Name 
Description 
MA.912.AR.1.1:  Identify and interpret parts of an equation or expression that represent a quantity in terms of a mathematical or realworld context, including viewing one or more of its parts as a single entity.Clarifications: Clarification 1: Parts of an expression include factors, terms, constants, coefficients and variables. Clarification 2: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business. 

MA.912.AR.1.2:  Rearrange equations or formulas to isolate a quantity of interest.Clarifications: Clarification 1: Instruction includes using formulas for temperature, perimeter, area and volume; using equations for linear (standard, slopeintercept and pointslope forms) and quadratic (standard, factored and vertex forms) functions. Clarification 2: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

Examples: Algebra 1 Example: The Ideal Gas Law PV = nRT can be rearranged as to isolate temperature as the quantity of interest. Example: Given the Compound Interest formula , solve for P. Mathematics for Data and Financial Literacy Honors Example: Given the Compound Interest formula , solve for t.
 
MA.912.AR.2.5:  Solve and graph mathematical and realworld problems that are modeled with linear functions. Interpret key features and determine constraints in terms of the context.Clarifications: Clarification 1: Key features are limited to domain, range, intercepts and rate of change.Clarification 2: Instruction includes the use of standard form, slopeintercept form and pointslope form. Clarification 3: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or setbuilder notation. Clarification 4: Within the Algebra 1 course, notations for domain, range and constraints are limited to inequality and setbuilder. Clarification 5: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

Examples: Algebra 1 Example: Lizzy’s mother uses the function C(p)=450+7.75p, where C(p) represents the total cost of a rental space and p is the number of people attending, to help budget Lizzy’s 16th birthday party. Lizzy’s mom wants to spend no more than $850 for the party. Graph the function in terms of the context.  
MA.912.AR.5.7:  Solve and graph mathematical and realworld problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.Clarifications: Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; constant percent rate of change; end behavior and asymptotes. Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or setbuilder notation. Clarification 3: Instruction includes understanding that when the logarithm of the dependent variable is taken and graphed, the exponential function will be transformed into a linear function. Clarification 4: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

Examples:
The graph of the function can be transformed into the straight line y=5t+2 by taking the natural logarithm of the function’s outputs.  
MA.912.DP.1.2:  Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.Clarifications: Clarification 1: Within the Probability and Statistics course, instruction includes the use of spreadsheets and technology.  
MA.912.DP.2.4:  Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and yintercept of the model. Use the model to solve realworld problems in terms of the context of the data.Clarifications: Clarification 1: Instruction includes fitting a linear function both informally and formally with the use of technology.Clarification 2: Problems include making a prediction or extrapolation, inside and outside the range of the data, based on the equation of the line of fit.
 
MA.912.DP.3.1:  Construct a twoway frequency table summarizing bivariate categorical data. Interpret joint and marginal frequencies and determine possible associations in terms of a realworld context.
Examples: Algebra 1 Example: Complete the frequency table below.
 Has an A in math  Doesn't have an A in math  Total  Plays an instrument  20   90  Doesn't play an instrument  20    Total    350 
Using the information in the table, it is possible to determine that the second column contains the numbers 70 and 240. This means that there are 70 students who play an instrument but do not have an A in math and the total number of students who play an instrument is 90. The ratio of the joint frequencies in the first column is 1 to 1 and the ratio in the second column is 7 to 24, indicating a strong positive association between playing an instrument and getting an A in math.
 
MA.912.F.1.2:  Given a function represented in function notation, evaluate the function for an input in its domain. For a realworld context, interpret the output.Clarifications: Clarification 1: Problems include simple functions in twovariables, such as f(x,y)=3x2y. Clarification 2: Within the Algebra 1 course, functions are limited to onevariable such as f(x)=3x.

