17.1: Assessment Tools and Application to Practice
By the end of this section, you should be able to:
- Differentiate among assessment tools and data sources (primary and secondary) used to evaluate the health status of populations, communities, and systems.
- Use a wide variety of sources and methods to access public health information.
- Conduct a community needs assessment considering self-resilient capabilities of a target population to identify and prioritize problems and health concerns.
Nurses gain a broad understanding of health issues during assessment and analysis. During assessment of an individual, the nurse gathers information about a client’s health condition and includes data from primary sources (head-to-toe assessment, client interview) and secondary sources (previous medical records, health professionals, family, or friends). Comparably, assessment of populations is termed community health assessment (CHA), or community health needs assessment (CHNA). In this instance, the client is the defined population or community. Nurses and other health care professionals use a comprehensive, systematic approach to gather community health data with the primary goal of implementing programs to benefit people in an area as a whole.
A CHA provides a comprehensive picture of a community’s current health status, identifying factors contributing to higher health risks or poorer health outcomes and available community resources to improve health (Public Health Accreditation Board [PHAB], 2022). The purpose of community health assessment and a subsequent community health improvement plan is to identify a community’s key health needs and address them through strategic intervention . Systematic processes are utilized to collect data, identify and analyze community health needs and assets, prioritize those needs, and provide a foundation for decision-making to implement a plan to address unmet needs (Centers for Disease Control and Prevention [CDC], 2023).
A CHA’s timing varies depending on the community’s needs. For example, public health departments seeking or maintaining PHAB accreditation must complete a community health assessment every 5 years. Some communities choose to conduct a CHA more often due to policy mandates. For example, the Affordable Care Act (ACA) requires nonprofit hospitals to conduct a CHA every 3 years. Communities may also conduct a partial or full CHA as needed. As noted in the chapter introduction, Tia wonders how the opioid crisis impacts the local community. To understand this issue clearly, Tia can conduct a partial CHA focusing on the opioid crisis. If a larger CHA is in process or was completed recently, such as within the past year, Tia can extract the data regarding drug use and overdose.
Community Health Assessment Models, Frameworks, and Tools
CHA models, frameworks, and tools guide community assessment and community health improvement. They provide a systematic, evidence-based process for organizing the assessment team; collecting and analyzing data; and planning, implementing, and evaluating community health improvement strategies. Most assessment and planning frameworks contain common actions. According to the CDC (2023), common elements of assessment and planning frameworks include the following:
- Organize and plan
- Engage the community
- Develop a goal or vision
- Conduct community health assessment(s)
- Prioritize health issues
- Develop a community health improvement plan
- Implement and monitor the community health improvement plan
- Evaluation process and outcomes
These common actions are evident within the frequently used CHA models, frameworks, and tools described in this chapter. This section reviews the Community Health Assessment toolkit, the Mobilizing for Action through Planning and Partnerships (MAPP) framework, the Community Health Assessment aNd Group Evaluation (CHANGE) tool, the PRECEDE-PROCEED model, and the Agency for Toxic Substances and Disease Registry (ATSDR) action model.
Community Health Assessment Toolkit
The American Hospital Association (AHA) developed the Association for Community Health Improvement Community Health Assessment toolkit to help nonprofit hospitals comply with Internal Revenue Service regulations for CHAs. The toolkit consists of nine steps for conducting a CHA and developing intervention strategies (AHA, 2017).
The Community Health Assessment Toolkit identifies community engagement as a central component of the CHA process. Community engagement is the process of working collaboratively with and through groups of people to identify the health needs of community residents and strategies to address them. To engage the community, the nurse must invite community partners to participate. Community partners , also called stakeholders , are all persons, agencies, and organizations that have an investment in the community’s health and in the local public health system (National Association of County and City Health Officials [NACCHO], 2016). This includes community members who benefit from health services and those that provide health services, such as informal or formal leaders from schools, faith-based organizations, businesses, social clubs, health care, transportation, and government. Community members may decide to establish a partnership , a relationship characterized by mutual cooperation and responsibilities among individuals and groups (Figure 17.2) (NACCHO, 2016). Partnerships may expand into coalition building. A coalition is a group of people and organizations that work to address community needs and solve community problems (PHAB, 2022). Planning Health Promotion and Disease Prevention Interventions further describes partnerships and coalitions.
Community engagement strengthens the CHA by including diverse perspectives; increasing collaboration and stronger partnerships; sharing a sense of ownership and resources; and improving communication among individuals from the community, community partner organizations, and hospitals. The Community Health Assessment toolkit enhances community engagement by establishing committees that collaborate at each step. Users of this toolkit sequentially follow the nine steps described in Table 17.1.
|
Community Health Assessment
Toolkit Steps |
Actions |
|---|---|
| Step 1: Reflect and Strategize |
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| Step 2: Identify and Engage Community Partners |
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| Step 3: Define the Community |
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| Step 4: Collect and Analyze Data |
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| Step 5: Prioritize Community Health Issues |
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| Step 6: Document and Communicate Results |
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| Step 7: Plan Implementation Strategies |
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| Step 8: Implement Strategies |
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| Step 9: Evaluate Progress |
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Conducting community health assessment through collaborative partnerships can positively impact the overall process. This video features key team members from two competing health systems and Penn State Hershey, an academic medical center, who participated in a Community Health Needs Assessment in Pennsylvania.
Watch the video, and then respond to the following questions.
- Why is it important to conduct a CHNA?
- What are the benefits of establishing collaborative partnerships to conduct a CHNA?
- What are the goals of a CHNA according to the speakers in the video?
Mobilizing for Action through Planning and Partnerships
Public health leaders can use the Mobilizing for Action through Planning and Partnerships (MAPP) framework for local-level community health improvement planning. The MAPP framework is community-driven and facilitates prioritizing public health issues and identifying resources to address them (NACCHO, 2023). MAPP emphasizes community engagement and collaboration for system-level planning. Originally consisting of six steps, the framework is undergoing redesign (NACCHO, 2020). The redesign includes the foundational principles of equity, inclusion, trusted relationships, community power, strategic collaborations, data-informed action, flexibility, and continuous improvement. The revised MAPP, shown in Table 17.2, provides a streamlined approach to community health assessment and community improvement and directs the nurse and program team through three phases consisting of multiple activities (NACCHO, 2023).
| Phases | Activities Completed | |
|---|---|---|
| 1 |
Build the Community Health
Improvement (CHI) Infrastructure |
|
| 2 | Tell the Community Story |
|
| 3 | Continuously Improve the Community |
|
Community Health Assessment aNd Group Evaluation
The CDC developed the Community Health Assessment and Group Evaluation (CHANGE) tool for community members who desire to improve their community’s health (CDC, 2010). CHANGE focuses on gathering and organizing data on community assets and potential areas for improvement to prioritize needs for multilevel changes in policies, systems, and the environment. An Action Guide with worksheets and templates assists community members through the eight action steps within the CHANGE tool (see Table 17.3).
The CHANGE tool divides the community into five sectors: community-at-large, community institution/organization, health care, school, and work site. The community-at-large sector includes the social and built community environments, such as safety, food access, and policies that affect health. The community institution/organization sector includes human services and facility access, such as the YMCA, senior centers, faith-based organizations, childcare, and colleges and universities. The health care sector includes emergency services, clinics, hospitals, and provider offices. The school sector includes primary and secondary learning institutions. The work site sector includes places of employment.
| CHANGE Tool Action Step | Actions Taken |
|---|---|
| 1: Assemble the Community Team |
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| 2: Develop Team Strategy |
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| 3: Review All Five Change Sectors |
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| 4: Gather Data |
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| 5: Review Data Gathered |
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| 6: Enter Data |
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| 7: Review Consolidated Data |
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| 8: Build the Community Action Plan |
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PRECEDE-PROCEED Model
The Green and Kreuter PRECEDE-PROCEED model uses a social-ecological, population-level approach to guide health promotion strategies. This model considers the impact of the social determinants of health (SDOH) and the community environment on the target population’s quality of life and needs (Porter, 2016). Members of the target population participate throughout each phase of the model.
PRECEDE stands for Predisposing, Reinforcing, Enabling Constructs in Educational/Environmental Diagnoses and Evaluations. The PRECEDE process occurs before implementation of an intervention and includes the following four phases:
- Define the outcome: Social and situational assessment of what the community wants and needs. Includes data collection and assessment.
- Identify the issue: Select the most important issue that can be influenced by an intervention. Includes analysis and prioritization.
- Examine factors that influence behavior, lifestyle, and responses to environment: This includes analysis of predisposing, enabling, and reinforcing factors that influence health promotion. See Health Promotion and Disease Prevention Strategies for further explanation of each factor.
- Identify best practices for intervention and organizational issues that could have an impact: Design an action plan.
PROCEED stands for Policy, Regulatory, and Organizational Constructs in Educational and Environmental Development. The four phases of PROCEED guide the implementation of the intervention itself. PROCEED is discussed further in Planning Health Promotion and Disease Prevention Interventions as a model used for programming planning, implementation, and evaluation.
Agency for Toxic Substances and Disease Registry Action Model
The Agency for Toxic Substances and Disease Registry (ATSDR) (2023) developed an Action Model for community members to identify community problems and create a plan to improve the community through redevelopment (see Figure 17.3). Redevelopment consists of making changes to an area to impact health outcomes, such as repairing sidewalks and buildings, removing harmful environmental exposures, or building a playground. For example, a community with increased adolescent obesity rates decides to redevelop a park to provide areas for exercise. They add basketball and tennis courts, walking trails, and outdoor exercise equipment to the park.
Before working through the Action Model, a team of community members who are interested in the identified issue or are impacted by the issue will play a role in redevelopment plans. A toolkit is available to walk community members through building a team and Action Model steps.
