ࡱ> y KbjbjEE ;''wBeh h 3338k_ 3f$[*.*(***/t'04[0CfEfEfEfEfEfEfhrk^Ef!w0Q/U/^w0w0Ef**ff666w0fR**Cf6w0Cf66nY"\*`M31Z /f|f0fZk2Jk@\\\k#] w0w06w0w0w0w0w0EfEf 5w0w0w0fw0w0w0w0kw0w0w0w0w0w0w0w0w0h q: Applied Math GLE Framework 2007-DraftCIP Code: Total Framework Hours:  FORMTEXT      Course: Applied MathExploratory:  FORMCHECKBOX  Preparatory:  FORMCHECKBOX  COMPONENTS AND COMPETENCIESPerformance Assessments: Assessments will come from the CORD Curriculum Study Guide and will include: Skills Drill Hands-on Testing Diagnostic (written) Testing Group ProjectsSTANDARDS AND COMPETENCIES-Year 2 Standard: Unit 13 Precision, Accuracy, and ToleranceTotal Learning Hours for Standard: 25 hrs Competency DescriptionDistinguish between counting and measuring, and between precision and accuracy.Read and write measurements to show precision an tolerance.Compare measurements to specified tolerances.Use significant digits to indicate the accuracy of a measurement.Use precision tools to make measurements.Calculate with measurements and round the result.Prerequisites from previous units 2, 3, 7, 8, 9Algebra 1 (Mathematics in Context)2.7Precision and Accuracy**Note: Unit 13 correlates with AMME (Applied Math Made Easy) Unit(s) integrated in units after 7.EALRs or GLEs (Taught & Assessed in Standards)Math1.1Understand and apply concepts and procedures from number sense1.1.1Understand and use scientific notation EXAMPLE: Read and translate numbers represented in scientific notation from calculators and other technology, texts, tables, and charts 1.1.1Understand and use scientific notation EXAMPLE: Use scientific notation in a given situation1.1.5Compute using scientific notation EXAMPLE: Use scientific notation to simplify a calculation1.1.5Compute using scientific notation EXAMPLE: Compute using scientific notation1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Calculate using order of operations on rational numbers1.2Understand and apply concepts and procedures from measurement1.2.3Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision EXAMPLE: Convert within a system while maintaining the same level of precision1.2.3Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision EXAMPLE: Use procedures to convert derived units of measure1.2.3Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision EXAMPLE: Explain why different situations require different levels of precision1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Determine when approximate measurements are sufficient and estimate a reasonable measurement at an appropriate level of precision1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Estimate quantities using derived units of measure1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Estimate derived units of measure1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Describe a procedure that would be an appropriate way to estimate a measurement1.5Understand and apply concepts and procedures from algebraic sense1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Write and/or simplify expressions including applying the distributive property1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Simplify an expression involving exponents1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Evaluate formulas or expressions that involve squares or cubes1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Use multiple algebraic properties to simplify expressions1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Use systems of equations to determine the optimal solution for a given situation1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Rearrange formulas to solve for a particular variable2.1Define problems2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Investigate the situation and determines if there is a problem to solve2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Define or clarify the question the problem presents2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Generate questions to be answered in order to solve the problem2.1.2Determine what information is missing or extraneous EXAMPLE: Determine what needed information is missing2.1.2Determine what information is missing or extraneous EXAMPLE: Differentiate between necessary and extraneous information2.1.3Identify what is known and unknown in complex situations EXAMPLE: Examine information to determine what is known and unknown2.2Construct solutions2.2.1Select and use relevant information to construct solutions EXAMPLE: Select and use relevant information from the problem2.2.1Select and use relevant information to construct solutions EXAMPLE: Determine whether a given solution shows the use of relevant information2.2.2Apply mathematical concepts and procedures from number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense to construct solutions EXAMPLE: Select and use appropriate concepts and procedures to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Select and use tools to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Apply a variety of strategies and approaches2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check work for mathematical accuracy2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Determine whether the solution is reasonable for the situation2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check the solution with an estimate or results from an alternate approach2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check to be certain the solution answers the question3.1Analyze information3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze mathematical information or results3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Integrate information from two or more sources3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze information to make a conjecture3.2Conclude3.2.1Draw and support conclusions, using inductive or deductive reasoning EXAMPLE: Use data or examples as evidence to support or contradict a conclusion or conjecture3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Check the viability and appropriate use of a selected procedure in a given situation 3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Evaluate a conclusion based on given information and/or procedures used and describes a revision as needed3.3Verify results3.3.1Justify results using inductive or deductive reasoning EXAMPLE: Justify results using evidence and information from the problem situation and/or known facts, patterns, relationships, and proportional reasoning3.3.2Evaluate reasonableness of results EXAMPLE: Check for reasonableness of results in a given situation3.3.2Evaluate reasonableness of results EXAMPLE: Verify that the solution to a realworld problem makes sense in relation to the situation3.3.3Validate thinking about mathematical ideas EXAMPLE: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning4.2Organize, represent, and share information4.2.1Organize, clarify, and refine mathematical information relevant to a given purpose EXAMPLE: Select a useful format and organize mathematical information for a given purpose4.2.2Represent mathematical information in graphs or other appropriate forms EXAMPLE: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2 or 3dimensional drawings, or other appropriate including title, labels, appropriate and consistent scales, and accurate display of data4.2.3Use mathematical language to explain or describe mathematical ideas and information in ways appropriate for audience and purpose EXAMPLE: Use both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures, or strategies appropriate for a given audience or purpose5.1Relate concepts and procedures within mathematics5.1.2Relate and use different mathematical models and representations of the same situation EXAMPLE: Explain or demonstrate how two or more different models represent the same mathematical idea5.2Relate mathematical concepts and procedures to other disciplines5.2.1Use mathematical patterns and ideas to extend mathematical thinking and modeling to other disciplines EXAMPLE: Provide examples of using mathematical thinking, patterns, ideas, and modeling in other disciplines5.3Relate mathematical concepts and procedures to realworld situations5.3.1Understand that mathematics is used extensively in daily life outside the classroom EXAMPLE: Describe situations in