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School District U‐46 Elgin, Illinois

Instructional Council Proposal Summary

High School Transitional Math

Proposal/Recommendation for Action

The purpose of this proposal is to recommend the adoption of three new high school transitional

mathematics courses, Transition to College Algebra, Transition to Quantitative Literacy and Statistics,

and Transition to Technical Math.

The Postsecondary and Workforce Readiness Act establishes a new statewide system for high school

seniors who are lacking a mathematical foundation from their previous education. Transitional math

instruction provides students with the mathematical knowledge and skills to meet their individualized

college and career goals and to be successful in college‐level math courses.

The proposed courses titles and descriptions are as follows:

Transition to College Algebra Grade Level: 12 Prerequisites: Completion of math graduation requirements and at least one of the following criteria:

B or better in Algebra 1 or a higher math course Math GPA of 2.5 or higher

Course Description: The Transition to College Algebra course is for students with career goals that require advanced algebraic skills. Successful completion of the course guarantees student placement into College Algebra or its equivalent at any Illinois community college and select universities. The main emphasis of the course is the understanding of functions (linear, polynomial, rational, radical, and exponential) and how they naturally arise through problem solving and authentic modeling situations. Essential algebraic topics include simplifying expressions, solving equations, and graphing functions, which will be explored deeply, allowing students to address any deficits.

Transition to Quantitative Literacy and Statistics Grade Level: 12 Prerequisites: Completion of math graduation requirements Course Description: The Transition to Quantitative Literacy and Statistics course is intended for students whose career goals do not involve occupations relating to College Algebra or Technical Math, as well as those students who have not yet selected a career goal. Successful completion of this course guarantees student placement into a credit‐bearing general education mathematics course or its equivalent at any Illinois community college and select universities. Essential topics include numeracy, algebra, and functions and modeling. At least one additional topic will be chosen from the following list: systems of equations and

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inequalities, probability and statistics, and proportional reasoning. This course is focused on attaining competency in general statistics, data analysis, quantitative literacy, and problem solving. Transition to Technical Math Grade Level: 12 Prerequisites: Completion of math graduation requirements and concurrent or prior enrollment in technical coursework. Content: The Transition to Technical Math course is for students who have career goals involving occupations in technical fields that do not require advanced algebraic or statistical skills. Successful completion of this course guarantees student placement into a credit‐bearing postsecondary mathematics course required for a community college career and technical education program. The mathematics in this course emphasizes the application of mathematics within career settings.

Rationale

Elgin Community College reports that 62.4% of high school graduates who enroll at their school have to

be placed into remedial mathematics courses, based upon the college’s placement exam. When looking

specifically at students from U‐46, approximantely 65% of our students are placed into a remedial math

course. This percentage has been fairly consistent for the past 12 years.

Year Total # of HS Grads at ECC

% in Remedial

# of U46 Students

Percent in

Remedial

2006 957 71.2% 537 68.1%

2007 927 67.7% 471 64.1%

2008 1,013 65.7% 497 64.9%

2009 1,136 65.9% 619 65.9%

2010 1,309 62.7% 715 62.8%

2011 1,296 62.9% 663 64.8%

2012 1,334 61.1% 728 62.6%

2013 1,296 58.3% 717 66.3%

2014 1,111 55.8% 593 61.5%

2015 1,154 56.2% 598 60.3%

2016 1,124 59.3% 571 65.0%

2017 1,037 62.2% 619 68.4%

Average 1,141 62.4% 611 64.6%

The use of transitional math courses during students’ senior year of high school will reduce the

remediation rates for our students. The transitional courses will also bridge the gap for students who

often opt out of math in their senior year, reducing their chances of needing remedial coursework. Upon

successful completion of a transitional math course in high school, students will receive guaranteed

placement into a credit bearing math course at any Illinois community college.

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The students who will be enrolled in a transitional math course will be those do not demonstrate college

readiness, as measured by multiple means including standardized test scores and course grades. The

transitional math courses are designed to address gaps in understanding by working on bigger problems,

emphasizing problem‐based learning, projects, communication, and integration of concepts, not just

skill acquisition. Contexts will be authentic, and whenever possible, apply to the student’s college or

career path. This approach will be motivating and engaging, and also sets the stage for the types of

problems a student will be exposed to when they reach college.

Description of Procedures

In May 2018, a call to committee was sent out to all teachers to participate in the curriculum process.

All applicants were accepted and include:

Joann Annable ‐ Elgin High School

Greg Anthony – Bartlett High School

Alex Camacho ‐ Elgin High School

Kari Foerster ‐ Elgin High School

William Hice – ROE/Dream Academy

Kenneth Kater ‐ Central School Programs

Liam Keigher ‐ Larkin High School

Jordan Kimbro ‐ Elgin High School

Alma Miho ‐ Bartlett High School

Maureen Toth ‐ Elgin High School

Kristen Wilmot ‐ South Elgin High School

Kameron Matthis – District Math Coach

Amy Ingente ‐ Math Coordinator

Within this group of teachers, all programs were represented, including Special Education, Dual

Language, and the District’s alternative high school programs.