Primary and Secondary Data Sources
A CHA consists of data and information from multiple sources. Required data includes information about the community’s demographics, health status, morbidity and mortality rates, socioeconomic characteristics, quality of life, community resources, behavioral factors, environment, and other social and structural determinants of health (PHAB, 2022). A comprehensive CHA needs a variety of primary and secondary data sources to gather information. In fact, PHAB requires public health departments to use primary and secondary data sources and include both quantitative and qualitative measures. Quantitative data are expressed by amounts in numerical terms. Qualitative data are expressed in word form, cannot be quantified, and describe perspectives of individuals and populations. CHA data and indicators should be valid, reliable, feasible, meaningful, and collected over time.
An assessor collects primary data directly from community members. PHAB considers primary data to be data for which collection is conducted, contracted, or overseen by the health department (PHAB, 2022). Collecting primary data can be time- and resource-intensive. Table 17.4 describes common primary data sources.
| Primary Data Source | Description |
|---|---|
| Participant observation |
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| Interview key informants |
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| Forum or town hall meeting |
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| Focus group |
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| Photovoice |
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| Survey |
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| Windshield survey |
|
Secondary data are obtained through an existing report on the community originally collected by another entity or for a purpose other than CHA. Secondary data are usually readily available and may be inexpensive for the assessor. Secondary sources include census data, vital statistics, health indicators, health profiles, and spatial data. Vital statistics are population data about births, deaths, marriages, and divorces. Health indicators are numerical measures of health outcomes, such as morbidity and mortality, that have been analyzed and are used to compare rates or trends of priority community health outcomes and determinants of health. They are usually attained through secondary data sources. Health indicators provide a snapshot of community health outcomes and allow for benchmarking. A benchmark is a standard or point of reference against which measurements can be compared.
Sources and Methods to Access Public Health Information
A comprehensive CHA contains public health data from various sources displayed in ways to identify trends and patterns. Public health information is also used to compare local data to state and national data, which can be used for benchmarking and to trend data to evaluate progress.
Spatial Data
One method to identify trends and patterns is using spatial data , which identifies the geographic location of phenomena. Spatial data provide an overview of the whole community in map form and facilitate comparing one part of the community to another. This is an important tool to use when conducting a CHA because geographic location can affect access to resources and exposure to health threats. Major differences in health outcomes, especially in mortality rates, have been found even between locations within 5 to 10 miles of each other (Couillard et al., 2021; Hollar, 2016; Pedigo et al., 2011).
A person’s geographical location influences their access to healthy foods, education, jobs, safe housing and neighborhoods, facilities that promote health, and health care resources. Individuals living in neighborhoods with greater economic resources have healthier lifestyles. By identifying locations where health disparities exist, even in the same community, nurses can recognize populations at risk for negative health outcomes. Additionally, spatial data helps identify the SDOH within a location that contribute to negative health outcomes. For example, a nurse finds that higher rates of tuberculosis occur in one community area. The nurse uses spatial data to locate the geographical area of tuberculosis diagnoses and assesses potential environmental factors that influence TB’s spread, such as housing and living conditions. The nurse prioritizes interventions by focusing on improving living conditions in the area.
This American Heart Association video explains why a person’s zip code may be more important than their genetic code.
Watch the video, and then respond to the following questions.
- Consider your community. What areas or locations might you compare using spatial data to clarify whether inequities exist?
- How does location relate to social determinants of health and other environmental factors that impact health?
Geographic information systems (GIS) are software and technology that can store, visualize, analyze, and interpret spatial data (CDC, 2019a). The software creates maps electronically using primary or secondary data to determine how location impacts disease and disability. Any data that can be mapped can be used and compared by location. This helps locate areas of communities where high rates of health problems occur.
Nurses and other health care professionals can use GIS maps to identify areas within a community—such as those with higher rates of opioid overdoses, for example—to target them for intervention. Additionally, it is possible to analyze the environment in that location for potential determinants of health that lead to increased opioid use and overdose. GIS tools and examples can be found on the CDC’s website.
This Queens University video describes how researchers are using GIS to create interactive maps to track information about a range of topics, such as population movement and infection rates of emerging diseases.
Watch the video, and then respond to the following questions.
- How can maps be used in community health assessment to determine health patterns?
- How were GIS and other assessment data used to predict the spread of COVID-19?
- How can GIS data be used to plan for intervention within a community?
Secondary Data Sources
Public health information sources provide data on local, state, and federal health indicators. During the CHA, the team can use these secondary sources to compare local health data to other municipalities, state, and federal health data for benchmarking. All are quantitative data sources. Table 17.5 describes frequently used secondary data sources and methods to access public health information.
| Secondary Data Source | Description |
|---|---|
|
Behavioral Risk Factor Surveillance Survey
(BRFSS)
https://www.cdc.gov/brfss/data_tools.htm |
|
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Population-Level Analysis and Community Estimates
(PLACES)
https://www.cdc.gov/places/ |
|
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CDC Wide-Ranging Online Data for Epidemiologic Research
(WONDER)
https://wonder.cdc.gov/ |
|
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National Center for Health Statistics: FastStats
https://www.cdc.gov/nchs/fastats/default.htm |
|
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U.S. Census
https://www.census.gov/ https://data.census.gov/ |
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Healthy People 2030
https://health.gov/healthypeople |
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County Health Rankings
https://www.countyhealthrankings.org/ |
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State Cancer Profile
https://statecancerprofiles.cancer.gov/ |
|
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State Health Access Data Assistance Center
https://www.shadac.org/ |
|
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State Health Assessment
See state public health department websites for state health assessments. |
|
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Tribal Health Assessment
See tribal health department websites for tribal health assessments. |
|
|
Local Health Assessment
See local health department websites for local community health assessments. |
|
Drug overdose deaths are one common health indicator measured within a CHA and are considered a national emergency. As such, a leading health indicator of Healthy People 2030 within Drug and Alcohol Use objectives is reducing drug overdose deaths . The target goal for this health indicator is 20.7 drug overdose deaths per 100,000 people, which was the baseline measure in 2018. In 2020, 28.3 drug overdose deaths per 100,000 individuals occurred; in 2021, 32.4 drug overdose deaths per 100,000 individuals occurred.
At this time, the 2020 and 2021 data signify that drug overdose deaths have increased in the United States. This aligns with the public health emergency declaration for the opioid crisis.
Conducting a Community Health Needs Assessment
The first steps of conducting a CHA, no matter the framework, model, or tool chosen as a guide, are planning, engaging the community, and recruiting the assistance of key community partners. After creating the team and determining team roles, the next step is defining the community and the data collection process.
A community may be defined by geography or place of residence, shared characteristics or demographics, or common interests. PHAB (2022) defines a community as a group of people with common characteristics; this can be defined by location, race, ethnicity, age, occupation, interest in particular problems or outcomes, or other common bonds. The definition of the community may change depending upon the context. For a CHA, the community should be defined by people, place or environment, and community systems. Table 17.6 clarifies data that fall under each category.
| Category | Data Included |
|---|---|
People:
|
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Place:
|
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Community systems:
|
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Data gathering is required to assist with defining the community. A rich CHA and definition of the community contain both quantitative and qualitative data, and PHAB requires a CHA to show evidence of both (PHAB, 2022). To provide a comprehensive picture of the community, the CHA should include several primary and secondary data collection methods to define the community. Refer to Table 17.4 for potential primary data sources and Table 17.5 for potential secondary data sources. Primary data sources may include qualitative data, quantitative data, or both. Secondary data sources are quantitative in nature.
The community health nurse focuses on data regarding areas of need. This includes mortality, morbidity, and other health outcome data, such as SDOH. A comprehensive review of access to education, healthy nutrition, transportation, healthy spaces, resources for exercise, health care services, economic opportunities, a healthy environment, and employment provides perspective on potential causes of negative health outcomes and areas for improvement.
The community health nurse should not focus only on data regarding areas of need, but on areas of strength and potential resources as well. The values and beliefs of the community, available resources, and current and potential funding are considered. Community values and beliefs are important to ensure community buy-in when programs are implemented to target an identified area of concern. Although statistical health data may indicate poor outcomes in one area, other health-related areas may be of greater concern and importance to community members. Evaluation of the adequacy of community systems should also occur. One method to assess the extent to which community agencies successfully provide support is the seven As (Truglio-Londrigan & Gallager, 2003):
- Awareness: Community members are aware that a service is needed and know where to attain that service.
- Access: Community members can contact the agency, can navigate the agency’s technology, and have no limitations in getting to the service.
- Availability: Service is offered at a time, location, and place that is convenient for community members.
- Affordability: Community members are able to pay for the service.
- Acceptability: Community members perceive that the service is meeting their needs.
- Appropriateness: Community members believe the service is suitable.
- Adequacy: Service is provided in sufficient quantity or degree.
Assigned individuals or groups within the CHA team carry out the work of data collection. Most often, the local public health department or health care system provides team leadership. Some CHA teams may decide to hire outside professionals to conduct the work of data collection and subsequent work writing in collaboration with the CHA team.
Most CHAs include surveys mailed to randomly selected community members. The team creates surveys in collaboration with various community partners and organizations that provide care to community members. Most often, these individuals and organizations have information that they need to determine if the care and programs they provide are still needed and effective. For example, a representative from the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) may be a part of the CHA team and ask that data regarding breastfeeding is collected. This ensures that the data collected is not only useful to the public health department, but to community partners as well.
Key interviews or focus groups add important qualitative information regarding the values and beliefs of the community. Examples of questions that may be asked to determine the values, beliefs, and concerns of community members include the following:
- What do you consider to be the major health concerns of the community?
- What do you consider to be the least important health issues of the community?
- What are some of the current efforts to address health concerns of the community?
- What do you consider to be strengths of the community?
- What do you consider to be challenges of the community?
- What do you consider to be needs of community members that are not being addressed?
- In your opinion, why are those needs not being addressed?
Youth data may be difficult to collect. School-age children complete multiple required assessments per year, which takes away from instruction. Additionally, parents must provide permission for assessment, which is not always granted. Often youth data are derived from either data collected by other agencies or organizations or by surveys completed by school-age youth enrolled in local schools. For example, the Ohio Healthy Youth Environment Survey (OHYES!) is a free survey schools can use to collect data from students in grades 7 to 12 (Ohio Department of Health, 2023). It includes questions about health, safety, and behavior health factors.
