Foundations of Mathematical Literacy (FML) Student Outcomes (Draft v 2.0) This is a problem solving and critical thinking experience ·Study Skills will be integrated throughout. ·Students should not fear to attempt to apply the mathematical skills they possess to model a situation, or discover a pattern in data. [I would hope to expect students to discover patterns in a variety of settings. Data is too limiting. Ed] ·The inclusion of authentic applications should be frequent and central to the experience. [Aplications don't help students understand or remember mathematics concepts or procedures. I would much prefer to see the idea of using contextual situations to teach concepts or procedures.] GENERAL STUDENT OUTCOMES of FML
The student should be able to: ·Judge the validity of logical arguments[will there be a section on logic?] ·Explain a mathematical argument in words, organize mathematical data into tables, organize mathematical data into graphs, and understand the meaning of simple mathematical formulas and equations ·Recognize that solving mathematical problems sometimes requires persistence and multiple approaches ·Communicate about mathematics ·Become fluent in the language of mathematics ·Employ and translate among multiple representations ·Develop reasoning and understanding ·Use mathematics to understand and solve a variety of authentic applications ·Appreciate that “Units matter” PREREQUISITE NUMERICAL SKILLS The student should be able to (prior to this FML experience):

1.Identify the value of each position in a number written in place value notation.
2.In a context, round a whole number to a given place value .
3.In a context, estimate the sum, difference, product or quotient of two whole numbers .
4.Demonstrate knowledge of addition, subtraction and multiplication facts for single digit whole numbers, and for very simple division (divisions which involve the multiplication facts for single digit numbers).
5.In a context, graph an integer on a number line .
6.Without context, follow the order of operations to evaluate numerical expressions that include one and two digit integers.
7.In a context, follow the order of operations to evaluate numerical expressions [Does this include knowledge of signed number computations? If yes, make explicit. If not, where is that covered?].
8.In a context, write a rational number as a fraction, decimal, or percent .
9.State equivalent decimal numbers and percents for frequently used fractions. [Where is ranking of decimals?]
10.In a context, add, subtract, multiply, and divide fractions with single digit whole number numerators and denominators.
11.Estimate the result of fraction arithmetic.
12.Solve problems in a real life context that involve percent including percent increase and decrease, retail, interest, and weighted grades.[Where are percent problems not in context covered?]
13.Identify and describe the characteristics of a triangle, rectangle, circle, and rectangular solid.
14.Find the perimeter and area of a triangle, rectangle, or circle.
15.Find the volume of a rectangular solid.
16.Obtain information from a table, bar graph, line graph, circle graph, or spreadsheet.

SPECIFIC STUDENT OUTCOMES of FML NUMERACY, ESTIMATION, AND MEASUREMENT

Magnitude and Place Value The student will be able to use the context of the problem to: oTranslate from place value notation to scientific notation and reverse. [use technology] oMultiply and divide numbers in scientific notation and report the product or quotient in scientific notation. [use technology] oOrder measurements including numbers written using the word names thousand, million, billion, and trillion, as well as tenths, hundredths, thousandths, etc. Reasonability and Estimate The student will be able to: ·Identify a reasonable place value for rounding the result of calculations done with real life measurements. ·Estimate the order of magnitude of a measurement in a real life context (Fermi problems.) ·Estimate the order of magnitude of a sum, difference, product or quotient of numbers in a context. ·Judge the reasonableness of results in all authentic application problems.

Measurement and Units The student will be able to: oUse units appropriately for measures of length, area and volume. oChange measurements and/or rates between the U.S. standard and metric systems. oExplain the units used in rates and make conversions between units. oBe able to estimate a total given a unit rate and the number of units oConvert measures (linear, area, liquid, mass, and volume) within and between the U.S. standard and metric systems. oUse estimation and computational skills with perimeter, area, and volume involving irregular shapes.

