1. Integrating Probability, Statistics and Genetics in Grade 7 Steven Blumsack Emeritus 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

2. 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

3. INTRODUCTION (*: Discussed today) Five lessons, each 1-2 class periods Includes: prior knowledge, assessments 1.Probability measures likelihood 2.* Uniform probability models 3.* Expected & Observed frequencies 4.* Hands-on Simulation of Inheritance Patterns 5.Computer simulation (Star Genetics)

4. 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

5. Lesson #2: Probability & Predictions MACC.7.SP.3.7. a.Develop uniform probability model to determine probability of events b.Develop a probability model by observing frequencies Experiment 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→REDYELLOW RED YELLOW

6. 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 events b.Develop a probability model by observing frequencies Practice of Science: Observation & Inference

7. 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

8. 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 RYRRYR YRYYRY YRYRYRYR YYRYYYYYYYRYYYYY

9. 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

10. Results of 8 Trials for 15 Experiments: RED=1 TRIAL # 123456789101112131415 1110010000010010 2000100101000010 3101000000001000 4000001000100001 5000010010010101 6011001000011001 7010010101000000 8110000100001000 total 342132312133123

11. Results of 15 Simulated Experiments 342132312133123 764242343453553 595255654466286 1310 111371189998 78 25% 50% Distribution of RED outcomes after 20 TRIALS Distribution of RED outcomes after 8 TRIALS 25% 50%

12. Comparison of Distributions for 8 Trials

13. Comparison of Distributions for 20 Trials

14. 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

15. Student Activity EORIGINAL FOR PARENT #1 e Each parent has chromosome pair for o H: hair o E: eyes o N: nose Students o choose features for dominant/recessive genes o replicate the chromosomes o split the replicated chromosome o randomly select chromosome from each parent o identify genotype (hair, eyes, nose) of alien baby o draw picture of alien baby

16. 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

17. 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

18. DISCUSSION!