Examples: Algebra 1 Example: The function models Alicia’s position in miles relative to a water stand x minutes into a marathon. Evaluate and interpret for a quarter of an hour into the race.  
MA.912.F.3.2:  Given a mathematical or realworld context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.Clarifications: Clarification 1: Instruction includes representing domain restrictions with inequality notation, interval notation or setbuilder notation.Clarification 2: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.
 
MA.912.FL.1.1:  Extend previous knowledge of operations of fractions, percentages and decimals to solve realworld problems involving money and business.Clarifications: Clarification 1: Problems include discounts, markups, simple interest, tax, tips, fees, percent increase, percent decrease and percent error.  
MA.912.FL.1.2:  Extend previous knowledge of ratios and proportional relationships to solve realworld problems involving money and business.
Examples: Example: A local grocery stores sells trail mix for $1.75 per pound. If the grocery store spends $0.82 on each pound of mix, how much will the store gain in gross profit if they sell 6.4 pounds in one day? Example: If Juan makes $25.00 per hour and works 40 hours per week, what is his annual salary?
 
MA.912.FL.2.2:  Solve realworld problems involving profits, costs and revenues using spreadsheets and other technology.Clarifications: Clarification 1: Instruction includes the connection to data. Clarification 2: Instruction includes displaying profits and costs over time in a table or graph and using the graph to predict profits. Clarification 3: Problems include maximizing profits, maximizing revenues and minimizing costs.

Examples: Example: A travel agency charges $2400 per person for a weeklong trip to London if the group has 16 people or less. For groups larger then 16, the price per person is reduced by $100 for each additional person. Create an expression describing the revenue as a function of the number of people in the group. Determine the number of people that maximizes the revenue.  
MA.912.FL.2.4:  Given current exchange rates, convert between currencies. Solve realworld problems involving exchange rates.Clarifications: Clarification 1: Instruction includes taking into account various fees, such as conversion fee, foreign transaction fee and dynamic concurrency conversion fee.  
MA.912.FL.2.5:  Develop budgets that fit within various incomes using spreadsheets and other technology.Clarifications: Clarification 1: Instruction includes budgets for a business and for an individual. Clarification 2: Instruction includes taking into account various cash management strategies, such as checking and savings accounts, and how inflation may affect these strategies.

Examples: Example: Develop a budget spreadsheet for your business that includes typical expenses such as rental space, transportation, utilities, inventory, payroll, and miscellaneous expenses. Add categories for savings toward your own financial goals, and determine the monthly income needed, before taxes, to meet the requirements of your budget.  
MA.912.FL.2.6:  Given a realworld scenario, complete and calculate federal income tax using spreadsheets and other technology.Clarifications: Clarification 1: Instruction includes understanding the difference between standardized deductions and itemized deductions. Clarification 2: Instruction includes the connection to piecewise linear functions with slopes relating to the marginal tax rates.
 
MA.912.FL.3.1:  Compare simple, compound and continuously compounded interest over time.Clarifications: Clarification 1: Instruction includes taking into consideration the annual percentage rate (APR) when comparing simple and compound interest.  
MA.912.FL.3.2:  Solve realworld problems involving simple, compound and continuously compounded interest.Clarifications: Clarification 1: Within the Algebra 1 course, interest is limited to simple and compound. 
Examples: Example: Find the amount of money on deposit at the end of 5 years if you started with $500 and it was compounded quarterly at 6% interest per year. Example: Joe won $25,000 on a lottery scratchoff ticket. How many years will it take at 6% interest compounded yearly for his money to double?
 
MA.912.FL.3.5:  Compare the advantages and disadvantages of using cash versus personal financing options.Clarifications:
Clarification 1: Instruction includes advantages and disadvantages for a business and for an individual.Clarification 2: Personal financing options include debit cards, credit cards, installment plans and loans.