Data collection ends when all planned assessment tasks are conducted and the data represent a comprehensive view of the community. The data are collated into a final written report and presented by topic. Most often, the CHA report contains topic areas such as health care access, adult health behaviors, chronic disease, social conditions, youth health, and demographics. The data are presented in written format, tables, graphs, and images to highlight areas of strength and concern. Examples of current CHA reports can be found on most public health department or health care system websites.
Read the scenario, and then answer the questions that follow.
After contacting community members, Tia joined an assessment team with the goal of implementing interventions to combat the opioid crisis. The team chose the PRECEDE-PROCEED model to guide its assessment and planning for intervention. During the first phase, social assessment, data regarding community needs and desires are collected. The team found that community members are concerned about the current opioid crisis and would like to reduce substance misuse and overdose death rates. During the second phase, epidemiological assessment, the team gathers data from primary and secondary sources and considers behavioral and environmental factors contributing to the opioid crisis. During the third phase, educational and ecological diagnosis, the team identifies predisposing, enabling, and reinforcing factors of the opioid crisis.'
1. The team plans to gather qualitative information from key community partners regarding the opioid crisis during the first step. Which of the following data collection strategies would be appropriate?
- Collecting survey responses from community members
- Using GIS to map incidences of opioid overdose deaths
- Gathering local overdose statistics to compare to national data
- Conducting a focus group with local emergency responders
2. Which of the following would be categorized as an enabling factor for addressing opioid misuse?
- A drug rehabilitation center is located within the community.
- Local media promotes community naloxone training.
- High school students gain knowledge of the consequences of opioid misuse.
- A cycle of drug misuse is linked to specific families in the community.


7.2: Energy in Living Systems - Electrons and Energy
- Describe the role played by electrons in energy production and storage
Electrons and Energy
The removal of an electron from a molecule via a process called oxidation results in a decrease in the potential energy stored in the oxidized compound. When oxidation occurs in the cell, the electron (sometimes as part of a hydrogen atom) does not remain un-bonded in the cytoplasm. Instead, the electron shifts to a second compound, reducing the second compound (oxidation of one species always occurs in tandem with reduction of another).
The shift of an electron from one compound to another removes some potential energy from the first compound (the oxidized compound) and increases the potential energy of the second compound (the reduced compound). The transfer of electrons between molecules via oxidation and reduction is important because most of the energy stored in atoms is in the form of high-energy electrons; it is this energy that is used to fuel cellular functions. The transfer of energy in the form of electrons allows the cell to transfer and use energy in an incremental fashion: in small packages rather than as a single, destructive burst.
Electron carriers
In living systems, a small class of molecules functions as electron shuttles: they bind and carry high-energy electrons between compounds in cellular pathways. The principal electron carriers we will consider are derived from the vitamin B group, which are derivatives of nucleotides. These compounds can be easily reduced (that is, they accept electrons) or oxidized (they lose electrons). Nicotinamide adenine dinucleotide (NAD) is derived from vitamin B3, niacin. NAD + is the oxidized form of niacin; NADH is the reduced form after it has accepted two electrons and a proton (which together are the equivalent of a hydrogen atom with an extra electron). It is noteworthy that NAD + must accept two electrons at once; it cannot serve as a one-electron carrier.
NAD + can accept electrons from an organic molecule according to the general equation:
RH (Reducing agent) + NAD + (Oxidizing agent) → NADH (Reduced) + R (Oxidized)
When electrons are added to a compound, the compound is reduced. A compound that reduces another is called a reducing agent. In the above equation, RH is a reducing agent and NAD + is reduced to NADH. When electrons are removed from a compound, the compound is oxidized. In the above equation, NAD + is an oxidizing agent and RH is oxidized to R. The molecule NADH is critical for cellular respiration and other metabolic pathways.
Similarly, flavin adenine dinucleotide (FAD + ) is derived from vitamin B 2 , also called riboflavin. Its reduced form is FADH 2 . A second variation of NAD, NADP, contains an extra phosphate group. Both NAD + and FAD + are extensively used in energy extraction from sugars, and NADP plays an important role in anabolic reactions and photosynthesis.
Key Points
- When electrons are added to a compound, the compound is reduced; a compound that reduces another is called a reducing agent.
- When electrons are removed from a compound, the compound is considered oxidized; a compound that oxidizes another is called an oxidizing agent.
- The transfer of energy in the form of electrons allows the cell to transfer and use energy in an incremental fashion.
- The principle electron carriers are NAD+ and NADH because they can be easily oxidized and reduced, respectively.
- NAD+ is the oxidized form of the niacin and NADH is the reduced form after it has accepted two electrons and a proton.
Key Terms
- oxidation : A reaction in which the atoms of an element lose electrons and the valence of the element increases.
- reduction : A reaction in which electrons are gained and valence is reduced; often by the removal of oxygen or the addition of hydrogen.
- nicotinamide adenine dinucleotide : (NAD) An organic coenzyme involved in biological oxidation and reduction reactions.
- electron shuttle : molecules that bind and carry high-energy electrons between compounds in cellular pathways


10.3: Photography
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- Last updated
- Save as PDF
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Photographer |
Focus Subject Matter |
General Format |
|---|---|---|
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Ansel Adams |
Nature, Landscape |
Prints |
|
Gordon Parks |
Fashion, Poverty, Sports, Portraits |
Magazine photos, Documentary |
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Dorothea Lange |
Social Issues |
Documentary |
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Margaret Bourke-White |
Social issues, World War 2 correspondent |
Magazine photos |
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Alfred Stieglitz |
Figures, Original paintings |
Prints, Exhibition |
When gazing at an Ansel Adams photograph in the visitor’s center at Grand Teton National Park and viewing the iconic Tetons and the Snake River (13.48) from 1942, one tries to think about hiking through the magical peaks of the Tetons, walking in the footsteps of Adams, and trying to visualize the images he skillfully captured. Ansel Adams (1902-1984) was one of America’s most famous photographers and a dedicated environmentalist. Using black and white film to capture the landscapes of America’s treasured national parks, he assisted in the preservation of thousands of acres of land. Born in San Francisco, California, and following his father’s devotion to the ideas of Ralph Waldo Emerson, he understood the beauty of the natural landscape in his neighborhood and developed an appreciation for the environment that would become his lifelong focus.
“To live a modest, moral life guided by a social responsibility to man and to nature” – Ralph Waldo Emerson
During the 1920s, Adams began his career in photography following the photo-secession movement of the famous photographer Alfred Stieglitz. In the days before Photoshop, what was captured on film was the photograph. The skill of photography was in the hands and eyes of the artist, and Adams had a gift of patience. A photographer cannot merely walk up to Half Dome in Yosemite Park and snap a beautiful photo, and it takes hours or days to capture the desired image based on the perfect light in the right season. In the 1930s, Adams traveled extensively to take photographs, his work demonstrating an experience level of a master. He produced books of his photographs; the book Taos Pueblo (13.49) was a pictorial of the western United States and one of his most inspiring books. The paper inside the book was created so Adams could print directly on the paper producing an extraordinary tonal range on a matte surface.
In the early 1940s, Adams contracted with the Department of the Interior to take photographs of America's national parks. Evening on McDonald Lake (13.50) is an image he captured of the lake in Glacier National Park during a momentary break in the clouds. Leaves at Glacier National Park (13.51) is a detailed close-up of the leave structure from one of the trees in the park. Adams recorded nature in photographs for almost sixty years and earned many awards for his spectacular images and his contribution to conservation.
Gordon Parks (1912-2006) was another American photographer and film director best known for his photographic essays for Life Magazine .  His parents died when he was a teenager, and he was on the streets to fend for himself. Buying his first camera from a pawn shop at age 25, Parker began to capture photographs of everyday life in Chicago. American Gothic (13.52) is a portrait of Ella Watson, who worked on the janitorial staff at the FSA building. The original American Gothic (13.53) by Grant Wood is clearly represented in Parks photograph, a parody to demonstrate the inequality in America. The photograph by Parks shows a single black mother holding both a mop and broom, which she used daily to clean offices. The civil rights movement in America was underway to give rights to all Americans. The final picture is one of Ella Watson and her family (13.54) at home after cleaning all night, sitting in the cramped quarters of her space.
Migrant Mother , an icon of the American depression, is one of the most recognized photographs from Dorothea Lange (1895-1965). Born in New Jersey, she contracted polio at a young age, which damaged her right leg, causing her to limp the rest of her life. Lange’s health contributed to her dramatic photographs because she was able to sit motionless for hours in one place. She never hurried and coupled with her courage, and she captured some of America's finest photographs.
Migrant Mother (13.55) was a series of photographs taken while on assignment for the Resettlement Administration of the Farm Security Administration Office. Lange was in Nipomo, California, when she noticed a mother with several children in a tent. She took five photos, each time closer than the last one until she produced the final photograph and the eyewitness to history.
Manzanar (13.56) was one of the Japanese Internment Camps based on Executive Order 9066 President Roosevelt authorized to remove and imprison Americans of Japanese descent forcibly. Lange was hired to photograph the massive relocation project and portray it as a necessity of American war requirements. Lange did not share the same opinion as to the government and struggled to justify her work, inspiring her to capture the suffering and misery of American citizens in the camps. Lange's work was refused and not published until 40 years later in a book after her death. Lange did not walk away from the injustice and photographed the real stories.
Another great American female photographer was Margaret Bourke-White (1904-1971). She is best known for her pictures in the Soviet Union and as the first foreign war photographer. Born in New York, her interest in photography started at an early age, and she worked in a commercial photography studio after college. Bourke-White was the first woman to fly with the US Air Force on a combat mission, and with the outbreak of World War II, she was already an established war correspondent. She took some of the critical images of the war (13.57) during her assignments, bringing the war into focus. She also went to India and Pakistan during their conflict and recorded events from each country, including the image of Gandhi sitting at a spinning wheel a few hours before he was assassinated.
