Interdisciplinary Math and Biology Module: Sickle Cell

INTERDISCIPLINARY MATH AND BIOLOGY MODULE: SICKLE CELL

By; REBECCA LANGOMES, FE ARENASA, JULITA BELCHES, JUDITH B. ABERGOS

CONTEXT

The purpose of this module is to provide a design of instruction- a framework in which the student plays a role within a simulation, acquiring knowledge and skills in the process of pursuing a meaningful lesson of sickle cell wherein there will be interdisciplinary concepts of mathematics (number patterns, function algebra, proportion, geometry , data analysis, statistics, probability and spatial sense) and biology (genetics).

ABSTRACT

Sickle cell anemia is a disease passed down through families in which red blood cells form an abnormal crescent shape. (Red blood cells are normally shaped like a disc.)

According to Bediako, Shawn, et.al, the present study examined an exploratory model of the confluence of racial centrality, pain, psychological variables, and health care use in a sample of African American adults with sickle cell disease.

SCD affects an estimated 70,000 to 100,000 Americans.

The disease occurs in about 1 out of every 500 African Americans births.

The disease occurs in about 1 out of every 36,000 Hispanic Americans births.

Sickle cell trait occurs in about 1 in 12 African Americans.

THEMES, CONCEPT/ BIG IDEAS:

Sickle cell anemia is caused by an abnormal type of hemoglobin called hemoglobin S. Hemoglobin S changes the shape of red blood cells, especially when the cells are exposed to low oxygen levels. The fragile, sickle-shaped cells deliver less oxygen to the body's tissues. They can also get stuck more easily in small blood vessels, and break into pieces that interrupt healthy blood flow.

Sickle cell anemia is inherited from both parents. If you inherit the hemoglobin S gene from one parent and normal hemoglobin (A) from your other parent, you will have sickle cell trait. People with sickle cell trait do not have the symptoms of sickle cell anemia.

GOALS AND OBJECTIVES:

The goals of the module are

BIOLOGY:

To demonstrate how sorting and recombination of genes results in genetic variation among offspring (Indicator 1) .
To demonstrate how traits are inherited including Punnett squares and pedigree analysis (Indicator 2)
To demonstrate the relationship between the structure of DNA and its role in determining traits (Indicator 3)
To demonstrate beneficial and harmful effects of genetic alteration (Indicator 4)

MATH:

a.Students will collect data and determine the percent frequency of specific genes in a given population.

b.Students will focus on learning to reason and construct proof by estimating and comparing with a real world model the frequency of sickle cell anemia in a population.

c.Students will communicate the mathematical data collected in their cooperative learning groups by sharing that data to formulate a class average and by using that information to support a debate on genetics.

d.Students will recognize the use of probability and percentages to analyze problems in real world situations.

e.Students will develop mathematical skills such as averaging, using tables and using formulas .

f.Students will use computational tools and strategies such as prediction, basic mathematical skills and algebraic formulas to analyze collected data.

g.Students will use genetic patterns and algebraic formulas to further their understanding of sickle cell anemia.

h.Students will create a statistical graph of the class data and explore spatially through handson activities and demonstrations.

i.Students will collect, predict, organize, and represent data to answer questions based on genetics. Students will discuss and support their opinions on the current topic of genetic testing of children in a classroom debate.

PRE-REQUISITE KNOWLEDGE:

BIOLOGY

Cell and its Structure
Biological Structure
Ecology

MATHEMATICS

Number patterns,
Algebra 1,
Geometry
Functions

Timeline: 4 LESSONS FOR ABOUT 2 WEEKS

LESSON PLANS

LESSON PLAN NO. 1
KNOWING SICKLE CELL
By: FE ARENASA, JUDITH BEBORA, JULITA BELCHES REBECCA LANGOMES
Course: BIOLOGY
Class: ______/ Date: ______
DAY______
Unit Title: GENETICS
Topic: WHAT IS SICKLE CELL?
Materials:
Video Clips : The Creation, What is sickle Cell?, Worksheets, Calculator
MSDE CORE Standards:
MATH:
Quantities★N -Q
Reason quantitatively and use units to solve problems.
1. Use units as a way to understand problems and to guide the solutionof multi-step problems; choose and interpret units consistently informulas; choose and interpret the scale and the origin in graphs and
data displays.
2. Define appropriate quantities for the purpose of descriptive modeling.
3. Choose a level of accuracy appropriate to limitations on measurementwhen reporting quantities.
BIIOLOGY
expectation 3.3
The student will analyze how traits are inherited and passed on from one generation to another.
Indicator:
3.3.1 The student will demonstrate that the sorting and recombination of genes during sexual reproduction has an effect on variation in offspring.
Lesson Objectives:
1.The Students will be able to describe sickle cell, reason and contrast proof by estimating and comparing with a real world and its frequency in its population.
2. Students will collect data and determine the percent frequency of specific genes in a given population.
Opening Activity/Warm-up:
Video Clip Showing: The creation: Students will make a cornell Note( worksheet #1) of the formation of the fetus.
Lesson Proper:
Engagement of Students:
Problem Solving: If there are 2 sperms out of 500 to develop a Zygote out, what is the percentage of creating a baby? Refer to video clip 1.
Exploration Activity: WICR ( Writing, Inquiring, Collaboration and Reading Strategy)
The class will be introduced to the topic of genetic diseases in a classroom discussion led by the classroom teacher.
Perform Part I and part II of the Gene Pool Lab:
Selection of Environment with or without Malaria.
Then you should compare this result by creating a tabulated data, plotting a graph, and determine the frequency .
Gene Pool lab-
For Teacher:
A Mutation Story link: /

This segment tells the story of a geneticmutationaffecting the population of West Africa. Although helpful in preventingmalaria, this mutation can also lead tosickle cell anemia. Sickle cell specialistDr. Ronald Nagelstresses the genetic diversity required for the survival of a species.
Credits:© 2001 WGBH Educational Foundation and Clear Blue Sky Productions, Inc. All rights reserved.
For Student Worksheet:
Gene Pool Lab link:
Part I. Selection in a malarial environment
Environment: Today, you are living in a poor country where malaria is a problem, and you cannot afford medication or treatment to combat the effects of sickle cell anemia.
Procedures:
*Note: The teacher will record class data on the board; EACH student must record this information on their data table.

Choose one HbA and one HbS hemoglobin allele from the gene pool. (Generation 0)
RANDOMLY choose a student with whom to “mate.”
Face your partner with both allele index cards behind your back.
Perform the “mating dance” as shown by your instructor.
Count to 3 and then reveal one allele.
The TWO alleles (one from each student) represent your first child.
Record your results on your scratch sheet.
Repeat steps 4-6 to produce a second offspring and record results.
NOTE: Individuals with TWO HbS alleles cannot survive in our environment. If you produce an offspring with TWO HbS alleles, re-mate until you produce an offspring that is either HbA/HbA or HbA/HbS.
It has also been found that HbA/HbS individuals survive at a higher rate than HbA/HbA individuals.
If you are HbA/HbA, flip a coin to determine if you will live or die.
Heads= HbA/HbA survivesTails= HbA/HbA dies
If you die, re-mate following instructions 4-6 until you have a child that survives.
The first generation now dies, and each partner assumes the identity of one of the two offspring. *You may need to return to the gene pool to fetch a new allele.
Determine which copies of hemoglobin alleles you have and QUICKLY move to the area designated below:

TWO HbA alleles= between lab bench 1 and 2
ONE HbA and ONE HbS allele= between lab bench 6 and 7

Teacher records # of each allele combination. This is generation 1.
Teacher will instruct you when you should go find another mate.
Repeat steps 2-13 for more generations as time allows. (Be sure that you are mating randomly.)

