Integrating Probability, Statistics and Genetics in Grade 7

Steven BlumsackEmeritus Professor, Mathematics (FSU)Assistant in Research: FCR-STEM (FSU)

We will work in terms of 3 (2 if necessary)Each team packet:

3 BLUE, 3 WHITE, 1 YELLOW, 1 PURPLE, 1 penny

RATIONALE• Integration of mathematics & science–Provides context in mathematics classroom–Opens door for deeper discussions in science–Reduces “Silos”

• Why Probability, Statistics, Genetics ?–Genetics rapidly developing field– Statistics crucial for mathematical literacy–Major increase in Prob/Stat in middle school

from NGSSS to Common Core

INTRODUCTION (*: Discussed today)

Five lessons, each 1-2 class periodsIncludes: prior knowledge, assessments1. Probability measures likelihood2. * Uniform probability models3. * Expected & Observed frequencies4. * Hands-on Simulation of Inheritance Patterns5. Computer simulation (Star Genetics)

Relevant Standards (Grade 7)

• CCSS Mathematical Practices: Most of the 8 • Mathematical Content: Clusters # standards in ( ) – Sampling to draw inferences (2)– Comparative inferences about 2 populations (2)– Probability models (4)

• Scientific Content: NGSSS– SC.7.L.16.1: Heredity, DNA, chromosomes, genes– SC.7.L.16.2: Genotype, phenotype probabilities– Practice of Science

Lesson #2: Probability & PredictionsMACC.7.SP.3.7. a. Develop uniform probability model to determine

probability of eventsb. Develop a probability model by observing frequenciesExperiment with a disc with distinct top/bottom.Predict the distribution of two RED, two YELLOW,

one RED-one YELLOW.Pairs: Investigate probabilities of possible outcomes.

FIRST TOSS↓ SECOND TOSS→ RED YELLOWREDYELLOW

Lesson #3: Likely Events

MACC.7.SP.2.3. Overlap of two data distributions.

MACC.7.SP.3.6. Approximate probability of a chance event by observing frequency

MACC.7.SP.3.7. a. Develop uniform probability model to

determine probability of eventsb. Develop a probability model by observing

frequencies

Practice of Science: Observation & Inference

Which Bag is It?• Two identical bags, each with 20 marbles–One (R5,25%) has 5 RED, 15 YELLOW–Other (R10,50%) has 10 RED, 10 YELLOW

• Teacher chooses one bag at random.• Alternative: Bag given to each pair of students.• Select one marble at a time, with replacement• Students observe & guess which bag was chosen• Indicate level of confidence in “guess”• Continue for a total of 20 selections

Demonstration: BLUE sheet for everyone• Record indicated color• After 1,2,5,8,12,20 trials indicate conjecture

regarding which bag (25% or 50% RED) and indicate CONFIDENCE in the conjecture!

Y Y

R Y R

Y R Y

Y R Y R

Y Y R Y Y Y Y Y

Spreadsheet Simulation

• For each of the two bags–15 experiments with 8 trials each–Uses random numbers in Excel worksheet–Determine number of RED for each experiment– Examine 15 results in histogram–Compare histograms of two bags– Extend to 20 trials each–Observe degree of overlap of distributions

Results of 8 Trials for 15 Experiments: RED=1

TRIAL # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0

2 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0

3 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0

4 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1

5 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1

6 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1

7 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0

8 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0

total 3 4 2 1 3 2 3 1 2 1 3 3 1 2 3

Results of 15 Simulated Experiments

3 4 2 1 3 2 3 1 2 1 3 3 1 2 3

7 6 4 2 4 2 3 4 3 4 5 3 5 5 3

5 9 5 2 5 5 6 5 4 4 6 6 2 8 6

13 10 10 11 13 7 11 8 9 9 9 8 11 7 8

25%

50%

Distribution of RED outcomes after 20 TRIALS

Distribution of RED outcomes after 8 TRIALS

25%

50%

Comparison of Distributions for 8 Trials

1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

R5R10

Comparison of Distributions for 20 Trials

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

1

2

3

4

5

6

R5R10

Lesson #4: Genetics & Meiosis• SC.L.16.2. Determine probabilities for genotype

and phenotype combinations

• Aliens have 3 pairs of chromosomes• Students assign characteristics for dominant and

recessive genes for hair, eyes, nose• Students draw pictures of faces of parents and

two alien babies

Student Activity

E ORIGINAL FOR PARENT #1e ORIGINAL FOR PARENT #1

• Each parent has chromosome pair for o H: hairo E: eyeso N: nose

• Students o choose features for dominant/recessive geneso replicate the chromosomes o split the replicated chromosomeo randomly select chromosome from each parento identify genotype (hair, eyes, nose) of alien babyo draw picture of alien baby

Activity Today: Everyone use White Sheet• Each team: Parent#1, Parent#2, Geneticist• Everyone: Choose characteristics for each gene and draw

pictures of both parents • Each parent replicates each chromosome pair for baby #1.• Geneticist flips coin to determine the chromosomes (e.g.

heads=top chromosome) for baby from each parent.• Team determines baby’s genotype.• Everyone draws face of baby#1.• Repeat for second baby• Team: compare characteristics of family members.• Everyone complete exercises #2 and #3

Acknowledgments

CONTRIBUTING COLLEAGUES–Danielle Sherdan, FCR-STEM –Jessica Palenchar, FCR-STEM–Robert Lengacher, FCR-STEM–Julie Brown, Leon District Schools–Julie Sear, Leon District Schools

DISCUSSION!