PROPORTIONAL REASONING The student will be able to: ·Know when it is more appropriate to use the actual number and when it is more appropriate to use a rate. For instance when comparing crime statistics between a medium sized and a large city the rate per 10,000 is probably more useful than the number of crimes. ·Use proportions in context EQUATIONS, INEQUALITIES, AND FUNCTIONS

Concept of Variable The student will be able to: oCorrectly use notation with variables (coefficients, exponents, subscripts) in mathematical expressions. oExplain the difference between a variable and a constant. oUse a variable to represent an unknown in a problem with context. oReplace variables in formulas with the correct numbers in an application and evaluate the formula. oIdentify the nature of a variable from the context as a place holder in a formula, or as an unknown for which to solve. Solve Problems involving Equations and Inequalities in Context The student will be able to: ·Determine whether one-variable, linear equations have 0, 1 or infinitely many solutions. [not that important] ·Solve linear equations and verify the solutions by [using an alternative method such as numerical or graphical] [Does "verify the solutions" imply that a student needs to know how to compute with decimals if the original equation has decimal coefficients? If so, where is that covered?] ·Use calculators and spreadsheets to evaluate complicated expressions. [doesn't add any educational value - agree] ·Explain what a solution to a one variable equation is. ·Evaluate whether numeric, graphic, or algebraic methods solve a particular equation most [appropriately.] ·Determine whether a numeric answer to an equation has enough precision for a problem in context. ·Solve any type of equation (chosen to have convenient solutions) using a table, or graph. ·Write a sentence explaining the meaning of the solution to an equation derived from a problem in context. Multiple Representations The student will be able to: oReport the input(s) and output(s) for a function; [??? identify/list input/output???] oExplain that an ordered pair on a graph represents the solution to a two-variable equation. oIdentify if a graph represents a particular function. Identify intercepts for linear functions without the aid of graphing technology. oConvert between graphical, tabular and symbolic representations of a two-variable, linear function. oCalculate ordered pairs that satisfy an equation using graphing technology. oCalculate sufficient ordered pairs to draw an accurate graph. [why would anyone want to do this? a total waste] oFind the slope for linear functions without the aid of technology. oIdentify intercepts for any function using graphing technology. oUse tables and graphs to identify an output corresponding to a given input, and to find an input corresponding to a given output. oUse tables and graphs to determine rates of change

Creating and Using Equations and Inequalities to Model Problem Situations The student will be able to: ·Use symbolic algebra to solve problems posed in paragraph form. [ solutions should be found using multiple methods] ·Write algebraic statements to describe problems. ·Explain the limitations of mathematical models. ·Solve problems involving inequalities in one variable. ·List graphical, tabular and symbolic properties of linear functions. [I don't know what these mean. Behaviors? Why list graphical, tabular and symbolic?? ditto below] ·List graphical, tabular and symbolic properties of exponential functions. ·List graphical, tabular and symbolic properties of a power fucntion. ·Detect whether data represents a linear function, an exponential function or apower function. [do you mean determine?] ·Investigate problems given in context using spreadsheets. ·Create spreadsheets that include cell references used appropriately as variables. ·Evaluate the fit of a line using proximity to the data and the context of the data. ·Model data in context using variables and parameters.

Rate of Change The student will be able to: oCompute the average rate of change from tabular data including the appropriate units. oApply the average rate of change to interpolate and extrapolate from tabular data including the appropriate units. oInterpret the meaning of slope and intercepts in the context of authentic application problems. Interpret slope in diverse settings and types of functions. oCalculate rate of change using [f(b)-f(a)]/(b-a) and interpret results with a context. [bad choice. it should be delta y/ delta x]

Formulas and Geometry The student will be able to: ·Evaluate formulas (input variables one side, output variable isolated) ·Report lengths, areas and volumes using the correct units. ·Choose correctly whether to use length, area or volume in a problem. ·Estimate lengths and volumes in UWS standard and metric units ·Calculate using UWS standard and metric units reporting answers with the correct units. ·Calculate perimeters, areas, volumes (in U.S. Standard or metric units) of basic and irregular shapes.

