktligt beskriva sambanden mellan begreppen. Dessutom växlar eleven med viss säkerhet mellan
olika representationer. Eleven kan med viss säkerhet använda begrepp och samband mellan begrepp för
att lösa matematiska problem och problemsituationer i karaktärsämnena i bekanta situationer. I arbetet
hanterar eleven n˚agra enkla procedurer och löser uppgifter av standardkaraktär med viss säkerhet, b˚ade
utan och med digitala verktyg.
The student can briefly describe the content of key concepts with the help of some examples as well as briefly
describing connections between concepts. Additionally, the student can interchange different methods of solution
with some certainty. The student can, with some certainty, use concepts and the connections between
them to solve problems, both mathematical and programme specific, in familiar situations. In working, the
student is able to carry out one-step procedures and complete standard tasks with some certainty, with and
without a digital device.
Eleven kan formulera, analysera och lösa matematiska problem av enkel karaktär. Dessa problem inkluderar
ett f˚atal begrepp och kräver enkla tolkningar. I arbetet gör eleven om realistiska problemsituationer
till matematiska formuleringar genom att tillämpa givna matematiska modeller. Eleven kan med enkla
omdömen utvärdera resultatets rimlighet samt valda modeller, strategier och metoder.
The student can formulate, analyse and solve mathematical problems of a simple character. These problems
include few concepts and demand simple interpretations. In working, the student is able reformulate realistic
problem situations in mathematical terms by using given mathematical models. The student can, using simple
judgements, evaluate the reasonableness of results, chosen models, strategies and methods.
Eleven kan föra enkla matematiska resonemang och värdera med enkla omdömen egna och andras resonemang
samt skilja mellan gissningar och välgrundade p˚ast˚aenden. Dessutom uttrycker sig eleven med viss
säkerhet i tal, skrift och handling med inslag av matematiska symboler och andra representationer.
The student can carry out simple mathematical reasoning and evaluate, using simple judgement, their own
and others reasoning, as well as differentiate between guesses and well founded statements. Additionally, the
student is able to express themselves, with some certainty, orally, in writing and kinaesthetically with some
mathematical symbols, terms and conventions.
Genom att ge exempel relaterar eleven n˚agot i kursens inneh˚all till dess betydelse inom andra ämnen,
yrkesliv, samhällsliv och matematikens kulturhistoria. Dessutom kan eleven föra enkla resonemang om exemplens
relevans.
Through giving examples, the student relates some elements of the course content to their meaning within
other subjects, professional and societal contexts, and the cultural history of mathematics. Additionally, the
student can carry out simple reasoning concerning the relevance of examples.
22

Grade C
Eleven kan utförligt beskriva innebörden av centrala begrepp med hjälp av n˚agra representationer samt
utförligt beskriva sambanden mellan begreppen. Dessutom växlar eleven med viss säkerhet mellan olika
representationer. Eleven kan med viss säkerhet använda begrepp och samband mellan begrepp för att
lösa matematiska problem och problemsituationer i karaktärsämnena. I arbetet hanterar eleven flera procedurer
och löser uppgifter av standardkaraktär med säkerhet, b˚ade utan och med digitala verktyg.
The student can thoroughly describe the content of key concepts with the help of some examples as well as
thoroughly describing connections between concepts. Additionally, the student can interchange different methods
of solution with some certainty. The student can, with some certainty, use concepts and the connections
between them to solve problems, both mathematical and programme specific. In working, the student is able to
carry out multi-step procedures and complete standard tasks with certainty, with and without a digital device.
Eleven kan formulera, analysera och lösa matematiska problem. Dessa problem inkluderar flera begrepp och
kräver avancerade tolkningar. I arbetet gör eleven om realistiska problemsituationer till matematiska formuleringar
genom att välja och tillämpa matematiska modeller. Eleven kan med enkla omdömen utvärdera
resultatets rimlighet samt valda modeller, strategier, metoder och alternativ till dem.
The student can formulate, analyse and solve mathematical problems. These problems include several concepts
and demand advanced interpretations. In working, the student is able reformulate realistic problem
situations in mathematical terms by choosing and applying mathematical models. The student can, using
simple judgements, evaluate the reasonableness of results, chosen models, strategies and methods, as well as
provide alternatives.
Eleven kan föra välgrundade matematiska resonemang och värdera med nyanserade omdömen egna och
andras resonemang samt skilja mellan gissningar och välgrundade p˚ast˚aenden. Dessutom uttrycker sig eleven
med viss säkerhet i tal, skrift och handling samt använder matematiska symboler och andra representationer
med viss anpassning till syfte och situation.
The student can carry out well-founded mathematical reasoning and evaluate, using nuanced judgement, their
own and others reasoning, as well as differentiate between guesses and well founded statements. Additionally,
the student is able to express themselves, with some certainty, orally, in writing and kinaesthetically, as well
using mathematical symbols, terms and conventions according to the purpose and context.
Genom att ge exempel relaterar eleven n˚agot i n˚agra av kursens delomr˚aden till dess betydelse inom andra
ämnen, yrkesliv, samhällsliv och matematikens kulturhistoria. Dessutom kan eleven föra välgrundade
resonemang om exemplens relevans.
Through giving examples, the student relates elements of the course content to their meaning within other
subjects, professional and societal contexts, and the cultural history of mathematics. Additionally, the student
can carry out well-founded reasoning concerning the relevance of examples.
23

