Investigations and Benchmark Lessons

    A benchmark is a lesson that is meant to help students better understand topics that they cannot grasp given the information, resources or time given. The students are lead by the teacher through the material in well structured lessons. There is more lecture in a bench mark than in an investigation. The information acquired is more general and less in depth than in an investigation. A benchmark provides students with new strategies, skill and information that they can use to learn difficult concepts in new projects. Benchmark lessons can include “direct instructional strategies” that are more teacher directed and focus on the teacher conveying information or demonstrating technique or process, or “indirect instructional strategies” that are more student centered and can include things like class discussions, and exploration of short scenarios. (Krajcik and Czeerniak, 2007)


An investigation is a lesson in the form of an inquiry that helps students gather needed information through project based learning. The investigation is centered around a driving question, were the students design and implement a method to solve the question. The teacher becomes the facilitator in an investigation while the students become responsible for the direction of the project. The information in an investigation is more in depth than a benchmark. "At its heart, inquiry is an active learning process in which students answer research questions through data analysis." (Smetana and Binns, 2005) 




Week 1
Survey Investigation
    Overview    
    Students investigate the frequency of traits in students families, the classroom, and the school in the form of surveys. Students will be asked to design survey questions, determine if they are proper for the information they’re seeking to attain, design ways of implementing the survey, compile, graph, and analyze the data to get a picture of the frequency of these traits in the population of the school and classroom. 

     Objectives and TEKS
 Design an appropriate survey question111.47.2e - formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions
Implement school-wide survey 111.39.1a - apply mathematics to problems arising in everyday life, society, and the workplace
112.34.2f - collect data individually or collaboratively, make measurements with precision and accuracy, record values using appropriate units, and calculate statistically relevant quantities to describe data, including mean, median, and range
 Choose and implement an appropriate sampling method for a survey111.47.2a - Compare and contrast the benefits of different sampling techniques, including random sampling and convenience sampling methods
 Identify the sample population 111.47.3d - describe and model variability using population and sampling distributions
 Create a graph of the sample data111.47.4b -represent and summarize data and justify the representation;
111.47.4d - compare and contrast different graphical or visual representations given the same data set 

 Implement and understand the results of statistical summaries and tests.111.47.4e - compare and contrast meaningful information derived from summary statistics given a data set;
112.34.2g - analyze, evaluate, make inferences, and predict trends from data 
 Identify and contrast categorical data and quantitative data111.47.4a - distinguish between categorical and quantitative data; 
 Create a report in LaTeX 110.31.1a - determine the meaning of grade-level technical academic English words in multiple content areas (e.g., science, mathematics, social studies, the arts) derived from Latin, Greek, or other linguistic roots and affixes; 
110.31.11b - analyze factual, quantitative, or technical data presented in multiple graphical sources.
110.31.13b - structure ideas in a sustained and persuasive way (e.g., using outlines, note taking, graphic organizers, lists) and develop drafts in timed and open-ended situations that include transitions and the rhetorical devices used to convey meaning;
110.31.13c - revise drafts to improve style, word choice, figurative language, sentence variety, and subtlety of meaning after rethinking how well questions of purpose, audience, and genre have been addressed;
110.31.13d - edit drafts for grammar, mechanics, and spelling; and
110.31.13e - revise final draft in response to feedback from peers and teacher and publish written work for appropriate audience
 Insert pictures from GeoGebra into LaTeX110.31.23c - uses graphics and illustrations to help explain concepts where appropriate;