One of the most significant influences on modern photography was Alfred Stieglitz (1864-1946). Stieglitz was an American photographer, owned the famous Stieglitz Gallery in New York City, and was married to Georgia O'Keefe. By the turn of the 20 th century, Stieglitz was an accomplished artist and began to photograph everyday scenes in New York City. Terminal (13.58) is a city street scene with a horse and trolley passing through the mountains of snow on the ground, steam seen rising off the horses and from their nostrils.
The Venetian Canal (13.59) and a portrait of Katherine Stieglitz (13.60) are two more examples of Stieglitz's artistic ability with the camera. The portrait of his daughter is black and white; however, the movement at the time was to colorize photographs by hand, giving them a colored photograph appearance. The photographs of Venice were taken during a nine-year trip to Europe and appeared in many magazines. The photo was taken using a straightforward printing method, without retouching. The soft focus of the photo comes from the early morning light, and the close-up is almost guaranteed with the small, tight Venetian canals.
When Stieglitz was near the end of his life, he was asked what he thought was the perfect photograph and he answered:
“I will be sitting with the plate of a picture I have just taken in my hands. It will be the picture I have always known that some day I would be able to take. It will be the perfect photograph, embodying all that I ever have wished to say. I will just have developed it; just have looked at it; just have seen that it was exactly what I wanted. The room will be empty, quiet. The walls will be bare – clean. I will sit looking at the picture. It will slip from my hands, and break as it falls to the ground. I will be dead. They will come. No one will ever have seen the picture nor know what it was.” [2]


3.1: Gaussian Elimination
The standard numerical algorithm to solve a system of linear equations is called Gaussian Elimination. We can illustrate this algorithm by example.
Consider the system of equations
\[\begin{aligned} &-3 x_{1}+2 x_{2}-x_{3}=-1 \\ &6 x_{1}-6 x_{2}+7 x_{3}=-7 \\ &3 x_{1}-4 x_{2}+4 x_{3}=-6 \end{aligned} \nonumber \]
To perform Gaussian elimination, we form an Augmented Matrix by combining the matrix \(A\) with the column vector \(b\) :
\[\left(\begin{array}{rrrr} -3 & 2 & -1 & -1 \\ 6 & -6 & 7 & -7 \\ 3 & -4 & 4 & -6 \end{array}\right) \nonumber \]
Row reduction is then performed on this matrix. Allowed operations are (1) multiply any row by a constant, (2) add multiple of one row to another row, (3) interchange the order of any rows. The goal is to convert the original matrix into an upper-triangular matrix
We start with the first row of the matrix and work our way down as follows. First we multiply the first row by 2 and add it to the second row, and add the first row to the third row:
\[\left(\begin{array}{rrrr} -3 & 2 & -1 & -1 \\ 0 & -2 & 5 & -9 \\ 0 & -2 & 3 & -7 \end{array}\right) \nonumber \]
We then go to the second row. We multiply this row by \(-1\) and add it to the third row:
\[\left(\begin{array}{rrrr} -3 & 2 & -1 & -1 \\ 0 & -2 & 5 & -9 \\ 0 & 0 & -2 & 2 \end{array}\right) \nonumber \]
The resulting equations can be determined from the matrix and are given by
\[\begin{aligned} -3 x_{1}+2 x_{2}-x_{3} &=-1 \\ -2 x_{2}+5 x_{3} &=-9 \\ -2 x_{3} &=2 \end{aligned} \nonumber \]
These equations can be solved by backward substitution, starting from the last equation and working backwards. We have
\[\begin{aligned} &-2 x_{3}=2 \rightarrow x_{3}=-1 \\ &-2 x_{2}=-9-5 x_{3}=-4 \rightarrow x_{2}=2 \\ &-3 x_{1}=-1-2 x_{2}+x_{3}=-6 \rightarrow x_{1}=2 \end{aligned} \nonumber \]
Therefore,
\[\left(\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right)=\left(\begin{array}{r} 2 \\ 2 \\ -1 \end{array}\right) \nonumber \]


16.3C: Planktonic Food Webs
- Differentiate planktonic food webs
Plankton communities are divided into broad categories of producer, consumer and recycler groups. However, determining the trophic level of some plankton is not straightforward. For example, although most dinoflagellates are either photosynthetic producers or heterotrophic consumers, many species are mixotrophic, depending upon circumstances.
Aside from representing the bottom few levels of a food chain that supports commercially important fisheries, plankton ecosystems play a role in the biogeochemical cycles of many important chemical elements, including the ocean’s carbon cycle.
Primarily by grazing on phytoplankton, zooplankton provide carbon to the planktic foodweb, either respiring it to provide metabolic energy, or upon death as biomass or detritus. Typically more dense than seawater, organic material tends to sink. In open-ocean ecosystems away from the coasts this transports carbon from surface waters to the deep. This process is known as the biological pump, and is one reason that oceans constitute the largest carbon sink on Earth.
It might be possible to increase the ocean’s uptake of carbon dioxide generated through human activities by increasing plankton production through “seeding”, primarily with the micronutrient iron. However, this technique may not be practical on a large scale. Ocean oxygen depletion and resultant methane production (caused by the excess production of remineralising at depth) is one potential drawback.
The growth of phytoplankton populations is dependent on light levels and nutrient availability. The chief factor limiting growth varies from region to region in the world’s oceans. On a broad scale, growth of phytoplankton in the oligotrophic tropical and subtropical gyres is generally limited by nutrient supply, while light often limits phytoplankton growth in subarctic gyres. Environmental variability at multiple scales influences the nutrient and light available for phytoplankton. As these organisms form the base of the marine food web, this variability in phytoplankton growth influences higher trophic levels. For example, at interannual scales phytoplankton levels temporarily plummet during El Nino periods, influencing populations of zooplankton, fish, sea birds, and marine mammals.
The effects of anthropogenic warming on the global population of phytoplankton is an area of active research. Changes in the vertical stratification of the water column, the rate of temperature-dependent biological reactions, and the atmospheric supply of nutrients are expected to have important impacts on future phytoplankton productivity. Additionally, changes in the mortality of phytoplankton due to rates of zooplankton grazing may be significant.
Freshly-hatched fish larvae are also plankton for a few days as long as they cannot swim against currents. Zooplankton are the initial prey item for almost all fish larvae as they switch from their yolk sacs to external feeding. Fish rely on the density and distribution of zooplankton to match that of new larvae, which can otherwise starve. Natural factors (e.g., current variations) and man-made factors (e.g. river dams) can strongly affect zooplankton, which can in turn strongly affect larval survival, and therefore breeding success.
Key Points
- Plankton communities represent the bottom few levels of a food chain that supports commercially important fisheries.
- Plankton ecosystems also play a crucial role in the biogeochemical cycles of many important chemical elements, including the ocean’s carbon cycle.
- The growth of phytoplankton populations is dependent on light levels and nutrient availability.
Key Terms
- plankton : Plankton (singular plankter) are any organisms that live in the water column and are incapable of swimming against a current. They provide a crucial source of food to many large aquatic organisms, such as fish and whales.
- ecosystems : Communities of living organisms (plants, animals and microbes) in conjunction with the nonliving components of their environment (things like air, water, and mineral soil), interacting as a system; linked together through nutrient cycles and energy flows.
- biogeochemical cycles : A biogeochemical cycle or substance turnover or cycling of substances is a pathway by which a chemical element or molecule moves through both biotic (biosphere) and abiotic (lithosphere, atmosphere, and hydrosphere) compartments of Earth. A cycle is a series of change which comes back to the starting point and which can be repeated.


4.5: Classifying Chemical Reactions - Combustion Reactions
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- Last updated
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- Scott Van Bramer
- Widener University
Learning Objectives
- Define combustion reactions
- Identify when a combustion reaction will occur
- Write a balanced chemical equation that describes what happens when a combustion reaction occurs
- Solve stoichometry problems with combustion reactions
Humans interact with one another in various and complex ways, and we classify these interactions according to common patterns of behavior. When two humans exchange information, we say they are communicating. When they exchange blows with their fists or feet, we say they are fighting. Faced with a wide range of varied interactions between chemical substances, scientists have likewise found it convenient (or even necessary) to classify chemical interactions by identifying common patterns of reactivity. This module will provide an introduction to combustion reactions, one of the most prevalent types of chemical reactions.
Combustion Reactions
Combustion reactions are another common class of reactions. These reactions provide the energy to drive your car, heat your home, and cook your food. Anytime something burns, it is a combustion reaction. These reactions are critical to our economy but they are also responsible for emitting 35 gigatons of CO 2 into the atmosphere in 2020. In a combustion reaction a fuel, like methane, reacts with oxygen to produce carbon dioxide and water. Almost all combustion reactions require additional oxygen, which comes from the atmosphere, with the reactants. In a combustion reaction all the carbon in the reactants is converted into carbon dioxide and all the hydrogen in the reactants is converted into water.
Example \(\PageIndex{1}\): Writing Equations for Combustion Reactions
Write balanced chemical equations for the combustion reaction described here:
- the combustion of methane, CH 4
- the combustion of ethane, C 2 H 6
Solution
(a) In addition to methane, CH 4 , the combustion reaction also requires oxygen from the atmosphere. The products of the combustion reaction will be H 2 O and CO 2 .
\[\ce{CH4}(g)+\ce{2O2}(g)\rightarrow \ce{CO2}(g)+\ce{2H2O}(l) \nonumber \]
(b) In addition to ethane, C 2 H 6 , the combustion reaction also requires oxygen from the atmosphere. The products of the combustion reaction will be H 2 O and CO 2 .
\[\ce{2C2H6}(g)+\ce{7O2}(g)\rightarrow \ce{4CO2}(g)+\ce{6H2O}(l) \nonumber \]
Notice that balancing the reaction requires doubling the number of ethane molecules so that the coefficient for oxygen is a whole number.