Grade A
Eleven kan utförligt beskriva innebörden av centrala begrepp med hjälp av flera representationer samt
utförligt beskriva sambanden mellan begreppen. Dessutom växlar eleven med säkerhet mellan olika representationer.
Eleven kan med säkerhet använda begrepp och samband mellan begrepp för att lösa komplexa
matematiska problem och problemsituationer i karaktärsämnena. I arbetet hanterar eleven flera procedurer
och löser uppgifter av standardkaraktär med säkerhet och p˚a ett effektivt sätt, b˚ade utan och med
digitala verktyg.
The student can thoroughly describe the content of key concepts with the help of several examples as well
as thoroughly describing connections between concepts. Additionally, the student can interchange different
methods of solution with certainty. The student can, with certainty, use concepts and the connections between
them to solve complex problems, both mathematical and programme specific. In working, the student is able to
carry out multi-step procedures and complete standard tasks effectively and with certainty, with and without
a digital device.
Eleven kan formulera, analysera och lösa matematiska problem av komplex karaktär. Dessa problem
inkluderar flera begrepp och kräver avancerade tolkningar. I problemlösning upptäcker eleven generella
samband som presenteras med symbolisk algebra. I arbetet gör eleven om realistiska problemsituationer
till matematiska formuleringar genom att välja, tillämpa och anpassa matematiska modeller. Eleven
kan utvärdera med nyanserade omdömen resultatets rimlighet samt valda modeller, strategier, metoder och
alternativ till dem.
The student can formulate, analyse and solve complex mathematical problems. These problems include several
concepts and demand advanced interpretations. In problem solving, the student finds general rules and
relationships which are presented algebraically using symbols. In working, the student is able reformulate
realistic problem situations in mathematical terms by choosing, applying and adapting mathematical models.
The student can, using nuanced judgements, evaluate the reasonableness of results, chosen models, strategies
and methods, as well as provide alternatives.
Eleven kan föra välgrundade och nyanserade matematiska resonemang, värdera med nyanserade omdömen
och vidareutveckla egna och andras resonemang samt skilja mellan gissningar och välgrundade p˚ast˚aenden.
Dessutom uttrycker sig eleven med säkerhet i tal, skrift och i handling samt använder matematiska symboler
och andra representationer med god anpassning till syfte och situation.
The student can carry out well-founded and nuanced mathematical reasoning and evaluate, using nuanced
judgement, further develop their own and others reasoning, as well as differentiate between guesses and well
founded statements. Additionally, the student is able to express themselves, with certainty, orally, in writing
and kinaesthetically, as well using mathematical symbols, terms and conventions well-suited to the purpose
and context.
Genom att ge exempel relaterar eleven n˚agot i n˚agra av kursens delomr˚aden till dess betydelse inom andra
ämnen, yrkesliv, samhällsliv och matematikens kulturhistoria. Dessutom kan eleven föra välgrundade
och nyanserade resonemang om exemplens relevans.
Through giving examples, the student relates elements of the course content to their meaning within other
subjects, professional and societal contexts, and the cultural history of mathematics. Additionally, the student
can carry out well-founded and nuanced reasoning concerning the relevance of examples.
24

Grade D
Betyget D innebär att kunskapskraven för E och till övervägande del för C är uppfyllda.
Grade D comprises all criteria for Grade E, and additionally the predominant criteria for Grade C are
fulfilled.
Grade B
Betyget B innebär att kunskapskraven för C och till övervägande del för A är uppfyllda.
Grade B comprises all criteria for Grade C, and additionally the predominant criteria for Grade A are
fulfilled.
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