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Figure It Out!

Grade 8, Mathematics

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Description of Unit

Students will choose a topic to investigate about which they can gather statistical data. They will survey an identified population and analyze the results. From their research, they will write a letter or article that uses the data to support solutions to the problem.

This guide links the Figure It Out! unit to the Texas Essential Knowledge and Skills (TEKS) for eighth graders. Figure It Out! is a mathematics unit that allows students to explore the uses of statistics in everyday life. Though a mathematics unit, Figure It Out! also teaches students skills in the other subject areas of English language arts, science, and social studies. For example, students use problem solving and critical thinking, which the Science TEKS include, and writing and research skills, which the English Language Arts and Reading and Social Studies TEKS address. The following document includes the applicable TEKS and the details of the Figure It Out! unit. The asterisks indicate that those TEKS are testable on the State of Texas Assessments of Academic Readiness (STAAR). The final section of this document presents the applicable Texas College and Career Readiness Standards adopted by the Texas Higher Education Coordinating Board (THECB) on January 24, 2008.

Phase I. Learning Experiences

This unit gives students an opportunity to develop survey research skills. Students identify an issue to investigate using survey research. They identify the issue, design a survey tool for collecting the data, analyze the data, and draw conclusions in an article that is written for an actual publication (e.g., school newspaper, community newspaper through a letter to the editor, teen magazine, online journal).

  1. Introduction. Students review one of the following Internet resources (or other similar resources) to become familiar with survey research and design:
    http://www.surveysystem.com/sdesign.htm
    http://www.dobney.com/Research/MR_basics.htm
  2. Students read an article that includes survey results. What are the questions that might have been asked in the survey? Each group generates a set of questions and shares the questions. Students review all of the questions that were generated, identify questions that may produce biased results, and select the most effective questions. As a class, they develop and administer a survey, analyze data, and report their findings. Students should compare how the class’s results were similar to or different from the published study.
  3. Sample problems. Students complete the sample statistics problems; Attachment #1.

Phase II. Independent Research

A. Research process

  1. Selecting a topic. Each student identifies a real-world problem which he/she wishes to investigate through a survey process (e.g., what solution do various groups of citizens favor for a current issue in the city or town, what solution do students, parents, and teachers favor for a pressing school issue, etc.).
  2. Asking guiding questions. Once the student has selected a topic, he/she should think of three to five guiding questions to explore, such as:
    1. What has been done in the past to address the problem?
    2. What are potential solutions?
    3. What do various groups see as solutions to the problems?
    4. How can each group be adequately surveyed?

      While these examples are general, the student’s questions should be specific to the chosen topic. The questions should lead him/her to form individual research-based opinions. The student should also develop a hypothesis or some possible answers to the questions.
  3. Designing and submitting a research proposal. The student should include numerous components in the research proposal:
    1. The real-world problem to be investigated
    2. Three to five guiding questions he/she will investigate
    3. Resources he/she will need to find answers to questions, such as previous studies on the topic and/or correspondence with experts on the subject
    4. A survey design, including who will be surveyed, numbers of various groups to be surveyed, how the survey questions will be tested, how the survey will be disseminated, what is an acceptable return rate, what the student will do to ensure that surveys are returned, and how data will be analyzed

      In the process of writing the research proposal, students may refine their guiding questions.
  4. Conducting the research. After the teacher has approved the student proposal, each student begins using the identified resources and other sources he/she may encounter. Research may encompass survey design or other survey research that has been done on the topic. During this stage, the student will need to keep a log, note cards, or resource process sheets of all the sources they use and what they learn from each one.
  5. Conducting the survey and analyzing the results. Each student should write and distribute the surveys, as identified in the research plan. When surveys are returned, the student should analyze them in terms of response rate, item response, and trend analysis. Then, the student should generate conclusions and offer recommendations.
  6. For students taking algebra: Students might want to design their survey so that they can easily relate two of the parameters (variables) in a graph form.