The committee met in June 2018 to develop the curriculum frameworks for the three transitions courses

identified in the Postsecondary and Workforce Readiness Act, aligning the curriculum to the State

recommended competencies and policies.

In June 2018, a sub‐group comprised of 5 teachers from the committee and 2 District administrators

also began meeting with Elgin Community College and the feeder high schools to develop a

memorandum of understanding and discuss portability requirements. These agreements will establish

expectations for each school partner and guarantees placement at any Illinois community college into

the appropriate math course(s) upon successful completion of the course.

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Description of Recommendation

The Postsecondary and Workforce Readiness Act defines benchmarks for projected readiness in college‐

level math. The Transitional Math Recommended Competencies and Policies document states the

following:

A high school junior who has successfully completed state math graduation requirements and

meets at least two of the following criteria is projected to be ready for college level coursework

in mathematics when arriving at a postsecondary institution in Illinois. This determination is

conditional based on enrollment in a senior year of math.

• B or better in Algebra 2 • C or better in a course higher than Algebra 2 • GPA ≥ 3.0 • Standardized Assessment: Math SAT or PSAT ≥ 530 or Math ACT > 22 • Placement test score (such as ALEKS, Accuplacer, Compass, local placement instrument, etc.) into college‐level math at the partner community college after taking their placement exam • PARCC math score of 4 or 5 • Teacher and/or advisor recommendation of college‐level math in the senior year

A high school junior who has successfully completed state math graduation requirements but

has not met at least two of the college‐level math projected readiness criteria will be projected

as NOT ready for college‐level math and will be given transitional math opportunities in relation

to their current math achievement and career interests. A student should consult with a teacher

and/or advisor to determine the appropriate transitional math pathway.

Transition to College Algebra

The Transition to College Algebra course is for students with career goals that require the application of

calculus or advanced algebraic skills. Essential algebraic topics are included in this transition course so

that they can be worked on deeply, allowing students to address any deficits. Students will simplify

expressions, solve equations, and graph functions in the following function families: Linear; Polynomial;

Rational; Radical; Exponential. Successful completion of the course guarantees student placement into

a College Algebra community college mathematics course.

By the end of this course, students will:

1. apply, analyze, and evaluate the characteristics of functions in mathematical and authentic

problem solving situations.

2. simplify expressions, solve equations, and graph functions from the linear, polynomial, rational,

and radical function families in mathematical and authentic problem solving situations.

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3. use their understanding of exponential functions of the form 𝑓 𝑥 𝐶𝑏 , for some constants

𝑏 0 and 𝐶, in mathematical and authentic problem solving situations.

4. create, solve, and reason with systems of equations and inequalities in mathematical and

authentic problem solving situations.

Transition to Quantitative Literacy and Statistics

The Transition to Quantitative Literacy and Statistics course is focused on attaining competency in

general statistics, data analysis, quantitative literacy, and problem solving. This pathway is intended for

students whose career goals do not involve occupations relating to College Algebra or Technical Math,

as well as those students who have not yet selected a career goal. Successful completion of this course

guarantees student placement into a credit‐bearing general education community college mathematics

course, including general education statistics, general education mathematics, quantitative literacy, or

elementary math modeling.


1. apply, analyze, and evaluate the characteristics of numbers in authentic modeling and problem

solving situations.

2. Perform operations on numbers and make use of those operations in authentic modeling and

problem solving situations.

3. propose various alternatives, determine reasonableness, and then select optimal estimates to

justify solutions.

4. demonstrate understanding of the characteristics of variables and expressions and apply this

knowledge in authentic modeling and problem solving situations.

5. perform operations on expressions in authentic modeling and problem solving situations.

6. create, solve, and reason with equations and inequalities in the context of authentic modeling

and problem solving situations.

7. apply, analyze and evaluate the characteristics of functions in authentic modeling and problem

solving situations.

8. build and use functions, including linear, nonlinear, and geometric models in authentic modeling

and problem solving situations.

9. evaluate mathematical models and explain the limitations of those models.

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Transition to Technical Math

The Transition to Technical Math course is for students who are enrolled in a Technical course during

their senior year and have career goals involving occupations in technical fields that do not require the

application of calculus, advanced algebraic, or advanced statistical skills. The mathematics in this course

emphasizes the application of mathematics within career settings. Successful completion of this course

guarantees student placement into a credit‐bearing postsecondary mathematics course required for a

community college career and technical education program.

The technical math competencies that follow are considered the core skills and contexts for this

transitional course. However, due to the highly varied career paths that exist in this pathway, it is

recommended to also include additional topics and contexts authentic to the career path.


1. use their understanding of operations with real numbers in authentic contexts.

2. perform unit conversions using dimensional analysis and proportions in both the standard and

metric systems and between both systems in authentic contexts.

3. use their understanding of exponents and radicals of real numbers to calculate quantities in

formulas and be able to explain the results.

4. use their understanding of graphs and charts in order to interpret them in contextualized

workplace scenarios.

5. use their understanding of geometry to find and analyze parameters of geometric figures in

authentic contexts.

6. use their understanding of geometry to correctly measure and apply the parts of geometric

figures in authentic contexts.

7. use their understanding of geometry to analyze authentic applications involving right triangles.