Recognize Patterns and Generalize The student will be able to: ÜPredict and analyze trends using patterns in data. PROBABILITY AND STATISTICS Basic Probability The student will be able to: oIdentify the sample space of an experiment. oUse basic rules of probability to calculate the probability of an event, including unions, intersections, and complement.

Central Tendency and Variability The student will be able to: ·Calculate measures of central tendency and variation. ·Recognize the differences between measures of central tendency, which measure is most appropriate to use and how to use multiple measures for better communication. ·Use measures of central tendency, measures of variation, and mathematical models to explain and/or interpret data.

Graphical Representations The student will be able to: oRecognize when graph scales can lead to misinterpretation of data, and how to correctly construct graph scales for basic situations. oUse statistical graphs and charts to identify and extract data and interpret their meaning oBe able to read and make decisions based upon data from lines graphs, bar graphs, histograms, box and whisker plots, scatterplots and pie charts (circle graph). oConstruct an appropriate graphical representation of a set of data. [use technology] oBe able to organize and display (discrete or continuous) data using a spreadsheet, and use the spreadsheet to create an appropriate chart or graph.

Student Outcomes

(Draft v 2.0)

This is a problem solving and critical thinking experience

· Study Skills will be integrated throughout.

· Students should not fear to attempt to apply the mathematical skills they possess to model a situation, or discover a pattern in data. [I would hope to expect students to discover patterns in a variety of settings. Data is too limiting. Ed]

· The inclusion of authentic applications should be frequent and central to the experience. [Aplications don't help students understand or remember mathematics concepts or procedures. I would much prefer to see the idea of using contextual situations to teach concepts or procedures.]

GENERAL STUDENT OUTCOMES of FMLThe student should be able to:

· Judge the validity of logical arguments [will there be a section on logic?]

· Explain a mathematical argument in words, organize mathematical data into tables, organize mathematical data into graphs, and understand the meaning of simple mathematical formulas and equations

· Recognize that solving mathematical problems sometimes requires persistence and multiple approaches

· Communicate about mathematics

· Become fluent in the language of mathematics

· Employ and translate among multiple representations

· Develop reasoning and understanding

· Use mathematics to understand and solve a variety of authentic applications

· Appreciate that “Units matter”

PREREQUISITE NUMERICAL SKILLSThe student should be able to (prior to this FML experience):

1. Identify the value of each position in a number written in place value notation.

2. In a context, round a whole number to a given place value .

3. In a context, estimate the sum, difference, product or quotient of two whole numbers .

4. Demonstrate knowledge of addition, subtraction and multiplication facts for single digit whole numbers, and for very simple division (divisions which involve the multiplication facts for single digit numbers).

5. In a context, graph an integer on a number line .

6. Without context, follow the order of operations to evaluate numerical expressions that include one and two digit integers.

7. In a context, follow the order of operations to evaluate numerical expressions [Does this include knowledge of signed number computations? If yes, make explicit. If not, where is that covered?].

8. In a context, write a rational number as a fraction, decimal, or percent .

9. State equivalent decimal numbers and percents for frequently used fractions. [Where is ranking of decimals?]

10. In a context, add, subtract, multiply, and divide fractions with single digit whole number numerators and denominators.

11. Estimate the result of fraction arithmetic.

12. Solve problems in a real life context that involve percent including percent increase and decrease, retail, interest, and weighted grades.[Where are percent problems not in context covered?]

13. Identify and describe the characteristics of a triangle, rectangle, circle, and rectangular solid.

14. Find the perimeter and area of a triangle, rectangle, or circle.

15. Find the volume of a rectangular solid.

16. Obtain information from a table, bar graph, line graph, circle graph, or spreadsheet.

SPECIFIC STUDENT OUTCOMES of FMLNUMERACY, ESTIMATION, AND MEASUREMENT

Magnitude and Place Value

The student will be able to use the context of the problem to:

o Translate from place value notation to scientific notation and reverse. [use technology]

o Multiply and divide numbers in scientific notation and report the product or quotient in scientific notation. [use technology]

o Order measurements including numbers written using the word names thousand, million, billion, and trillion, as well as tenths, hundredths, thousandths, etc.

