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Concepts of Genetics

William S. Klug, Michael R. Cummings, Charlotte A. Spencer

Chapter 4

Extensions of Mendelian Genetics - all with Video Answers

Educators

Chapter Questions

03:36

Problem 1

In this chapter, we focused on extensions and modifications of Mendelian principles and ratios. In the process, we encountered many opportunities to consider how this information was acquired. On the basis of these discussions, what answers would you propose to the following fundamental questions?
(a) How were early geneticists able to ascertain inheritance patterns that did not fit typical Mendelian ratios?
(b) How did geneticists determine that inheritance of some phenotypic characteristics involves the interactions of two or more gene pairs? How were they able to determine how many gene pairs were involved?
(c) How do we know that specific genes are located on the sexdetermining chromosomes rather than on autosomes?
(d) For genes whose expression seems to be tied to the sex of individuals, how do we know whether a gene is X-linked in contrast to exhibiting sex-limited or sex-influenced inheritance?

Celine Ibrahim
Celine Ibrahim
Numerade Educator
07:02

Problem 2

Review the Chapter Concepts list on p. 62 These all relate to exceptions to the inheritance patterns encountered by Mendel. Write a short essay that explains why multiple
and lethal alleles often result in a modification of the classic Mendelian monohybrid and dihybrid ratios.

Jessica Honkomp
Jessica Honkomp
Numerade Educator
02:12

Problem 3

In shorthorn cattle, coat color may be red, white, or roan. Roan is an intermediate phenotype expressed as a mixture of red and white hairs. The following data were obtained from various crosses:
How is coat color inherited? What are the genotypes of parents and offspring for each cross?

Bryan Valdivia
Bryan Valdivia
Numerade Educator
02:22

Problem 4

In foxes, two alleles of a single gene, $P$ and $p$, may result in lethality $(P P),$ platinum coat $(P p),$ or silver coat $(p p) .$ What ratio is obtained when platinum foxes are interbred? Is the $P$ allele behaving domi-
nantly or recessively in causing (a) lethality;
(b) platinum coat color?

Bryan Valdivia
Bryan Valdivia
Numerade Educator
01:16

Problem 5

In mice, a short-tailed mutant was discovered. When it was crossed to a normal long-tailed mouse, 4 offspring were short-tailed and 3 were long-tailed. Two short-tailed mice from the $\mathrm{F}_{1}$ generation were selected and crossed. They produced 6 short-tailed and 3 long-tailed mice. These genetic experiments were repeated three times with approximately the same results. What genetic ratios are illustrated? Hypothesize the mode of inheritance and diagram the crosses.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:28

Problem 6

List all possible genotypes for the $\mathrm{A}, \mathrm{B}, \mathrm{AB},$ and $\mathrm{O}$ phenotypes. Is the mode of inheritance of the $\mathrm{ABO}$ blood types representative of dominance, recessiveness, or codominance?

Parvati Devi
Parvati Devi
Numerade Educator
04:19

Problem 7

With regard to the ABO blood types in humans, determine the genotype of the male parent and female parent shown here: Male parent: Blood type B; mother type O Female parent: Blood type A; father type B Predict the blood types of the offspring that this couple may have and the expected proportion of each.

Jessica Wooten
Jessica Wooten
Numerade Educator
02:04

Problem 8

In a disputed parentage case, the child is blood type $0,$ while the mother is blood type A. What blood type would exclude a male from being the father? Would the other blood types prove that a particular male was the father?

John Barone
John Barone
Numerade Educator
03:55

Problem 9

The $A$ and $B$ antigens in humans may be found in water-soluble form in secretions, including saliva, of some individuals (Se/Se and Se/se) but not in others (se/se). The population thus contains "secretors" and "nonsecretors."
(a) Determine the proportion of various phenotypes (blood type and ability to secrete) in matings between individuals that are blood type $A B$ and type $O,$ both of whom are Selse.
(b) How will the results of such matings change if both parents are heterozygous for the gene controlling the synthesis of the H substance $(H h) ?$

Bryan Valdivia
Bryan Valdivia
Numerade Educator
01:00

Problem 10

In chickens, a condition referred to as "creeper" exists whereby the bird has very short legs and wings and appears to be creeping when it walks. If creepers are bred to normal chickens, one-half of the offspring are normal and one-half are creepers. Creepers never breed true. If bred together, they yield two-thirds creepers and one-third normal. Propose an explanation for the inheritance of this condition.

