21
Title of lesson: Inheritance Patterns GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish (University of Alabama at Birmingham) 1 Final Report December 2008 The workshop: The Geneticist-Educator Network of Alliances (GENA) Workshop we attended on August 4-8, 2008 at the Montclair State University PRISM Facility in Montclair, NJ was a unique opportunity, in particular for the scientist among us, to refresh our knowledge about pedagogical approaches to the teaching of genetics in K-12 and to learn the standards required by the State of Alabama for the teaching of Genetics in high school. The open, pleasant atmosphere at the workshop allowed a great deal of interaction which resulted in groups helping each other with information about resources available for their respective lesson. At the end of the workshop, we had a very clear idea of the lesson plan we wanted to develop and had prepared an outline. Developing the lesson plan: Upon our return home, we worked on developing the details of the lesson plan. Sonya and Ada met to discuss the plan in Ada’s office at the University of Alabama at Birmingham. After revising the lesson plan, we submitted it to GENA for review. In September, we received Mike and Angie’s comments. One question was about the following statement in the lesson plan we had submitted, i.e., “it is important to review [inheritance patterns] with the students before they begin their exploration activities”. Mike and Angie asked whether the students will already have learned about these patterns?”. This was, of course, a mistake and that sentence has been taken out from the revised Lesson Plan we attach to this report. Another question was whether Ada Elgavish will be presenting during class. Since most of the lesson was not structured as a frontal lecture but more as activities followed by discussions, both Sonya and Ada participated in the discussion. We thank Mike and Angie for their suggestion to start the pedigree exploration activities with inquiry questions. This worked well. Implementation of the lesson plan: At the beginning of December, Sonya and Ada met at the P.D. Jackson- Olin High School in Ensley, Alabama, where Sonya teaches the seniors Genetics, 16 students per class. First, we discussed Mike and Angie’s comments and revised the lesson plan. Ada was able to visit the well-equipped computer lab which would allow students to work independently, if needed. We opted for having the students work on activities in pairs, which allowed them to discuss the activities while they were working on them. Sonya and Ada worked together in the two following days to implement the lesson plan. Before the first lesson started, students were asked to answer the short questionnaire attached. Following this, each student received the handout attached, which is a version of the Lesson Plan modified for the students. Students were given a defined amount of time to work on each activity on their own, after which each activity was discussed. After the first day, students were asked to prepare one page report on a genetic disorder of their choice. At the beginning of the second lesson, two students read their reports. The rest of the second lesson proceeded as described in detail in the Lesson Plan. At the end of the second class, the students were provided with the same questionnaire they had answered the day before. The number of points acquired by each of the students is in the Table attached. Critique of the first implementation of the lesson plan: Part A of the questionnaire we administered was designed to test whether students had the basic prerequisite knowledge before the lesson was taught. Part B of the questionnaire was designed to test whether student knowledge had been improved by the lesson. Comparing the mean scores on part A before and after the lesson showed that there was no significant difference (see t-test attached). As shown in the Table of data attached, all the students could answer some of the questions asked, indicating that they had received the prerequisite instruction. We found that 31.3% of the students had a perfect score on Part A of the test before the lesson whereas 35.7% of the students had perfect

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Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

1

Final Report

December 2008

The workshop: The Geneticist-Educator Network of Alliances (GENA) Workshop we attended on August 4-8,

2008 at the Montclair State University PRISM Facility in Montclair, NJ was a unique opportunity, in particular

for the scientist among us, to refresh our knowledge about pedagogical approaches to the teaching of genetics in

K-12 and to learn the standards required by the State of Alabama for the teaching of Genetics in high school.

The open, pleasant atmosphere at the workshop allowed a great deal of interaction which resulted in groups

helping each other with information about resources available for their respective lesson. At the end of the

workshop, we had a very clear idea of the lesson plan we wanted to develop and had prepared an outline.

Developing the lesson plan: Upon our return home, we worked on developing the details of the lesson plan.

Sonya and Ada met to discuss the plan in Ada’s office at the University of Alabama at Birmingham. After

revising the lesson plan, we submitted it to GENA for review. In September, we received Mike and Angie’s

comments. One question was about the following statement in the lesson plan we had submitted, i.e., “it is

important to review [inheritance patterns] with the students before they begin their exploration activities”. Mike

and Angie asked whether the students will already have learned about these patterns?”. This was, of course, a

mistake and that sentence has been taken out from the revised Lesson Plan we attach to this report. Another

question was whether Ada Elgavish will be presenting during class. Since most of the lesson was not structured

as a frontal lecture but more as activities followed by discussions, both Sonya and Ada participated in the

discussion. We thank Mike and Angie for their suggestion to start the pedigree exploration activities with

inquiry questions. This worked well.

