# CTE Resource Center - Verso - Electronics Systems I Task 1446406906

CTE Resource Center - Verso

Virginia’s CTE Resource Center

Apply mathematical skills to job-specific tasks.

Definition

Application could include
  • performing calculations (e.g., percentages, fractions, addition, subtraction, averages, measurement, conversions, monetary transactions)
  • applying mathematical processes to accomplish job-specific tasks (e.g., estimating required supplies, completing expense reports)
  • managing personal finance (e.g., understanding wage rates, paycheck deductions, taxes, sales receipts).

Process/Skill Questions

  • What mathematical skills are required to attain an entry-level job in a specific field? What mathematical skills are required for higher-level jobs within that field?
  • What resources are available to assist in the improvement of mathematical skills?
  • Why are mathematical skills considered communication skills?

Related Standards of Learning

English

6.4

The student will read and determine the meanings of unfamiliar words and phrases within authentic texts.
  1. Identify word origins and derivations.
  2. Use roots, affixes, synonyms, and antonyms to expand vocabulary.
  3. Use context and sentence structure to determine meanings and differentiate among multiple meanings of words.
  4. Identify and analyze the construction and impact of figurative language.
  5. Use word-reference materials.
  6. Extend general and cross-curricular vocabulary through speaking, listening, reading, and writing.

6.6

The student will read and demonstrate comprehension of a variety of nonfiction texts.
  1. Skim materials using text features such as type, headings, and graphics to predict and categorize information.
  2. Identify main idea.
  3. Summarize supporting details.
  4. Create an objective summary including main idea and supporting details.
  5. Draw conclusions and make inferences based on explicit and implied information.
  6. Identify the author’s organizational pattern(s).
  7. Identify transitional words and phrases that signal an author’s organizational pattern.
  8. Differentiate between fact and opinion.
  9. Identify cause and effect relationships.
  10. Analyze ideas within and between selections providing textual evidence.
  11. Use reading strategies to monitor comprehension throughout the reading process.

6.7

The student will write in a variety of forms to include narrative, expository, persuasive, and reflective with an emphasis on narrative and reflective writing.
  1. Engage in writing as a recursive process.
  2. Choose audience and purpose.
  3. Use a variety of prewriting strategies to generate and organize ideas.
  4. Organize writing to fit mode or topic.
  5. Write narratives to include characters, plot, setting, and point of view.
  6. Establish a central idea incorporating evidence and maintaining an organized structure.
  7. Compose a thesis statement for expository and persuasive writing.
  8. Write multiparagraph compositions with elaboration and unity.
  9. Use transition words and phrases.
  10. Select vocabulary and information to enhance the central idea, tone, and voice.
  11. Expand and embed ideas by using modifiers, standard coordination, and subordination in complete sentences.
  12. Revise writing for clarity of content including specific vocabulary and information.

7.4

The student will read and determine the meanings of unfamiliar words and phrases within authentic texts.
  1. Identify word origins and derivations.
  2. Use roots, affixes, synonyms, and antonyms to expand vocabulary.
  3. Identify and analyze the construction and impact of figurative language.
  4. Identify connotations.
  5. Use context and sentence structure to determine meanings and differentiate among multiple meanings of words.
  6. Use word-reference materials to determine meanings and etymology.
  7. Extend general and cross-curricular vocabulary through speaking, listening, reading, and writing.

7.6

The student will read and demonstrate comprehension of a variety of nonfiction texts.
  1. Skim materials using text features including type, headings, and graphics to predict and categorize information.
  2. Identify an author’s organizational pattern using textual clues, such as transitional words and phrases.
  3. Make inferences and draw logical conclusions using explicit and implied textual evidence.
  4. Differentiate between fact and opinion.
  5. Identify the source, viewpoint, and purpose of texts.
  6. Describe how word choice and language structure convey an author’s viewpoint.
  7. Identify the main idea.
  8. Summarize text identifying supporting details.
  9. Create an objective summary including main idea and supporting details.
  10. Identify cause and effect relationships.
  11. Organize and synthesize information for use in written and other formats.
  12. Analyze ideas within and between selections providing textual evidence.
  13. Use reading strategies to monitor comprehension throughout the reading process.