Joanna Quigley
Joanna Quigley
Numerade Educator
03:00

Problem 11

In rabbits, a series of multiple alleles controls coat color in the following way: $C$ is dominant to all other alleles and causes full color The chinchilla phenotype is due to the $c^{\mathrm{ch}}$ allele, which is dominant to all alleles other than $C .$ The $c^{h}$ allele, dominant only to $c^{a}$ (albino), results in the Himalayan coat color. Thus, the order of dominance is $C>c^{\kappa h}>c^{h}>c^{a} \cdot$ For each of the following three cases, the phenotypes of the $P_{1}$ generations of two crosses are shown, as well as the phenotype of one member of the $F_{1}$ generation.

Mikayla Stephens
Mikayla Stephens
Numerade Educator
03:22

Problem 12

Three gene pairs located on separate autosomes determine flower color and shape as well as plant height. The first pair exhibits incomplete dominance, where the color can be red, pink (the heterozygote), or white. The second pair leads to personate (dominant) or peloric (recessive) flower shape, while the third gene pair produces either the dominant tall trait or the recessive dwarf trait. Homozygous plants that are red, personate, and tall are crossed to those that are white, peloric, and dwarf. Determine the $F_{1}$ genotype(s) and phenotype(s). If the $\mathrm{F}_{1}$ plants are interbred, what proportion of the offspring will exhibit the same phenotype as the $F_{1}$ plants?

Shiksha Dutta
Shiksha Dutta
Numerade Educator
06:39

Problem 13

As in Problem $12,$ flower color may be red, white, or pink, and flower shape may be personate or peloric. For the following crosses, determine the $P_{1}$ and $F_{1}$ genotypes:
(a) red, peloric $\times$ white, personate
1
$\mathrm{F}_{1}:$ all pink, personate
(b) red, personate $\times$ white, peloric
1
$\mathrm{F}_{1}:$ all pink, personate
(c) pink, personate $\times$ red, peloric $\rightarrow \mathrm{F}_{1} \quad\left\{\begin{array}{l}1 / 4 \mathrm{red}, \text { personate } \\ 1 / 4 \mathrm{red}, \text { peloric } \\ 1 / 4 \mathrm{pink}, \text { peloric } \\ 1 / 4 \mathrm{pink}, \text { personate }\end{array}\right.$
(d) pink, personate $\times$ white, peloric $\rightarrow \mathrm{F}_{1}\left\{\begin{array}{l}1 / 4 \text { white, personate } \\ 1 / 4 \text { white, peloric } \\ 1 / 4 \text { pink, personate } \\ 1 / 4 \text { pink, peloric }\end{array}\right.$
(c) What phenotypic ratios would result from crossing the $\mathrm{F}_{1}$ of
(a) to the $F_{1}$ of $(b) ?$

Carlene Jimenez
Carlene Jimenez
Numerade Educator
05:34

Problem 14

Horses can be cremello (a light cream color), chestnut (a brownish color), or palomino (a golden color with white in the horse's tail and mane). Of these phenotypes, only palominos never breed true.
$\begin{array}{ll}\text { cremello } \times \text { palomino } & \longrightarrow \begin{array}{l}1 / 2 \text { cremello } \\ 1 / 2 \text { palomino }\end{array} \\ \text { chestnut } \times \text { palomino } \longrightarrow & \begin{array}{l}1 / 2 \text { chestnut } \\ 1 / 2 \text { palomino }\end{array} \\ \text { palomino } \times \text { palomino } \longrightarrow & \begin{array}{l}1 / 4 \text { chestnut } \\ 1 / 2 \text { palomino }\end{array} \\ & 1 / 4 \text { cremello }\end{array}$
(a) From the results given above, determine the mode of inheritance by assigning gene symbols and indicating which genotypes yield which phenotypes.
(b) Predict the $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ results of many initial matings between cremello and chestnut horses.

