Transcript Mapping Points in a Plane

Probability and Betweenness of
Points: The Genetic Ruler
Kevin DeVizia & Mark Nebzydoski
Delaware Valley High School
Milford, PA
The Delaware Valley Program
•
scientists vs. lab assistants
•
student-initiated research vs. canned
experiments
•
link math and science
•
scheduling
•
www.dvsd.org/honorsmathsci
NCTM’s Connections Standard

Instructional programs from prekindergarten
through grade 12 should enable all students
to:
– recognize and use connections among
mathematical ideas;
– understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole;
– recognize and apply mathematics in
contexts outside of mathematics.
The Delaware Valley Program
9th grade: Biology / Geometry
 10th grade: Chemistry / Algebra 2
 11th grade: Physics / Precalculus
 Statistics taught throughout

Some Biology/Geometry Links

Statistical Inference & Experimental Design
 Similarity/Proportion & Anatomical
Morphology
 Sequences/Recursion & Population Ecology
 Probability/Combinatorics & Genetics
Mapping Points

Given a set of points and the distances
shown, sketch a map of how the points
might appear in the plane and describe
the geometry of the shape they form.
Justify your response in each case:
–
–
–
–
1.
2.
3.
4.
AB = 5, BC = 5, AC = 5
AB = 3, BC = 4, AC = 5
AB = 2, BC = 3, AC = 4
AB = 2, BC = 3, AC = 5
More Problems in Placing
Points
Sometimes an atlas will show a set of
distances between pairs of cities in a chart
like this…
More Problems in Placing
Points

Try mapping the points designated in this
chart; justify the geometry involved.
More Problems in Placing
Points

Try mapping the points designated in this
chart; justify the geometry involved.
More Problems in Placing
Points

Try mapping the points designated in this
chart… Hint: these points are collinear.
Gene Mapping

An ordered list of genetic loci along a
particular chromosome
 First done by Thomas Hunt Morgan and
later used in the Human Genome Project
Linked Genes
•
Genes located on the same chromosome,
linked genes, tend to be inherited
together because the chromosome is
passed along as a unit.
•
Results of crosses with linked genes
deviate from those expected according to
independent assortment.
First Use of Gene Mapping

Thomas Hunt Morgan observed this linkage
and its deviations when he followed the
inheritance of characters for body color and
wing size.
 The wild-type body color is gray (b+) and the
mutant black (b).
 The wild-type wing size is normal (vg+) and
the mutant has vestigial wings (vg).
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings
b+b vg+vg
X
b b vg vg
(Assuming independent assortment)
(Genes on different chromosomes)
b+vg+
b+vg
b vg+
b vg
b vg
b+b vg+vg b+b vg vg
b b vg+vg b b vg vg
b vg
b+b vg+vg b+b vg vg
b b vg+vg b b vg vg
b vg
b+b vg+vg b+b vg vg
b b vg+vg b b vg vg
b vg
b+b vg+vg b+b vg vg
b b vg+vg b b vg vg
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings
A Gene Mapping Problem

Consider genes X, Y, and Z. If the
percent recombination
–
between X and Y is 10,
– between X and Z is 4,
– between Z and Y is 6,

then what is the order of the genes on
the chromosome?
A Gene Mapping Problem

mah=mahogany eyes, h=hairy body,
se=sepia eyes, e=ebony body
mah
0
h
10
0
se
3.5
6.5
0
e
19.5
9.5
16
0
mah
h
se
e
A Gene Mapping Problem
(with a twist)

Ye=yellow body, Ve=Vermillion eyes,
MW=miniature wings, Wh=white eyes
Ye
0
Wh
1
0
Ve
32.2
30
0
MW
35.5
32.7
3
0
Ye
Wh
Ve
MW
An Explanation of the Twist
Using multiple crosses of this type with
different genes percentages of
recombination can be generated.
 b – cn = 9%
 cn – vg = 9.5%
 b – vg = 17%

An Explanation of the Twist
Fig. 15.6
Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings
For More Information…

www.dvsd.org/honorsmathsci