7.7

The student will write in a variety of forms to include narrative, expository, persuasive, and reflective with an emphasis on expository and persuasive writing.
  1. Engage in writing as a recursive process.
  2. Choose intended audience and purpose.
  3. Use a variety of prewriting strategies to generate and organize ideas.
  4. Organize writing structure to fit form or topic.
  5. Establish a central idea incorporating evidence, while maintaining an organized structure and a formal style.
  6. Compose a thesis statement for persuasive writing that includes a position.
  7. Clearly state a position and organize reasons and evidence, using credible sources.
  8. Distinguish between fact and opinion to support a position.
  9. Write multiparagraph compositions with elaboration and unity.
  10. Use transition words and phrases within and between paragraphs.
  11. Develop and modify the central idea, tone, and voice to fit the audience and purpose.
  12. Expand and embed ideas by using modifiers, standard coordination, and subordination in complete sentences.
  13. Use clauses and phrases for sentence variety.
  14. Revise writing for clarity of content including specific vocabulary and information.

8.4

The student will apply knowledge of word origins, and figurative language to extend vocabulary development within authentic texts.
  1. Identify and analyze the construction and impact of an author’s use of figurative language.
  2. Use context, structure, and connotations to determine meaning and differentiate among multiple meanings of words and phrases.
  3. Use roots, affixes, synonyms, and antonyms to determine the meaning(s) of unfamiliar words and technical vocabulary.
  4. Identify the meaning of common idioms.
  5. Use word-reference materials to determine meanings and etymology.
  6. Discriminate between connotative and denotative meanings and interpret the connotation.
  7. Extend general and cross-curricular vocabulary through speaking, listening, reading, and writing.

8.6

The student will read, comprehend, and analyze a variety of nonfiction texts.
  1. Identify an author’s organizational pattern using textual clues, such as transitional words and phrases.
  2. Apply knowledge of text features and organizational patterns to analyze selections.
  3. Skim materials to develop an overview or locate information.
  4. Make inferences and draw conclusions based on explicit and implied information using evidence from text as support.
  5. Analyze the author’s qualifications, viewpoint, word choice, and impact.
  6. Analyze details for relevance and accuracy.
  7. Differentiate between fact and opinion.
  8. Identify the main idea.
  9. Summarize the text identifying supporting details.
  10. Identify cause and effect relationships.
  11. Evaluate, organize, and synthesize information for use in written and other formats.
  12. Analyze ideas within and between selections providing textual evidence.
  13. Use reading strategies to monitor comprehension throughout the reading process.

8.7

The student will write in a variety of forms to include narrative, expository, persuasive, and reflective with an emphasis on expository and persuasive writing.
  1. Engage in writing as a recursive process.
  2. Choose intended audience and purpose.
  3. Use prewriting strategies to generate and organize ideas.
  4. Organize writing structure to fit form or topic.
  5. Establish a central idea incorporating evidence, maintaining an organized structure and formal style.
  6. Compose a thesis statement for persuasive writing that advocates a position.
  7. Clearly state and defend a position with reasons and evidence, from credible sources.
  8. Identify a counterclaim and provide a counter - argument.
  9. Distinguish between fact and opinion to support a position.
  10. Organize information to provide elaboration and unity.
  11. Develop and modify the central idea, tone, and voice to fit the audience and purpose.
  12. Revise writing for clarity of content, word choice, sentence variety, and transitions among paragraphs.

9.5

The student will read and analyze a variety of nonfiction texts.
  1. Apply knowledge of text features and organizational patterns to understand, analyze, and gain meaning from texts.
  2. Make inferences and draw conclusions based on explicit and implied information using evidence from text as support.
  3. Analyze the author’s qualifications, viewpoint, and impact.
  4. Recognize an author’s intended purpose for writing and identify the main idea.
  5. Summarize, paraphrase, and synthesize ideas, while maintaining meaning and a logical sequence of events, within and between texts.
  6. Identify characteristics of expository, technical, and persuasive texts.
  7. Identify a position/argument to be confirmed, disproved, or modified.
  8. Evaluate clarity and accuracy of information.
  9. Analyze, organize, and synthesize information in order to solve problems, answer questions, complete a task, or create a product.
  10. Differentiate between fact and opinion and evaluate their impact.
  11. Analyze ideas within and between selections providing textual evidence.
  12. Use the reading strategies to monitor comprehension throughout the reading process.