Bryan Lynn
Bryan Lynn
Numerade Educator
06:08

Problem 15

With reference to the eye color phenotypes produced by the recessive, autosomal, unlinked brown and scarlet loci in Drosophila (see Figure 4.10 ), predict the $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ results of the following $\mathrm{P}_{1}$ crosses. (Recall that when both the brown and scarlet alleles are homozygous, no pigment is produced, and the eyes are white.)
(a) wild type $\times$ white
(b) wild type $\times$ scarlet
(c) brown $\times$ white

Khalida Dawar
Khalida Dawar
Numerade Educator
View

Problem 16

Pigment in mouse fur is only produced when the $C$ allele is present. Individuals of the $c c$ genotype are white. If color is present, it may be determined by the $A, a$ alleles. $A A$ or $A a$ results in agouti color, while a results in black coats.
(a) What $F_{1}$ and $F_{2}$ genotypic and phenotypic ratios are obtained from a cross between $A A C C$ and aacc mice?
(b) In three crosses between agouti females whose genotypes were unknown and males of the aacc genotype, the following phenotypic ratios were obtained:

Kaela Piechowicz
Kaela Piechowicz
Numerade Educator
01:47

Problem 17

In rats, the following genotypes of two independently assorting autosomal genes determine coat color:
A third gene pair on a separate autosome determines whether or not any color will be produced. The $C C$ and Cc genotypes allow color according to the expression of the $A$ and $B$ alleles. However, the $c c$ genotype results in albino rats regardless of the $A$ and $B$ alleles present. Determine the $F_{1}$ phenotypic ratio of the following crosses:
(a) $A A b b C C \quad \times \quad$ aaBBcc
(b) $A a B B C C \quad \times \quad A A B b c c$
(c) $A a B b C c \quad \times \quad$ AaBbcc
(d) $A a B B C c \quad \times \quad$ AaBBCc
(e) $A A B b C c \quad \times \quad$ AABbcc

Anand Jangid
Anand Jangid
Numerade Educator
01:47

Problem 18

Given the inheritance pattern of coat color in rats described in Problem $17,$ predict the genotype and phenotype of the parents who produced the following offspring:
(a) $9 / 16$ gray: $3 / 16$ yellow: $3 / 16$ black: $1 / 16$ cream
(b) $9 / 16$ gray: $3 / 16$ yellow: $4 / 16$ albino
(c) $27 / 64$ gray: $16 / 64$ albino: $9 / 64$ yellow: $9 / 64$ black: $3 / 64$ cream
(d) $3 / 8$ black: $3 / 8$ cream: $2 / 8$ albino
(e) $3 / 8$ black: $4 / 8$ albino: $1 / 8$ cream

Anand Jangid
Anand Jangid
Numerade Educator
04:47

Problem 19

In a species of the cat family, eye color can be gray, blue, green, or brown, and each trait is true breeding. In separate crosses involving homozygous parents, the following data were obtained: (a) Analyze the data. How many genes are involved? Define gene symbols and indicate which genotypes yield each phenotype. (b) In a cross between a gray-eyed cat and one of unknown genotype and phenotype, the $\mathrm{F}_{1}$ generation was not observed. However, the $\mathrm{F}_{2}$ resulted in the same $\mathrm{F}_{2}$ ratio as in cross $\mathrm{C}$. Determine the genotypes and phenotypes of the unknown $\mathrm{P}_{1}$ and $\mathrm{F}_{1}$ cats.

Protim Das
Protim Das
Numerade Educator
04:29

Problem 20

In a plant, a tall variety was crossed with a dwarf variety. All $\mathrm{F}_{1}$ plants were tall. When $\mathrm{F}_{1} \times \mathrm{F}_{1}$ plants were interbred, $9 / 16$ of the $\mathrm{F}_{2}$ were tall and $7 / 16$ were dwarf.
(a) Explain the inheritance of height by indicating the number of gene pairs involved and by designating which genotypes yield tall and which yield dwarf. (Use dashes where appropriate.)
(b) What proportion of the $F_{2}$ plants will be true breeding if self- fertilized? List these genotypes.