which mathematics can be used to solve problems with local, national, or international implications5.3.2Understand that mathematics is used in many occupations or careers EXAMPLE: Describe specific examples of mathematics associated with a given career5.3.2Understand that mathematics is used in many occupations or careers EXAMPLE: Explain the mathematics used by workers in a specific jobWritingReading1.2Use vocabulary (word meaning) strategies to comprehend textScienceCommunicationsSocial StudiesArtHealth and FitnessSKILLSSuggested Activities: Refer to Unit 13 Teachers Guide for suggested lab activities that will teach the following state leadership standards.Leadership: Group Skills 2.3 The student will analyze the complex responsibilities of the leader and follower and demonstrate the ability to both lead and follow.2.4 The student will demonstrate skills that assist in understanding and accepting responsibility to family, community, and business and industry.2.7 The student will demonstrate the ability to train others to understand the established rules and expectations, rationale, and consequences and to follow those rules and expectations.2.8 The student will demonstrate the ability to incorporate and utilize the principles of group dynamics in a variety of settings.Leadership: Community and Career Skills 3.2 The student will demonstrate social responsibility in family, community and business and industry.3.4 The student will understand the organizational skills necessary to be a successful leader and citizen and practice those skills in real-life.3.6The student will understand the importance and utilize the components and structure of community-based organizations.Employability: 1.1 The student will demonstrate the ability to identify, organize, plan and allocate resources. This means that the student is able to demonstrate allocating time, money, materials, space and staff.Time: selects goal-relevant activities, ranks them, allocates time, and prepares and follows schedules. Money: uses or prepares budgets, makes forecasts, keeps records, and makes adjustments to meet objectives. Human Resources: assesses skills and distributes work accordingly, evaluates performance and provides feedback.1.2 The student will demonstrate the ability to acquire and use information in family, community, business and industry settings. This means that the students can acquire and evaluate data, organize and maintain files, interpret and communicate, and use computers to process information.Acquire and Evaluate Information. Organize and Maintain Information. Interpret and Communicate Information1.4 The students will demonstrate an ability to work with a variety of technologies, identify or solve problems with equipment, including computers and other technology. This means that the student can select equipment and tools, apply technology to specific tasks, and maintain and troubleshoot equipment.Selects Technology: chooses procedures, tools or equipment including computers and related technology. Applies Technology to Task: understands overall intent and proper procedures for setup and operation of equipment. Maintains and Troubleshoots Equipment: prevents, identifies, or solves problems with equipment, including computers and other technology. Relevance to Work: Refer to CORD Unit 13 Teachers Guide, exercises 1 40, for Relevance to Work (area of application and difficulty) Standard: Unit 14 Solving Problems with Powers and RootsTotal Learning Hours for Standard: 25 hrs Competency DescriptionRead and write numbers expressed as powers 1.1, 1.1.1, 1.1.5, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.2.3, 1.2.5, 1.2.6, 1.3, 1.3.1, 1.3.2, 1.5, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.3, 5.3.2Estimate the values of numbers written as powers 1.1, 1.1.1, 1.1.5, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.2.3, 1.2.5, 1.2.6, 1.3, 1.3.1, 1.3.2, 1.5, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.3, 5.3.2Read and write numbers expressed as roots 1.1, 1.1.1, 1.1.5, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.2.3, 1.2.5, 1.2.6, 1.3, 1.3.1, 1.3.2, 1.5, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.3, 5.3.2Find powers and roots of numbers using a calculator 1.1, 1.1.1, 1.1.5, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.2.3, 1.2.5, 1.2.6, 1.3, 1.3.1, 1.3.2, 1.5, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.3, 5.3.2Solve problems that involve numbers and powers and roots 1.1, 1.1.1, 1.1.5, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.2.3, 1.2.5, 1.2.6, 1.3, 1.3.1, 1.3.2, 1.5, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.3, 5.3.2Prerequisites from previous units 1, 2, 7, 8, 11, 12Algebra 1 (Mathematics in Context)10.4Additional properties of exponents.**Note: Unit 14 correlates with AMME (Applied Math Made Easy) Unit(s) 16 and 17Note Bridges: Powers and Roots (Chapter 10)Bridges: Math Activities, Math Labs, Technology, PortfolioEALRs or GLEs (Taught & Assessed in Standards)Math1.1Understand and apply concepts and procedures from number sense1.1.1Understand and use scientific notation Explain the meaning of scientific notation using words, pictures, symbols, or numbers1.1.1Understand and use scientific notation EXAMPLE: Express and/or use equivalents among fractions, decimals, percents, integers, positive integer exponents, square roots, and/or numbers written in scientific notation1.1.1Understand and use scientific notation EXAMPLE: Read and translate numbers represented in scientific notation from calculators and other technology, texts, tables, and charts1.1.1Understand and use scientific notation Use scientific notation in a given situation1.1.5Compute using scientific notation EXAMPLE: Use scientific notation to simplify a calculation1.1.5Compute using scientific notation EXAMPLE: Compute using scientific notation1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Calculate using order of operations on rational numbers1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Use properties to reorder and rearrange expressions to compute more efficiently1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Apply strategies to complete multistep computations fluently1.1.8Apply estimation strategies in situations involving multistep computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers EXAMPLE: Select, explain, and justify situations involving rational numbers where estimates are sufficient and others for which an exact value is required1.1.8Apply estimation strategies in situations involving multistep computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers EXAMPLE: Use a variety of estimation strategies to predict or to verify the reasonableness of calculated results1.1.8Apply estimation strategies in situations involving multistep computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers EXAMPLE: Describe a strategy used for estimation using multistep computations1.2Understand and apply concepts and procedures from measurement1.2.1Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume EXAMPLE: Determine and/or describe the impact of a change in two linear dimensions on perimeter, area, surface area, and/or volume1.2.1Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume EXAMPLE: Describe how changes in one or more linear dimensions affect perimeter, area, and/or volume in real world situations1.2.1Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume EXAMPLE: Determine the change in one or more linear dimensions given a change in perimeter, area, surface area, and/or volume1.2.3Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision EXAMPLE: Convert within a system while maintaining the same level of precision1.2.3Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision EXAMPLE: Use procedures to convert derived units of measure1.2.3Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision EXAMPLE: Explain why different situations require different levels of precision1.2.5Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids EXAMPLE: Use formulas to determine and label the volume of a compound figure1.2.5Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids EXAMPLE: Use formulas to determine and label the surface area of a compound figure1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Estimate quantities