9.6

The student will write in a variety of forms to include expository, persuasive, reflective, and analytic with an emphasis on persuasion and analysis.
  1. Engage in writing as a recursive process.
  2. Plan, organize, and write for a variety of audiences and purposes.
  3. Objectively introduce and develop topics, incorporating evidence and maintaining an organized structure and a formal style.
  4. Blend multiple forms of writing including embedding a narrative to produce effective essays.
  5. Communicate clearly the purpose of the writing using a thesis statement.
  6. Compose a thesis for persuasive writing that advocates a position.
  7. Clearly state and defend a position using reasons and evidence from credible sources as support.
  8. Identify counterclaims and provide counter - arguments.
  9. Determine the best kind of evidence to use for a claim, and effectively use fact and opinion to support a position.
  10. Use textual evidence to compare and contrast multiple texts.
  11. Arrange paragraphs in a logical progression, using transitions between paragraphs and ideas.
  12. Revise writing for clarity of content, accuracy, and depth of information.

10.5

The student will read, interpret, analyze, and evaluate nonfiction texts.
  1. Analyze text features and organizational patterns to evaluate the meaning of texts.
  2. Recognize an author’s intended audience and purpose for writing.
  3. Skim materials to develop an overview and locate information.
  4. Compare and contrast informational texts for intent and content.
  5. Interpret and use data and information in maps, charts, graphs, timelines, tables, and diagrams.
  6. Draw conclusions and make inferences on explicit and implied information using textual support as evidence.
  7. Analyze and synthesize information in order to solve problems, answer questions, and generate new knowledge.
  8. Analyze ideas within and between selections providing textual evidence.
  9. Summarize, paraphrase, and synthesize ideas, while maintaining meaning and a logical sequence of events, within and between texts.
  10. Use reading strategies throughout the reading process to monitor comprehension.

10.6

The student will write in a variety of forms to include persuasive, reflective, interpretive, and analytic with an emphasis on persuasion and analysis.
  1. Engage in writing as a recursive process.
  2. Plan and organize writing to address a specific audience and purpose.
  3. Adjust writing content, technique, and voice for a variety of audiences and purposes.
  4. Communicate clearly the purpose of the writing using a thesis statement.
  5. Objectively introduce and develop topics, incorporating evidence and maintaining an organized structure and a formal style.
  6. Compose a thesis statement for persuasive writing that advocates a position.
  7. Clearly state and defend a position using reasons and sufficient evidence from credible sources as support.
  8. Identify counterclaims and provide counter - arguments.
  9. Show relationships among claims, reasons, and evidence and include a conclusion that follows logically from the information presented.
  10. Blend multiple forms of writing including embedding a narrative to produce effective essays.
  11. Elaborate ideas clearly through word choice.
  12. Use textual evidence to compare and contrast multiple texts.
  13. Revise writing for clarity of content, accuracy, and depth of information.
  14. Write and revise to a standard acceptable both in the workplace and in postsecondary education.

11.5

The student will read, interpret, analyze, and evaluate a variety of nonfiction texts including employment documents and technical writing.
  1. Apply information from texts to clarify understanding of concepts.
  2. Read and correctly interpret an application for employment, workplace documents, or an application for college admission.
  3. Analyze technical writing for clarity.
  4. Paraphrase and synthesize ideas within and between texts.
  5. Draw conclusions and make inferences on explicit and implied information using textual support.
  6. Analyze multiple texts addressing the same topic to determine how authors reach similar or different conclusions.
  7. Analyze false premises, claims, counterclaims, and other evidence in persuasive writing.
  8. Recognize and analyze use of ambiguity, contradiction, paradox, irony, sarcasm, overstatement, and understatement in text.
  9. Generate and respond logically to literal, inferential, evaluative, synthesizing, and critical thinking questions about the text(s).

11.6

The student will write in a variety of forms, to include persuasive/argumentative, reflective, interpretive, and analytic with an emphasis on persuasion/argumentation.
  1. Apply components of a recursive writing process for multiple purposes to create a focused, organized, and coherent piece of writing to address a specific audience and purpose.
  2. Produce arguments in writing developing a thesis that demonstrates knowledgeable judgments, addresses counterclaims, and provides effective conclusions.
  3. Organize claims, counterclaims, and evidence in a sustained and logical sequence.
  4. Adapt evidence, vocabulary, voice, and tone to audience, purpose, and situation.
  5. Use words, phrases, clauses, and varied syntax to create a cohesive argument.
  6. Blend multiple forms of writing including embedding narratives to produce effective essays.
  7. Revise writing for clarity of content, accuracy and depth of information.
  8. Write and revise to a standard acceptable both in the workplace and in postsecondary education.