8. use algebra to analyze authentic contexts that involve linear equations and inequalities.

9. represent perimeter, volume, and area as a function of a single variable in authentic contexts.

10. apply formulas to solve problems in authentic contexts.

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Recommendations for Implementation

2018‐2019

Continue collaboration with Elgin Community College and surrounding High School Districts to

o Complete the Memorandum of Understanding and Portability Documentation

o Develop common assessments

o Select resources to support the curriculum

January 2019 – Begin registration for the three transitional math courses

Summer 2019 – Provide professional development for teachers about the new curriculum

2019‐2020

Full Implementation

Ongoing professional development

Professional development will be provided for teachers during summer 2019 and on the District

Collaboration Days. These sessions will include a description of the new curriculum, as well as best

practices to support students. The District Math Coach will also make classroom visits and provide

ongoing support as it is needed throughout the school year.

Evaluation

STAR Math will be used to benchmark and progress monitor students’ growth. District Common

Assessment Data will be reviewed to ensure students’ proficiency in the course competencies. Cohort

data will also reviewed to monitor long term performance in subsequent math courses at Elgin

Community College.

Appendix

Curriculum Documents

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Transition to Quantitative Literacy and Statistics ‐ Numeracy & Proportional Reasoning

Stage 1 Desired Results

ESTABLISHED GOALS QL‐N1. Students can apply, analyze, and evaluate the characteristics of numbers in authentic modeling and problem solving situations. QL‐N2. Students can perform operations on numbers and make use of those operations in authentic modeling and problem solving situations. QL‐N3. Students can propose various alternatives, determine reasonableness, and then select optimal estimates to justify solutions.

Transfer

Students will be able to independently use their learning to…

Examine an authentic problem/situation involving numbers to initiate and execute a plan.

Evaluate and explain the reasonableness of a solution.

Meaning

UNDERSTANDINGSStudents will understand that…

Estimation builds logical understanding and is an essential part of problem solving to justify solutions

Fractions, decimals and percentages may represent the same value

Part‐whole relationships exist in real life contexts

Demonstrating measurement sense includes predicting, estimating and solving problems with appropriate units

Organizing numbers helps analyze data and make decisions

ESSENTIAL QUESTIONSStudents will keep considering…

How do we know when we have found a solution?

How do we determine if an answer is reasonable?

What are all the ways to represent a number?

How do we best represent part and whole relationships?

How can we summarize data to make decisions?

What units are most appropriate for this solution?

Acquisition

Students will know…

Operations with whole numbers, integers, fractions, and decimals

The effect of operations on numbers in words and symbols

Part‐whole representations

Place values and numbers written in scientific notation

Mean, median and mode

Various data displays

Estimation strategies

Students will be skilled at…

Basic computations and estimations without a calculator

Justifying estimates

Applying quantitative reasoning

Converting between units

Converting between fractions, decimals and percentages

Interpreting data displays

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Stage 2 ‐ Evidence

PWR CCSS Proficiency Criteria Assessment Evidence

QL‐N1 abf

5.NF 6.NS NQ.1 NQ.2

In authentic modeling and problem solving situations(no calculator – keep numbers reasonable and do mental math)

Convert between words, numbers, and operations (contextual, not algebraic equations)

Explain the effect of operations (eg. tripling, half, squaring, fraction operations, etc.)

Apply mathematical properties in numeric and algebraic contexts (eg. 4+n‐2+5=11+3+5, 4 more than twice her age)

Demonstrate measurement sense that includes o Predicting using appropriate units (eg. in the thousands) o Estimating using appropriate units (eg. 2000) o Solving problems using appropriate units (eg. 2143)

Performance Taskhttps://robertkaplinsky.com/work/stars‐in‐the‐universe/ Other Evidence

Quizzes and Tests

Short answer to prompts

Observations and dialogues

Formative checks for understanding

QL‐N2

7.NS.3 7.RP.3

In authentic modeling and problem solving situations(no calculator – keep numbers reasonable and do mental math)

Use basic arithmetic operations without a calculator to solve problems with

o whole numbers o integers o fractions o decimals

Solve problems involving part‐whole relationships and rates

QL‐N3 4.OA.3

In authentic modeling and problem solving situations

Assess the reasonableness of an answer using mental computation and estimation strategies, including rounding

Justify estimates o Propose various estimates o Select optimal estimates

QL‐N1ef 8.EE.3‐4


Use magnitude in the contexts of o Place values (ten times larger/smaller) o Numbers written in scientific notation o Fractions (with negative exponents written as positive exponents

in the denominator)

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Transition to Quantitative Literacy and Statistics ‐ Algebra


ESTABLISHED GOALS QL‐A1. Students can demonstrate understanding of the characteristics of variables and expressions and apply this knowledge in authentic modeling and problem solving situations. QL‐A2. Students can perform operations on expressions in authentic modeling and problem solving situations. QL‐A3. Students can create, solve, and reason with equations and inequalities in the context of authentic modeling and problem solving situations.

Transfer


Examine an authentic problem/situation and use algebraic reasoning to initiate and execute a plan.

Evaluate and explain the reasonableness of a solution.