using derived units of measure1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Select and use a procedure to find a reasonable estimate for and label the volumes of prisms and cylinders1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Estimate conversions between yards and meters and quarts and liters1.2.6Understand and apply estimation strategies to obtain reasonable measurements at an appropriate level of precision EXAMPLE: Describe a procedure that would be an appropriate way to estimate a measurement1.3Understand and apply concepts and procedures from geometric sense1.3.1Understand the properties of and the relationships among 1dimensional, 2dimensional, and 3dimensional shapes and figures EXAMPLE: Make and test conjectures about 2dimensional and 3dimensional shapes and their individual attributes and relationships using physical, symbolic, and technological models1.3.1Understand the properties of and the relationships among 1dimensional, 2dimensional, and 3dimensional shapes and figures EXAMPLE: Use the relationship between similar figures to determine the scale factor1.3.1Understand the properties of and the relationships among 1dimensional, 2dimensional, and 3dimensional shapes and figures EXAMPLE: Match or draw a 3dimensional figure that could be formed by folding a given net1.3.2Use the properties of and relationships among 1dimensional, 2dimensional, and 3dimensional shapes and figures including prisms, cylinders, cones, and pyramids EXAMPLE: Match or draw 3dimensional objects from different views using the same properties and relationships1.3.2Use the properties of and relationships among 1dimensional, 2dimensional, and 3dimensional shapes and figures including prisms, cylinders, cones, and pyramids EXAMPLE: Sort, classify, and label 2dimensional and 3dimensional shapes according to characteristics including faces, edges, and vertices, using actual and virtual modeling1.3.2Use the properties of and relationships among 1dimensional, 2dimensional, and 3dimensional shapes and figures including prisms, cylinders, cones, and pyramids EXAMPLE:Construct geometric figures, including angle bisectors, perpendicular bisectors, and triangles given specific characteristic, using a variety of tools and technologies1.5Understand and apply concepts and procedures from algebraic sense1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Use variables to write expressions and equations to represent situations that can be described using repeated addition or repeated multiplication1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Write equations in recursive form for additive or multiplicative models1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Match an expression or equation to a given realworld situation and explain the meaning of a variable1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Differentiate between and explain correct vs. incorrect representations of algebraic situations1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Describe the meaning of a variable in a formula, expression, equation, or inequality1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Write and/or simplify expressions including applying the distributive property1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Simplify an expression involving exponents1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Evaluate formulas or expressions that involve squares or cubes1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Use multiple algebraic properties to simplify expressions1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Rearrange formulas to solve for a particular variable1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Interpret solutions of systems of equations1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Solve, or write and solve, multistep equations1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Use systems of equations to determine the optimal solution for a given situation2.1Define problems2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Investigate the situation and determines if there is a problem to solve2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Define or clarify the question the problem presents2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Generate questions to be answered in order to solve the problem2.1.3Identify what is known and unknown in complex situations EXAMPLE: Examine information to determine what is known and unknown2.2Construct solutions2.2.1Select and use relevant information to construct solutions EXAMPLE: Select and use relevant information from the problem2.2.1Select and use relevant information to construct solutions EXAMPLE: Determine whether a given solution shows the use of relevant information2.2.2Apply mathematical concepts and procedures from number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense to construct solutions EXAMPLE: Select and use appropriate concepts and procedures to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Select and use tools to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Apply a variety of strategies and approaches2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check work for mathematical accuracy2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Determine whether the solution is reasonable for the situation2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check the solution with an estimate or results from an alternate approach2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check to be certain the solution answers the question3.1Analyze information3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze mathematical information or results3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Integrate information from two or more sources3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze information to make a conjecture3.2Conclude3.2.1Draw and support conclusions, using inductive or deductive reasoning EXAMPLE: Use data or examples as evidence to support or contradict a conclusion or conjecture3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Check the viability and appropriate use of a selected procedure in a given situation 3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Evaluate a conclusion based on given information and/or procedures used and describes a revision as needed3.3Verify results3.3.1Justify results using inductive or deductive reasoning EXAMPLE: Justify results using evidence and information from the problem situation and/or known facts, patterns, relationships, and proportional reasoning3.3.2Evaluate reasonableness of results EXAMPLE: Check for reasonableness of results in a given situation3.3.2Evaluate reasonableness of results EXAMPLE: Verify that the solution to a realworld problem makes sense in relation to the situation3.3.3Validate thinking about mathematical ideas EXAMPLE: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning4.1 Gather Information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Determine appropriate mathematical information needed for a specific purpose or audience4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Describe the general procedures, not a survey, to gather exactly the mathematical information sought and no irrelevant information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Follow a plan, not a survey, to collect mathematical information for a given audience and purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, graphs, diagrams, and models for a purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Write or identify questions to be answered using data sources such as magazines, newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales receipts4.2Organize, represent, and share information4.2.1Organize, clarify, and refine mathematical information relevant to a given purpose EXAMPLE: Select a useful format and organize mathematical information for a given purpose4.2.2Represent mathematical information in graphs or other appropriate forms EXAMPLE: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2 or 3dimensional drawings, or other appropriate including title, labels, appropriate and consistent scales, and accurate display of data4.2.3Use mathematical language to explain or describe mathematical ideas and information in ways appropriate for