Implementation of the lesson plan: At the beginning of December, Sonya and Ada met at the P.D. Jackson-

Olin High School in Ensley, Alabama, where Sonya teaches the seniors Genetics, 16 students per class. First,

we discussed Mike and Angie’s comments and revised the lesson plan. Ada was able to visit the well-equipped

computer lab which would allow students to work independently, if needed. We opted for having the students

work on activities in pairs, which allowed them to discuss the activities while they were working on them.

Sonya and Ada worked together in the two following days to implement the lesson plan. Before the first lesson

started, students were asked to answer the short questionnaire attached. Following this, each student received

the handout attached, which is a version of the Lesson Plan modified for the students. Students were given a

defined amount of time to work on each activity on their own, after which each activity was discussed. After the

first day, students were asked to prepare one page report on a genetic disorder of their choice. At the beginning

of the second lesson, two students read their reports. The rest of the second lesson proceeded as described in

detail in the Lesson Plan. At the end of the second class, the students were provided with the same questionnaire

they had answered the day before. The number of points acquired by each of the students is in the Table

attached.

Critique of the first implementation of the lesson plan: Part A of the questionnaire we administered was

designed to test whether students had the basic prerequisite knowledge before the lesson was taught. Part B of

the questionnaire was designed to test whether student knowledge had been improved by the lesson.

Comparing the mean scores on part A before and after the lesson showed that there was no significant

difference (see t-test attached). As shown in the Table of data attached, all the students could answer some of

the questions asked, indicating that they had received the prerequisite instruction. We found that 31.3% of the

students had a perfect score on Part A of the test before the lesson whereas 35.7% of the students had perfect

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

2

scores on part A after the lesson. The small improvement after the lesson was not significant (p value=0.796;

see z-test report of statistical analysis for Part A attached).

We found that, in the weeks before the implementation, constraints of the students’ schedule of exams had

forced Sonya to start teaching some of the concepts we were planning to teach using this lesson plan. Therefore,

it was not surprising that 13% of the students had a perfect score on part B of the questionnaire before the

lesson was taught. This proportion increased significantly after the lesson to 50% of students with a perfect

score on part B (p value = 0.028; see z-test on part B attached). We had originally planned to examine whether

there is a correlation between the student’s prerequisite knowledge (scores on part A before the lesson) and the

student’s acquisition of the concepts taught in the lesson (scores on part B after the lesson). Unfortunately,

many of the students forgot to sign their tests and this correlation could not be evaluated in this study.

The following documents are submitted with this report:

(1) Detailed lesson plan for teachers

(2) Handout for students

(3) Questionnaire (for student)

(4) Questionnaire with answers (for teacher)

(5) Table with results of the test

(6) Statistical analysis of the data

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

1

Prep: Copy handouts for each pair; ensure that each computer is signed in at the resource websites

Duration: The lesson requires two classes, 90 minutes each.

Introduction

The main objective of this lesson is to teach basic Mendelian patterns of inheritance and basic pedigree analysis.

Two classes (90 min each) will be required. The following basic concepts of genetics are a necessary

prerequisite: basic DNA structure, gene, allele, chromosome, homozygote, heterozygote, mitosis and meiosis.

The major concepts that will be taught in this lesson are:

• Dominant character manifests in a heterozygote (represented by capital letters)

• Recessive character manifests in a homozygote but not in a heterozygote (represented by small

letters)

• Codominance occurs when both alleles are equally strong and neither is masked by the other. When

both alleles are present they are both expressed in the phenotype resulting in a “blended” phenotype.

An example of codominance is found in chicken. When white chicken are crossed with black

chicken, the result is not a grey chicken, but a chicken with both black and white feathers.

(represented by capital letters and subscripts)

• Incomplete dominant (a.k.a. semi-dominant) character occurs when the phenotype of the

heterozygote is an intermediate phenotype. An example is found in carnations. When pure bred

white carnations are crossed with pure bred red carnations, the result is a pink carnation.

(represented by different capitalized letters).

• Multiple allelism: The existence of several known alleles of a gene. For example, the ABO blood

group consist of 3 types of alleles A, B, and O, any of which can pair resulting in a phenotype.

• Basic Mendelian pedigree patterns: Autosomal dominant, autosomal recessive, X-linked

dominant, X-linked recessive, Y-linked

• Pedigree: A family tree illustrating the inheritance of particular genotypes or phenotypes

Several inheritance patterns are presented in this lesson. It is important to stress that inheritance of the traits

used in this lesson have been simplified to serve as examples. Students need to be reminded that actual

inheritance is more complex to address concerns about their own traits.