Meaning


Variables and expressions represent quantities in real world situations

There is a relationship between zeros and factors in real world situations

Equations and inequalities describe relationships in real world situations

Solving equations and inequalities builds logical understanding and is an essential part of problem solving to justify solutions in real world situations

Changing variable values has an effect on an algebraic relationship in real world situations


What is an appropriate method to solve a problem?

How can variables be used to represent quantities in real world situations?

How can I translate an authentic context to an algebraic expression?

What are the differences between expressions, equations, and inequalities? When are they used in in real world situations?

Why is it helpful to rewrite expressions in equivalent forms?

Acquisition


Variables represent real world quantities or attributes

Parts of expressions, including terms, factors and coefficients

Zeros and factors of polynomials

Expressions, equations, and inequalities


Developing and solving expressions, equations and inequalities

Comparing and contrasting equations and expressions

Justifying reasoning while solving equations

Performing operations on polynomials

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Creating equivalent forms of expressions



QL‐A1 A.CED.1 A.CED.3 N.Q.2 6.EE.2 A.SSE.1 A.SSE.2 A.SSE.3


Use variables to accurately represent quantities or attributes

Predict and confirm the effect that changes in variable values have in an algebraic relationship

Interpret parts of expressions o Terms o Factors o Coefficients

Write expressions and/or rewrite expressions in equivalent forms to solve problems

Performance Task:Defined STEM: Computer Manufacturer Defined STEM: Food Truck Entrepreneur Other Evidence

Quizzes and Tests




QL‐A2 A.APR.1 A.APR.2


Perform arithmetic operations (addition, subtraction, multiplication) on polynomials in authentic tasks

Demonstrate the relationship between zeros and factors of polynomials

QL‐A3 A.CED.1 F.IF.9 A.REI.1


Create equations and inequalities that describe numbers or relationships

Compare and contrast expressions and equations

Use and justify reasoning while solving equations

Develop and solve equations and inequalities in one variable

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Transition to Quantitative Literacy and Statistics ‐ Functions


ESTABLISHED GOALS QL‐FM1. Students can apply, analyze and evaluate the characteristics of functions in authentic modeling and problem solving situations. QL‐FM2. Students can build and use functions including linear, nonlinear, and geometric models in authentic modeling and problem solving situations. QL‐FM3. Students can evaluate mathematical models and explain the limitations of those models.

Transfer


Apply mathematical knowledge to analyze and model mathematical relationships in the context of a situation in order to make decisions, draw conclusions, and solve problems.

Evaluate and explain the appropriateness of a model.

Meaning


Authentic problem/situation can be modeled in multiple ways (descriptions, tables, graphs, and equations)

A function models a relationship between quantities in real world situations

Changing variable values has an effect on an algebraic relationship in real world situations


What model best represents this situation?

How do I know if this is the best representation?

How do I know that I have chosen an appropriate function?

How do I know if I need more than one function? How do I know when I need to combine functions?

What are the limitations of the chosen models?

Acquisition


Linear, polynomial, exponential, and logarithmic functions

Functions have a single output

Functions can be built from existing functions

Different representations of functions (descriptions, tables, graphs, and equations)

Characteristics of functions

Relationship between variables

Variables represent real world quantities or attributes


Graphical analysis

Modeling with geometry

Modeling with linear and non‐linear functions

Compare models

Interpreting functions

Identifying the reasonableness of a model

Describing relationships

Transferring between different representations of functions

Using models to solve problems

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QL‐FM1

N.Q.2 A.CED.1 F.BF.1 F.IF.2 F.IF.8 F.IF.1 F.IF.4 F.IF.7 F.IF.9

In authentic modeling and problem solving situations, which may include linear, polynomial, exponential, logarithmic functions

Use variables to represent quantities or attributes

Predict and confirm the effect that changes in variable values have in an algebraic relationship

Identify if a relation is a function

Identify what the parts of the function represent in a given situation

Identify and analyze functions using different representations (descriptions, tables, graphs, and equations)

o Maximum / Minimum o Increasing / Decreasing o Intercepts o Domain / Range o End behavior (if appropriate)

Performance Task:Defined STEM: Automobile Efficiency Expert Defined STEM: Earth Scientist Defined STEM: Wind Energy Specialist Other Evidence

Quizzes and Tests




QL‐FM2

A.CED.1 A.CED.2 F.BF.1 F.LE.1 F.LE.2 A.SSE.1 G.MG


Represent common types of functions using words, algebraic symbols, graphs, and tables. Types of functions include:

o Linear o Polynomial o Exponential o Logarithmic

Translate a context into a mathematical representation

Translate a mathematical representation into a context

For linear, polynomial, exponential and logarithmic functions o Build a function that models a relationship between two quantities o Build new functions from existing functions o Compare two functions o Use created functions to solve problems

Apply geometric concepts in modeling situations (eg. volume, perimeter, similarity, Pythagorean Theorem, etc.)