12.5

The student will read, interpret, analyze, and evaluate a variety of nonfiction texts.
  1. Use critical thinking to generate and respond logically to literal, inferential, and evaluative questions about the text(s).
  2. Identify and synthesize resources to make decisions, complete tasks, and solve specific problems.
  3. Analyze multiple texts addressing the same topic to determine how authors reach similar or different conclusions.
  4. Recognize and analyze use of ambiguity, contradiction, paradox, irony, overstatement, and understatement in text.
  5. Analyze false premises claims, counterclaims, and other evidence in persuasive writing.

12.6

The student will write in a variety of forms to include persuasive/argumentative reflective, interpretive, and analytic with an emphasis on persuasion/argumentation.
  1. Apply components of a recursive writing process for multiple purposes to create a focused, organized, and coherent piece of writing to address a specific audience and purpose.
  2. Produce arguments in writing that develop a thesis to demonstrate knowledgeable judgments, address counterclaims, and provide effective conclusions.
  3. Use a variety of rhetorical strategies to clarify and defend a position organizing claims, counterclaims, and evidence in a sustained and logical sequence.
  4. Blend multiple forms of writing including embedding a narrative to produce effective essays.
  5. Adapt evidence, vocabulary, voice, and tone to audience, purpose, and situation.
  6. Use words, phrases, clauses, and varied syntax to connect all parts of the argument creating cohesion from the information presented.
  7. Revise writing for clarity of content, depth of information, and technique of presentation.
  8. Write and revise to a standard acceptable both in the workplace and in postsecondary education.
  9. Write to clearly describe personal qualifications for potential occupational or educational opportunities.

History and Social Science

CE.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. analyzing and interpreting evidence from primary and secondary sources, including charts, graphs, and political cartoons;
  2. analyzing how political and economic trends influence public policy, using demographic information and other data sources;
  3. analyzing information to create diagrams, tables, charts, graphs, and spreadsheets;
  4. determining the accuracy and validity of information by separating fact and opinion and recognizing bias;
  5. constructing informed, evidence-based arguments from multiple sources;
  6. determining multiple cause-and-effect relationships that impact political and economic events;
  7. taking informed action to address school, community, local, state, national, and global issues;
  8. using a decision-making model to analyze and explain the costs and benefits of a specific choice;
  9. applying civic virtue and democratic principles to make collaborative decisions; and
  10. defending conclusions orally and in writing to a wide range of audiences, using evidence from sources.

CE.4

The student will demonstrate personal character traits that facilitate thoughtful and effective participation in civic life by

  1. practicing trustworthiness and honesty;
  2. practicing courtesy and respect for the rights of others;
  3. practicing responsibility, accountability, and self-reliance;
  4. practicing respect for the law;
  5. practicing patriotism;
  6. practicing thoughtful decision making; and
  7. practicing service to the school and/or local community.

CE.14

The student will apply social science skills to understand personal finance and career opportunities by

  1. identifying talents, interests, and aspirations that influence career choice;
  2. identifying human capital such as attitudes and behaviors that strengthen the individual work ethic and promote career success;
  3. identifying human capital such as abilities, skills, and education and the changing supply of and demand for them in the economy;
  4. examining the impact of technological change and globalization on career opportunities;
  5. describing the importance of education to lifelong personal finances; and
  6. analyzing the financial responsibilities of citizenship, including evaluating common forms of credit, savings, investments, purchases, contractual agreements, warranties, and guarantees.

GOVT.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. planning inquiries by synthesizing information from diverse primary and secondary sources;
  2. analyzing how political and economic trends influence public policy, using demographic information and other data sources;
  3. comparing and contrasting historical, cultural, economic, and political perspectives;
  4. evaluating critically the quality, accuracy, and validity of information to determine misconceptions, fact and opinion, and bias;
  5. constructing informed, analytic arguments using evidence from multiple sources to introduce and support substantive and significant claims;
  6. explaining how cause-and-effect relationships impact political and economic events;
  7. taking knowledgeable, constructive action, individually and collaboratively, to address school, community, local, state, national, and global issues;
  8. using a decision-making model to analyze the costs and benefits of a specific choice, considering incentives and possible consequences;
  9. applying civic virtues and democratic principles to make collaborative decisions; and
  10. communicating conclusions orally and in writing to a wide range of audiences, using evidence from multiple sources and citing specific sources.