audience and purpose EXAMPLE: Use both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures, or strategies appropriate for a given audience or purpose5.1Relate concepts and procedures within mathematics5.1.1Relate concepts and procedures from two or more content strands, including number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense, in a given problem or situation EXAMPLE: Use concepts and procedures from two or more content strands in a given problem or situation 5.3Relate mathematical concepts and procedures to realworld situations5.3.2Understand that mathematics is used in many occupations or careers EXAMPLE: Explain the mathematics used by workers in a specific job5.3.2Understand that mathematics is used in many occupations or careers EXAMPLE: Describe specific examples of mathematics associated with a given career5.3.2Understand that mathematics is used in many occupations or careers EXAMPLE: Explain the mathematical requirements to enter a given careerWritingReading1.2Use vocabulary (word meaning) strategies to comprehend textScienceCommunicationsSocial StudiesArtHealth and FitnessSKILLSSuggested Activities: Refer to Unit 14 Teachers Guide for suggested lab activities that will teach the following state leadership standards.Leadership: Group Skills: Refer to Unit 13 GLE Framework above.Employability: Refer to Unit 13 GLE Framework above.Relevance to Work: Refer to CORD Unit 14 Teachers Guide, exercises 1 40, for Relevance to Work (area of application and difficulty) Unit 15 Kevin said he had unit 15 done Thursday at the afternoon session. Standard: Unit 16 Solving Problems that Involve Linear EquationsTotal Learning Hours for Standard: 25 hrs Competency DescriptionTranslate a problem into an equation 1.1, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.3, 1.3.3, 1.5, 1.5.1, 1.5.2, 1.5.4, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1Recognize and work with the parts of an equation 1.1, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.3, 1.3.3, 1.5, 1.5.1, 1.5.2, 1.5.4, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1Simplify and solve an equation 1.1, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.3, 1.3.3, 1.5, 1.5.1, 1.5.2, 1.5.4, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1Check the solutions of the equation and the problem 1.1, 1.1.6, 1.1.8, 1.2, 1.2.1, 1.3, 1.3.3, 1.5, 1.5.1, 1.5.2, 1.5.4, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1Prerequisites from previous units 1, 2, 7, 8, 11, 12, 14, 15Algebra 1 (Mathematics in Context)3.1The Multiplication and Division Properties of Equality3.2Solving Proportions and Percent EquationsGeometry Mathematics in Context Chapter 77.1Distance on the Coordinate Plane7.2Vectors on the Coordinate Plane7.3The Slope Formula7.4Linear Equations7.5Coordinate Proof7.6Coordinates in Space**Note: Unit 16 correlates with AMME (Applied Math Made Easy) Unit(s) 8Note Bridges: Solving Equations (Chapter 4)Bridges: Math Activities, Math Labs, Technology, PortfolioEALRs or GLEs (Taught & Assessed in Standards)Math1.1Understand and apply concepts and procedures from number sense1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Calculate using order of operations on rational numbers1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Use properties to reorder and rearrange expressions to compute more efficiently1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Apply strategies to complete multistep computations fluently1.1.8Apply estimation strategies in situations involving multistep computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers EXAMPLE: Select, explain, and justify situations involving rational numbers where estimates are sufficient and others for which an exact value is required1.1.8Apply estimation strategies in situations involving multistep computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers EXAMPLE: Use a variety of estimation strategies to predict or to verify the reasonableness of calculated results1.1.8Apply estimation strategies in situations involving multistep computations of rational numbers using addition, subtraction, multiplication, division, powers, and square roots to predict or determine reasonableness of answers EXAMPLE: Describe a strategy used for estimation using multistep computations1.2Understand and apply concepts and procedures from measurement1.2.1Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume EXAMPLE: Determine and/or describe the impact of a change in two linear dimensions on perimeter, area, surface area, and/or volume1.2.1Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume EXAMPLE: Describe how changes in one or more linear dimensions affect perimeter, area, and/or volume in real world situations1.2.1Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume EXAMPLE: Determine the change in one or more linear dimensions given a change in perimeter, area, surface area, and/or volume1.3Understand and apply concepts and procedures from geometric sense1.3.3Use geometric properties to determine and plot points on a coordinate grid EXAMPLE: Determine geometric properties of twodimensional objects using coordinates on a grid1.3.3Use geometric properties to determine and plot points on a coordinate grid EXAMPLE: Determine the location of a set of points that satisfy given conditions1.3.3Use geometric properties to determine and plot points on a coordinate grid EXAMPLE: Represent real life situations on a coordinate grid or describes the location of a point that satisfies given conditions1.3.3Use geometric properties to determine and plot points on a coordinate grid EXAMPLE: Use tools and technology to draw objects on a coordinate grid based on given properties1.3.3Use geometric properties to determine and plot points on a coordinate grid EXAMPLE: Write ordered pairs to describe the locations of points or objects on a coordinate grid1.5Understand and apply concepts and procedures from algebraic sense1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Represent, extend, or create a pattern or sequence between sets of numbers representing a linear function1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Identify, extend, or create a geometric sequence or pattern1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Translate among equivalent numerical, graphical, and algebraic forms of a linear function1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Create a pattern that has the same rule as a given pattern1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Describe or represent linear and exponential patterns in words or algebraic symbols1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Determine an equation of a line from a set of ordered pairs1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Write an equation or rule to describe a sequence1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Write an expression, equation, or inequality with two variables representing a linear and/or nonlinear model of a realworld problem1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Use variables to write expressions and equations to represent situations that can be described using repeated addition or repeated multiplication1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Write equations in recursive form for additive or multiplicative models1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Match an expression or equation to a given realworld situation and explain the meaning of a variable1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Differentiate between and explain correct vs. incorrect representations of algebraic situations1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Describe the meaning of a variable in a formula, expression, equation, or inequality1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Rearrange formulas to solve for a particular variable1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Interpret solutions of systems of equations1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Solve, or write and solve, multistep equations1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Use systems of equations to determine the optimal solution for a given situation2.1Define problems2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Investigate the situation and determines if there