QL‐FM3

S.ID.6 In authentic modeling and problem solving situations

Identify the reasonableness of a linear model for given data and consider alternative models

Explain limitations of models in real‐world scenarios or relationships

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Transition to Quantitative Literacy ‐ Probability and Statistics


Established Goals: Interpreting categorical and quantitative data

Summarize, represent and interpret data on a single count or measurement variable

Summarize, represent and interpret data on two categorical and quantitative variables

Interpret linear models Make inference san justify conclusions from data Conditional probability and the rules of probability

Understand independence and conditional probability and use them to interpret data

Use the rules of probability to compute probabilities of compound events

Using probability to make decisions

Calculate expected values and use them to solve problems

Use probability to evaluate outcomes of decisions

Transfer


Make predictions and decisions on real world events based on sampling, statistics and probability

Meaning

UNDERSTANDINGS Students will understand that…

Data can be represented in multiple ways

Data can be organized and analyzed to solve problems and make decisions

Data can be interpreted many ways

Probability can help predict outcomes

Probability can be analyzed and used to make fair decisions in real‐world situations

Statistics and probability are used in everyday life


How can I tell if a representation or interpretation of data is misleading?

What is the best way to represent a set of data?

What is the relationship between data sets? Is there a correlation?

What predictions can be made based on the patterns I see/knowledge of past events in the data set?

Acquisition


Scatterplot, two‐way frequency table, histogram, boxplot, circle graph, dot plot, pictograph,

Measures of central tendency

Shape, center, spread

Correlation coefficient

Causation

Sample space

Independent and conditional probability

Probability rules


Using technology to represent and analyze data

Representing data with multiple models

Analyzing, comparing and interpreting data

Fitting a function to data

Recognizing possible associations and trends

Use sample data to make inferences about a population

Evaluate reports based on data

Describing sample space

Determining independent and conditional probabilities

Using probability to analyze and make fair decisions

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S.ID.2 S.ID.2 S.ID.5 S.ID.6 S.ID.8


Represent and analyze data to solve problems, make decisions, and

predictions using:

o Scatterplot

o Two‐way frequency table

o Histogram

o Boxplot

o Circle graph

o Dot plot

Analyze data using the following statistical concepts

o Measures of central tendency

o Shape, center, spread

o Correlation coefficient

Performance Task: Defined STEM: Recycling Wins, Defined STEM: Sabermetrician: Baseball Stats Defined STEM: Tunnel Team Other Evidence

Quizzes and Tests




S.CP.1 S.CP.2 S.CP.3 S.CP.5 S.CP.6 S.CP.7 S.CP.8 S.MD.6 S.MD.7

Use probability to predict outcomes and make fair decisions in real‐

world situations

o Sample space

o Independent vs. dependent vs. mutually exclusive events

o Independent probability

o Conditional probability

o Probability rules (and/or)

Performance Task: Defined STEM: Carnival Game Designer Other Evidence

Quizzes and Tests




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Transition to College Algebra ‐ Linear Functions


ESTABLISHED GOALS CA‐A1. Students can apply, analyze, and evaluate the characteristics of functions in mathematical and authentic problem solving situations CA‐A2. Students can simplify expressions, solve equations, and graph functions from the linear, polynomial, rational, and radical function families in mathematical and authentic problem solving situations. CA‐A4. Students can create, solve, and reason with systems of equations and inequalities in mathematical and authentic problem solving situations.

Transfer


Use appropriate linear mathematical models to solve real life applications

Meaning


A linear function can be used to model real world situations

There is a relationship between graphs and equations

The equation of a line can be represented in multiple ways

The solution to an inequality can be represented in multiple ways

The solution to a system can be found using various methods

Systems of equations and inequalities can be used to model real world situations

ESSENTIAL QUESTIONS

What function models this situation and what are the key features?

How do I know if I found all the solutions?

Which form of the equation is the best representation for this situation?

What is the relationship between parallel and perpendicular lines?

Which method is best to solve this system of equations?

Acquisition


The equation of a line in various forms

The relationship between a function and its graph

Linear equations and inequalities

Systems of equations

Domain and range


Rewriting and analyzing equations to reveal key information

Create linear equations and inequalities to model authentic real world situations

Solving equations and inequalities

Solving systems graphically and algebraically

Graphing linear equations and

inequalities

Justifying and explain their mathematical thinking

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CA‐A1 F.IF.1 F.IF.2 F.IF.4 A.SSE.1 F.BF.1 F.IF.5 F.BF.3 F.IF.9

For functions in mathematical and authentic problem solving situations

Explain the concept of a function and use function notation

Interpret the dependent and independent variables in the context of functions

Create and interpret expressions for functions, including selecting appropriate domains for these functions

Understand the relationship between a function and its graph

Find the domain and range of a function

Analyze functions using different representations (graphic, numeric, algebraic, verbal)

Performance Task: Defined STEM: Dream Job Defined STEM: Hydroelectric Engineer: The Xayaburi Dam Project And The People Of Laos Other Evidence

Quizzes and Tests




CA‐A2 F.IF.4 A.SSE.4 8.EE.5 8.EE.6 F.IF.7 A.CED.2 8.EE.8 A.REI.3 G.GPE.5

In mathematical and authentic problem solving situations

Identify dependent and independent variables in linear relationships to model authentic situations