Exercise \(\PageIndex{1}\)
Write the balanced equation for the combustion of methanol, CH 3 OH
- Answer
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\[\ce{2CH3OH}(l)+\ce{3O2}(g)\rightarrow \ce{2CO2}(g)+\ce{4H2O}(l) \nonumber \]
Combustion in Biological Systems
Similar reactions also occur in biological systems. The overall chemical reaction that occurs in aerobic respiration is basically the same as the combustion of glucose. In biological systems these reactions are broken down into small steps to control the release of energy. The overall reaction for the combustion of glucose is:
\[\ce{C6H12O6}(s)+\ce{6O2}(g)\rightarrow \ce{6CO2}(g)+\ce{6H2O}(l) \nonumber \]
Combustion Analysis
The elemental composition of hydrocarbons and related compounds may be determined via a gravimetric method known as combustion analysis . In a combustion analysis, a weighed sample of the compound is heated to a high temperature under a stream of oxygen gas, resulting in its complete combustion to yield gaseous products of known identities. The complete combustion of hydrocarbons, for example, will yield carbon dioxide and water as the only products. The gaseous combustion products are swept through separate, preweighed collection devices containing compounds that selectively absorb each product (Figure \(\PageIndex{1}\)). The mass increase of each device corresponds to the mass of the absorbed product and may be used in an appropriate stoichiometric calculation to derive the mass of the relevant element.
Example \(\PageIndex{2}\): Combustion Analysis
Polyethylene is a hydrocarbon polymer used to produce food-storage bags and many other flexible plastic items. A combustion analysis of a 0.00126-g sample of polyethylene yields 0.00394 g of CO 2 and 0.00161 g of H 2 O. What is the empirical formula of polyethylene?
Solution
The primary assumption in this exercise is that all the carbon in the sample combusted is converted to carbon dioxide, and all the hydrogen in the sample is converted to water:
\[\mathrm{C_xH_y}(s)+\ce{excess\: O2}(g)\rightarrow x\ce{CO2}(g)+ \dfrac{y}{2} \ce{H2O}(g) \nonumber \]
Note that a balanced equation is not necessary for the task at hand. To derive the empirical formula of the compound, only the subscripts x and y are needed.
First, calculate the molar amounts of carbon and hydrogen in the sample, using the provided masses of the carbon dioxide and water, respectively. With these molar amounts, the empirical formula for the compound may be written as described in the previous chapter of this text. An outline of this approach is given in the following flow chart:
\[\mathrm{mol\: C=0.00394\:g\: CO_2\times\dfrac{1\:mol\: CO_2}{44.01\: g/mol}\times\dfrac{1\:mol\: C}{1\:mol\: CO_2}=8.95\times10^{-5}\:mol\: C} \nonumber \]
\[\mathrm{mol\: H=0.00161\:g\: H_2O\times\dfrac{1\:mol\: H_2O}{18.02\:g/mol}\times\dfrac{2\:mol\: H}{1\:mol\: H_2O}=1.79\times10^{-4}\:mol\: H} \nonumber \]
The empirical formula for the compound is then derived by identifying the smallest whole-number multiples for these molar amounts. The H-to-C molar ratio is
\[\mathrm{\dfrac{mol\: H}{mol\: C}=\dfrac{1.79\times10^{-4}\:mol\: H}{8.95\times10^{-5}\:mol\: C}=\dfrac{2\:mol\: H}{1\:mol\: C}} \nonumber \]
and the empirical formula for polyethylene is CH 2 .
Exercise \(\PageIndex{2}\)
A 0.00215-g sample of polystyrene, a polymer composed of carbon and hydrogen, produced 0.00726 g of CO 2 and 0.00148 g of H 2 O in a combustion analysis. What is the empirical formula for polystyrene?
- Answer
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CH
Summary
Chemical reactions are classified according to similar patterns of behavior. A large number of important reactions are included in three categories: precipitation, acid-base, and combustion. Precipitation reactions involve the formation of one or more insoluble products. Acid-base reactions involve the transfer of hydrogen ions between reactants.
Glossary
- combustion analysis
- gravimetric technique used to determine the elemental composition of a compound via the collection and weighing of its gaseous combustion products
- combustion reaction
- vigorous redox reaction producing significant amounts of energy in the form of heat and, sometimes, light
Contributors and Attributions
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


5.7: The Role of Teachers/Educators
Curriculum
Curriculum can be defined as the goals for children's development and learning, what teachers do to achieve the goals, the content children are to learn, processes, and activities through which children learn, the environment or context in which teaching and learning occur. What types of curriculum models (ex. emergent, project-based) or theories (ex. Montessori, Piaget, Vygotsky) have you heard about?
Teaching Philosophy
A quality curriculum provides a vision of what a program should look like and a framework for making decisions about how to achieve that vision. Educators need to be able to define their vision and how they provide learning to meet the needs of all learners. This vision should include the following:
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Create learning environments to allow students to be critical observers of their environment.
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Value Difference
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Recognize Injustice
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Question and Call to Action
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Critically evaluate and modify curriculum, materials, and teaching strategies.
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Expand personal and professional knowledge.
Expectations
Do no harm is an expression you may have heard in regards to medical professions but also applies to education and other fields of study. The National Association for the Education of Young Children (NAEYC) has created the "Code of Ethical Conduct and Statement of Commitment" (May 2011) which identifies the core values and responsibilities early care and educational settings should have and strive to meet in supporting children, families, educators, and community. Please click Code of Ethics to view.
Teacher Performance Expectations and Assessment
Teacher Performance Assessment
There are several advantages of performance assessments (Linn & Miller 2005). First, the focus is on complex learning outcomes that often cannot be measured by other methods. Second, performance assessments typically assess process or procedure as well as the product. For example, the teacher can observe if the students are repairing the machine using the appropriate tools and procedures as well as whether the machine functions properly after the repairs. Third, well designed performance assessments communicate the instructional goals and meaningful learning clearly to students. For example, if the topic in a fifth grade art class is one-point perspective the performance assessment could be drawing a city scene that illustrates one point perspective. (www.sanford-artedventures.com) . This assessment is meaningful and clearly communicates the learning goal. This performance assessment is a good instructional activity and has good content validity— common with well designed performance assessments (Linn & Miller 2005).
One major disadvantage with performance assessments is that they are typically very time consuming for students and teachers. This means that fewer assessments can be gathered so if they are not carefully devised fewer learning goals will be assessed— which can reduce content validity. State curriculum guidelines can be helpful in determining what should be included in a performance assessment. For example, Eric, a dance teacher in a high school in Tennessee learns that the state standards indicate that dance students at the highest level should be able to do demonstrate consistency and clarity in performing technical skills by:
- performing complex movement combinations to music in a variety of meters and styles
- performing combinations and variations in a broad dynamic range
- demonstrating improvement in performing movement combinations through self-evaluation
- critiquing a live or taped dance production based on given criteria
- ( www.tn.gov/education/instruction/academic-standards/arts-education.html )
Eric devises the following performance task for his eleventh grade modern dance class .
In groups 0/4-6 students will perform a dance at least 5 minutes in length. The dance selected should be multifaceted so that all the dancers can demonstrate technical skills, complex movements, and a dynamic range (Items 1-2). Students will videotape their rehearsals and document how they improved through self evaluation (Item 3). Each group will view and critique the final performance of one other group in class (Item 4). Eric would need to scaffold most steps in this performance assessment. The groups probably would need guidance in selecting a dance that allowed all the dancers to demonstrate the appropriate skills; critiquing their own performances constructively; working effectively as a team, and applying criteria to evaluate a dance.
Another disadvantage of performance assessments is they are hard to assess reliably which can lead to inaccuracy and unfair evaluation. As with any constructed response assessment, scoring rubrics are very important. An example of holistic and analytic scoring rubrics designed to assess a completed product are in Tables in previous sections. A rubric designed to assess the process of group interactions is in Table 1.11.1
Table 1.11.1 : Example of group interaction rubric
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Score |
Time management |
Participation and performance in roles |
Shared involvement |
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0 |
Group did not stay on task and so task was not completed. |
Group did not assign or share roles. |
Single individual did the task. |
|
1 |
Group was off-task the majority of the time but task was completed. |
Groups assigned roles but members did not use these roles. |
Group totally disregarded comments and ideas from some members. |
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2 |
Group stayed on task most of the time. |
Groups accepted and used some but not all roles. |
Group accepted some ideas but did not give others adequate consideration. |
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3 |
Group stayed on task throughout the activity and managed time well. |
Group accepted and used roles and actively participated. |
Groups gave equal consideration to all ideas. |
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4 |
Group defined their own approach in a way that more effectively managed the activity. |
Group defined and used roles not mentioned to them. Role changes took place that maximized individuals’ expertise. |
Groups made specific efforts to involve all group members including the reticent members. |
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Source : Adapted from Group Interaction ( GI) SETUP ( 2003). Issues, Evidence and You. Ronkonkomo, NY Lab-Aids. |
This rubric was devised for middle grade science but could be used in other subject areas when assessing group process. In some performance assessments several scoring rubrics should be used. In the dance performance example above Eric should have scoring rubrics for the performance skills, the improvement based on self evaluation, the team work, and the critique of the other group. Obviously, devising a good performance assessment is complex and Linn and Miller (2005) recommend that teachers should:
• Create performance assessments that require students to use complex cognitive skills. Sometimes teachers devise assessments that are interesting and that the students enjoy but do not require students to use higher level cognitive skills that lead to significant learning. Focusing on high level skills and learning outcomes is particularly important because performance assessments are typically so time consuming.
• Ensure that the task is clear to the students. Performance assessments typically require multiple steps so students need to have the necessary prerequisite skills and knowledge as well as clear directions. Careful scaffolding is important for successful performance assessments.
• Specify expectations of the performance clearly by providing students scoring rubrics during the instruction. This not only helps students understand what it expected but it also guarantees that teachers are clear about what they expect. Thinking this through while planning the performance assessment can be difficult for teachers but is crucial as it typically leads to revisions of the actual assessment and directions provided to students.
• Reduce the importance of unessential skills in completing the task. What skills are essential depends on the purpose of the task. For example, for a science report, is the use of publishing software essential? If the purpose of the assessment is for students to demonstrate the process of the scientific method including writing a report, then the format of the report may not be significant. However, if the purpose includes integrating two subject areas, science and technology, then the use of publishing software is important.
