Download 1 © 2013 AIMS Education Foundation Topic Heredity Key Question

NCTM Standards 2000*
• Predict the probability of outcomes of simple experiments and test the predictions
• Design investigations to address a question and
consider how data-collection methods affect the
nature of the data set
• Collect data using observations, surveys, and
experiments
• Represent data using tables and graphs such as
line plots, bar graphs, and line graphs
• Use proportionality and a basic understanding of
probability to make and test conjectures about the
results of experiments and simulations
Topic
Heredity
Key Question
What kind of offspring will our Teddy Bear parents
produce?
Learning Goals
Students will:
• recognize that characteristics passed from parents
to child are predictable, and
• simulate the mixing of genetic codes to determine
the possible outcomes from two parents.
Math
Data analysis
probability
statistics
sampling
graphing
bar graphs
Guiding Documents
Project 2061 Benchmarks
• Some likenesses between children and parents, such
as eye color in human beings, or fruit or flower color in
plants, are inherited. Other likenesses, such as people’s
table manners or carpentry skills, are learned.
• For offspring to resemble their parents, there must
be a reliable way to transfer information from one
generation to the next.
Science
Life science
heredity
NRC Standards
• Many characteristics of an organisms are inherited
from the parents of the organisms, but other characteristics result from an individual’s interactions with
the environment. Inherited characteristics include the
color of flowers and the number of limbs of an animal.
Other features, such as the ability to ride a bicycle, are
learned through interactions with the environment
and cannot be passed on to the next generation.
• Every organism requires a set of instructions for
specifying its traits. Heredity is the passage of these
instructions from one generation to another.
• Heredity information is contained in genes, located
in the chromosomes of each cell. Each gene carries
a single unit of information. An inherited trait of an
individual can be determined by one or by many
genes, and a single gene can influence more than
one trait. A human cell contains many thousands
of different genes.
Integrated Processes
Observing
Classifying
Collecting and organizing data
Comparing and contrasting
Generalizing
Inferring
Materials
Teddy Bear Counters (see Management 3)
Paper bag or box, one per student group
Student pages
Background Information
Traits are passed between generations by genetic
coding of chromosomes. One or more gene pairs may
control a trait. Each parent contributing one gene forms
a pair of genes. With a simple genetic characteristic,
one gene pair controls the trait. If a gene’s trait is more
prominent in the individual, that gene is said to code
for the dominant trait. If the gene’s trait is less prominent in the individual, the gene is said to code for the
recessive trait.
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© 2013 AIMS Education Foundation
The ability to curl your tongue is a trait that is controlled by one gene pair. A dominant gene will allow
you to curl your tongue. A recessive gene will not give
you this ability. If either or both of the genes in your
pair is dominant you will be able to curl your tongue.
If both the genes in your pair are recessive, you will
not be able to curl your tongue.
When both genes are the same, they are called
homogeneous. If both parents are homogeneous for the
recessive trait, all offspring will display the recessive trait
because they have only recessive genes. If both parents
are homogeneous for the dominant trait, all the offspring
will display the dominant trait because they have only
the dominant genes. When the gene pair is mixed with a
dominant and recessive gene, it is called heterogeneous.
Individuals that have heterogeneous genes display only
the dominant trait. Many people who curl the their tongues
(dominant trait) have heterogeneous genes (one dominant, one recessive). The offspring of heterogeneous parents show either recessive or dominant traits depending
on which gene was passed on to the child. The mixture of
traits in the offspring then is the result of the chance event
of the recessive or dominant trait being passed on to the
child. This mixture can be predicted using probability.
This investigation is a simulation of experiments
done by Gregor Mendel in the early 1800s. Mendel’s
work formed the foundation of the study of heredity.
Mendel studied pea plants and recognized that dwarf
plants always produced dwarf plants, while tall plants
produce both dwarf and tall offspring. With pea
plants, tall is a dominant trait. Dwarf plants have
pure recessive genes.