Explain the relationship between lines and their equations

Graph a line using slope‐intercept form of the linear equation

Determine the equation of a line from its graph

Determine the equation of a line from point‐slope formula

Use graphs of lines to identify solutions to linear equations

Solve linear inequalities o Writing solution sets in interval notation o Graphing solution sets on number lines o Interpreting solutions in context

Use and explain slope relationships for parallel and perpendicular lines

CA‐A4 A.REI.6 A.CED.2 A.CED.4 A.REI.11 A.CED.3 A.REI.2


Solve and create models for systems of linear equations using both graphical and algebraic methods (limit to two equations and two variables, without matrices)

Use linear inequalities and systems of linear inequalities in two unknowns to create models

Graphically identify solutions sets to linear inequalities or systems of inequalities

Performance Task:Basketball Math Other Evidence

Quizzes and Tests




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Transition to College Algebra ‐ Exponential Functions


ESTABLISHED GOALS CA‐A1. Students can apply, analyze, and evaluate the characteristics of functions in mathematical and authentic problem solving situations CA‐A3. Students can use their understanding of exponential functions of the form f(x) = C bx, for some constants b > 0 and C, in mathematical and authentic problem solving situations.

Transfer

Students will be able to independently use their learning to… Use appropriate exponential mathematical models to solve real life applications

Meaning


An exponential function can be used to model real world situations


Exponential functions behave differently from other functions

ESSENTIAL QUESTIONS


How do I know my solution is reasonable and complete?

How do the properties of this function differ from the properties of another?

Acquisition


Exponential models

Graphs of exponential functions

Domain and range


Creating exponential models

Solving exponential models

Justifying the function they used to model an authentic real world situation

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Performance Task Defined STEM: Exponential Decay Other Evidence

Quizzes and Tests




CA‐A3 F.LE.1 F.IF.7 F.BF.4 F.BF.5 F.LE.4


Create and solve simple models involving exponential equations

Distinguish exponential rate of change from other rates of change

Graph and recognize the graph of exponential functions of the form f(x) = a∙bx

Solve exponential equations numerically and algebraically

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Transition to College Algebra ‐ Quadratic Functions


ESTABLISHED GOALS CA‐A1. Students can apply, analyze, and evaluate the characteristics of functions in mathematical and authentic problem solving situations CA‐A2. Students can simplify expressions, solve equations, and graph functions from the linear, polynomial, rational, and radical function families in mathematical and authentic problem solving situations.

Transfer

Students will be able to independently use their learning to… Use appropriate quadratic mathematical models to solve real life applications

Meaning


A quadratic function can be used to model real world situations


Quadratic functions behave differently from other functions

ESSENTIAL QUESTIONS




Acquisition


Quadratic models

Graphs of quadratic functions

The relationship between zeros and factors

Domain and range


Creating quadratic functions

Solving quadratic equations and inequalities

Graphing quadratic functions (by hand and with technology)

Rewriting quadratic functions to reveal key features


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Performance Tasks: Defined STEM: Rocket Golf Course Designer Defined STEM: Architect Using Ancient Design Symbols Defined STEM: Grain Farmer Defined STEM: Green Construction Defined STEM: Regional Transportation & Railroad Director Other Evidence

Quizzes and Tests




CA‐A2 A.CED.1 A.SSE.2 A.REI.4 F.IF.7 F.IF.8

In mathematical and authentic problem solving situations.

Create and solve models involving quadratic equations.

Apply standard factoring techniques to quadratics, including identifying non‐factorable expressions

Solve quadratic equations by o Factoring o Completing the square o Quadratic Formula

Graph quadratic functions

Determine the quadratic function from a graph

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Transition to College Algebra ‐ Polynomial Functions



Transfer

Students will be able to independently use their learning to… Use appropriate polynomial mathematical models to solve real life applications

Meaning


A polynomial function can be used to model real world situations


Polynomial functions behave differently from other functions

ESSENTIAL QUESTIONS




Acquisition


Polynomial models

Graphs of polynomial functions

The relationship between zeros and factors

Domain and range


Creating polynomial functions

Graphing polynomial functions

Solving polynomial equations and inequalities

Rewriting polynomial functions to reveal key features


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Performance Tasks: Defined STEM: Slow Those Trucks Down! Defined STEM: Automotive Finance Manager Other Evidence

Quizzes and Tests




CA‐A2 A.CED.1 A.SSE.2 A.APR.2 A.APR.3 A.SSE.3 A.APR.6


Create and solve models involving polynomial equations.

Apply standard factoring techniques to polynomials, including identifying non‐factorable expressions

Understand the relationship between zeros and factors of a polynomial of degree 2 and higher

Solve polynomial equations and inequalities of degree 2 and higher

Analyze graphs of polynomial functions using technology o Zeros o y‐intercept o Turning points (i.e., relative maximum/minimum) o Domain and range

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Transition to College Algebra ‐ Radical Functions



Transfer

Students will be able to independently use their learning to… Use appropriate radical mathematical models to solve real life applications