Examples: Example: Compare paying for a tank of gasoline in the following ways: cash; credit card and paying over 2 months; credit card and paying balance in full each month.  
MA.912.FL.3.6:  Calculate the finance charges and total amount due on a bill using various forms of credit using estimation, spreadsheets and other technology.Clarifications: Clarification 1: Instruction includes how annual percentage rate (APR) and periodic rate are calculated per month and the connection between the two percentages. 
Examples: Example: Calculate the finance charge each month and the total amount paid for 5 months if you charged $500 on your credit card but you can only afford to pay $100 each month. Your credit card has a monthly periodic finance rate of 1.5% and an annual finance rate of 17.99%.  
MA.912.FL.3.9:  Compare the advantages and disadvantages of different types of mortgage loans by manipulating a variety of variables and calculating fees and total cost using spreadsheets and other technology.Clarifications: Clarification 1: Instruction includes understanding various considerations that qualify a buyer for a loan, such as DebttoIncome ratio. Clarification 2: Fees include discount prices, origination fee, maximum brokerage fee on a net or gross loan, documentary stamps and prorated expenses. Clarification 3: Instruction includes a cost comparison between a higher interest rate and fewer mortgage points versus a lower interest rate and more mortgage points. Clarification 4: Instruction includes a cost comparison between the length of the mortgage loan, such as 30year versus 15year.
Clarification 5: Instruction includes adjustable rate loans, tax implications and equity for mortgages.
 
MA.912.FL.3.10:  Analyze credit scores qualitatively. Explain how shortterm and longterm purchases, including deferred payments, may increase or decrease credit scores. Explain how credit scores influence buying power.Clarifications: Clarification 1: Instruction includes how each of the following categories affects a credit score: past payment history, amount of debt, public records information, length of credit history and the number of recent credit inquiries.Clarification 2: Instruction includes how a credit score affects qualification and interest rate for a home mortgage.
 
MA.912.FL.3.11:  Given a realworld scenario, establish a plan to pay off debt.Clarifications: Clarification 1: Instruction includes the comparison of different plans to pay off the debt. Clarification 2: Instruction includes pay off plans for a business and for an individual.

Examples: Example: Suppose you currently have a balance of $4500 on a credit card that charges 18% annual interest. What monthly payment would you have to make in order to pay off the card in 3 years, assuming you do not make any more charges to the card?  
MA.912.FL.4.1:  Calculate and compare various options, deductibles and fees for various types of insurance policies using spreadsheets and other technology.Clarifications: Clarification 1: Insurances include medical, car, homeowners, life and rental car. Clarification 2: Instruction includes types of insurance for a business and for an individual.
 
MA.912.FL.4.4:  Collect, organize and interpret data to determine an effective retirement savings plan to meet personal financial goals using spreadsheets and other technology.Clarifications: Clarification 1: Instruction includes students researching the latest information on different retirement options. Clarification 2: Instruction includes the understanding of the relationship between salaries and retirement plans. Clarification 3: Instruction includes retirement plans from the perspective of a business and of an individual.
Clarification 4: Instruction includes the comparison of different types of retirement plans, including IRAs, pensions and annuities.

Examples: Example: Investigate historical rates of return for stocks, bonds, savings accounts, mutual funds, as well as the relative risks for each type of investment. Organize your results in a table showing the relative returns and risks of each type of investment over short and long terms, and use these data to determine a combination of investments suitable for building a retirement account sufficient to meet anticipated financial needs.  
MA.912.NSO.1.1:  Extend previous understanding of the Laws of Exponents to include rational exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions involving rational exponents.Clarifications: Clarification 1: Instruction includes the use of technology when appropriate.
Clarification 2: Refer to the K12 Formulas (Appendix E) for the Laws of Exponents.
Clarification 3: Instruction includes converting between expressions involving rational exponents and expressions involving radicals.Clarification 4:Within the Mathematics for Data and Financial Literacy course, it is not the expectation to generate equivalent numerical expressions.  
MA.912.NSO.1.2:  Generate equivalent algebraic expressions using the properties of exponents.
Examples: The expression is equivalent to the expression which is equivalent to .  
MA.K12.MTR.1.1:  Actively participate in effortful learning both individually and collectively. Mathematicians who participate in effortful learning both individually and with others:
 Analyze the problem in a way that makes sense given the task.
 Ask questions that will help with solving the task.
 Build perseverance by modifying methods as needed while solving a challenging task.
 Stay engaged and maintain a positive mindset when working to solve tasks.
 Help and support each other when attempting a new method or approach.
Clarifications: Teachers who encourage students to participate actively in effortful learning both individually and with others:
 Cultivate a community of growth mindset learners.
 Foster perseverance in students by choosing tasks that are challenging.
 Develop students’ ability to analyze and problem solve.
 Recognize students’ effort when solving challenging problems.
 