This investigation simulates the offspring of two
heterogeneous parents. The two equal amounts of
colored Teddy Bear Counters (20) represent the equal
representation of dominant and recessive genes in the
parents. Drawing two bears simulates the contribution of one gene from each parent. If red and blue
are the colors, there are four possible outcomes in
the draw. Only possibility is for both bears to be the
same color—red-red or blue-blue. These represent two
homogeneous offspring. The other possibilities are redblue or blue-red, which represent two heterogeneous
offspring. These possibilities mean that in a large sample,
one-fourth should both be red, one-half should be mixed,
and one-fourth should be both blue.
When working with probability, it is important to
gather information from a large number of events.
Mendel often studied as many as 17,000 plants before
arriving at a generalization. The requirement of using a
large number of trials should be discussed and stressed
as students complete this investigation. During the simulation each student group will repeat the investigation
four times. The average will then be computed. Next,
the average results from all groups will be pooled. This
will yield a significant number of trials and the average
result should closely approximate those Mendel found
with pea plants.
Just as Mendel found that about one-fourth of the
results were pure tall, one-half hybrid, and one-fourth
pure dwarf, students will find that one-fourth of the
results consist of pairs where both are of the first color,
one-half are mixed, and the remaining one-fourth are
pairs of the second color. (Hint: use the terminology
of first and second colors rather than color names,
this helps avoid confusion since different groups will
probably use different colors.)
Students will learn how heredity is passed from
parent to offspring through genes and will be able to
generalize the pattern of distribution. However, they
will have more difficulty understanding the probability
controlling the outcome. Piaget conducted a similar
investigation using marbles. He wanted to determine
at what age students formed intuitive notions of probability. He placed an equal number of marbles of each
of two colors in a bag and mixed them thoroughly. He
told children that he would draw the marbles out in
pairs. He asked them to predict which event was most
likely among the following:
both would be the first color;
both would be the second color; or,
there would be one of each color.
He found that generally students before age 12 would
make guesses, usually wrong, with little reason for doing
so. However, at age 12 many of them began to reason
that the most likely event would be a mixed pair.
Recognize what understanding is most appropriate
for your students. Before beginning this investigation,
ask your students to make predictions as to the most
common result and have them explain the reason for
the answer.
Key Vocabulary:
Trait: a characteristic that is inherited from parents
DNA: the material that carries our traits
Gene: a part of the DNA that has our traits on it
Management
1. The best results will be obtained if there are six
to eight student groups each performing independent investigations.
2. Learning groups of three to four students work
best. Each student should be assigned a job:
drawer, grapher, recorder, calculator. The assignments can rotate after each test.
3. Each group will need 40 Teddy Bear Counters,
20 each of two colors. The AIMS Friendly Bears
or other objects of uniform size and shape may
be substituted for Teddy Bear Counters. Have
students put the bears into a paper bag or box.
Procedure
1.Discuss the Key Questions and relate the simulation to a parents’ genes being selected and paired
and passed on to the offspring.
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© 2013 AIMS Education Foundation
2. Explain the procedure and divide the class into the
desired number of collaborative learning groups
and assign tasks.
3. Make sure that each group has a bag or box of
20 Teddy Bear Counters in each of two colors.
4. Explain to the students that the bears will be drawn
out in pairs and not put back into the bag or box
until the trial ends; 20 pairs will be drawn. Before
beginning the investigation, ask the students to
record their predictions of how many of the 20
events will occur for each of the three results.
5. Instruct the students to mix the bears thoroughly,
pointing out that such mixing is necessary to
produce random results.
6. Have students draw out bears in pairs, classifying
each pair as it is placed on the sorting bar graph
(page 2).
7. After all pairs have been classified, have students
place the numerical information in the table.
8. Tell students to complete four trials before they
find the average and graph the results.
9. Have all the groups share their results. Collect the
data from all of the groups.
10. Have students find the average result of all the
trials and graph the information.
Connecting Learning
1. How do your results compare for the four trials?
[different for each trial, but most in mixed pairs]
2. Why is the average a better predictor of what is likely
to happen? [It balances the highs and lows.]