Jessica Wooten
Jessica Wooten
Numerade Educator
01:31

Problem 21

In a unique species of plants, flowers may be yellow, blue, red, or mauve. All colors may be true breeding. If plants with blue flowers are crossed to red-flowered plants, all $\mathrm{F}_{1}$ plants have yellow flowers. When these produced an $\mathrm{F}_{2}$ generation, the following ratio was observed: $9 / 16$ yellow: $3 / 16$ blue: $3 / 16$ red: $1 / 16$ mauve
In still another cross using true-breeding parents, yellow-flowered plants are crossed with mauve-flowered plants. Again, all $\mathrm{F}_{1}$ plants had yellow flowers and the $\mathrm{F}_{2}$ showed a 9: 3: 3: 1 ratio, as just shown.
(a) Describe the inheritance of flower color by defining gene symbols and designating which genotypes give rise to each of the four phenotypes.
(b) Determine the $F_{1}$ and $F_{2}$ results of a cross between truebreeding red and true-breeding mauve-flowered plants.

Anand Jangid
Anand Jangid
Numerade Educator
01:09

Problem 22

Five human matings $(1-5),$ identified by both maternal and paternal phenotypes for $\mathrm{ABO}$ and $\mathrm{MN}$ blood-group antigen status, are shown on the left side of the following table:
Each mating resulted in one of the five offspring shown in the right-hand column (a-e). Match each offspring with one correct set of parents, using each parental set only once. Is there more than one set of correct answers?

Christina Sorrentino
Christina Sorrentino
Numerade Educator
01:15

Problem 23

A husband and wife have normal vision, although both of their fathers are red-green color-blind, an inherited X-linked recessive condition. What is the probability that their first child will be
(a) a normal son,
(b) a normal daughter,
(c) a color-blind son,
(d) a color-blind daughter?

Zachary Papazian
Zachary Papazian
Numerade Educator
01:04

Problem 24

In humans, the ABO blood type is under the control of autosomal multiple alleles. Color blindness is a recessive X-linked trait. If two parents who are both type A and have normal vision produce a son who is color-blind and is type 0 , what is the probability that their next child will be a female who has normal vision and is type $0 ?$

Danielle Ashley
Danielle Ashley
Numerade Educator
05:41

Problem 25

In Drosophila, an X-linked recessive mutation, scalloped (sd) causes irregular wing margins. Diagram the $F_{1}$ and $F_{2}$ results if $(a)$ a scalloped female is crossed with a normal male; (b) a scalloped male is crossed with a normal female. Compare these results with
those that would be obtained if the scalloped gene were autosomal.

John Barone
John Barone
Numerade Educator
07:25

Problem 26

Another recessive mutation in Drosophila, ebony (e), is on an autosome (chromosome 3) and causes darkening of the body compared with wild-type flies. What phenotypic $F_{1}$ and $F_{2}$ male and female ratios will result if a scalloped-winged female with normal body color is crossed with a normal-winged ebony male? Work out this problem by both the Punnett square method and the forked-line method.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
06:08

Problem 27

In Drosophila , the X-linked recessive mutation vermilion (v) causes bright red eyes, in contrast to the brick-red eyes of wild type. A separate autosomal recessive mutation, suppressor of vermilion $(s u-v),$ causes flies homozygous or hemizygous for $v$ to have wildtype eyes. In the absence of vermilion alleles, su-v has no effect on eye color. Determine the $F_{1}$ and $F_{2}$ phenotypic ratios from a cross between a female with wild-type alleles at the vermilion locus, but who is homozygous for $s u$ -v, with a vermilion male who has wildtype alleles at the su-v locus.

Khalida Dawar
Khalida Dawar
Numerade Educator
06:08

Problem 28

While vermilion is X-linked in Drosophila and causes the eye color to be bright red, brown is an autosomal recessive mutation that
causes the eye to be brown. Flies carrying both mutations lose all pigmentation and are white-eyed. Predict the $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ results of the following crosses:
(a) vermilion females $\times$ brown males
(b) brown females $\times$ vermilion males
(c) white females $\times$ wild-type males

Khalida Dawar
Khalida Dawar
Numerade Educator
05:20

Problem 29

In a cross in Drosophila involving the X-linked recessive eye mutation white and the autosomally linked recessive eye mutation sepia (resulting in a dark eye), predict the $F_{1}$ and $F_{2}$ results of crossing true-breeding parents of the following phenotypes:
(a) white females $\times$ sepia males
(b) sepia females $\times$ white males Note that white is epistatic to the expression of sepia.