MA.K12.MTR.2.1:  Demonstrate understanding by representing problems in multiple ways. Mathematicians who demonstrate understanding by representing problems in multiple ways:  Build understanding through modeling and using manipulatives.
 Represent solutions to problems in multiple ways using objects, drawings, tables, graphs and equations.
 Progress from modeling problems with objects and drawings to using algorithms and equations.
 Express connections between concepts and representations.
 Choose a representation based on the given context or purpose.
Clarifications: Teachers who encourage students to demonstrate understanding by representing problems in multiple ways:  Help students make connections between concepts and representations.
 Provide opportunities for students to use manipulatives when investigating concepts.
 Guide students from concrete to pictorial to abstract representations as understanding progresses.
 Show students that various representations can have different purposes and can be useful in different situations.
 
MA.K12.MTR.3.1:  Complete tasks with mathematical fluency. Mathematicians who complete tasks with mathematical fluency:  Select efficient and appropriate methods for solving problems within the given context.
 Maintain flexibility and accuracy while performing procedures and mental calculations.
 Complete tasks accurately and with confidence.
 Adapt procedures to apply them to a new context.
 Use feedback to improve efficiency when performing calculations.
Clarifications: Teachers who encourage students to complete tasks with mathematical fluency: Provide students with the flexibility to solve problems by selecting a procedure that allows them to solve efficiently and accurately.
 Offer multiple opportunities for students to practice efficient and generalizable methods.
 Provide opportunities for students to reflect on the method they used and determine if a more efficient method could have been used.
 
MA.K12.MTR.4.1:  Engage in discussions that reflect on the mathematical thinking of self and others. Mathematicians who engage in discussions that reflect on the mathematical thinking of self and others:  Communicate mathematical ideas, vocabulary and methods effectively.
 Analyze the mathematical thinking of others.
 Compare the efficiency of a method to those expressed by others.
 Recognize errors and suggest how to correctly solve the task.
 Justify results by explaining methods and processes.
 Construct possible arguments based on evidence.
Clarifications: Teachers who encourage students to engage in discussions that reflect on the mathematical thinking of self and others: Establish a culture in which students ask questions of the teacher and their peers, and error is an opportunity for learning.
 Create opportunities for students to discuss their thinking with peers.
 Select, sequence and present student work to advance and deepen understanding of correct and increasingly efficient methods.
 Develop students’ ability to justify methods and compare their responses to the responses of their peers.
 
MA.K12.MTR.5.1:  Use patterns and structure to help understand and connect mathematical concepts. Mathematicians who use patterns and structure to help understand and connect mathematical concepts:  Focus on relevant details within a problem.
 Create plans and procedures to logically order events, steps or ideas to solve problems.
 Decompose a complex problem into manageable parts.
 Relate previously learned concepts to new concepts.
 Look for similarities among problems.
 Connect solutions of problems to more complicated largescale situations.
Clarifications: Teachers who encourage students to use patterns and structure to help understand and connect mathematical concepts: Help students recognize the patterns in the world around them and connect these patterns to mathematical concepts.
 Support students to develop generalizations based on the similarities found among problems.
 Provide opportunities for students to create plans and procedures to solve problems.
 Develop students’ ability to construct relationships between their current understanding and more sophisticated ways of thinking.
 