is a problem to solve2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Define or clarify the question the problem presents2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Generate questions to be answered in order to solve the problem2.1.2Determine what information is missing or extraneous EXAMPLE: Differentiate between necessary and extraneous information2.1.3Identify what is known and unknown in complex situations EXAMPLE: Examine information to determine what is known and unknown2.2Construct solutions2.2.1Select and use relevant information to construct solutions EXAMPLE: Select and use relevant information from the problem2.2.1Select and use relevant information to construct solutions EXAMPLE: Determine whether a given solution shows the use of relevant information2.2.2Apply mathematical concepts and procedures from number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense to construct solutions EXAMPLE: Select and use appropriate concepts and procedures to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Select and use tools to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Apply a variety of strategies and approaches2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check work for mathematical accuracy2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Determine whether the solution is reasonable for the situation2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check the solution with an estimate or results from an alternate approach2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check to be certain the solution answers the question3.1Analyze information3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze mathematical information or results3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Integrate information from two or more sources3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze information to make a conjecture3.2Conclude3.2.1Draw and support conclusions, using inductive or deductive reasoning EXAMPLE: Use data or examples as evidence to support or contradict a conclusion or conjecture3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Check the viability and appropriate use of a selected procedure in a given situation 3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Evaluate a conclusion based on given information and/or procedures used and describes a revision as needed3.3Verify results3.3.1Justify results using inductive or deductive reasoning EXAMPLE: Justify results using evidence and information from the problem situation and/or known facts, patterns, relationships, and proportional reasoning3.3.2Evaluate reasonableness of results EXAMPLE: Check for reasonableness of results in a given situation3.3.2Evaluate reasonableness of results EXAMPLE: Verify that the solution to a realworld problem makes sense in relation to the situation3.3.3Validate thinking about mathematical ideas EXAMPLE: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning4.1 Gather Information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Determine appropriate mathematical information needed for a specific purpose or audience4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Describe the general procedures, not a survey, to gather exactly the mathematical information sought and no irrelevant information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Follow a plan, not a survey, to collect mathematical information for a given audience and purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, graphs, diagrams, and models for a purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Write or identify questions to be answered using data sources such as magazines, newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales receipts4.2Organize, represent, and share information4.2.1Organize, clarify, and refine mathematical information relevant to a given purpose EXAMPLE: Select a useful format and organize mathematical information for a given purpose4.2.2Represent mathematical information in graphs or other appropriate forms EXAMPLE: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2 or 3dimensional drawings, or other appropriate including title, labels, appropriate and consistent scales, and accurate display of data4.2.3Use mathematical language to explain or describe mathematical ideas and information in ways appropriate for audience and purpose EXAMPLE: Use both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures, or strategies appropriate for a given audience or purpose5.1Relate concepts and procedures within mathematics5.1.1Relate concepts and procedures from two or more content strands, including number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense, in a given problem or situation EXAMPLE: Use concepts and procedures from two or more content strands in a given problem or situation WritingReading1.2Use vocabulary (word meaning) strategies to comprehend textScienceCommunicationsSocial StudiesArtHealth and FitnessSKILLSSuggested Activities: Refer to Unit 16 Teachers Guide for suggested lab activities that will teach the following state leadership standards.Leadership: Group Skills: Refer to Unit 13 GLE Framework above.Employability: Refer to Unit 13 GLE Framework above.Relevance to Work: Refer to CORD Unit 16 Teachers Guide, exercises 1 40, for Relevance to Work (area of application and difficulty) Standard: Unit 17 Graphing DataTotal Learning Hours for Standard: 25 hrs Competency DescriptionGraph data as points on a coordinate system 1.5, 1.5.5Graph as equation 1.5, 1.5.2 Find the slope of a graphed line 1.1, 1.1.6, 1.3.3, 1.4, 1.4.5, 1.5, 1.5.1, 1.5.2, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3, 3.3.3, 4.1, 4.1.1, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.5.1Find the intercepts of a graphed line 1.1, 1.1.6, 1.3.3, 1.4, 1.4.5, 1.5, 1.5.1, 1.5.2, 1.5.4, 1.5.5, 1.5.6, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3, 3.3.3, 4.1, 4.1.1, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.5.1Prerequisites from previous units 1, 2, 4, 14, 15, 16Algebra 1 (Mathematics in Context)4.1Coordinates and Graphs4.3The Slope of a Line**Note: Unit 17 correlates with AMME (Applied Math Made Easy) Unit(s) 14Note Bridges: Graphing on the Coordinate Plane (Chapter 8)Bridges: Math Activities, Math Labs, Technology, PortfolioEALRs or GLEs (Taught & Assessed in Standards)Math1.1Understand and apply concepts and procedures from number sense1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Calculate using order of operations on rational numbers1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Use properties to reorder and rearrange expressions to compute more efficiently1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Apply strategies to complete multistep computations fluently1.4Understand and apply concepts and procedures from probability and statistics1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Determine whether the underlying model for a set of data is linear1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Determine whether an equation for a line is appropriate for a given set of data and supports the judgment with data1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Match an equation with a set of data or a graphic display1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Identify trends in a set of data in order to make a prediction based on the information1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Determine whether a prediction is reasonable based on the given data or graph1.5Understand and apply concepts and procedures from algebraic sense1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Represent, extend, or create a pattern or sequence between sets of numbers representing a linear function1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Create a pattern that has the same rule as a given pattern1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Translate among equivalent numerical, graphical, and algebraic forms of a linear function1.5.1Apply knowledge of patterns or sequences to represent linear functions (W) and/or exponential functions EXAMPLE: Describe or represent linear and exponential patterns in words or algebraic symbols1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Determine an equation of a line from a set of ordered