B. The product

The student shows what he/she has learned through one of the following written products:

  1. A letter to a person or organization with responsibility for the problem. In the letter, the student should summarize the results of his/her survey, as well as including the survey methodology. Students should also include supplementary materials (such as graphs, tables, and/or visual depictions of the system) with the letter.
  2. An article that summarizes the results of the research. The student should use graphs, tables, or visual depictions of the system to illustrate the results of the survey, the survey process, and conclusions. The article should be submitted to a publication (e.g., school newspaper, community newspaper through a letter to the editor, teen magazine, online journal).
  3. For students taking algebra: Students should graph two of the parameters (variables) of their survey, create and find an equation of best fit, write a description of the relationship between the two parameters, and make some analyses and predictions.
  4. Whatever product is chosen, the student must complete a Reference List/Works Cited Page that includes at least ten references.

C. Communication

The student demonstrates what he/she has learned through one of the following types of presentations, to last no more than fifteen minutes:

  1. A formal presentation to a panel of experts. In the class, form panels of “experts”—groups of students or adults—who will read the student’s letter or article, listen to his/her presentation, and ask questions. The student may provide some questions to the panel, but others should be generated by the panel members.
  2. An informal class presentation in which the student presents his/her expertise to the class. A question-and-answer session should follow the presentation.

D. Submission

  1. A cover sheet
  2. The research proposal
  3. A log, note cards, or resource process sheets
  4. Data summary
  5. The letter or article
  6. A Works Cited Page with at least ten references
  7. An audio or video recording of presentation, including the Q&A session
  8. A response to the student letter or article, if received

This unit may address the following TEKS.

110.24., English Language Arts and Reading, Grade 8, Adopted 2017

110.24(b)(2)
Developing and sustaining foundational language skills: listening, speaking, reading, writing, and thinking--vocabulary. The student uses newly acquired vocabulary expressively.
110.24(b)(5)(C)
make, correct, or confirm predictions using text features, characteristics of genre, and structures;
110.24(b)(5)(G)
evaluate details read to determine key ideas;
110.24(b)(6)(I)
reflect on and adjust responses as new evidence is presented
110.24(b)(6)(J)
defend or challenge the authors' claims using relevant text evidence.
110.24(b)(6)(F)
respond using newly acquired vocabulary as appropriate;
110.24(b)(6)(E)
interact with sources in meaningful ways such as notetaking, annotating, freewriting, or illustrating;
110.24(b)(6)(A)
describe personal connections to a variety of sources, including self-selected texts;
110.24(b)(8)(D)(iii)
multiple organizational patterns within a text to develop the thesis;
110.24(b)(8)(D)(i)
the controlling idea or thesis with supporting evidence;
110.24(b)(8)(D)(ii)
features such as footnotes, endnotes, and citations
110.24(b)(8)(E)(iii)
identifying the intended audience or reader
110.24(b)(8)(E)(ii)
identifying and explaining the counter argument
110.24(b)(8)(F)
analyze characteristics of multimodal and digital texts.
110.24(b)(11)(C)
compose multi-paragraph argumentative texts using genre characteristics and craft
110.24(b)(12)(E)
differentiate between primary and secondary sources;
110.24(b)(12)(F)
synthesize information from a variety of sources;
110.24(b)(9)
Author's purpose and craft: listening, speaking, reading, writing, and thinking using multiple texts. The student uses critical inquiry to analyze the authors' choices and how they influence and communicate meaning within a variety of texts. The student analyzes and applies author's craft purposefully in order to develop his or her own products and performances.
110.24(b)(10)
Composition: listening, speaking, reading, writing, and thinking using multiple texts--writing process. The student uses the writing process recursively to compose multiple texts that are legible and uses appropriate conventions.
110.24(b)(1)
Developing and sustaining foundational language skills: listening, speaking, discussion, and thinking--oral language. The student develops oral language through listening, speaking, and discussion.
110.24(b)(12)
Inquiry and research: listening, speaking, reading, writing, and thinking using multiple texts. The student engages in both short-term and sustained recursive inquiry processes for a variety of purposes.

111.28, Mathematics, Grade 8

111.28(b)(1)
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.28(b)(2)
Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms.
111.28(b)(8)
Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.
111.28(b)(11)
Measurement and data. The student applies mathematical process standards to use statistical procedures to describe data.