MA.K12.MTR.6.1:  Assess the reasonableness of solutions. Mathematicians who assess the reasonableness of solutions:  Estimate to discover possible solutions.
 Use benchmark quantities to determine if a solution makes sense.
 Check calculations when solving problems.
 Verify possible solutions by explaining the methods used.
 Evaluate results based on the given context.
Clarifications: Teachers who encourage students to assess the reasonableness of solutions: Have students estimate or predict solutions prior to solving.
 Prompt students to continually ask, “Does this solution make sense? How do you know?”
 Reinforce that students check their work as they progress within and after a task.
 Strengthen students’ ability to verify solutions through justifications.
 
MA.K12.MTR.7.1:  Apply mathematics to realworld contexts. Mathematicians who apply mathematics to realworld contexts:  Connect mathematical concepts to everyday experiences.
 Use models and methods to understand, represent and solve problems.
 Perform investigations to gather data or determine if a method is appropriate.
• Redesign models and methods to improve accuracy or efficiency.
Clarifications: Teachers who encourage students to apply mathematics to realworld contexts: Provide opportunities for students to create models, both concrete and abstract, and perform investigations.
 Challenge students to question the accuracy of their models and methods.
 Support students as they validate conclusions by comparing them to the given situation.
 Indicate how various concepts can be applied to other disciplines.
 
ELA.K12.EE.1.1:  Cite evidence to explain and justify reasoning.Clarifications: K1 Students include textual evidence in their oral communication with guidance and support from adults. The evidence can consist of details from the text without naming the text. During 1st grade, students learn how to incorporate the evidence in their writing.23 Students include relevant textual evidence in their written and oral communication. Students should name the text when they refer to it. In 3rd grade, students should use a combination of direct and indirect citations. 45 Students continue with previous skills and reference comments made by speakers and peers. Students cite texts that they’ve directly quoted, paraphrased, or used for information. When writing, students will use the form of citation dictated by the instructor or the style guide referenced by the instructor. 68 Students continue with previous skills and use a style guide to create a proper citation. 912 Students continue with previous skills and should be aware of existing style guides and the ways in which they differ.
 
ELA.K12.EE.2.1:  Read and comprehend gradelevel complex texts proficiently.Clarifications: See Text Complexity for gradelevel complexity bands and a text complexity rubric.  
ELA.K12.EE.3.1:  Make inferences to support comprehension.Clarifications: Students will make inferences before the words infer or inference are introduced. Kindergarten students will answer questions like “Why is the girl smiling?” or make predictions about what will happen based on the title page.
Students will use the terms and apply them in 2nd grade and beyond.  
ELA.K12.EE.4.1:  Use appropriate collaborative techniques and active listening skills when engaging in discussions in a variety of situations.Clarifications: In kindergarten, students learn to listen to one another respectfully.In grades 12, students build upon these skills by justifying what they are thinking. For example: “I think ________ because _______.” The collaborative conversations are becoming academic conversations. In grades 312, students engage in academic conversations discussing claims and justifying their reasoning, refining and applying skills. Students build on ideas, propel the conversation, and support claims and counterclaims with evidence.
 
ELA.K12.EE.5.1:  Use the accepted rules governing a specific format to create quality work.Clarifications: Students will incorporate skills learned into work products to produce quality work. For students to incorporate these skills appropriately, they must receive instruction. A 3rd grade student creating a poster board display must have instruction in how to effectively present information to do quality work.  
ELA.K12.EE.6.1:  Use appropriate voice and tone when speaking or writing.Clarifications: In kindergarten and 1st grade, students learn the difference between formal and informal language. For example, the way we talk to our friends differs from the way we speak to adults. In 2nd grade and beyond, students practice appropriate social and academic language to discuss texts.  
ELD.K12.ELL.MA.1:  English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. 
ELD.K12.ELL.SI.1:  English language learners communicate for social and instructional purposes within the school setting. 