Meaning


A radical function can be used to model real world situations


Radical functions behave differently from other functions

ESSENTIAL QUESTIONS




Acquisition


Radical equations

Rules of exponents

Graphs of radical functions

Domain and range


Converting between radical and rational exponents

Simplifying radical and rational exponents

Solving radical equations

Graphing radical equations

25











Performance Task: Captain Red Ickle’s Booty Other Evidence

Quizzes and Tests




CA‐A2 A.REI.2 F.IF.7 N.RN.2 N.RN.1 A.SSE.3


Create and solve models involving radical equations

Convert between radical and rational exponent notation

Simplify expressions involving radical and rational exponents using appropriate exponent rules

Solve equations involving radical expressions

Analyze graphs of radical functions using technology o Zeros o y‐intercept o Domain and range

26

Transition to College Algebra ‐ Rational Functions



Transfer

Students will be able to independently use their learning to… Use appropriate rational mathematical models to solve real life applications

Meaning


A rational function can be used to model real world situations


Rational functions behave differently from other functions

ESSENTIAL QUESTIONS




Acquisition


Rational equations

Graphs of rational functions

Domain and range


Simplifying rational expressions

Solving rational equations and inequalities

Create rational functions to model an authentic situation

Graphing rational functions

27











Performance Task: Defined STEM: Dream Job Salary Other Evidence

Quizzes and Tests




CA‐A2 A.REI.2 A.APR.7


Create and solve models involving rational equations

Simplify rational expressions

Solve rational equations

Solve rational inequalities algebraically

Analyze graphs of rational functions using technology o Zeros o y‐intercept o Asymptotes o Domain

28

Transition to Technical Math ‐ Number Systems & Basic Algebra


ESTABLISHED GOALS TM‐NS1. Students can use their understanding of operations with real numbers in authentic contexts. TM‐NS2. Students can perform unit conversions using dimensional analysis and proportions in both the standard and metric systems and between both systems in authentic contexts. TM‐NS3. Students can use their understanding of exponents and radicals of real numbers in order to calculate quantities in formulas and be able to explain the results. TM‐NS4. Students can use their understanding of graphs and charts in order to interpret them in contextualized workplace scenarios. TM‐BA1. Students can use algebra to analyze authentic contexts that involve linear equations and inequalities. TM‐BA3. Students can apply formulas to solve problems in authentic contexts.

Transfer


Work with measurement, estimation, formulas to solve authentic applications in their field of study.

Engage in using mathematical models to solve real world problems through effective and accurate use of mathematical notations, vocabulary, and reasoning in their field of study.

Meaning


Computing unit rates are associated with ratios and proportional relationships

Mental computations, estimation and rounding strategies will help with assessing reasonableness of answers and efficiency in career fields

Using visual models/artifacts will help draw and justify conclusions in career fields

Non‐perfect square and cube roots are irrational

Linear equations, linear inequalities, and formulas can be used to solve problems in their field of study

ESSENTIAL QUESTIONS

How do I know my answer is reasonable for the context of the problem?

How do I know I am using appropriate units?

How do I know I am reading and interpreting a model correctly?

When is it appropriate to use estimation strategies? When do I need to have a more precise answer?

How do I know I chose an appropriate method/model for this situation?

How do linear equations and inequalities represent this situation?

What formula(s) can be used in this situation?

Acquisition


Proportions

Graph and chart displays

Square roots and cube roots are inverse operations of numbers that are squared or cubed respectively

Estimating strategies

Unit conversions with proportions

Equation/inequality/formulas

Radicals and integer exponents

Fractions, numbers, and percentages


Analyzing proportional relationships

Analyzing graphs and charts

Justifying decisions based on data

Converting between measurements

Computing basic computations mentally using the properties of real numbers

Applying properties of operations to linear expressions

Solving equations, inequalities, and formulas

Using estimating strategies

Converting units of measure

Assessing the reasonableness of their solution

How to decide what formulas are appropriate

29

Stage 2 ‐ Evidence PWR CCSS Proficiency Criteria Assessment Evidence

TM‐NS1 7.RP.2 7.RP.3 6.RP.2 6.RP.3 7.EE.3 8.NS.2

In authentic contexts

Use proportional relationships to solve problems

Compute unit rates in like or different units of o Fractions o Decimals o Percents o Ratios of lengths o Ratios of areas

Apply properties of operations to calculate values using numbers in any form

Convert numbers between forms as appropriate

Assess the reasonableness of answers using mental computation, estimation and rounding strategies

Use rational approximations of irrational numbers to compare the size of irrational numbers and estimate the value of expressions (e.g., π/2 is slightly larger than 1.5)

Performance Task:Defined Stem: Fuel Efficient Cars Defined Stem: Marketing Facial Products Defined Stem: School Store Defined STEM: Food Truck Entrepreneur Defined STEM: Nutritionist Defined STEM: Baker Defined STEM: Catering Company Other Evidence • Quizzes and Tests • Short answer to prompts • Observations and dialogues • Formative checks for understanding

TM‐NS2 S.MD.1 6.RP.3

In authentic contexts

Convert like measurement units within a given measurement system (e.g., inches to feet) in solving authentic multistep problems

Convert like measurement units between systems (e.g., inches to centimeters) in solving authentic multistep problems

Use ratio reasoning (dimensional analysis) to convert measurement units including, but not limited to, distances and rates

Manipulate and transform units appropriately when multiplying or dividing quantities