pairs1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Write an expression, equation, or inequality with two variables representing a linear and/or nonlinear model of a realworld problem1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Write an equation or rule to describe a sequence1.5.2Determine an equation or rule for a linear function represented in a pattern, table, graph, or model EXAMPLE: Write an equation for a line given a graph of the line1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Use variables to write expressions and equations to represent situations that can be described using repeated addition or repeated multiplication1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Write equations in recursive form for additive or multiplicative models1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Match an expression or equation to a given realworld situation and explain the meaning of a variable1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Differentiate between and explain correct vs. incorrect representations of algebraic situations1.5.4Use variables to write expressions, linear equations and inequalities that represent situations involving rational numbers, whole number powers, and square roots EXAMPLE: Describe the meaning of a variable in a formula, expression, equation, or inequality1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Rearrange formulas to solve for a particular variable1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Interpret solutions of systems of equations1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Solve, or write and solve, multistep equations1.5.6Apply properties to solve multistep equations and systems of equations EXAMPLE: Use systems of equations to determine the optimal solution for a given situation2.1Define problems2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Investigate the situation and determines if there is a problem to solve2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Define or clarify the question the problem presents2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Generate questions to be answered in order to solve the problem2.1.2Determine what information is missing or extraneous EXAMPLE: Differentiate between necessary and extraneous information2.1.3Identify what is known and unknown in complex situations EXAMPLE: Examine information to determine what is known and unknown2.2Construct solutions2.2.1Select and use relevant information to construct solutions EXAMPLE: Select and use relevant information from the problem2.2.1Select and use relevant information to construct solutions EXAMPLE: Determine whether a given solution shows the use of relevant information2.2.2Apply mathematical concepts and procedures from number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense to construct solutions EXAMPLE: Select and use appropriate concepts and procedures to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Select and use tools to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Apply a variety of strategies and approaches2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check work for mathematical accuracy2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Determine whether the solution is reasonable for the situation2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check the solution with an estimate or results from an alternate approach2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check to be certain the solution answers the question3.1Analyze information3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze mathematical information or results3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Integrate information from two or more sources3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze information to make a conjecture3.2Conclude3.2.1Draw and support conclusions, using inductive or deductive reasoning EXAMPLE: Use data or examples as evidence to support or contradict a conclusion or conjecture3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Check the viability and appropriate use of a selected procedure in a given situation 3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Evaluate a conclusion based on given information and/or procedures used and describes a revision as needed3.3Verify results3.3.1Justify results using inductive or deductive reasoning EXAMPLE: Justify results using evidence and information from the problem situation and/or known facts, patterns, relationships, and proportional reasoning3.3.2Evaluate reasonableness of results EXAMPLE: Check for reasonableness of results in a given situation3.3.2Evaluate reasonableness of results EXAMPLE: Verify that the solution to a realworld problem makes sense in relation to the situation3.3.3Validate thinking about mathematical ideas EXAMPLE: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning4.1 Gather Information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Determine appropriate mathematical information needed for a specific purpose or audience4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Describe the general procedures, not a survey, to gather exactly the mathematical information sought and no irrelevant information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Follow a plan, not a survey, to collect mathematical information for a given audience and purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, graphs, diagrams, and models for a purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Write or identify questions to be answered using data sources such as magazines, newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales receipts4.2Organize, represent, and share information4.2.1Organize, clarify, and refine mathematical information relevant to a given purpose EXAMPLE: Select a useful format and organize mathematical information for a given purpose4.2.2Represent mathematical information in graphs or other appropriate forms EXAMPLE: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2 or 3dimensional drawings, or other appropriate including title, labels, appropriate and consistent scales, and accurate display of data4.2.3Use mathematical language to explain or describe mathematical ideas and information in ways appropriate for audience and purpose EXAMPLE: Use both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures, or strategies appropriate for a given audience or purpose5.1Relate concepts and procedures within mathematics5.1.1Relate concepts and procedures from two or more content strands, including number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense, in a given problem or situation EXAMPLE: Use concepts and procedures from two or more content strands in a given problem or situation WritingReading1.2Use vocabulary (word meaning) strategies to comprehend textScienceCommunicationsSocial StudiesArtHealth and FitnessSKILLSSuggested Activities: Refer to Unit 17 Teachers Guide for suggested lab activities that will teach the following state leadership standards.Leadership: Group Skills: Refer to Unit 13 GLE Framework above.Employability: Refer to Unit 13 GLE Framework above.Relevance to Work: Refer to CORD Unit 17 Teachers Guide, exercises 1 40, for Relevance to Work (area of application and difficulty) Unit 18 Standard: Unit 19 Working with StatisticsTotal Learning Hours for Standard: 25 hrs Competency DescriptionDistinguish between mean, mode and median measures of central tendency 1.1, 1.1.5, 1.1.6, 1.4, 1.4.3, 1.4.6, 1.5.5, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3, 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.1.2, 5.2, 5.2.1, 5.2.2, 5.3, 5.3.1, 5.3.2Calculate the mean, mode and median for a set of data 1.1, 1.1.5, 1.1.6, 1.4, 1.4.3, 1.4.6, 1.5.5, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3., 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.1.2, 5.2, 5.2.1, 5.2.2, 5.3, 5.3.1, 5.3.2Draw a histogram to represent frequency distributions of data 3.1, 3.1.1, 4.2.1, 4.2.2Distinguish between range, trend, and standard deviation as measures of variability 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 4.1.2, 5.1Interpret the characteristics of a normal curve 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 4.1.2, Calculate the range and standard deviation to describe a set of data 1.1, 1.1.5, 