This lesson will be an opportunity to discuss and dispel several misconceptions. For example:

• Having a mutation always means looking different

• All gene modifications lead to retardation

• All diseases are caused by alterations in one gene (introduce the concept of polygenic inheritance)

At the end of this lesson, students will be able to:

• Understand basic terms associated with Mendelian patterns of inheritance

• Interpret simple, basic Mendelian patterns of inheritance

• Predict whether an unborn child may display a disease phenotype based on the analysis of simple

pedigrees

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

2

For the Teacher

FIRST CLASS (90 minutes)

Engagement (30 min)- The topic “Patterns of inheritance” will be introduced by projecting for the students

the presentation at the link below entitled Recovering the Romanovs. Go to the DNA Interactive website

www.dnai.org > Applications > Recovering the Romanovs. You will have to sign in. Sign in before the class.

In the class, go only over the part “The Romanov family”. A pedigree is being built, as the story is told. Use the

key link to explain the symbols used in a pedigree. Encourage students to watch the rest of the story at home.

Ask the students why do they think that it might be important to have the type of information provided by a

pedigree such as the one they had just seen.

Exploration and Explanation (75 minutes) –

Activity #1 (20 minutes): Start by watching a short animation introducing the concept of a pedigree and

the meaning of each symbol. Go to http://www.dnalc.org/mediashowcase/index.html?q=genes&s=Search.

You will have to sign in. Sign in before the class. In the Search box enter Pedigree. Select “making a

pedigree”. This is a passive activity. Concepts learned will be practiced in the next activities.

Activity #2 (20 minutes): The objective of this activity is to analyze and interpret pedigrees. Students

will work with the Table in Appendix 1 as a handout. In the left column are provided simple pedigrees.

Students will be asked to describe the pattern they see in the middle column. After the Elaboration step in

the second class, students will be asked to complete the third column for homework.

Activity #3 (20 minutes): Activity will start in class. You will have to sign in. Sign in before the class.

Students will be provided with the link below, but will be encouraged to search additional links using the

key words Mendel, inheritance, pedigree.

http://learn.genetics.utah.edu/units/disorders/whataregd/ What are genetic disorders?

Homework: For homework, each student will write a 1 page report on a genetic disorder and its mode

of inheritance. 3 selected students selected at random will present their work for the class at the beginning of

the second class.

For comprehension, students will be asked to read a chapter in the textbook and answer questions (Human

Genetics pages 88-94).

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

3

SECOND CLASS (90 minutes)

Elaboration (55 minutes)

• (30 minutes) All students submit their 1 page reports. 3 students selected at random present their report

to the class. The discussion that follows will provide an opportunity for formative assessment.

• (25 minutes) Teacher lectures on patterns of inheritance and basic concepts of probability (Punnett

Squares). Material on the websites below will be used.

o Mendel’s principles : http://anthro.palomar.edu/mendel/mendel_1.htm

o The probability of genetics: http://anthro.palomar.edu/mendel/mendel_2.htm

o Patterns of inheritance: Material at the following links will be used to teach the basic patterns

of inheritance

� Autosomal dominant: (Example: Huntington’s disease )

http://learn.genetics.utah.edu/units/disorders/whataregd/hunt/index.cfm

� Autosomal recessive: (Example: Sickle Cell Disease)

http://learn.genetics.utah.edu/units/disorders/whataregd/sicklecell/index.cfm

� X-linked inheritance: (Example: Severe Combined Immunodeficiency)

http://learn.genetics.utah.edu/units/disorders/whataregd/scid/index.cfm

Evaluation (35 minutes)

Formative assessment 35 minutes)

� To test for understanding of basic terms, the flashcards at the following link will be used:

http://anthro.palomar.edu/mendel/flashcards_1.htm

� Hands-on to test understanding of patterns of inheritance, pedigree analysis and probability of

genetics

o Students will be provided with examples of pedigrees and asked to determine the mode of

inheritance

o Students will be provided with examples of pedigrees and will be asked to predict the

possible phenotype of an offspring

o Exercise using Punnett squares at http://www.athro.com/evo/gen/punexam.html

Homework: Students will be asked to complete the third column in the Table provided for Activity #3 and

to solve “puzzles” using Punnett squares.

Summative assessment will be a test given later in the semester which will include activities similar to those

in their formative assessment, but with different pedigrees.