Mendel Benchmark Lesson
    Overview 
    Students will be introduced to the history behind genetics beginning with Mendel and his experiments with pea plants.  This will begin a scientific discussion and exploration of traits, recessive v. dominant, genotypes and phenotypes, homozygosity and heterozygosity, and concepts of codominance v. incomplete dominance. Students will learn how Punnett squares represent the variation in genotype and phenotype in an offspring generation and solve several simple 2x2 Punnett squares using the the parents’ given genotype for several traits.
    Objectives and TEKS
Predict how hanging genotype will affect the phenotype of an individual.112.34.6f - predict possible outcomes of various genetic combinations such as monohybrid crosses, dihybrid crosses, and non-Mendelian inheritance
Describe Mendel's findings on heredity, including discovery of alleles112.34.3f - research and describe the history of biology and contributions of scientists
Describe and differentiate between recessive and dominant alleles, genotypes and phenotypes, and homozygous and heterozygous genotypes 112.34.3b - communicate and apply scientific information extracted from various sources such as current events, news reports, published journal articles, and marketing materials 

Identify and use dominant vs. recessive traits 
hoose and implement an appropriate sampling method for a survey
112.34.6f - predict possible outcomes of various genetic combinations such as monohybrid crosses, dihybrid crosses, and non-Mendelian inheritance

Week 2
Punnett Square Benchmark Lesson 
    Overview 
    Students will learn to use simple Punnett squares to calculate the proportion of living offsprings with a genetic disease that is dominant and a disease that is recessive. Having been introduced to simple 2x2 Punnett squares, students will now undertake more complex 4x4 Punnett squares to be able to make their own Punnett Squares from a description of the parents being crossed. Students will be introduced to meiosis and how it is responsible for the different combinations of genotype in individuals. Students will calculate expected proportions of certain genotypes and phenotypes in the first generation of offsprings. Students will be able to make predictions about the number of students in their class with these particular traits. The students will then take data from the classroom and compare it with their predictions.
    Objectives and TEKS 
Create 2x2 and 4x4 Punnett Squares 112.34.6f - predict possible outcomes of various genetic combinations such as monohybrid crosses, dihybrid crosses, and non-Mendelian inheritance
Explain results of Punnett Squares by means of a ratio of phenotypes and genotypes
 111.34.1b - gather and record data and use data sets to determine functional relationships between quantities
Determine the phenotype of individuals based on genotypes from Punnett Squares 112.34.6f - predict possible outcomes of various genetic combinations such as monohybrid crosses, dihybrid crosses, and non-Mendelian inheritance
 Explain how meiosis leads to the pattern we see in Punnett Squares 112.34.c6g - recognize the significance of meiosis to sexual reproduction

Predict how hanging genotype will affect the phenotype of an individual.112.34.6f - predict possible outcomes of various genetic combinations such as monohybrid crosses, dihybrid crosses, and non-Mendelian inheritance
 Communicate the difference between theoretical and empirical probabilities111.47.5b - describe the relationship between theoretical and empirical probabilities using the Law of Large Numbers;
 Calculate the Probability  of a particular gene occurring given a circumstance111.47.5a - determine probabilities, including the use of a two-way table;
E
Chi^2 BenchMark Lesson
Students will be given data and asked to infer from it. Once the question is posed and students have struggled with it, the instructor will introduce the idea of the Chi^2 test.
Objectives and TEKS 
Use and interpret a chi^2 test 111.47.6f - explain how sample a sample statistic provides evidence against a claim about a population parameter when using a hypothesis test
111.47.6h - explain the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis in the context of the situation;
Create a null and alternative hypothesis statement 111.47.6g -construct null and alternative hypothesis statements about a population parameter;
Create a report in LaTeX 110.31.1a - determine the meaning of grade-level technical academic English words in multiple content areas (e.g., science, mathematics, social studies, the arts) derived from Latin, Greek, or other linguistic roots and affixes; 
110.31.11b - analyze factual, quantitative, or technical data presented in multiple graphical sources.
110.31.13b - structure ideas in a sustained and persuasive way (e.g., using outlines, note taking, graphic organizers, lists) and develop drafts in timed and open-ended situations that include transitions and the rhetorical devices used to convey meaning;
110.31.13c - revise drafts to improve style, word choice, figurative language, sentence variety, and subtlety of meaning after rethinking how well questions of purpose, audience, and genre have been addressed;
110.31.13d - edit drafts for grammar, mechanics, and spelling; and
110.31.13e - revise final draft in response to feedback from peers and teacher and publish written work for appropriate audiences.
 Insert pictures from GeoGebra into LaTeX 110.31.23c - uses graphics and illustrations to help explain concepts where appropriate;


Week 3
Survey Investigation
Continuation of week one survey investigation.