1.1.6, 1.4,1.4.3, 1.4.6, 1.5.5, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2.2.1, 2.2.2, 2.2.3, 2.2.4, 3.1, 3.1.1, 3.2, 3.2.1, 3.2.2, 3.3, 3.3.1, 3.3.2, 3.3.3., 4.1, 4.1.1, 4.1.2, 4.2, 4.2.1, 4.2.2, 4.2.3, 5.1, 5.1.1, 5.1.2, 5.2, 5.2.1, 5.2.2, 5.3, 5.3.1, 5.3.2Prerequisites from previous units 1, 2, 4, 11, 15, 16, 17Algebra 1 (Mathematics in Context)7.1Measuring of Central Tendency**Note: Unit 19 correlates with AMME (Applied Math Made Easy) Unit(s) 21Note Bridges: Working with Data (Chapter 2)Bridges: Math Activities, Math Labs, Technology, PortfolioEALRs or GLEs (Taught & Assessed in Standards)Math1.1Understand and apply concepts and procedures from number sense1.1.5Compute using scientific notation EXAMPLE: Use scientific notation to simplify a calculation1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Use properties to reorder and rearrange expressions to compute more efficiently1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Calculate using order of operations on rational numbers1.4Understand and apply concepts and procedures from probability and statistics1.4.3Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled EXAMPLE: Determine whether claims made about results are based on biased data due to sampling1.4.3Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled EXAMPLE: Collect data using appropriate questions, samples, and/or methods to control for bias1.4.3Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled EXAMPLE: Examine sources of bias in data collection questions, samples, and/or methods and describe how such bias can be controlled1.4.3Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled EXAMPLE: Examine methods and technology used to investigate a research question1.4.3Determine possible sources of bias in questions, data collection methods, samples, and/or measures of central tendency and describe how such bias can be controlled EXAMPLE: Determine how data collection methods impact the accuracy of the results1.4.6Determine and explain how the same set of data can support different points of view EXAMPLE: Explain how the same set of data can support different points of view.1.4.6Determine and explain how the same set of data can support different points of view EXAMPLE: Explain, using data, how statistics have been used or misused to support a point of view or argument.1.4.6Determine and explain how the same set of data can support different points of view EXAMPLE: Use statistics to support different points of view. 1.4.6Determine and explain how the same set of data can support different points of view EXAMPLE: Use a set of statistics to develop a logical point of view1.5Understand and apply concepts and procedures from algebraic sense1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Simplify an expression involving exponents2.1Define problems2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Investigate the situation and determines if there is a problem to solve2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Define or clarify the question the problem presents2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Generate questions to be answered in order to solve the problem2.1.2Determine what information is missing or extraneous EXAMPLE: Differentiate between necessary and extraneous information2.1.3Identify what is known and unknown in complex situations EXAMPLE: Examine information to determine what is known and unknown2.2Construct solutions2.2.1Select and use relevant information to construct solutions EXAMPLE: Select and use relevant information from the problem2.2.1Select and use relevant information to construct solutions EXAMPLE: Determine whether a given solution shows the use of relevant information2.2.2Apply mathematical concepts and procedures from number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense to construct solutions EXAMPLE: Select and use appropriate concepts and procedures to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Select and use tools to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Apply a variety of strategies and approaches2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check work for mathematical accuracy2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Determine whether the solution is reasonable for the situation2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check the solution with an estimate or results from an alternate approach2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check to be certain the solution answers the question3.1Analyze information3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze mathematical information or results. 3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Integrate information from two or more sources.3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Compare mathematical information in tables, charts, graphs, text, diagrams, figures, or pictorial representations. 3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Differentiate between valid and invalid analysis of mathematical information or results. 3.1.1Analyze, compare, and integrate mathematical information from multiple sources EXAMPLE: Analyze information to make a conjecture3.2Conclude3.2.1Draw and support conclusions, using inductive or deductive reasoning EXAMPLE: Use data or examples as evidence to support or contradict a conclusion or conjecture3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Check the viability and appropriate use of a selected procedure in a given situation 3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Evaluate a conclusion based on given information and/or procedures used and describes a revision as needed3.3Verify results3.3.1Justify results using inductive or deductive reasoning EXAMPLE: Justify results using evidence and information from the problem situation and/or known facts, patterns, relationships, and proportional reasoning3.3.2Evaluate reasonableness of results EXAMPLE: Check for reasonableness of results in a given situation3.3.2Evaluate reasonableness of results EXAMPLE: Verify that the solution to a realworld problem makes sense in relation to the situation3.3.3Validate thinking about mathematical ideas EXAMPLE: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoning4.1 Gather Information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Determine appropriate mathematical information needed for a specific purpose or audience4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Describe the general procedures, not a survey, to gather exactly the mathematical information sought and no irrelevant information4.1.1Develop, select, and/or apply an efficient system for collecting mathematical information EXAMPLE: Follow a plan, not a survey, to collect mathematical information for a given audience and purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Extract and use mathematical information from various sources such as pictures, symbols, text, tables, charts, graphs, diagrams, and models for a purpose4.1.2Extract mathematical information from multiple sources EXAMPLE: Write or identify questions to be answered using data sources such as magazines, newspapers, menus, sales or travel brochures, TV or bus schedules, and/or sales receipts4.2Organize, represent, and share information4.2.1Organize, clarify, and refine mathematical information relevant to a given purpose EXAMPLE: Select a useful format and organize mathematical information for a given purpose4.2.2Represent mathematical information in graphs or other appropriate forms EXAMPLE: Represent mathematical information using pictures, tables, Venn diagrams, scatter plots, 2 or 3dimensional drawings, or other appropriate including title, labels, appropriate and consistent scales, and accurate display of data4.2.3Use mathematical language to explain or describe mathematical ideas and information in ways appropriate for audience and purpose EXAMPLE: Use both everyday and mathematical language and notation to explain, defend, or present mathematical ideas, facts, procedures, or strategies appropriate for a given audience or purpose5.1Relate concepts and procedures within mathematics5.1.1Relate concepts and procedures from two or more content strands, including number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense, in a given problem or situation