Bryan Valdivia
Bryan Valdivia
Numerade Educator
04:58

Problem 30

Consider the three pedigrees below, all involving a single human trait.
(a) Which combination of conditions, if any, can be excluded? dominant and X-linked
dominant and autosomal
recessive and X-linked
recessive and autosomal
(b) For each combination that you excluded, indicate the
single individual in generation II (e.g., II-1, II-2 ) that was most instrumental in your decision to exclude it. If none were excluded, answer "none apply."
(c) Given your conclusions in part (a), indicate the genotype of the following individuals:
II-1, II-6, II-9
If more than one possibility applies, list all possibilities. Use the
symbols $A$ and $a$ for the genotypes.

John Barone
John Barone
Numerade Educator
05:43

Problem 31

In goats, the development of the beard is due to a recessive gene. The following cross involving true-breeding goats was made and carried to the $\mathrm{F}_{2}$ generation:
Offer an explanation for the inheritance and expression of this trait, diagramming the cross. Propose one or more crosses to test your hypothesis.

Mikayla Stephens
Mikayla Stephens
Numerade Educator
01:37

Problem 32

Predict the $F_{1}$ and $F_{2}$ results of crossing a male fowl that is cockfeathered with a true-breeding hen-feathered female fowl. Recall that these traits are sex limited.

Danielle Ashley
Danielle Ashley
Numerade Educator
03:54

Problem 33

Two mothers give birth to sons at the same time at a busy urban hospital. The son of mother 1 is afflicted with hemophilia, a dis- ease caused by an X-linked recessive allele. Neither parent has the disease. Mother 2 has a normal son, despite the fact that the father has hemophilia. Several years later, couple 1 sues the hospital, claiming that these two newborns were swapped in the nursery following their birth. As a genetic counselor, you are called to testify. What information can you provide the jury concerning the allegation?

Chelsi Marolf
Chelsi Marolf
Numerade Educator
05:25

Problem 34

Discuss the topic of phenotypic expression and the many factors that impinge on it.

Bryan Valdivia
Bryan Valdivia
Numerade Educator
01:38

Problem 35

Contrast penetrance and expressivity as the terms relate to phenotypic expression.

Theodore Donnell
Theodore Donnell
Numerade Educator
05:31

Problem 36

Labrador retrievers may be black, brown (chocolate), or golden (yellow) in color (see chapter-opening photo on p. 62 ). While each color may breed true, many different outcomes are seen when numerous litters are examined from a variety of matings where the parents are not necessarily true breeding. Following are just some of the many possibilities.
Propose a mode of inheritance that is consistent with these data, and indicate the corresponding genotypes of the parents in each mating. Indicate as well the genotypes of dogs that breed true for each color

John Barone
John Barone
Numerade Educator
02:33

Problem 37

A true-breeding purple-leafed plant isolated from one side of
El Yunque, the rain forest in Puerto Rico, was crossed to a truebreeding white variety found on the other side. The $\mathrm{F}_{1}$ offspring were all purple. A large number of $\mathrm{F}_{1} \times \mathrm{F}_{1}$ crosses produced the following results:
\[
\text { purple: } 4219 \quad \text { white: } 5781 \quad(\text { Total }=10,000)
\]
Propose an explanation for the inheritance of leaf color. As a geneticist, how might you go about testing your hypothesis? Describe the genetic experiments that you would conduct.

John Barone
John Barone
Numerade Educator
02:16

Problem 38

In Dexter and Kerry cattle, animals may be polled (hornless) or horned. The Dexter animals have short legs, whereas the Kerry
animals have long legs. When many offspring were obtained from matings between polled Kerrys and horned Dexters, half were found to be polled Dexters and half polled Kerrys. When these two types of $\mathrm{F}_{1}$ cattle were mated to one another, the following $\mathrm{F}_{2}$ data were obtained:
$3 / 8$ polled Dexters
$3 / 8$ polled Kerrys
$1 / 8$ horned Dexters
$1 / 8$ horned Kerrys
A geneticist was puzzled by these data and interviewed farmers who had bred these cattle for decades. She learned that Ker-
rys were true breeding. Dexters, on the other hand, were not true breeding and never produced as many offspring as Kerrys. Provide a genetic explanation for these observations.