     Objectives and TEKS
 Create a graph of the sample data111.47.4b -represent and summarize data and justify the representation; 
111.47.4d - compare and contrast different graphical or visual representations given the same data set 

 Implement and understand the results of statistical summaries and tests.111.47.4e - compare and contrast meaningful information derived from summary statistics given a data set;
112.34.2g - analyze, evaluate, make inferences, and predict trends from data 
 Identify and contrast categorical data and quantitative data111.47.4a - distinguish between categorical and quantitative data; 
 Create a report in LaTeX 110.31.1a - determine the meaning of grade-level technical academic English words in multiple content areas (e.g., science, mathematics, social studies, the arts) derived from Latin, Greek, or other linguistic roots and affixes; 
110.31.11b - analyze factual, quantitative, or technical data presented in multiple graphical sources.
110.31.13b - structure ideas in a sustained and persuasive way (e.g., using outlines, note taking, graphic organizers, lists) and develop drafts in timed and open-ended situations that include transitions and the rhetorical devices used to convey meaning;
110.31.13c - revise drafts to improve style, word choice, figurative language, sentence variety, and subtlety of meaning after rethinking how well questions of purpose, audience, and genre have been addressed;
110.31.13d - edit drafts for grammar, mechanics, and spelling; and
110.31.13e - revise final draft in response to feedback from peers and teacher and publish written work for appropriate audience
Give a presentation 
  110.31.23a - marshals evidence in support of a clear thesis statement and related claims;
110.31.23b - provides an analysis for the audience that reflects a logical progression of ideas and a clearly stated point of view;
110.31.24a - listen responsively to a speaker by taking notes that summarize, synthesize, or highlight the speaker's ideas for critical reflection and by asking questions related to the content for clarification and elaboration;
110.31.24c - evaluate the effectiveness of a speaker's main and supporting ideas

Hardy-Weinberg Investigation
    Overview   
    The Hardy Weinberg principle will be addressed in terms of populations and quadratic equations.  We will list, discuss, and explain the requirements for stable genotype and allele frequencies in a population, and students will become familiar with the results of the equation. The equation will be used to predict the frequency of specific traits within the classroom and world population, discussing the validity of the results when considering the required assumptions. The assumptions will also be used as a segue into an inquiry on a recently popular topic: the question of whether red hair as a trait is dying out.  The topic will be introduced by asking the students if they think red hair is going extinct, and will be given time to think and come up with evidence to support their thoughts.  Students will then be given time to research the topic using the internet to determine if they are correct and gather evidence.  
Through a presentation, we will cover population dynamics and the factors that lead to changes in population size.  From this, students will be given three sets of data and will be asked to calculate the population size for different period of time.  After graphing they should see a trend in the data, and will be asked to come up with a plausible scenario that would match the trend seen in the graph.  They will compile these three graphs into either a poster or a powerpoint presentation and perform a gallery walk of their findings.    
    Objectives and TEKS 
Explain why the Hardy-Weinberg Equilibrium is an ideal case, and will not work unless each assumption is met.
112.34.c3e - evaluate models according to their limitations in representing biological objects or events; and
Explain how absence of any assumption would disrupt the equilibrium. 112.34.c7f - analyze and evaluate the effects of other evolutionary mechanisms, including genetic drift, gene flow, mutation, and recombination
Identify and describe the components of the equation, p and q. 111.32.3a - use symbols to represent unknowns and variables 