Because performance assessments take time it is tempting to include multiple skills without carefully considering if all the skills are essential to the learning goals.
References
Derman-Sparks, L., Edwards, J. O., & National Association for the Education of Young Children. (2010). Anti-bias education for young children and ourselves. Washington, DC: National Association for the Education of Young Children.
Code of Ethical Conduct and Statement of Commitment: Washington, D.C.: National Association for the Education of Young Children, 2011.
TED Talk, 2013. Rita Pierson: Every Kid needs a Champion . [video] Available at: < http://www.ted.com/talks/rita_pierso...pt?language=en >


22.7A: The Liver
The liver makes bile, which is essential for the digestion of fats.
- Summarize the roles of the liver in digestion
Key Points
- The liver is a vital organ with a wide range of functions, including detoxification, protein synthesis, and the production of bile, which is necessary for digestion.
- The bile produced by the liver is essential for the digestion of fats. Bile is formed in the liver and either stored in the gallbladder or released directly into the small intestine.
Key Terms
- liver : A large organ in the body that stores and metabolizes nutrients, destroys toxins, and produces bile. It is responsible for thousands of biochemical reactions.
- bile : A bitter, brownish-yellow or greenish-yellow secretion produced by the liver, stored in the gallbladder, and discharged into the duodenum, where it aids the process of digestion.
The Role of the Liver
The liver normally weighs between 1.3—3.0 kilograms and is a soft, pinkish-brown organ. It is the second-largest organ in the body, and is located on the right side of the abdomen.
Human liver : Photo of recently removed human liver.
The liver plays a major role in metabolism and has a number of functions in the body, including glycogen storage, plasma protein synthesis, and drug detoxification. It also produces bile, which is important for digestion.
The liver is supplied by two main blood vessels on its right lobe: the hepatic artery and the portal vein. The portal vein brings venous blood from the spleen, pancreas, and small intestine so that the liver can process the nutrients and byproducts of food digestion.
Bile
The bile produced in the liver is essential for the digestion of fats. Bile is formed in the liver, and it is stored in the gallbladder or released directly into the small intestine. After being stored in the gallbladder, the bile becomes more concentrated than when it left the liver; this increases its potency and intensifies its effect in digesting fats.


9.4A: Muscle Metabolism
Muscle contraction occurs via metabolism of adenosine triphosphate (ATP) derived primarily from the simple sugar glucose.
- Explain the process involved in muscle metabolism during aerobic exercise
Key Points
- ATP is required for muscle contraction. Four sources of this substance are available to muscle fibers: free ATP, phosphocreatine, glycolysis and cellular respiration.
- A small amount of free ATP is available in the muscle for immediate use.
- Phosphocreatine provides phosphates to ADP molecules, producing high-energy ATP molecules. It is present in low levels in the muscle.
- Glycolysis converts glucose to pyruvate, water and NADH, producing two molecules of ATP. Excess pyruvate is converted to lactic acid which causes muscle fatigue.
- Cellular respiration produces further molecules of ATP from pyruvate in the mitochondria. It is also required to resynthesize glycogen from lactic acid and restore stores of phosphocreatine and ATP in the muscle.
Key Terms
- phosphocreatine : A phosphorylated creatine molecule that serves as a rapidly mobilizable reserve of high-energy phosphates in skeletal muscle.
- ATP : The molecule containing high-energy bonds used to transfer energy between systems within a cell.
Muscle contractions are fueled by adenosine triphosphate (ATP), an energy-storing molecule. Four potential sources of ATP power muscle contractions.
Free ATP
Low levels of ATP exist within the muscle fibers and can immediately provide energy for contraction. However, the pool is very small and after a few muscle twitches will be exhausted.
Phosphocreatine
Phosphocreatine, also known as creatine phosphate, can rapidly donate a phosphate group to ADP to form ATP and creatine under anaerobic conditions. Enough phosphocreatine is present in the muscle to provide ATP for up to 15 seconds of contraction.
The reaction of phosphocreatine + ADP to ATP + creatine is reversible. During periods of rest, the store of phosphocreatine is regenerated from ATP.
Glycolysis
Glycolysis is the metabolic reaction which produces two molecules of ATP through the conversion of glucose into pyruvate, water, and NADH in the absence of oxygen.
The glucose for glycolysis can be provided by the blood supply, but is more often converted from glycogen in the muscle fibers. If glycogen stores in the muscle fibers are expended, glucose can be created from fats and proteins. However, this conversion is not as efficient.
Pyruvate is continually processed into lactic acid. With pyruvate accumulation, the amount of lactic acid produced is also increased. This lactic acid accumulation in the muscle tissue reduces the pH, making it more acidic and producing the stinging feeling in muscles when exercising. This inhibits further anaerobic respiration, inducing fatigue.
Glycolysis alone can provide energy to the muscle for approximately 30 seconds, although this interval can be increased with muscle conditioning.
Cellular Respiration
While the pyruvate generated through glycolysis can accumulate to form lactic acid, it can also be used to generate further molecules of ATP. Mitochondria in the muscle fibers can convert pyruvate into ATP in the presence of oxygen via the Krebs Cycle, generating an additional 30 molecules of ATP.
Cellular respiration is not as rapid as the above mechanisms; however, it is required for exercise periods longer than 30 seconds. Cellular respiration is limited by oxygen availability, so lactic acid can still build up if pyruvate in the Krebs Cycle is insufficient.
Cellular respiration plays a key role in returning the muscles to normal after exercise, converting the excess pyruvate into ATP and regenerating the stores of ATP, phosphocreatine, and glycogen in the muscle that are required for more rapid contractions.


2: Minerals
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- 2.4: Silicate Minerals
- The vast majority of the minerals that make up the rocks of Earth’s crust are silicate minerals. These include minerals such as quartz, feldspar, mica, amphibole, pyroxene, olivine, and a variety of clay minerals. The building block of all of these minerals is the silica tetrahedron, a combination of four oxygen atoms and one silicon atom. As we’ve seen, it’s called a tetrahedron because planes drawn through the oxygen atoms form a shape with 4 surfaces.
Thumbnail: A ball of lustrous, royal-blue cavansite blades is set on a starkly contrasting snow-white crust on basalt matrix on this fine specimen from recent finds at the Wagholi Quarry of India. (CC-SA-BY 3.0; Rob Lavinsky from iRocks.com).


39.13: Transport of Gases in Human Bodily Fluids - Transport of Oxygen in the Blood
- Describe how oxygen is bound to hemoglobin and transported to body tissues
Transport of Oxygen in the Blood
Although oxygen dissolves in blood, only a small amount of oxygen is transported this way. Only 1.5 percent of oxygen in the blood is dissolved directly into the blood itself. Most oxygen, 98.5 percent, is bound to a protein called hemoglobin and carried to the tissues.
Hemoglobin
Hemoglobin, or Hb, is a protein molecule found in red blood cells (erythrocytes) made of four subunits: two alpha subunits and two beta subunits. Each subunit surrounds a central heme group that contains iron and binds one oxygen molecule, allowing each hemoglobin molecule to bind four oxygen molecules. Molecules with more oxygen bound to the heme groups are brighter red. As a result, oxygenated arterial blood where the Hb is carrying four oxygen molecules is bright red, while venous blood that is deoxygenated is darker red.
It is easier to bind a second and third oxygen molecule to Hb than the first molecule. This is because the hemoglobin molecule changes its shape, or conformation, as oxygen binds. The fourth oxygen is then more difficult to bind. The binding of oxygen to hemoglobin can be plotted as a function of the partial pressure of oxygen in the blood (x-axis) versus the relative Hb-oxygen saturation (y-axis). The resulting graph, an oxygen dissociation curve, is sigmoidal, or S-shaped. As the partial pressure of oxygen increases, the hemoglobin becomes increasingly saturated with oxygen.
Factors That Affect Oxygen Binding
The oxygen-carrying capacity of hemoglobin determines how much oxygen is carried in the blood. In addition, other environmental factors and diseases can also affect oxygen-carrying capacity and delivery; the same is true for carbon dioxide levels, blood pH, and body temperature. When carbon dioxide is in the blood, it reacts with water to form bicarbonate (HCO 3 − ) and hydrogen ions (H + ). As the level of carbon dioxide in the blood increases, more H + is produced and the pH decreases. The increase in carbon dioxide and subsequent decrease in pH reduce the affinity of hemoglobin for oxygen. The oxygen dissociates from the Hb molecule, shifting the oxygen dissociation curve to the right. Therefore, more oxygen is needed to reach the same hemoglobin saturation level as when the pH was higher. A similar shift in the curve also results from an increase in body temperature. Increased temperature, such as from increased activity of skeletal muscle, causes the affinity of hemoglobin for oxygen to be reduced.
Diseases such as sickle cell anemia and thalassemia decrease the blood’s ability to deliver oxygen to tissues and its oxygen-carrying capacity. In sickle cell anemia, the shape of the red blood cell is crescent-shaped, elongated, and stiffened, reducing its ability to deliver oxygen. In this form, red blood cells cannot pass through the capillaries. This is painful when it occurs. Thalassemia is a rare genetic disease caused by a defect in either the alpha or the beta subunit of Hb. Patients with thalassemia produce a high number of red blood cells, but these cells have lower-than-normal levels of hemoglobin. Therefore, the oxygen-carrying capacity is diminished.
Key Points
- Hemoglobin is made up of four subunits and can bind up to four oxygen molecules.
- Carbon dioxide levels, blood pH, body temperature, environmental factors, and diseases can all affect oxygen’s carrying capacity and delivery.
- A decrease in the oxygen-carrying ability of hemoglobin is observed with an increase in carbon dioxide and temperature, as well as a decrease in pH within the body.
- Sickle cell anemia and thalassemia are two hereditary diseases that decrease the blood’s oxygen-carrying capacity.