Hailey Tomashek
Hailey Tomashek
Numerade Educator
05:08

Problem 39

A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering "rib-it rib-it" and has purple eyes. The other line croaks more softly by muttering "knee-deep knee-deep" and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing $\mathrm{F}_{1}$ frogs that were all utterers and had blue eyes. A large $\mathrm{F}_{2}$ generation then yielded the following ratios:
(a) How many total gene pairs are involved in the inheritance of both traits? Support your answer.
(b) Of these, how many are controlling eye color? How can you tell? How many are controlling croaking?
(c) Assign gene symbols for all phenotypes and indicate the genotypes of the $P_{1}$ and $F_{1}$ frogs.
(d) Indicate the genotypes of the six $F_{2}$ phenotypes.
(e) After years of experiments, the geneticist isolated purebreeding strains of all six $\mathrm{F}_{2}$ phenotypes. Indicate the $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ phenotypic ratios of the following cross using these pure-breeding strains: blue-eyed, "knee-deep" mutterer $\times$ purple-eyed, "rib-it" utterer.
(f) One set of crosses with his true-breeding lines initially caused the geneticist some confusion. When he crossed truebreeding purple-eyed, "knee-deep" mutterers with truebreeding green-eyed, "knee-deep" mutterers, he often got different results. In some matings, all offspring were blue-eyed, "knee-deep" mutterers, but in other matings all offspring were purple-eyed, "knee-deep" mutterers. In still a third mating, 1/2 blue-eyed, "knee-deep" mutterers and 1/2 purple-eyed, “knee-deep" mutterers were observed. Explain why the results differed.
(g) In another experiment, the geneticist crossed two purple-eyed, "rib-it" utterers together with the results shown here:
What were the genotypes of the two parents?

James Kiss
James Kiss
Numerade Educator
02:49

Problem 40

The following pedigree is characteristic of an inherited condition known as male precocious puberty, where affected males show signs of puberty by age $4 .$ Propose a genetic explanation of this phenotype.

Prashant Bana
Prashant Bana
Numerade Educator
01:26

Problem 41

Students taking a genetics exam were expected to answer the following question by converting data to a "meaningful ratio" and then solving the problem. The instructor assumed that the final ratio would reflect two gene pairs, and most correct answers did. Here is the exam question: "Flowers may be white, orange, or brown. When plants with white flowers are crossed with plants with brown flowers, all the $F_{1}$ flowers are white. For $F_{2}$ flowers, the following data were obtained:
Convert the $F_{2}$ data to a meaningful ratio that allows you to explain the inheritance of color. Determine the
number of genes involved and the genotypes that yield each phenotype."
(a) Solve the problem for two gene pairs. What is the final $\mathrm{F}_{2}$ ratio?
(b) A number of students failed to reduce the ratio for two gene pairs as described above and solved the problem using three gene pairs. When examined carefully, their solution was deemed a valid response by the instructor. Solve the problem using three gene pairs.
(c) We now have a dilemma. The data are consistent with two alternative mechanisms of inheritance. Propose an experiment that executes crosses involving the original parents that would distinguish between the two solutions proposed by the students. Explain how this experiment would resolve the dilemma.

Anand Jangid
Anand Jangid
Numerade Educator
02:21

Problem 42

In four o'clock plants, many flower colors are observed. In a cross involving two true-breeding strains, one crimson and the other white, all of the $\mathrm{F}_{1}$ generation were rose color. In the $\mathrm{F}_{2}$, four new phenotypes appeared along with the $P_{1}$ and $F_{1}$ parental colors. The following ratio was obtained:
Propose an explanation for the inheritance of these flower colors.

Eric Goldman
Eric Goldman
Numerade Educator
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Problem 43

Below is a partial pedigree of hemophilia in the British Royal Family descended from Queen Victoria, who is believed to be the original "carrier" in this pedigree. Analyze the pedigree and indicate which females are also certain to be carriers. What is the probability that Princess Irene is a carrier?

Kaela Piechowicz
Kaela Piechowicz
Numerade Educator