USI.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship, by

  1. analyzing and interpreting artifacts and primary and secondary sources to understand events in United States history;
  2. analyzing and interpreting geographic information to determine patterns and trends in United States history;
  3. interpreting charts, graphs, and pictures to determine characteristics of people, places, or events in United States history;
  4. using evidence to draw conclusions and make generalizations;
  5. comparing and contrasting historical, cultural, and political perspectives in United States history;
  6. determining relationships with multiple causes or effects in United States history;
  7. explaining connections across time and place;
  8. using a decision-making model to identify the costs and benefits of a specific choice made;
  9. identifying the rights and responsibilities of citizenship and the ethical use of material or intellectual property; and
  10. investigating and researching to develop products orally and in writing.

USII.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. analyzing and interpreting artifacts and primary and secondary sources to understand events in United States history;
  2. analyzing and interpreting geographic information to determine patterns and trends in United States history;
  3. interpreting charts, graphs, and pictures to determine characteristics of people, places, or events in United States history;
  4. using evidence to draw conclusions and make generalizations;
  5. comparing and contrasting historical, cultural, and political perspectives in United States history;
  6. determining relationships with multiple causes or effects in United States history;
  7. explaining connections across time and place;
  8. using a decision-making model to identify costs and benefits of a specific choice made;
  9. identifying the rights and responsibilities of citizenship and the ethical use of material or intellectual property; and
  10. investigating and researching to develop products orally and in writing.

VUS.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. synthesizing evidence from artifacts and primary and secondary sources to obtain information about events in Virginia and United States history;
  2. using geographic information to determine patterns and trends in Virginia and United States history;
  3. interpreting charts, graphs, and pictures to determine characteristics of people, places, or events in Virginia and United States history;
  4. constructing arguments, using evidence from multiple sources;
  5. comparing and contrasting historical, cultural, economic, and political perspectives in Virginia and United States history;
  6. explaining how indirect cause-and-effect relationships impact people, places, and events in Virginia and United States history;
  7. analyzing multiple connections across time and place;
  8. using a decision-making model to analyze and explain the incentives for and consequences of a specific choice made;
  9. identifying the rights and responsibilities of citizenship and ethical use of material and intellectual property; and
  10. investigating and researching to develop products orally and in writing.

WG.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. synthesizing evidence from artifacts and primary and secondary sources to obtain information about the world’s countries, cities, and environments;
  2. using geographic information to determine patterns and trends to understand world regions;
  3. creating, comparing, and interpreting maps, charts, graphs, and pictures to determine characteristics of world regions;
  4. evaluating sources for accuracy, credibility, bias, and propaganda;
  5. using maps and other visual images to compare and contrast historical, cultural, economic, and political perspectives;
  6. explaining indirect cause-and-effect relationships to understand geospatial connections;
  7. analyzing multiple connections across time and place;
  8. using a decision-making model to analyze and explain the incentives for and consequences of a specific choice made;
  9. identifying the rights and responsibilities of citizenship and the ethical use of material or intellectual property; and
  10. investigating and researching to develop products orally and in writing.

WHI.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. synthesizing evidence from artifacts and primary and secondary sources to obtain information about events in world history;
  2. using geographic information to determine patterns and trends to understand world history;
  3. interpreting charts, graphs, and pictures to determine characteristics of people, places, or events in world history;
  4. evaluating sources for accuracy, credibility, bias, and propaganda;
  5. comparing and contrasting historical, cultural, economic, and political perspectives in world history;
  6. explaining how indirect cause-and-effect relationships impacted people, places, and events in world history;
  7. analyzing multiple connections across time and place;
  8. using a decision-making model to analyze and explain the incentives for and consequences of a specific choice made;
  9. identifying the rights and responsibilities of citizens and ethical use of materials and intellectual property; and
  10. investigating and researching to develop products orally and in writing.

WHII.1

The student will demonstrate skills for historical thinking, geographical analysis, economic decision making, and responsible citizenship by

  1. synthesizing evidence from artifacts and primary and secondary sources to obtain information about events and life in world history;
  2. using geographic information to determine patterns and trends in world history;
  3. interpreting charts, graphs, and pictures to determine characteristics of people, places, or events in world history;
  4. evaluating sources for accuracy, credibility, bias, and propaganda;
  5. comparing and contrasting historical, cultural, economic, and political perspectives in world history;
  6. explaining how indirect cause-and-effect relationships impacted people, places, and events in world history;
  7. analyzing multiple connections across time and place;
  8. using a decision-making model to analyze and explain the incentives for and consequences of a specific choice made;
  9. identifying the rights and responsibilities of citizens and ethical use of materials and intellectual property; and
  10. investigating and researching to develop products orally and in writing.