Part II. Selection in an environment WITHOUT malaria
Environment: Today, you are living in a poor country where malaria is NOT a problem, and you cannot afford medication or treatment to combat the effects of sickle cell anemia.
Follow the procedures above as in part I. with the following CHANGES:

In this environment, HbA/HbS individuals have LOWER fitness (survival and reproductive success) than HbA/HbA
Replace procedure 10. above with the following:
If you are HbA/HbS, flip a coin to determine if you will live or die.
Heads= HbA/HbS survivesTails= HbA/HbS dies
If you die, re-mate following instructions 4-6 until you have a child that survives.
Complete the data table, graphs and post lab analysis for Part II.

Part I-Data Tables and Graphs: For each generation, record the # of individuals with each of the three possible allele combinations and then determine the frequency.
Population size= ______(number of individuals in the class
I. Effects of selection in a malarial environment

HbA/HbA

HbA/HbS

/ HbS/HbS
Generation / # / Frequency / # / Frequency / # / Frequency
0 / 1.0
1
2
3
4
5
6
7
8
9
10
HbA= normal hemoglobin alleleHbS= mutated hemoglobin allele
Graphs: You need to create a scale for the axes. Use the grid below to graph changes in frequency of each of the allele combinations over time. Use different colors for each line; fill in the legend to show what each color line represents.

Changes in the frequency of allele combinations in malarial environment

Time (generations)

Explanation:
Answer the Post Lab analysis part of Gene Pool Lab.
In this discussion the teacher and students will share what they know about genetic diseases and how they relate to the information shown in the 2nd video clip: What is sickle cell? Explain the frequency of malarial environment where sickle cell develops.

Extension/ Elaborate:
Think about this: Economic Cost
During 2005, medical expenditures for children with sickle cell disease averaged $11,702 for children with Medicaid coverage and $14,772 for children with employer-sponsored insurance. 40% of both groups had at least one hospital stay.
Sickle cell disease is a major public health concern. From 1989 through 1993, there was an average of 75,000 hospitalizations due to sickle cell disease in the United States, costing approximately $475 million.
How this data affects the economy? Explain. Point for debate: In this time of recession, will you agree that the government will increase the budget for the hospitalization due to sickle cell disease?

Evaluation/Assessment:

How did you find out the frequency ? What mathematical operations do you used?
Why do we need to find out frequency of sickle cell? What is the mathematical impact to the real world? If one for every 12 African American people has sickle cell, what is the percentage that has sickle cell when there of 656 students in our school?
Homework:
 Use google engine to compare a person with or without sickle cell diseases.
Make a documentary report for at least 2 or more websites
Accommodation and Modification:

Extended Time Response; Verbatim Instruction.
Provide calculator devices, highlighting of text, cornell note format is provided, reward system
Highlighting of text. Genetic flow should be discussed verbatim
Provide open ended sentences ready for explanation part. Simplifying instructions.
Give more pictures to visualize which is a sickle cell or a normal blood cell

WARM- UP WORKSHEET #1

CORNELL NOTE

Name ______date ______

TOPIC: ______
Questions / Notes/Answers from the video clip
1. What are these little tiny objects found at the beginning of the video?
2. How can you identify if these are sperms?
3. Where does the fertilization of the egg occur?
4. How does fertilized egg grow or multiply?
5. In what way that the characteristics from the parents will be transmitted to the newly developed fetus?

WORKSHEET#2 Lesson plan no. 1

Answer the Pre lab questions : Gene Pool Lab

Pre-lab: Read over the information at the following four web link: Watch the PBS Evolution Web Video (A mutation story) and read the backgrounder that is provided with the video, A case study of the effects of mutation, the “bad” gene, sickle cell anemia: the first molecular look at a disease and LW pp 49-51. Use information from the readings and web video to answer the following questions.

