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Integrating Probability, Statistics and Genetics in Grade 7

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. RATIONALE.

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Integrating Probability, Statistics and Genetics in Grade 7

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  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 • Probability measures likelihood • * Uniform probability models • * Expected & Observed frequencies • * Hands-on Simulation of Inheritance Patterns • 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. • Develop uniform probability model to determine probability of events • 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.

  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. • Develop uniform probability model to determine probability of events • 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 R Y R Y RY Y R Y R Y Y R Y Y Y Y Y

  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

  11. Results of 15 Simulated Experiments Distribution of RED outcomes after 8 TRIALS 25% 50% Distribution of RED outcomes after 20 TRIALS 25% 50%

  12. Comparison of Distributions for 8Trials

  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 • Each parent has chromosome pair for • H: hair • E: eyes • N: nose • Students • choose features for dominant/recessive genes • replicate the chromosomes • split the replicated chromosome • randomly select chromosome from each parent • identify genotype (hair, eyes, nose) of alien baby • 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!

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