3. Which event (colors of bears) occurred most
frequently? [mixed pairs]
4. How did the class average compare to your
group’s average?
5. How many times more often does a mixed pair
occur than a pair of one of the colors? [twice as
often as either of the colors]
6. If the 20 pairs represent 20 offspring, what fraction of the offspring will share the dominant trait
with the parents? (Colored counters represent the
dominant and recessive genes. Let the first color
represent the dominant gene. If a pair of genes
has one dominant gene, the offspring will show
that trait.)
7. What fraction of the 20 offspring will not share the
trait with their parent?
8. Why do offspring tend to have the same traits as
their parents?
9. What are you wondering now?
* Reprinted with permission from Principles and Standards for
School Mathematics, 2000 by the National Council of Teachers
of Mathematics. All rights reserved.
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© 2013 AIMS Education Foundation
Key Question
What kind of offspring will
our Teddy Bear parents
produce?
Learning Goals
Students will:
• recognize that characteristics passed from parents
to child are predictable, and
• simulate the mixing of genetic codes to determine
the possible outcomes from two parents.
Key Vocabulary
Trait: a characteristic that is inherited from parents
DNA: the material that carries our traits
Gene: a part of the DNA that has our traits on it
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© 2013 AIMS Education Foundation
1. Put 20 counters of a first color and 20 of a second color into a bag or box.
2. Mix them well.
3. You will pull the counters out in pairs. Before you start, predict how many of the
20 pairs there will be of each combination.
Number of pairs where both are the first color:
Number of pairs where there is one of each color:
Number of pairs where both are the second color:
4. Draw out two counters at a time, classify the
pair, and place both counters in the proper
column on the bar graph on the next page.
5. After all the counters have been drawn, count
the number of pairs in each category and
record in the table.
6. Complete four trials and then average them.
Test Number
First Color
Mixed Pairs
Second Color
ONE
TWO
THREE
FOUR
TOTAL
AVERAGE
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© 2013 AIMS Education Foundation
First Color
Mixed Colors
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Second Color
© 2013 AIMS Education Foundation
Graph the results for each of the four tests.
Test
Number
Result
Number of Occurrences
1 2 3 4 5 6 7 8 9 10 11 12131415
First Color
Mixed Pairs
Second Color
First Color
Mixed Pairs
Second Color
First Color
Mixed Pairs
Second Color
First Color
Mixed Pairs
Second Color
AVERAGE
First Color
Mixed Pairs
Second Color
1. How do the number of occurrences for the type of events compare between trials?
2. Why is the average a better predictor of what is likely to happen?
3. Which event occurred most frequently?
4. How much more often did the most common event happen
than either of the other two events?
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© 2013 AIMS Education Foundation
Collect the average results from the other groups.
Calculate the average for the class.
Group Number
First Color
Mixed Pairs Second Color
ONE
TWO
THREE
FOUR
FIVE
SIX
SEVEN
EIGHT
TOTAL
AVERAGE
Graph the class averages.
DESCRIPTION
Number of Occurrences
1 2 3 4 5 6 7 8 9 10 11 12131415
First Color
Mixed Pairs
Second Color
5. How did the class average compare to your group’s average?
6. How many times more often does a mixed pair occur than a pair of one of the colors?
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CO
N
NE
C T I NG
Connecting Learning
LEA
RN
1. How do your results compare
for the four trials?
I NG
2. Why is the average a better
predictor of what is likely to
happen?
3. Which event (colors of bears) occurred
most frequently?
4. How did the class average
compare to your group’s
average?
5. How many times more
often does a mixed pair
occur than a pair of one
of the colors?
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© 2013 AIMS Education Foundation
CO
N
NE
C T I NG
Connecting Learning
LEA
RN
I NG
6. If the 20 pairs represent 20
offspring, what fraction of the
offspring will share the dominant trait with the parents?
7. What fraction of the 20 offspring will
not share the trait with their parent?
8. Why do offspring tend to have the
same traits as their parents?
9. What are you
wondering now?
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© 2013 AIMS Education Foundation
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