Mathematics

6.1

The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b.

6.2

The student will
  1. represent and determine equivalencies among fractions, mixed numbers, decimals, and percents; and
  2. compare and order positive rational numbers.

6.5

The student will
  1. multiply and divide fractions and mixed numbers;
  2. solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers; and
  3. solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.

6.6

  1. add, subtract, multiply, and divide integers;
  2. solve practical problems involving operations with integers; and
  3. simplify numerical expressions involving integers.

6.12

The student will
  1. represent a proportional relationship between two quantities, including those arising from practical situations;
  2. determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table;
  3. determine if a proportional relationship exists between two quantities; and
  4. make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs.

6.13

The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable.

6.14

The student will
  1. represent a practical situation with a linear inequality in one variable; and
  2. solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line.

7.1

The student will
  1. investigate and describe the concept of negative exponents for powers of ten;
  2. compare and order numbers greater than zero written in scientific notation;
  3. compare and order rational numbers;
  4. determine square roots of perfect squares; and
  5. identify and describe absolute value of rational numbers.

7.2

The student will solve practical problems involving operations with rational numbers.

7.3

The student will solve single-step and multistep practical problems, using proportional reasoning.

7.4

The student will
  1. describe and determine the volume and surface area of rectangular prisms and cylinders; and
  2. solve problems, including practical problems, involving the volume and surface area of rectangular prisms and cylinders.

7.5

The student will solve problems, including practical problems, involving the relationship between corresponding sides and corresponding angles of similar quadrilaterals and triangles.

7.6

The student will
  1. compare and contrast quadrilaterals based on their properties; and
  2. determine unknown side lengths or angle measures of quadrilaterals.

7.8

The student will
  1. determine the theoretical and experimental probabilities of an event; and
  2. investigate and describe the difference between the experimental probability and theoretical probability of an event.

7.9

The student, given data in a practical situation, will
  1. represent data in a histogram;
  2. make observations and inferences about data represented in a histogram; and
  3. compare histograms with the same data represented in stem-and-leaf plots, line plots, and circle graphs.

7.11

The student will evaluate algebraic expressions for given replacement values of the variables.

7.12

The student will solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable.

7.13

The student will solve one- and two-step linear inequalities in one variable, including practical problems, involving addition, subtraction, multiplication, and division, and graph the solution on a number line.

8.4

The student will solve practical problems involving consumer applications.

8.5

The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.

8.6

The student will
  1. solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids; and
  2. describe how changing one measured attribute of a rectangular prism affects the volume and surface area.

8.8

The student will construct a three-dimensional model, given the top or bottom, side, and front views.

8.9

The student will
  1. verify the Pythagorean Theorem; and
  2. apply the Pythagorean Theorem.

8.10

The student will solve area and perimeter problems, including practical problems, involving composite plane figures.

8.11

The student will
  1. compare and contrast the probability of independent and dependent events; and
  2. determine probabilities for independent and dependent events.

8.12

The student will
  1. represent numerical data in boxplots;
  2. make observations and inferences about data represented in boxplots; and
  3. compare and analyze two data sets using boxplots.

8.13

The student will
  1. represent data in scatterplots;
  2. make observations about data represented in scatterplots; and
  3. use a drawing to estimate the line of best fit for data represented in a scatterplot.

8.14

The student will
  1. evaluate an algebraic expression for given replacement values of the variables; and
  2. simplify algebraic expressions in one variable.

8.15

The student will
  1. determine whether a given relation is a function; and
  2. determine the domain and range of a function.

8.16

The student will
  1. recognize and describe the graph of a linear function with a slope that is positive, negative, or zero;
  2. identify the slope and y-intercept of a linear function, given a table of values, a graph, or an equation in y = mx + b form;
  3. determine the independent and dependent variable, given a practical situation modeled by a linear function;
  4. graph a linear function given the equation in y = mx + b form; and
  5. make connections between and among representations of a linear function using verbal descriptions, tables, equations, and graphs.