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

4

References:

1. Lewis. R., Human Genetics: Concepts and Applications, 7th edition, McGraw Hill pp.88-94.

2. Lewis, R. Human Genetics: Case Workbook. 7th edition, McGraw Hill pp.88-94.

3. Kearns, MW, Davis, TM, McKell, SH. Genetics and Biotechnology: Laboratory Manual, 2008-

2009, UAB Center for Community Outreach Development and Birmingham City Schools

4. Weaver, RF, Hedrick, PW. Basic Genetics. Wm. C. Brown Publishers, 1991.

5. Strachan, T, Read, AP. Mendelian pedigree patterns In Human Molecular Genetics. 3rd Edition,

Garland Science, Taylor and Francis Group, London and New York, pp. 102-119, 2003.

6. Information found on the following websites has also been used:

o http://www.dnalc.org/mediashowcase/index.html?q=genes&s=Search

o http://learn.genetics.utah.edu/units/disorders/whataregd/

o http://learn.genetics.utah.edu/units/disorders/whataregd/hunt/index.cfm

o http://learn.genetics.utah.edu/units/disorders/whataregd/sicklecell/index.cfm

o http://learn.genetics.utah.edu/units/disorders/whataregd/scid/index.cfm

o http://wwhttp://www.athro.com/evo/gen/punexam.html

o w.kumc.edu/gec/lpneurga.html Basic Human Inheritance Pattern Activity

o http://anthro.palomar.edu/mendel/mendel_2.htm

o http://anthro.palomar.edu/mendel/mendel_1.htm

o http://anthro/palomar.edu/mendel/flashcards_1.htm Flash Cards for Basic Principles of

Genetics

o http://www.kumc.edu/gec/lpfloor.html Births Defects, Genetic disorders, and Pedigree

Analysis

o http://www.dnai.org/teacherguide/guide.html Recovering the Romanovs

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

5

APPENDIX 1 (Student Handout)

Patterns of Inheritance

The main objective of this activity is to learn basic Mendelian patterns of inheritance and basic pedigree

analysis. Pedigrees were kindly provided by Bruce Korf, MD, PhD, Chairman, Department of Genetics,

University of Alabama at Birmingham.

Instructions:

(a) As you progress through this activity, make a note of any terms you do not know and look their meaning

up in your class notes, your textbook or on the internet. Enter the terms and their meaning in the table

below:

Term Meaning

(b) In the left column of the table below, you will see pedigrees similar to that of the Romanov family you

saw at the beginning of the class. Answer the following questions first.

o What does the square mean?

o What does the circle mean?

o What does the filled circle or square mean?

o What does the line connecting the symbols (circles or squares) mean?

o What does the line connecting the vertical lines to symbols mean?

(a) Taking into consideration the meaning of the symbols and the lines, what do you think each pedigree

tells us about that family? Write your answer in the center column. You will fill the right column after

class tomorrow.

Pedigree What do you see? Conclusion

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

6

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

7

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

8

APPENDIX 1 (Teacher)

Patterns of Inheritance

The main objective of this activity is to learn basic Mendelian patterns of inheritance and basic pedigree

analysis. Pedigrees were kindly provided by Bruce Korf, MD, PhD, Chairman, Department of Genetics,

University of Alabama at Birmingham.

Instructions: (b) As you progress through this activity, make a note of any terms you do not know and look their meaning

up in your class notes, your textbook or on the internet. Enter the terms and their meaning in the table

below:

Term Meaning

(c) In the left column of the table below, you will see pedigrees similar to that of the Romanov family you

saw at the beginning of the class. Answer the following questions first.

o What does the square mean?

o What does the circle mean?

o What does the filled circle or square mean?

o What does the line connecting the symbols (circles or squares) mean?

o What does the line connecting the vertical lines to symbols mean?

(a) Taking into consideration the meaning of the symbols and the lines, what do you think each pedigree

tells us about that family? Write your answer in the center column. You will fill the right column after

class tomorrow.

Pedigree What do you see? Conclusion

Autosomal recessive

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

9

Autosomal dominant

Autosomal dominant

(limited to males)

Autosomal Recessive

consanguinity

X-linked dominant

Autosomal recessive

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

10

X-linked recessive

Autosomal recessive

(pseudodominant)

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

1

Questionnaire (For student)

Part A (each correct answer is worth 2 points)

Please choose the correct answer and click in the square next to it to record it. There is only one correct answer

for each of the terms.

DNA adenosine

deoxyribonucleic acid

cytosine

gene

gene complete set of genetic information from a genetic system

the set of codons and the amino acids they stand for

basic unit of heredity

chromosome

allele basic unit of heredity

chromosome

a particular form of a gene

heterozygote

chromatid copies of a chromosome produced in cell division

the material of chromosomes

basic unit of heredity

coding strand

Chromosome number is maintained during mitosis Yes

No

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Priget (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

2

Part B (each correct answer is worth 2 points)

Please choose the correct answer and click in the square next to it to record it. There is only one correct answer

for each of the terms.