Key Terms
- thalassemia : an inherited disorder in which the person produces a high number of red blood cells, but the cells have lower levels of hemoglobin
- sickle cell anemia : a hereditary blood disorder, characterized by red blood cells that assume an abnormal, rigid, sickle shape
- heme : the component of hemoglobin responsible for binding oxygen; consists of an iron ion that binds oxygen and a porphyrin ring that binds the globin molecules; one molecule binds one molecule of oxygen


34.11: The Self-Reliant Baby Driver (Spoiler Alert!) – Where is American Literature Now?
Edgar Wright is well known for his ground-breaking work in filmography. With his newest film, not only did he break further untapped ground, but he broke straight into some good ‘ol American idealism. Specifically, in his newest film, Baby Driver, Wright makes connections to the themes expressed in Ralph Waldo Emerson’s “Self-Reliance.” You heard me. Wright draws off the same ideals Emerson highlights in his essay.
Let’s start with Emerson’s views. The text stresses exactly what the title proclaims: self-reliance. The idea of relying on oneself is indeed a noble one. Yet, there are further implications to Emerson’s ideal type of reliance. In laying his groundwork, Emerson does mention that “[a] man should learn to detect and watch the gleam of light which flashes across his mind from within, more than the lustre of the firmament of bards and sages” (1). In plain English, this means that a man should trust himself. He should not blindly follow the ideologies of others. The saying “to thine own self be true” comes to mind. Emerson requires that every man follow his own path, his own north star “more than the lustre of the firmament of the bards and sages.”
For Baby, the main character of Baby Driver , this statement rings true. While working for a crime syndicate as a get-away driver, there are several instances where we see his self-reliant nature. While driving away from the robbery of an armored truck, a civilian gets involved and tries to chase down the thieves. During the car chase, one of the criminals being driven, Bats, has a clear chance to shoot at the civilian. Before he can, Baby cuts the wheel and drives the crew to safety. After, Bats confronts Baby to ask if he did this to save the man who was chasing them. When Baby doesn’t answer directly, Bats replies “The moment you catch feelings is the moment you catch a bullet” (Wright). This scene shows a dynamic difference between Baby and the criminals he drives for. Every other criminal in this crime ring has no problem killing others to get what they want: money. Yet Baby purposefully avoids death if he can manage it, refusing to let civilians be harmed on his watch. Even though everyone around him falls into all sorts of criminal actions, Baby keeps the majority of his moral principles. He refuses to kill the innocent. In this way, he is self-reliant. Regardless of what others think, he stands his ground, even while being threatened by characters like Bats. Despite the “lustre” of the ideology that Bats and company lead, Baby finds his own path.
Emerson brings up a controversial point in his essay: the idea that the others don’t matter.  You are your own person regardless of what others think. If you’re mean, be mean. Believe what you believe. Do not let others try to define you. However, Emerson states this in a way that is much less like a motivational poster: “What I must do is all that concerns me, not what the people think” (5). He quite literally tells the reader that the thoughts of others are not his concern. He is a man who is all about his own actions. And to be self-reliant, one must detach from the judgement of others.
In Edgar Wright’s films, the main characters often have quirks. In Baby Driver , this quirk is a huge theatrical device. It is also much talked about between the different characters. Having been in a car accident in a young age, Baby suffers from acute tinnitus, meaning there is always a low buzzing in his ears. For that and other reasons, Baby listens to music; he has a large library of tunes to choose from. It’s not occasional either, this motif continues practically every moment of the film. Baby never stops listening to music. However, the criminals that he works with are constantly alluding to this quirk being a mental issue, based on the constant immersion in his music. At one point, Bats even remarks “He’s a looney. Just like his tunes” (Wright). Regardless, there is no end to Baby’s listening. Not only does he ignore his fellow degenerates, he barely seems to notice their commentary. Even when the others get in his face, he gives them a blank stare. Baby doesn’t care about the thoughts of his companions. He is only concerned with what he must do, “not what the people think.”
While many of us in class disagreed with the blunt message Emerson was sending in “Self-Reliance,” a lot of those ideals are alive and well today. Everyone has their own code that they live by, and most don’t bother with what others think about that code. In terms of American Literature, we see this sort of thing in advertising all the time. “Be You,” and “Believe in Yourself” are motivational slogans we print on practically everything today. We also see it in all sorts of texts, like Baby Driver. America is full to bursting with ideas of being self-reliant and being yourself in all circumstances. At the end of it all, America still promotes many of the ideologies within Self-Reliance.


1.3: The Average Rate of Change of a Function
- What do we mean by the average rate of change of a function on an interval?
- What does the average rate of change of a function measure? How do we interpret its meaning in context?
- How is the average rate of change of a function connected to a line that passes through two points on the curve?
Given a function that models a certain phenomenon, it's natural to ask such questions as “how is the function changing on a given interval” or “on which interval is the function changing more rapidly?” The concept of average rate of change enables us to make these questions more mathematically precise. Initially, we will focus on the average rate of change of an object moving along a straight-line path.
For a function \(s\) that tells the location of a moving object along a straight path at time \(t\text{,}\) we define the average rate of change of \(s\) on the interval \([a,b]\) to be the quantity
Note particularly that the average rate of change of \(s\) on \([a,b]\) is measuring the change in position divided by the change in time .
Let the height function for a ball tossed vertically be given by \(s(t) = 64 - 16(t-1)^2\text{,}\) where \(t\) is measured in seconds and \(s\) is measured in feet above the ground.
- Compute the value of \(AV_{[1.5,2.5]}\text{.}\)
- What are the units on the quantity \(AV_{[1.5,2.5]}\text{?}\) What is the meaning of this number in the context of the rising/falling ball?
- In Desmos , plot the function \(s(t) = 64 - 16(t-1)^2\) along with the points \((1.5,s(1.5))\) and \((2.5, s(2.5))\text{.}\) Make a copy of your plot on the axes in Figure 1.3.1, labeling key points as well as the scale on your axes. What is the domain of the model? The range? Why?
4. Work by hand to find the equation of the line through the points \((1.5,s(1.5))\) and \((2.5, s(2.5))\text{.}\) Write the line in the form \(y = mt + b\) and plot the line in Desmos , as well as on the axes above.
5. What is a geometric interpretation of the value \(AV_{[1.5,2.5]}\) in light of your work in the preceding questions?
6. How do your answers in the preceding questions change if we instead consider the interval \([0.25, 0.75]\text{?}\) \([0.5, 1.5]\text{?}\) \([1,3]\text{?}\)
Defining and interpreting the average rate of change of a function
In the context of a function that measures height or position of a moving object at a given time, the meaning of the average rate of change of the function on a given interval is the average velocity of the moving object because it is the ratio of change in position to change in time . For example, in Preview Activity \(\PageIndex{1}\) , the units on \(AV_{[1.5,2.5]} = -32\) are “feet per second” since the units on the numerator are “feet” and on the denominator “seconds”. Morever, \(-32\) is numerically the same value as the slope of the line that connects the two corresponding points on the graph of the position function, as seen in Figure \(\PageIndex{2}\) The fact that the average rate of change is negative in this example indicates that the ball is falling.
While the average rate of change of a position function tells us the moving object's average velocity, in other contexts, the average rate of change of a function can be similarly defined and has a related interpretation. We make the following formal definition.
For a function \(f\) defined on an interval \([a,b]\text{,}\) the average rate of change of \(f\) on \([a,b]\) is the quantity
\[ AV_{[a,b]} = \frac{f(b) - f(a)}{b-a}\text{.} \nonumber \]
In every situation, the units on the average rate of change help us interpret its meaning, and those units are always “units of output per unit of input.” Moreover, the average rate of change of \(f\) on \([a,b]\) always corresponds to the slope of the line between the points \((a,f(a))\) and \((b,f(b))\text{,}\) as seen in Figure \(\PageIndex{3}\)
According to the US census, the populations of Kent and Ottawa Counties in Michigan where GVSU is located 1 from 1960 to 2010 measured in \(10\)-year intervals are given in the following tables.
| 1960 | 1970 | 1980 | 1990 | 2000 | 2010 |
| 363,187 | 411,044 | 444,506 | 500,631 | 574,336 | 602,622 |
| 1960 | 1970 | 1980 | 1990 | 2000 | 2010 |
| 98,719 | 128,181 | 157,174 | 187,768 | 238,313 | 263,801 |
Let \(K(Y)\) represent the population of Kent County in year \(Y\) and \(W(Y)\) the population of Ottawa County in year Y.
- Compute \(AV_{[1990,2010]}\) for both \(K\) and \(W\text{.}\)
- What are the units on each of the quantities you computed in (a.)?
- Write a careful sentence that explains the meaning of the average rate of change of the Ottawa county population on the time interval \([1990,2010]\text{.}\) Your sentence should begin something like “In an average year between 1990 and 2010, the population of Ottawa County was \(\ldots\)”
- Which county had a greater average rate of change during the time interval \([2000,2010]\text{?}\) Were there any intervals in which one of the counties had a negative average rate of change?
- Using the given data, what do you predict will be the population of Ottawa County in 2018? Why?
The average rate of change of a function on an interval gives us an excellent way to describe how the function behaves, on average. For instance, if we compute \(AV_{[1970,2000]}\) for Kent County, we find that
which tells us that in an average year from 1970 to 2000, the population of Kent County increased by about \(5443\) people. Said differently, we could also say that from 1970 to 2000, Kent County was growing at an average rate of \(5443\) people per year. These ideas also afford the opportunity to make comparisons over time. Since
we can not only say that Kent county's population increased by about \(7370\) in an average year between 1990 and 2000, but also that the population was growing faster from 1990 to 2000 than it did from 1970 to 2000.
Finally, we can even use the average rate of change of a function to predict future behavior. Since the population was changing on average by \(7370.5\) people per year from 1990 to 2000, we can estimate that the population in 2002 is
We have already seen that it is natural to use words such as “increasing” and “decreasing” to describe a function's behavior. For instance, for the tennis ball whose height is modeled by \(s(t) = 64 - 16(t-1)^2\text{,}\) we computed that \(AV_{[1.5,2.5]} = -32\text{,}\) which indicates that on the interval \([1.5,2.5]\text{,}\) the tennis ball's height is decreasing at an average rate of \(32\) feet per second. Similarly, for the population of Kent County, since \(AV_{[1990,2000]} = 7370.5\text{,}\) we know that on the interval \([1990,2000]\) the population is increasing at an average rate of \(7370.5\) people per year.