111.39, Algebra I

111.39(c)(1)
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
111.39(c)(2)
Linear functions, equations, and inequalities. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.
111.39(c)(4)
Linear functions, equations, and inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.
111.39(c)(12)
Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

112.28., Science, Grade 8, Adopted 2021

112.28(b)(1)
Scientific and engineering practices. The student, for at least 40% of instructional time, asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to answer questions, explain phenomena, or design solutions using appropriate tools and models. The student is expected to:
112.28(b)(4)
Scientific and engineering practices. The student knows the contributions of scientists and recognizes the importance of scientific research and innovation on society. The student is expected to:

113.20, Social Studies, Grade 8

113.20(b)(10)
Geography. The student understands the location and characteristics of places and regions of the United States, past and present.
113.20(b)(23)
Culture. The student understands the relationships between and among people from various groups, including racial, ethnic, and religious groups, during the 17th, 18th, and 19th centuries.
113.20(b)(24)
Culture. The student understands the major reform movements of the 19th century.
113.20(b)(27)
Science, technology, and society. The student understands the impact of science and technology on the economic development of the United States.
113.20(b)(29)
Social studies skills. The student applies critical-thinking skills to organize and use information acquired through established research methodologies from a variety of valid sources, including electronic technology.
113.20(b)(30)
Social studies skills. The student communicates in written, oral, and visual forms.
113.20(b)(31)
Social studies skills. The student uses problem-solving and decision-making skills, working independently and with others, in a variety of settings.

This unit may address the following Texas College and Career Readiness Standards.

Science:

S.I.A.1
Utilize skepticism, logic, and professional ethics in science.
S.I.A.2
Use creativity and insight to recognize and describe patterns in natural phenomena.
S.I.A.3
Formulate appropriate questions to test understanding of natural phenomena.
S.I.A.4
Rely on reproducible observations of empirical evidence when constructing, analyzing, and evaluating explanations of natural events and processes.
S.I.B.1
Design and conduct scientific investigations in which hypotheses are formulated and tested.
S.I.C.1
Collaborate on joint projects.
S.I.E.1
Use several modes of expression to describe or characterize natural patterns and phenomena. These modes of expression include narrative, numerical, graphical, pictorial, symbolic, and kinesthetic.
S.I.E.2
Use essential vocabulary of the discipline being studied.
S.II.A.1
Understand the real number system and its properties.
S.II.A.3
Understand ratios, proportions, percentages, and decimal fractions, and translate from any form to any other.
S.II.A.6
Estimate results to evaluate whether a calculated result is reasonable.
S.II.A.7
Use calculators, spreadsheets, computers, etc., in data analysis.
S.II.B.1
Carry out formal operations using standard algebraic symbols and formulae.
S.II.B.2
Represent natural events, processes, and relationships with algebraic expressions and algorithms.
S.II.E.1
Understand descriptive statistics.
S.II.F.1
Select and use appropriate Standard International (SI) units and prefixes to express measurements for real world problems.
S.II.F.2
Use appropriate scientific digits.
S.III.A.1
Use correct applications of writing practices in scientific communication.
S.III.B.1
Read technical and scientific articles to gain understanding of interpretations, apparatuses, techniques or procedures, and data.
S.III.B.2
Set up apparatuses, carry out procedures, and collect specified data from a given set of appropriate instructions.
S.III.B.3
Recognize scientific and technical vocabulary in the field of study and use this vocabulary to enhance clarity of communication.
S.III.B.4
List, use , and give examples of specific strategies before, during, and after reading to improve comprehension.
S.III.C.1
Prepare and present scientific/technical information in appropriate formats for various audiences.
S.III.D.1
Use search engines, databases, and other digital electronic tools effectively to locate information.
S.III.D.2
Evaluate quality, accuracy, completeness, reliability, and currency of information from any source.
S.V.E.1
Use models to make predictions.
S.V.E.2
Use scale to relate models and structures.

Social Studies:

SS.I.F.1
 Use a variety of research and analytical tools to explore questions or issues thoroughly and fairly.
SS.IV.A.1
 Identify and analyze the main idea(s) and point(s)-of-view in sources.
SS.IV.A.2
 Situate an informational source in its appropriate contexts (contemporary, historical, cultural).
SS.IV.A.3
 Evaluate sources from multiple perspectives.
SS.IV.A.4
 Understand the differences between a primary and secondary source and use each appropriately to conduct research and construct arguments.
SS.IV.A.5
 Read narrative texts critically.
SS.IV.A.6
 Read research data critically.
SS.IV.B.1
 Use established research methodologies.
SS.IV.B.3
 Gather, organize, and display the results of data and research.
SS.IV.B.4
 Identify and collect sources.
SS.IV.C.1
 Understand and interpret presentations (e.g., speeches, lectures, informal presentations) critically.
SS.IV.D.1
 Construct a thesis that is supported by evidence.
SS.IV.D.2
 Recognize and evaluate counter-arguments.
SS.V.A.1
 Use appropriate oral communication techniques depending on the context or nature of the interaction.
SS.V.A.2
 Use conventions of standard written English.
SS.V.B.1
 Attribute ideas and information to source materials and authors.

