Introduction to Math Topics in Biology
Introduction:
The
purpose of this exercise is to allow explore the rules of probability.
Objectives:
o
Define the terms: allele,
dominant, recessive, and incomplete dominance.
o
Identify frequencies of allele combinations for single gene crosses.
o
Understand how to calculate the probability of different types of genetic
events.
Materials:
each group of students will need:
2 or more coins of different denominations
2 or more dice
Probability
Activity:
Using
two six-sided dice, perform the following exercises to explore the laws of
probability. Show all of your
calculations!
a.
Roll a single six-sided die. What
is the probability of rolling a four?
What is the probability of rolling a four?
d.
Roll one die 12 times: record
your results: one(s______,
two(s) ______,
three(s) ______, four(s) ______,
five(s) ______, six(es) ______.
What is the probability of rolling a one (single dot) on the thirteenth
roll?
e.
Roll two dice together
(simultaneously).
What is the probability rolling seven?
What is the probability rolling two (one dot on each die)?
What is the probability of rolling a one and a two together?
f.
If you rolled a six-sided die
and a ten-sided die,
what is the probability of rolling a one and a two together?
Introduction:
The
purpose of this exercise is to allow students to observe how single genetic
traits get combined. Student groups will use beads (or beans) to represent gene
alleles and a random selection method.
Objectives:
o
Define the terms allele, dominant, recessive, and incomplete dominance.
o
Identify frequencies of allele combinations for single gene crosses.
o
Understand the proportions involved with genetics and simple gene
crosses.
Materials:
each group of students will need:
4 large beakers
100-200 colored (red) beads
100-200 clear beads
genetics
Activity:
Students
will observe how single genetic traits are combined, using non-biological
alleles (beads of different colors).
A
red bead represents the red allele, R.
A
clear bead represents the white allele, r.
In
this case RR=red, Rr=red, rr=white.
b.
Put all (100-200) red beads in one beaker (beaker 1), this represents the
homozygous red parent. Put all
(100-200) clear beads in one beaker (beaker 2), this represents the homozygous
white parent. This represents the P
(parent) generation.
c.
Select one bead from each beaker. This
pair should be tallied (recorded). Put
this pair in beaker 3. Select
another pair of beads (one from beaker 1 and one from beaker 2). Put this pair in beaker 4.
d.
Continue step 2 until you have 50 pairs each in beakers 3 & 4.
(100 total pairs.) Record the number of RR, rr and Rr pairs you selected in step
three. This represents the F1
generation.
e.
Select one bead from each beaker. Continue
to select pairs until all the beads have been selected. Record the number of RR, rr, and Rr.
f.
Now assume the beads represent alleles for flower color.
a.
Assume that R is dominant and r is recessive.
What color are the flowers in the F1 generation (and how many of each
color)? What color are the flowers in the F2 generation (and how many of each
color)?
b.
Assume that R and r show incomplete dominance.
What color are the flowers in the F1 generation (and how many of each
color)? What color are the flowers in the F2 generation (and how many of each
color)?