We make the following formal definitions to clarify what it means to say that a function is increasing or decreasing.
Let \(f\) be a function defined on an interval \((a,b)\) (that is, on the set of all \(x\) for which \(a \lt x \lt b\)). We say that \(f\) is increasing on \ ((a,b)\) provided that the function is always rising as we move from left to right. That is, for any \(x\) and \(y\) in \((a,b)\text{,}\) if \(x \lt y\text{,}\) then \(f(x) \lt f(y)\text{.}\)
Similarly, we say that \(f\) is decreasing on \((a,b)\) provided that the function is always falling as we move from left to right. That is, for any \(x\) and \(y\) in \((a,b)\text{,}\) if \(x \lt y\text{,}\) then \(f(x) \gt f(y)\text{.}\)
If we compute the average rate of change of a function on an interval, we can decide if the function is increasing or decreasing on average on the interval, but it takes more work 2 to decide if the function is increasing or decreasing always on the interval.
Let's consider two different functions and see how different computations of their average rate of change tells us about their respective behavior. Plots of \(q\) and \(h\) are shown in Figures 1.3.8 and 1.3.9.
1. Consider the function \(q(x) = 4-(x-2)^2\text{.}\) Compute \(AV_{[0,1]}\text{,}\) \(AV_{[1,2]}\text{,}\) \(AV_{[2,3]}\text{,}\) and \(AV_{[3,4]}\text{.}\) What do your last two computations tell you about the behavior of the function \(q\) on \([2,4]\text{?}\)
2. Consider the function \(h(t) = 3 - 2(0.5)^t\text{.}\) Compute \(AV_{[-1,1]}\text{,}\) \(AV_{[1,3]}\text{,}\) and \(AV_{[3,5]}\text{.}\) What do your computations tell you about the behavior of the function \(h\) on \([-1,5]\text{?}\)
3. On the graphs in Figures 1.3.8 and 1.3.9, plot the line segments whose respective slopes are the average rates of change you computed in (a) and (b).
True or false: Since \(AV_{[0,3]} = 1\text{,}\) the function \(q\) is increasing on the interval \((0,3)\text{.}\) Justify your decision.
5. Give an example of a function that has the same average rate of change no matter what interval you choose. You can provide your example through a table, a graph, or a formula; regardless of your choice, write a sentence to explain.
It is helpful be able to connect information about a function's average rate of change and its graph. For instance, if we have determined that \(AV_{[-3,2]} = 1.75\) for some function \(f\text{,}\) this tells us that, on average, the function rises between the points \(x = -3\) and \(x = 2\) and does so at an average rate of \(1.75\) vertical units for every horizontal unit. Moreover, we can even determine that the difference between \(f(2)\) and \(f(-3)\) is
since \(\frac{f(2)-f(-3)}{2-(-3)} = 1.75\text{.}\)
Sketch at least two different possible graphs that satisfy the criteria for the function stated in each part. Make your graphs as significantly different as you can. If it is impossible for a graph to satisfy the criteria, explain why.
- \(f\) is a function defined on \([-1,7]\) such that \(f(1) = 4\) and \(AV_{[1,3]} = -2\text{.}\)
2. \(g\) is a function defined on \([-1,7]\) such that \(g(4) = 3\text{,}\) \(AV_{[0,4]} = 0.5\text{,}\) and \(g\) is not always increasing on \((0,4)\text{.}\)
3. \(h\) is a function defined on \([-1,7]\) such that \(h(2) = 5\text{,}\) \(h(4) = 3\) and \(AV_{[2,4]} = -2\text{.}\)
Summary
-
For a function \(f\) defined on an interval \([a,b]\text{,}\) the average rate of change of \(f\) on \([a,b]\) is the quantity
\[ AV_{[a,b]} = \frac{f(b) - f(a)}{b-a}\text{.} \nonumber \]
- The value of \(AV_{[a,b]} = \frac{f(b) - f(a)}{b-a}\) tells us how much the function rises or falls, on average, for each additional unit we move to the right on the graph. For instance, if \(AV_{[3,7]} = 0.75\text{,}\) this means that for additional \(1\)-unit increase in the value of \(x\) on the interval \([3,7]\text{,}\) the function increases, on average, by \(0.75\) units. In applied settings, the units of \(AV_{[a,b]}\) are “units of output per unit of input”.
- The value of \(AV_{[a,b]} = \frac{f(b) - f(a)}{b-a}\) is also the slope of the line that passes through the points \((a,f(a))\) and \((b,f(b))\) on the graph of \(f\text{,}\) as shown in Figure 1.3.3.
Exercises
A cold can of soda is removed from a refrigerator. Its temperature \(F\) in degrees Fahrenheit is measured at \(5\)-minute intervals, as recorded in the following table.
| \(t\) (minutes) | \(0\) | \(5\) | \(10\) | \(15\) | \(20\) | \(25\) | \(30\) | \(35\) |
| \(F\) (Fahrenheit temp) | \(37.00\) | \(44.74\) | \(50.77\) | \(55.47\) | \(59.12\) | \(61.97\) | \(64.19\) | \(65.92\) |
- Determine \(AV_{[0,5]}\text{,}\) \(AV_{[5,10]}\text{,}\) and \(AV_{[10,15]}\text{,}\) including appropriate units. Choose one of these quantities and write a careful sentence to explain its meaning. Your sentence might look something like “On the interval \(\ldots\text{,}\) the temperature of the soda is \(\ldots\) on average by \(\ldots\) for each \(1\)-unit increase in \(\ldots\)”.
- On which interval is there more total change in the soda's temperature: \([10,20]\) or \([25,35]\text{?}\)
- What can you observe about when the soda's temperature appears to be changing most rapidly?
- Estimate the soda's temperature when \(t = 37\) minutes. Write at least one sentence to explain your thinking.
The position of a car driving along a straight road at time \(t\) in minutes is given by the function \(y = s(t)\) that is pictured in Figure \(\PageIndex{11}\) The car's position function has units measured in thousands of feet. For instance, the point \((2,4)\) on the graph indicates that after 2 minutes, the car has traveled 4000 feet.
In everyday language, describe the behavior of the car over the provided time interval. In particular, carefully discuss what is happening on each of the time intervals \([0,1]\text{,}\) \([1,2]\text{,}\) \([2,3]\text{,}\) \([3,4]\text{,}\) and \([4,5]\text{,}\) plus provide commentary overall on what the car is doing on the interval \([0,12]\text{.}\)
Compute the average rate of change of \(s\) on the intervals \([3,4]\text{,}\) \([4,6]\text{,}\) and \([5,8]\text{.}\) Label your results using the notation “\(AV_{[a,b]}\)” appropriately, and include units on each quantity.
On the graph of \(s\text{,}\) sketch the three lines whose slope corresponds to the values of \(AV_{[3,4]}\text{,}\) \(AV_{[4,6]}\text{,}\) and \(AV_{[5,8]}\) that you computed in (b).
Is there a time interval on which the car's average velocity is \(5000\) feet per minute? Why or why not?
Is there ever a time interval when the car is going in reverse? Why or why not?
Consider an inverted conical tank (point down) whose top has a radius of \(3\) feet and that is \(2\) feet deep. The tank is initially empty and then is filled at a constant rate of \(0.75\) cubic feet per minute. Let \(V=f(t)\) denote the volume of water (in cubic feet) at time \(t\) in minutes, and let \(h= g(t)\) denote the depth of the water (in feet) at time \(t\text{.}\) It turns out that the formula for the function \(g\) is \(g(t) = \left( \frac{t}{\pi} \right)^{1/3}\text{.}\)
- In everyday language, describe how you expect the height function \(h = g(t)\) to behave as time increases.
- For the height function \(h = g(t) = \left( \frac{t}{\pi} \right)^{1/3}\text{,}\) compute \(AV_{[0,2]}\text{,}\) \(AV_{[2,4]}\text{,}\) and \(AV_{[4,6]}\text{.}\) Include units on your results.
- Again working with the height function, can you determine an interval \([a,b]\) on which \(AV_{[a,b]} = 2\) feet per minute? If yes, state the interval; if not, explain why there is no such interval.
- Now consider the volume function, \(V = f(t)\text{.}\) Even though we don't have a formula for \(f\text{,}\) is it possible to determine the average rate of change of the volume function on the intervals \([0,2]\text{,}\) \([2,4]\text{,}\) and \([4,6]\text{?}\) Why or why not?
<1> Grand Rapids is in Kent, Allendale in Ottawa.
<2> Calculus offers one way to justify that a function is always increasing or always decreasing on an interval.


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Ableism
Discrimination on the basis of physical, mental, or emotional impairment or blocked access to the fulfillment of needs and in particular, full participation in social life.
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Bias
Prejudice for or against one thing, person or group compared to another, usually in a way considered to be unfair.
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Biological determinism
can be defined as a general theory, which holds that a group’s biological or genetic makeup shapes its social, political, and economic destiny.
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Classism
Discrimination on the basis of social class, or blocked access to material wealth and social status.

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Heteronormativity
The everyday, taken-for-granted ways in which heterosexuality is privileged and normalized.
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Homophobia
—the fear, hatred, or prejudice against gay people.
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Implicit bias
attitudes towards people or groups of people or associate stereotypes with them without our conscious knowledge.
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Intersectionality
Seeing systems of oppression working in concert, rather than separately and independently. Also, the complex, cumulative way in which the multiple forms of discrimination (e.g. racism, sexism, classism) combine, overlap or intersect the experiences of marginalized individuals or groups.
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Social constructionism
is a theory of knowledge that holds that characteristics typically thought to be immutable and solely biological—such as gender, race, class, ability, and sexuality—are products of human definition and interpretation shaped by cultural and historical contexts.