EXAMPLE: Use concepts and procedures from two or more content strands in a given problem or situation WritingReading1.2Use vocabulary (word meaning) strategies to comprehend textScienceCommunicationsSocial StudiesArtHealth and FitnessSKILLSSuggested Activities: Refer to Unit 19Teachers Guide for suggested lab activities that will teach the following state leadership standards.Leadership: Group Skills: Refer to Unit 13 GLE Framework above.Employability: Refer to Unit 13 GLE Framework above.Relevance to Work: Refer to CORD Unit 19 Teachers Guide, exercises 1 40, for Relevance to Work (area of application and difficulty) Standard: Unit 20 Working with ProbabilitiesTotal Learning Hours for Standard: 30 hrs Competency DescriptionFind the probability of some simple events 1.1, 1.1.5, 1.4, 1.4.1, 1.4.2, 1.5.5, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.2, 2,2,1, 2.2.2, 2.2.3, 2.2.4, 3.2, 3.2.1, 3.3, 3.3.1, 3.3.2, 3.3.3Count the number of ways an event can happen 1.1, 1.1.5, 1.4, 1.4.1, 1.4.2, 2.1, 2.1.1, 2.1.2, 2.1.3, 3.2, 3.2.1, 3.3, 3.3.1, 3.3.2, 3.3.3Draw diagrams and charts to help find probability 1.4, 1.4.5, 2.1, 2.1.1, 2.1.2, 2.1.3, 2,2,1, 2.2.2, 2.2.3, 2.2.4, 3.3, 3.3.1, 3.3.2, 3.3.3Use your calculator to find probabilities 1.1, 1.1.5, 1.1.6, 1.4, 1.4.1, 1.4.2, 1.4.5, 1.5.5, 2.1, 2.1.1, 2.1.2, 2.1.3, 2,2,1, 2.2.2, 2.2.3, 2.2.4, 3.2, 3.2.1, 3.3, 3.3.1, 3.3.2, 3.3.3Prerequisites from previous units 1, 2, 4, 9, 15, 19Algebra 1 (Mathematics in Context)6.1Probability6.3Principal of Counting**Note: Unit 20 correlates with AMME (Applied Math Made Easy) Unit(s) 21Note Bridges: Ratio Proportion and Probabilities (Chapter 6); Supplemental materials must be used for calculator use and creating diagrams and charts and graphs.Bridges: Math Activities, Math Labs, Technology, PortfolioEALRs or GLEs (Taught & Assessed in Standards)Math1.1Understand and apply concepts and procedures from number sense1.1.5Compute using scientific notation EXAMPLE: Use scientific notation to simplify a calculation1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Use properties to reorder and rearrange expressions to compute more efficiently1.1.6Complete multistep computations with combinations of rational numbers using order of operations and addition, subtraction, multiplication, division, powers, and square roots EXAMPLE: Calculate using order of operations on rational numbers1.4Understand and apply concepts and procedures from probability and statistics1.4.1Understand the concepts of dependent and independent events EXAMPLE: Describe whether the outcome of a first event affects the probability of a later event1.4.1Understand the concepts of dependent and independent events EXAMPLE: Describe the difference between dependent and independent events1.4.1Understand the concepts of dependent and independent events EXAMPLE: Describe the relationship between theoretical probability and empirical frequency of dependent events using simulations with and without technology1.4.2Use procedures to compute the probability of dependent and independent events EXAMPLE: Determine the sample space for independent or dependent events1.4.2Use procedures to compute the probability of dependent and independent events EXAMPLE: Determine probabilities of dependent and independent events1.4.2Use procedures to compute the probability of dependent and independent events EXAMPLE: Determine the outcomes and probability of multiple independent or dependent events1.4.2Use procedures to compute the probability of dependent and independent events EXAMPLE: Modify or revise a simple game based on independent probabilities so that all players have an equal probability of winning1.4.2Use procedures to compute the probability of dependent and independent events EXAMPLE: Create a simple game based on conditional probabilities1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Match an equation with a set of data or a graphic display1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Determine whether an equation for a line is appropriate for a given set of data and supports the judgment with data1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Determine whether a prediction is reasonable based on the given data or graph1.4.5Use bivariate data in tables and displays to predict mathematical relationships EXAMPLE: Identify trends in a set of data in order to make a prediction based on the information1.5Understand and apply concepts and procedures from algebraic sense1.5.5Apply algebraic properties to simplify expressions involving whole number exponents EXAMPLE: Simplify an expression involving exponents2.1Define problems2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Investigate the situation and determines if there is a problem to solve2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Define or clarify the question the problem presents2.1.1Formulate questions to be answered to solve a problem EXAMPLE: Generate questions to be answered in order to solve the problem2.1.2Determine what information is missing or extraneous EXAMPLE: Differentiate between necessary and extraneous information2.1.3Identify what is known and unknown in complex situations EXAMPLE: Examine information to determine what is known and unknown2.2Construct solutions2.2.1Select and use relevant information to construct solutions EXAMPLE: Select and use relevant information from the problem2.2.1Select and use relevant information to construct solutions EXAMPLE: Determine whether a given solution shows the use of relevant information2.2.2Apply mathematical concepts and procedures from number sense, measurement, geometric sense, probability and statistics, and/or algebraic sense to construct solutions EXAMPLE: Select and use appropriate concepts and procedures to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Select and use tools to construct a solution2.2.3Apply a variety of strategies and approaches to construct solutions EXAMPLE: Apply a variety of strategies and approaches2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check work for mathematical accuracy2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Determine whether the solution is reasonable for the situation2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check the solution with an estimate or results from an alternate approach2.2.4Determine whether a solution is viable, is mathematically correct, and answers the question(s) EXAMPLE: Check to be certain the solution answers the question3.2Conclude3.2.1Draw and support conclusions, using inductive or deductive reasoning EXAMPLE: Use data or examples as evidence to support or contradict a conclusion or conjecture3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Check the viability and appropriate use of a selected procedure in a given situation 3.2.2Evaluate procedures and conclusions to make needed revisions EXAMPLE: Evaluate a conclusion based on given information and/or procedures used and describes a revision as needed3.3Verify results3.3.1Justify results using inductive or deductive reasoning EXAMPLE: Justify results using evidence and information from the problem situation and/or known facts, patterns, relationships, and proportional reasoning3.3.2Evaluate reasonableness of results EXAMPLE: Check for reasonableness of results in a given situation3.3.2Evaluate reasonableness of results EXAMPLE: Verify that the solution to a realworld problem makes sense in relation to the situation3.3.3Validate thinking about mathematical ideas EXAMPLE: Justify or refute claims and supporting arguments using data, models, known facts, patterns, relationships, counter examples, and/or proportional reasoningWritingReading1.2Use vocabulary (word meaning) strategies to comprehend textScienceCommunicationsSocial StudiesArtHealth and FitnessSKILLSSuggested Activities: Refer to Unit 20 Teachers Guide for suggested lab activities that will teach the following state leadership standards.Leadership: Group Skills: Refer to Unit 13 GLE Framework above.Employability: Refer to Unit 13 GLE Framework above.Relevance to Work: Refer to CORD Unit 20 Teachers Guide, exercises 1 40, for Relevance to Work (area of application and difficulty)       Page  PAGE 1 of  NUMPAGES 30 2007 Draft Washington Applied Math Council  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