What causes an ineffective hemoglobin protein (poor transporter of oxygen) to be produced?

Designate a normal hemoglobin allele as HbA and the mutated hemoglobin allele as HbS.

Which combination(s) of alleles will cause an individual to show severe effects of sickle cell anemia?

Which combination(s) of alleles produce individuals that show NO affects of sickle cell anemia?

3.Describe the effect of having one normal and one mutated hemoglobin (Hb) allele.

4. In the absence of medication, what do you think would happen to individuals with both copies of the mutated

allele? Explain.

5. Explain why the mutated allele is not wiped out of the African populations.

LESSON PLAN NO. 2

Sickle Cell and Malaria- A Mathematical Representation

By: FE ARENASA, JUDITH BEBORA, JULITA BELCHES REBECCA LANGOMES

Course: BIOLOGY
Class: ______/ Date: _____ DAY______
Unit Title: GENETICS
Topic: Sickle Cell and Malaria- A Mathematical Representation
Materials:
Sickle cell disease data link:

Evolution of sickle cell malaria link:

MSDE CORE Standards:
MATH:
FUNCTIONS:
Reason quantitatively and use units to solveproblems:
1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the
input x. The graph of f is the graph of the equation y = f(x).
2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a
context.
BIIOLOGY
expectation 3.3
The student will analyze how traits are inherited and passed on from one generation to another.
Indicator:
3.3.2 The student will illustrate and explain how expressed traits are passed from parent to offspring.
3.2.2 The student will conclude that cells exist within a narrow range of environmental conditions and changes to that environment, either naturally occurring or induced, may cause changes in the metabolic activity of the cell or organism.
1.4.4 The student will determine the relationships between quantities and develop the mathematical model that describes these relationships.
Lesson Objectives:
1. Students will communicate the mathematical data collected in their cooperative learning groups by sharing that data to formulate a class average and by using that information to support a debate on genetics.
2. Students will predict the births and deaths of sickle cell mutation by using algebraic expressions;
3. Students will use computational tools and strategies by using prediction, basic mathematical skills and algebraic formulas to analyze collected data.
Opening Activity/Warm-up:
Writing Literacy: Create a paragraph as reaction of your research( base from their homework)
Use the Writing Literacy format attached hereto. ( worksheet # 1 lesson plan 2)
Lesson Proper:
Engagement of Students:
Watching video on the relationship of malaria and sickle cell:
Let them read the student reading assignment. Resource: A Study of Malaria and Sickle Cell Anemia:
A Hands-on Mathematical Investigation
Link:
Exploration Activity: WICR ( Writing, Inquiring, Collaboration and Reading Strategy)
Do the activity focus on simulation of genetic processes.
Activity title: Modeling a Population where Malaria is a Risk: A Physical Model

Worksheet # 2 Lesson Plan 2 is attached hereto.
Explanation:
Making a Mathematical Model of the Population
1. You have simulated the birth of a population by looking at 30 random "births" and modeling death events with given probabilities. Study your table and those of other groups. Compare each others' results. The purpose of the simulation was to help you understand the genetic process and the way the incidence of the two diseases affects the survival rates of the children. In the following, you will investigate how the size of the surviving population depends on the fraction of alleles in the parent population that are N. For example,
suppose 60% of the alleles in the parent population are N and 40% are S. (This could be represented by a cup containing 6 N beads and 4 S beads.) Imagine that you are going to draw beads from the cup at random, replacing beads after each draw, to get 30 births, a total of 60 beads, two beads (thus two alleles) for each new birth
Instead of simulating births and deaths, you will predict them with numerical expressions based on probabilities using the fractions you know describe the situation. You want to know the number of NN individuals that should be expected in a total of 30 births if the fraction of N alleles in the adult population is n= 0.6 . To compute this number, multiply the probability that one parent will contribute an N allele times the probability that the other parent will contribute an N allele times the number of births:
0.6 x 0.6 x 30 = 10.8 NN children
2. Use the tree or the area model in Figure 1a) or b) to help compute the expected number of children born with "NS" and the expected number of children born with SS.