Solve for p and q using the Hardy-Weinberg Equilibrium equation; 
(p+q)^= p^2 + 2pq + q^2 = 1
 111.32.4a - find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations 
111.32.9d - analyze graphs of quadratic functions and draw conclusions
111.32.10a - solve quadratic equations using concrete models, tables, graphs, and algebraic methods 
Determine how birth rates, death rates, immigration/emigration rates, and other limiting factors such as resource availability, predation, etc. lead to changes in a population.112.34.7f - analyze and evaluate the effects of other evolutionary mechanisms, including genetic drift, gene flow, mutation, and recombination
112.34.c7 - analyze and evaluate how the elements of natural selection, including inherited variation, the potential of a population to produce more offspring than can survive, and a finite supply of environmental resources, result in differential reproductive success
Graph population growth or decline patterns for each scenario. 122.34.2g - analyze, evaluate, make inferences, and predict trends from data 111.32.2c - interpret situations in terms of given graphs or creates situations that fit given graphs 
Create poster explaining findings and graphs. 112.34.2g - analyze, evaluate, make inferences, and predict trends from data
Perform internet search to find reliable information112.34.3a - in all fields of science, analyze, evaluate, and critique scientific explanations by using empirical evidence, logical reasoning, and experimental and observational testing, including examining all sides of scientific evidence of those scientific explanations, so as to encourage critical thinking by the student
112.34.3b - communicate and apply scientific information extracted from various sources such as current events, news reports, published journal articles, and marketing materials;
Perform gallery walk and present findings to classmates.  112.34.2h - communicate valid conclusions supported by the data through methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technology-based reports.

Week 4
Survey Investigation
Continuation of week one survey investigation.
     Objectives and TEKS
Create a graph of the sample data111.47.4b -represent and summarize data and justify the representation; 
111.47.4d - compare and contrast different graphical or visual representations given the same data set 

 Implement and understand the results of statistical summaries and tests.111.47.4e - compare and contrast meaningful information derived from summary statistics given a data set;
112.34.2g - analyze, evaluate, make inferences, and predict trends from data 
 Identify and contrast categorical data and quantitative data111.47.4a - distinguish between categorical and quantitative data; 
 Create a report in LaTeX 110.31.1a - determine the meaning of grade-level technical academic English words in multiple content areas (e.g., science, mathematics, social studies, the arts) derived from Latin, Greek, or other linguistic roots and affixes; 
110.31.11b - analyze factual, quantitative, or technical data presented in multiple graphical sources.
110.31.13b - structure ideas in a sustained and persuasive way (e.g., using outlines, note taking, graphic organizers, lists) and develop drafts in timed and open-ended situations that include transitions and the rhetorical devices used to convey meaning;
110.31.13c - revise drafts to improve style, word choice, figurative language, sentence variety, and subtlety of meaning after rethinking how well questions of purpose, audience, and genre have been addressed;
110.31.13d - edit drafts for grammar, mechanics, and spelling; and
110.31.13e - revise final draft in response to feedback from peers and teacher and publish written work for appropriate audience
 Give a presentation 
  110.31.23a - marshals evidence in support of a clear thesis statement and related claims;
110.31.23b - provides an analysis for the audience that reflects a logical progression of ideas and a clearly stated point of view;
110.31.24a - listen responsively to a speaker by taking notes that summarize, synthesize, or highlight the speaker's ideas for critical reflection and by asking questions related to the content for clarification and elaboration;
110.31.24c - evaluate the effectiveness of a speaker's main and supporting ideas
 Use and interpret a chi^2 test 
 111.47.6f - explain how sample a sample statistic provides evidence against a claim about a population parameter when using a hypothesis test
111.47.6h - explain the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis in the context of the situation;



1. Krajcik, J. & Czerniak, C. (2007). Chapter 8: Instructional Strategies that Support Inquiry in Teaching Science in Elementary and Middle School: A Project-Based Approach (Third Edition). New York: Routledge
        2. Bell, R. Smetana, L. & Binns. I. (2005). Simplifying inquiry instruction. The Science Teacher