Dominant character character manifest in humans only

character manifest in the heterozygote

character manifest only in plants

chromosome

Autosomal recessive an affected person usually has at least one affected parent

character manifest in the heterozygote

affects mainly males

affects either sex, but more females than males

Pedigree mode of inheritance

family tree illustrating inheritance of a particular phenotype

symbol

genotype

Punnett squares type of chromosomal changes

diagram used to predict the outcome of a cross

monohybrid cross

autosomal dominant

When two heterozygous parents (Bb X Bb) are crossed, the probability of a child having

the bb phenotype is:

50%

100%

25%

30%

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Privet (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

1

Questionnaire (For teacher)

Objectives:

Before the lesson is taught, the purpose of this questionnaire is to determine: (a) whether students had

the required prerequisite knowledge when the lesson was taught (Part A); and (b) whether they were

already familiar with the terms to be taught in this lesson before the lesson (Part B).

After the lesson is taught, the purpose of this questionnaire will be to determine: (a) whether student’s

knowledge was improved by the lesson; (b) in cases in which knowledge was not improved, it will

evaluate whether the lack of the required prerequisite knowledge may have been the reason.

Procedure:

Students will be asked to fill this questionnaire before and after the lesson is taught. Each correct answer

will be scored 2 points. The following endpoints will be calculated: (a) Total points for Part A for each

student; (b) Total points for Part B for each student; (c) Total points for the entire exam for each student.

Some of the statistical analyses that will be carried out using Sigma Stat are below:

(a) To determine whether students’ knowledge of the material taught in the lesson improved after the lesson was taught: We will determine whether there is a statistical

difference between the mean (or median) of the total number of points obtained before the

lesson in Part B and the total number of points obtained after the lesson in Part B. We will

also compare the proportion of students with perfect scores (10 points out of 10) before and

after the lesson.

(b) To determine whether in cases in which knowledge was not improved, the reason was the lack of the required prerequisite knowledge. Pearson’s correlation coefficient will be

calculated to determine whether there is a correlation between the total number of points

obtained by each student in Part A (before the lesson) and the total number of points obtained

by each student, respectively, in Part B (after the lesson)

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Privet (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

2

Part A (each correct answer is worth 2 points)

Please choose the correct answer and click in the square next to it to record it. There is only one correct answer

for each of the terms.

DNA adenosine

Deoxyribonucleic acid

Cytosine

Gene

Gene complete set of genetic information from a genetic system

the set of codons and the amino acids they stand for

basic unit of heredity

chromosome

allele basic unit of heredity

chromosome

a particular form of a gene

heterozygote

chromatid copies of a chromosome produced in cell division

the material of chromosomes

basic unit of heredity

coding strand

Chromosome number is maintained during mitosis Yes

No

Title of lesson: Inheritance Patterns

GENA Partners: Sonya Privet (P.D. Jackson-Olin High School, Birmingham, AL) and Ada Elgavish

(University of Alabama at Birmingham)

3

Part B (each correct answer is worth 2 points)

Please choose the correct answer and click in the square next to it to record it. There is only one correct answer

for each of the terms.

Dominant character character manifest in humans only

character manifest in the heterozygote

character manifest only in plants

chromosome

Autosomal recessive an affected person usually has at least one affected parent

character manifest in the heterozygote

affects mainly males

affects either sex, but more females than males

Pedigree mode of inheritance

family tree illustrating inheritance of a particular phenotype

symbol

genotype

Punnett squares type of chromosomal changes

diagram used to predict the outcome of a cross

monohybrid cross

autosomal dominant

When two heterozygous parents (Bb X Bb) are crossed, the probability of a child having

the bb phenotype is:

50%

100%

25%

30%

GENA results December 2008** saved: c:\Genetics\GENA\test

Part A* Part B Total Part A Part B Total

6 8 14 8 8 16

10 8 18 6 8 14

10 6 16 4 2 6

10 6 16 8 10 18

2 8 10 10 10 20

8 8 16 8 10 18

6 8 14 2 4 6

6 8 14 10 6 16

6 8 14 10 10 20

10 6 16 10 10 20

2 4 6 10 10 20

8 10 18 6 8 14

4 2 6 6 8 14

6 8 14 8 10 18

10 10 20

6 8 14

** Some of the students did not write their name. Therefore results "after" do not correspond to results "before" for each student respectively

* Part A and B are for the same student

Before the lesson After the lesson