TM‐NS3 6.EE.2 A.APR.1 8.EE.2 8.NS.1

For formulas in authentic problems, including exponential and radical formulas

Evaluate expressions at specific values for their variables

Perform arithmetic operations, including those involving whole‐number exponents, using order of operations

Work with radicals and integer exponents, applying rules of exponents

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number

Evaluate square roots of small perfect squares and cube roots of small perfect cubes

Know that square roots and cubed roots of non‐perfect squares and cubes are irrational and understand what irrational numbers are

TM‐NS4 S.ID.1 In contextualized workplace scenarios

30

S.ID.2 7.SP.2 5.OA.3 F.LE.1 S.IC.B

Draw and justify conclusions from graphics such as o order forms o bar charts o pie charts o diagrams o flow charts o maps o dashboards

From graphs and charts, identify and interpret o Trends o Patterns o Relationships

Identify types of graphs that best represent a given set of data, including o Bar graphs

o Pie graphs

o Line graphs

Make and justify decisions based on data.

TM‐BA1 6.EE.3 7.EE.1 A.REI.3 A.CED.1 A.CED.2

In authentic contexts that involve linear equations and inequalities

Add, subtract, factor, and expand linear expressions with rational coefficients

Solve linear equations and inequalities in one variable

Use linear equations to model authentic contexts

TM‐BA3 6.EE.1 6.EE.2 N.Q.1 N.Q.2 A.CED.4

In authentic contexts:


Analyze and use units to solve multistep problems and justify the solution

Choose and interpret units in formulas

Apply appropriate formulas

31

Transition to Technical Math ‐ Geometry


ESTABLISHED GOALS TM‐G1. Students can use their understanding of geometry to find and analyze parameters of geometric figures in authentic contexts. TM‐G2. Students can use their understanding of geometry to correctly measure and apply the parts of geometric figures in authentic contexts. TM‐G3. Students can use their understanding of geometry to analyze authentic applications involving right triangles. TM‐BA2. Represent perimeter, volume, and area as a function of a single variable in authentic contexts. TM‐BA3. Students can apply formulas to solve problems in authentic contexts.

Transfer


Apply geometric concepts to their field of study

Understand spatial relationships in real world situations

Meaning


Figures can be measured by perimeter, area, and volume

Angle relationships, Pythagorean theorem, and ratios can be used to find unknown measurements in their field of study

Similar figures can be used to create scale models

Coordinate grids can be used to represent values for a given situation

Changing the value of one quantity effects the value of another

ESSENTIAL QUESTIONS

What geometric concepts apply to this real world situation? What information do I need to know to solve this problem?

Why are scale models helpful in real world situations?

How do I know my solution is appropriate for the situation?

How precise does my solution need to be?

Acquisition


Area, perimeter and volume formulas

Units/scales of measure

Scale drawings

Coordinate grid

Pythagorean Theorem

Right triangle ratios (sine, cosine, tangent, and inverses)

Supplementary, complementary, vertical, adjacent, corresponding, alternate interior, alternate exterior angles

perimeter, circumference, diagonals, diameter


Evaluate expressions, that arise from formulas in real world situations

Accurately measuring parts of geometric figures

Creating geometric models

Creating equations from real world situations

Graphing coordinates/figures

Converting units of measure

Use the relationship between two quantities to solve problems in real world situations

32



TM‐G1 6.G1‐4 7.G.4 7.G.6 8.G.9

In authentic contexts:Use perimeter, area, and volume formulas to calculate measurements of geometric figures

Performance Task:Defined STEM: Design Architect: Building a Fun Zone Defined STEM: Astronomer Design a Telescope Defined STEM: Crime Scene Investigation Other Evidence

Quizzes and Tests Short answer to prompts Observations and dialogues Formative checks for understanding

TM‐G2 7.G.5 7.G.1 6.NS.8 2.MD.1 3.MD.3 3.MD.8 4.MD.6 6.NS.8 5.G.2

For geometric figures in authentic contexts

Use facts about angles to solve for an unknown angle o Supplementary o Complementary o Vertical o Adjacent o Corresponding o Alternate interior o Alternate exterior

Accurately measure parts of geometric figures using the correct measurement tool o Sides o Perimeter/Circumference o Diagonals o Diameter o Angles

Solve problems involving scale drawings of geometric figures including o Computing lengths o Computing areas o Reproducing a scale drawing at a different scale

Graph and interpret points in the coordinate plane

TM‐G3 8.G.7 G.SRT.8

In authentic applications involving right triangles

Use the Pythagorean Theorem to solve for a side of right triangles

Use trig ratios and their inverses to solve for unknown sides and angles in right triangles

TM‐BA2 G.GMD.3 6.EE.9 A.CED.4

In authentic contexts involving perimeter, volume and area

Use variables to represent two quantities involving geometric figures that change in relationship to one another

Write an equation to express one quantity in terms of the other quantity (independent and dependent variable)

Rearrange formulas to highlight a quantity of interest

TM‐BA3 6.EE.1 6.EE.2

In authentic contexts:


33

N.Q.1 N.Q.2 A.CED.4

Analyze and use units to solve multistep problems and justify the solution

Choose and interpret units in formulas

Apply appropriate formulas