8.17

The student will solve multistep linear equations in one variable with the variable on one or both sides of the equation, including practical problems that require the solution of a multistep linear equation in one variable.

8.18

The student will solve multistep linear inequalities in one variable with the variable on one or both sides of the inequality symbol, including practical problems, and graph the solution on a number line.

A.1

The student will
  1. represent verbal quantitative situations algebraically; and
  2. evaluate algebraic expressions for given replacement values of the variables.

A.3

The student will simplify
  1. square roots of whole numbers and monomial algebraic expressions;
  2. cube roots of integers; and
  3. numerical expressions containing square or cube roots.

A.4

The student will solve
  1. multistep linear and quadratic equations in one variables algebraically;
  2. quadratic equations in one variables algebraically;
  3. literal equations for a specified variable;
  4. systems of two linear equations in two variables algebraically and graphically; and
  5. practical problems involving equations and systems of equations.

A.5

The student will
  1. solve multistep linear inequalities in one variable algebraically and represent the solution graphically;
  2. represent the solution of linear inequalities in two variables graphically;
  3. solving practical problems involving inequalities; and
  4. represent the solution to a system of inequalities graphically.

A.7

The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
  1. determining whether a relation is a function;
  2. domain and range;
  3. zeros of a function;
  4. x- and y-intercepts;
  5. finding the values of a function for elements in its domain; and
  6. making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

A.8

The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

A.9

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions.

AFDA.1

The student will investigate and analyze linear, quadratic, exponential, and logarithmic function families and their characteristics. Key concepts include
  1. domain and range;
  2. intervals in which the function is increasing or decreasing;
  3. absolute maxima and minima;
  4. zeros;
  5. intercepts;
  6. values of a function for elements in its domain;
  7. connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs;
  8. end behavior; and
  9. vertical and horizontal asymptotes.

AFDA.3

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems using models of linear, quadratic, and exponential functions.

AFDA.5

The student will determine optimal values in problem situations by identifying constraints and using linear programming techniques.

AFDA.8

The student will design and conduct an experiment/survey. Key concepts include
  1. sample size;
  2. sampling technique;
  3. controlling sources of bias and experimental error;
  4. data collection; and
  5. data analysis and reporting.

AII.3

The student will solve
  1. absolute value linear equations and inequalities;
  2. quadratic equations over the set of complex numbers;
  3. equations containing rational algebraic expressions; and
  4. equations containing radical expressions.

AII.7

The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include
  1. domain, range, and continuity;
  2. intervals in which a function is increasing or decreasing;
  3. extrema;
  4. zeros;
  5. intercepts;
  6. values of a function for elements in its domain;
  7. connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs;
  8. end behavior;
  9. vertical and horizontal asymptotes;
  10. inverse of a function; and
  11. composition of functions algebraically and graphically.

AII.9

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear, quadratic, and exponential functions.

AII.10

The student will represent, create, and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

COM.1

The student will design and apply computer programs to solve practical problems in mathematics arising from business and applications in mathematics.

COM.7

The student will select and call library functions to process data, as appropriate.

Science

6.1

The student will demonstrate an understanding of scientific reasoning, logic, and the nature of science by planning and conducting investigations in which
  1. observations are made involving fine discrimination between similar objects and organisms;
  2. precise and approximate measurements are recorded;
  3. scale models are used to estimate distance, volume, and quantity;
  4. hypotheses are stated in ways that identify the independent and dependent variables;
  5. a method is devised to test the validity of predictions and inferences;
  6. one variable is manipulated over time, using many repeated trials;
  7. data are collected, recorded, analyzed, and reported using metric measurements and tools;
  8. data are analyzed and communicated through graphical representation;
  9. models and simulations are designed and used to illustrate and explain phenomena and systems; and
  10. current applications are used to reinforce science concepts.

BIO.1

The student will demonstrate an understanding of scientific reasoning, logic, and the nature of science by planning and conducting investigations in which
  1. observations of living organisms are recorded in the lab and in the field;
  2. hypotheses are formulated based on direct observations and information from scientific literature;
  3. variables are defined and investigations are designed to test hypotheses;
  4. graphing and arithmetic calculations are used as tools in data analysis;
  5. conclusions are formed based on recorded quantitative and qualitative data;
  6. sources of error inherent in experimental design are identified and discussed;
  7. validity of data is determined;
  8. chemicals and equipment are used in a safe manner;
  9. appropriate technology including computers, graphing calculators, and probeware is used for gathering and analyzing data, communicating results, modeling concepts, and simulating experimental conditions;
  10. research utilizes scientific literature;
  11. differentiation is made among a scientific hypothesis, theory, and law;
  12. alternative scientific explanations and models are recognized and analyzed; and
  13. current applications of biological concepts are used.