3. Let represent the fraction of the alleles of the parents that are N. Let represent the total number of 30 children that are expected to survive both malaria and sickle cell anemia, assuming that two-thirds of the NN children die of malaria and none ofthe SS children survive sickle cell anemia. Find . Completing the column of Table 2 under "0.6" will help you organize your information.
Solution:
Find 4 and . (For each, complete a tree diagram similar to Figure 1 and then complete the columns of Table 2 under "0.4" and "0.3".)
Show and explain your solution:
Extension/ Elaborate:
 Now write the function ƒ(n) for the number of the 30 children who achieve adulthood, where n is the fraction of N alleles in the gene pool. You have probably written your expressions for the last column of Table 2 in terms of both s and n. Rewrite your expressions in terms of n only. This will help you to develop your expression of ƒ(n) . Recall that all the alleles are either S or N, so if n is the fraction of one type, you can easily express s in terms of n.
Factor the function ƒ(n) .
Graph
Graph the function. Label units on horizontal and vertical axes. What do the numbers on the horizontal axis represent? What do the numbers on the vertical axis represent? How do the -intercepts relate to the factors?
What is the domain of your function ƒ(n), in this context? That is, what values of n in this context? That is what values of n are possible in the real world?
Watching more videos:
e=related
=related
elated

Evaluation/Assessment: Practice test
A Model with Varying Sickle Cell Survival Rate
Suppose that 90% of NN children survive malaria and that 40% of SS children survive sickle cell anemia. Remember that all of the "NS" children survive both diseases. Assume 1000 children are born.
a. Develop a function ƒ(n) for the total number of children who survive both diseases if n is the fraction of N alleles among the parents and s= 1-n is the fraction of S alleles among the parents. The following tree diagram and/or area model may help.

B. Find the zeros of ƒ(n). (Note that the roots do not have real world significance)
C. Use the roots to find the n -value that maximizes the function ƒ(n). This –value gives the genetic makeup that maximizes the number of children that survive.
d. Graph ƒ(n). Include the roots of ƒ(n) in your graph, even though these values have no physical significance.
Summary
One reason that the sickle cell allele occurs with relatively high frequency in some human populations is that, in areas where the malaria parasite thrives, the presence of the sickle cell allele results in the survival of a larger fraction of the population. This is termed a "survival advantage." It is believed that this type of relationship exists for other diseases and genetic traits. For example, there is some evidence that people with just one of the alleles that causes cystic fibrosis have an increased chance of surviving cholera. Another important aspect of the relationship between a disease and a new allele for a trait is worth noting. Genetic mutations occur randomly over time, and a large population can generate a large, diverse number of mutated genes.If the population of a species is small, such as in the case of an endangered species, there are fewer potential opportunities for beneficial genetic mutations to occur that could help the species to survive new dangers. Genetic diversity helps a species survive.
Question: Based from mathematical representation, what are the factors that affect the population of sickle cell patients?
Based from the mathematical representation, can we consider SCD curable?
------
HOMEWORK:
Research on genetic testing. Make a report about this topic.
______
Accommodation and Modification:

Extended time response.
Provide calculator devices
Separate mathematical instruction should be provided by writing the steps in a separate text.
Highlighting of text especially the formula and equation.

Worksheet #1 Lesson plan 2
WRITING LITERACY ABOUT SICKLE CELL
Websites where your research taken: ______
In your paragraph below include the following items to describe sickle cell disease?

What is sickle cell? Is this a communicable disease?
How sickle cell diseases transfer from one offspring to another?
Can Sickle cell disease be attain from malaria victims? Give 2 or more supporting details about this.
Describe the physical characteristics of a person who has sickle cell.

______

SIMULATION ACTIVITY