Cross-Disciplinary Standards:

CDS.I.A.1
 Engage in scholarly inquiry and dialogue.
CDS.I.A.2
 Accept constructive criticism and revise personal views when valid evidence warrants.
CDS.I.B.1
 Consider arguments and conclusions of self and others.
CDS.I.B.2
 Construct well-reasoned arguments to explain phenomena, validate conjectures, or support positions.
CDS.I.B.3
 Gather evidence to support arguments, findings, or lines of reasoning.
CDS.I.B.4
 Support or modify claims based on the results of an inquiry.
CDS.I.D.1
 Self-monitor learning needs and seek assistance when needed.
CDS.I.D.2
 Use study habits necessary to manage academic pursuits and requirements.
CDS.I.D.3
 Strive for accuracy and precision.
CDS.I.D.4
 Persevere to complete and master tasks.
CDS.I.E.1
 Work independently.
CDS.I.E.2
 Work collaboratively.
CDS.I.F.1
 Attribute ideas and information to source materials and people.
CDS.I.F.2
 Evaluate sources for quality of content, validity, credibility, and relevance.
CDS.I.F.3
 Include the ideas of others and the complexities of the debate, issue, or problem.
CDS.I.F.4
 Understand and adhere to ethical codes of conduct.
CDS.II.A.1
 Use effective prereading strategies.
CDS.II.A.2
 Use a variety of strategies to understand the meanings of new words.
CDS.II.A.3
 Identify the intended purpose and audience of the text.
CDS.II.A.4
 Identify the key information and supporting details.
CDS.II.A.5
 Analyze textual information critically.
CDS.II.A.6
 Annotate, summarize, paraphrase, and outline texts when appropriate.
CDS.II.A.7
 Adapt reading strategies according to structure of texts.
CDS.II.A.8
 Connect reading to historical and current events and personal interest.
CDS.II.B.1
 Write clearly and coherently using standard writing conventions.
CDS.II.B.2
 Write in a variety of forms for various audiences and purposes.
CDS.II.B.3
 Compose and revise drafts.
CDS.II.C.1
 Understand which topics or questions are to be investigated.
CDS.II.C.2
 Explore a research topic.
CDS.II.C.3
 Refine research topic based on preliminary research and devise a timeline for completing work.
CDS.II.C.4
 Evaluate the validity and reliability of sources.
CDS.II.C.5
 Synthesize and organize information effectively.
CDS.II.C.6
 Design and present an effective product.
CDS.II.C.7
 Integrate source material.
CDS.II.C.8
 Present final product.
CDS.II.D.1
 Identify patterns or departures from patterns among data.
CDS.II.D.2
 Use statistical and probabilistic skills necessary for planning an investigation and collecting, analyzing, and interpreting data
CDS.II.D.3
 Present analyzed data and communicate findings in a variety of formats.
CDS.II.E.1
 Use technology to gather information.
CDS.II.E.2
 Use technology to organize, manage, and analyze information.
CDS.II.E.3
 Use technology to communicate and display findings in a clear and coherent manner.
CDS.II.E.4
 Use technology appropriately.

English Language Arts:

ELA.I.A.5
Edit writing for audience, purpose, context, and style, assuring that it conforms to Standard American English, when appropriate.
ELA.I.A.4
Review feedback and revise each draft by organizing it more logically and fluidly, refining key ideas, and using language more precisely and effectively.
ELA.I.A.2
Generate ideas, gather information, and manage evidence relevant to the topic and purpose.
ELA.I.A.3
Evaluate relevance, quality, sufficiency, and depth of preliminary ideas and information; organize material generated; and formulate a thesis or purpose statement.
ELA.II.B.4
Make inferences about the denotative and connotative meanings of unfamiliar words using context clues.
ELA.II.B.3
Use reference guides to confirm the meanings of new words or concepts.
ELA.II.B.1
Identify new words and concepts acquired through study of their relationships to other words and concepts.
ELA.II.A.2
Use text features to form an overview of content and to locate information.
ELA.II.A.4
Make evidence-based inferences about a text’s meaning, intent, and values.
ELA.II.A.5
Analyze and evaluate implicit and explicit arguments in a variety of texts for the quality and coherence of evidence and reasoning.
ELA.II.A.7
Compare and analyze how features of genre are used across texts.
ELA.II.B.2
Apply knowledge of roots and affixes to infer the meanings of new words.
ELA.III.A.5
Plan and deliver focused, coherent presentations that convey clear and distinct perspectives and demonstrate sound reasoning.
ELA.III.A.4
Adjust delivery, vocabulary, and length of message for particular audiences, purposes, and contexts.
ELA.III.A.2
Engage in reasoned dialogue, including with people who have different perspectives.
ELA.III.A.1
Participate actively, effectively, and respectfully in one-on-one oral communication as well as in group discussions.
ELA.III.A.3
Understand how style, register, and content of spoken language vary in different contexts and influence the listener’s understanding.
ELA.IV.A.5
Recognize fillers, intentional pauses, and placeholders in speech (e.g., um) and make inferences in context.
ELA.IV.A.4
Comprehend detailed instructions, explanations, and directions in a range of contexts (e.g., specialized contexts such as workplace procedures and operating instructions).
ELA.IV.A.2
Listen critically and respond appropriately.
ELA.IV.A.1
Use a variety of active listening strategies to enhance comprehension.
ELA.IV.A.3
Develop an awareness of rhetorical and stylistic choices used to convey a message.
ELA.V.C.1
Integrate and organize material effectively.
ELA.V.B.3
Assess the relevance and credibility of sources.
ELA.V.B.1
Explore and collect a range of potential sources.
ELA.V.A.1
Articulate and investigate research questions.
ELA.V.A.2
Explore and refine a research topic.
ELA.V.A.3
Devise a plan for completing work on time.
ELA.V.B.2
Distinguish between and among primary and secondary sources.

Mathematics:

M.I.C.2
Convert units within and between systems of measurement.
M.I.B.1
Use estimation to check for errors and reasonableness of solutions.
M.I.A.1
Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
M.I.A.2
Perform computations with rational and irrational numbers.
M.I.B.2
Interpret the relationships between the different representations of numbers.
M.I.C.1
Select or use the appropriate type of method, unit, and tool for the attribute being measured.
M.V.C.1
Analyze data sets using graphs and summary statistics.
M.V.C.3
Make predictions using summary statistics.
M.V.C.4
Identify and explain misleading uses of data.
M.V.C.2
Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
M.V.B.3
Compute and describe the study data with measures of center and basic notions of spread.
M.V.A.1
Formulate a statistical question, plan an investigation, and collect data.
M.V.B.1
Classify types of data.
M.V.B.2
Construct appropriate visual representations of data.
M.V.B.4
Describe patterns and departure from patterns in the study data.
M.VII.C
Logical reasoning
M.VII.D
Real-world problem solving
M.VII.C.2
Understand attributes and relationships with inductive and deductive reasoning.
M.VII.A.1
Analyze given information.
M.VII.D.1
Interpret results of the mathematical problem in terms of the original real-world situation.
M.VII.D.2
Evaluate the problem-solving process.
M.VII.A.2
Formulate a plan or strategy.
M.VII.A.5
Evaluate the problem-solving process.
M.VII.A.3
Determine a solution.
M.VII.B.1
Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
M.VII.A.4
Justify the solution.
M.VIII.C.2
ate and use representations to organize, record, and communicate mathematical ideas.
M.VIII.C.3
Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
M.VIII.C.1
Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
M.VIII.B.1
Model and interpret mathematical ideas and concepts using multiple representations.
M.VIII.A.1
Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
M.VIII.A.2
Use mathematical language to represent and communicate the mathematical concepts in a problem.
M.VIII.A.3
Use mathematical language for reasoning, problem solving, making connections, and generalizing.
M.VIII.B.2
Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
M.IX.B.2
Understand and use appropriate mathematical models in the natural, physical, and social sciences.
M.IX.B.1
Use multiple representations to demonstrate links between mathematical and real-world situations.
M.IX.A.1
Connect and use multiple key concepts of mathematics in situations and problems.
M.IX.A.2
Connect mathematics to the study of other disciplines.
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