CH.1

The student will investigate and understand that experiments in which variables are measured, analyzed, and evaluated produce observations and verifiable data. Key concepts include
  1. designated laboratory techniques;
  2. safe use of chemicals and equipment;
  3. proper response to emergency situations;
  4. manipulation of multiple variables, using repeated trials;
  5. accurate recording, organization, and analysis of data through repeated trials;
  6. mathematical and procedural error analysis;
  7. mathematical manipulations including SI units, scientific notation, linear equations, graphing, ratio and proportion, significant digits, and dimensional analysis;
  8. use of appropriate technology including computers, graphing calculators, and probeware for gathering data, communicating results, and using simulations to model concepts;
  9. construction and defense of a scientific viewpoint; and
  10. the use of current applications to reinforce chemistry concepts.

ES.1

The student will plan and conduct investigations in which
  1. volume, area, mass, elapsed time, direction, temperature, pressure, distance, density, and changes in elevation/depth are calculated utilizing the most appropriate tools;
  2. technologies including computers, probeware, and geospatial technologies are used to collect, analyze, and report data and to demonstrate concepts and simulate experimental conditions;
  3. scales, diagrams, charts, graphs, tables, imagery, models, and profiles are constructed and interpreted;
  4. maps and globes are read and interpreted, including location by latitude and longitude;
  5. variables are manipulated with repeated trials; and
  6. current applications are used to reinforce Earth science concepts.

LS.1

The student will demonstrate an understanding of scientific reasoning, logic, and the nature of science by planning and conducting investigations in which
  1. data are organized into tables showing repeated trials and means;
  2. a classification system is developed based on multiple attributes;
  3. triple beam and electronic balances, thermometers, metric rulers, graduated cylinders, and probeware are used to gather data;
  4. models and simulations are constructed and used to illustrate and explain phenomena;
  5. sources of experimental error are identified;
  6. dependent variables, independent variables, and constants are identified;
  7. variables are controlled to test hypotheses, and trials are repeated;
  8. data are organized, communicated through graphical representation, interpreted, and used to make predictions;
  9. patterns are identified in data and are interpreted and evaluated; and
  10. current applications are used to reinforce life science concepts.

PH.1

The student will plan and conduct investigations using experimental design and product design processes. Key concepts include
  1. the components of a system are defined;
  2. instruments are selected and used to extend observations and measurements;
  3. information is recorded and presented in an organized format;
  4. the limitations of the experimental apparatus and design are recognized;
  5. the limitations of measured quantities are recognized through the appropriate use of significant figures or error ranges;
  6. models and simulations are used to visualize and explain phenomena, to make predictions from hypotheses, and to interpret data; and
  7. appropriate technology including computers, graphing calculators, and probeware is used for gathering and analyzing data and communicating results.

PS.1

The student will demonstrate an understanding of scientific reasoning, logic, and the nature of science by planning and conducting investigations in which
  1. chemicals and equipment are used safely;
  2. length, mass, volume, density, temperature, weight, and force are accurately measured;
  3. conversions are made among metric units, applying appropriate prefixes;
  4. triple beam and electronic balances, thermometers, metric rulers, graduated cylinders, probeware, and spring scales are used to gather data;
  5. numbers are expressed in scientific notation where appropriate;
  6. independent and dependent variables, constants, controls, and repeated trials are identified;
  7. data tables showing the independent and dependent variables, derived quantities, and the number of trials are constructed and interpreted;
  8. data tables for descriptive statistics showing specific measures of central tendency, the range of the data set, and the number of repeated trials are constructed and interpreted;
  9. frequency distributions, scatterplots, line plots, and histograms are constructed and interpreted;
  10. valid conclusions are made after analyzing data;
  11. research methods are used to investigate practical problems and questions;
  12. experimental results are presented in appropriate written form; and
  13. models and simulations are constructed and used to illustrate and explain phenomena;
  14. current applications of physical science concepts are used.

Other Related Standards

Instructional Resources for Workplace Readiness Skills

Mathematical Resources