Reasonability and Estimate

The student will be able to:

· Identify a reasonable place value for rounding the result of calculations done with real life measurements.

· Estimate the order of magnitude of a measurement in a real life context (Fermi problems.)

· Estimate the order of magnitude of a sum, difference, product or quotient of numbers in a context.

· Judge the reasonableness of results in all authentic application problems.

Measurement and Units

The student will be able to:

o Use units appropriately for measures of length, area and volume.

o Change measurements and/or rates between the U.S. standard and metric systems.

o Explain the units used in rates and make conversions between units.

o Be able to estimate a total given a unit rate and the number of units

o Convert measures (linear, area, liquid, mass, and volume) within and between the U.S. standard and metric systems.

o Use estimation and computational skills with perimeter, area, and volume involving irregular shapes.

PROPORTIONAL REASONINGThe student will be able to:

· Know when it is more appropriate to use the actual number and when it is more appropriate to use a rate. For instance when comparing crime statistics between a medium sized and a large city the rate per 10,000 is probably more useful than the number of crimes.

· Use proportions in context

EQUATIONS, INEQUALITIES, AND FUNCTIONSConcept of Variable

The student will be able to:

o Correctly use notation with variables (coefficients, exponents, subscripts) in mathematical expressions.

o Explain the difference between a variable and a constant.

o Use a variable to represent an unknown in a problem with context.

o Replace variables in formulas with the correct numbers in an application and evaluate the formula.

o Identify the nature of a variable from the context as a place holder in a formula, or as an unknown for which to solve.

Solve Problems involving Equations and Inequalities in Context

The student will be able to:

· Determine whether one-variable, linear equations have 0, 1 or infinitely many solutions. [not that important]

· Solve linear equations and verify the solutions by [using an alternative method such as numerical or graphical] [Does "verify the solutions" imply that a student needs to know how to compute with decimals if the original equation has decimal coefficients? If so, where is that covered?]

· Use calculators and spreadsheets to evaluate complicated expressions. [doesn't add any educational value - agree]

· Explain what a solution to a one variable equation is.

· Evaluate whether numeric, graphic, or algebraic methods solve a particular equation most [appropriately.]

· Determine whether a numeric answer to an equation has enough precision for a problem in context.

· Solve any type of equation (chosen to have convenient solutions) using a table, or graph.

· Write a sentence explaining the meaning of the solution to an equation derived from a problem in context.

Multiple Representations

The student will be able to:

o Report the input(s) and output(s) for a function; [??? identify/list input/output???]

o Explain that an ordered pair on a graph represents the solution to a two-variable equation.

o Identify if a graph represents a particular function. Identify intercepts for linear functions without the aid of graphing technology.

o Convert between graphical, tabular and symbolic representations of a two-variable, linear function.

o Calculate ordered pairs that satisfy an equation using graphing technology.

o Calculate sufficient ordered pairs to draw an accurate graph. [why would anyone want to do this? a total waste]

o Find the slope for linear functions without the aid of technology.

o Identify intercepts for any function using graphing technology.

o Use tables and graphs to identify an output corresponding to a given input, and to find an input corresponding to a given output.

o Use tables and graphs to determine rates of change

Creating and Using Equations and Inequalities to Model Problem Situations

The student will be able to:

· Use symbolic algebra to solve problems posed in paragraph form. [ solutions should be found using multiple methods]

· Write algebraic statements to describe problems.

· Explain the limitations of mathematical models.

· Solve problems involving inequalities in one variable.

· List graphical, tabular and symbolic properties of linear functions. [I don't know what these mean. Behaviors? Why list graphical, tabular and symbolic?? ditto below]

· List graphical, tabular and symbolic properties of exponential functions.

· List graphical, tabular and symbolic properties of a power fucntion.

· Detect whether data represents a linear function, an exponential function or a power function. [do you mean determine?]

· Investigate problems given in context using spreadsheets.

· Create spreadsheets that include cell references used appropriately as variables.

· Evaluate the fit of a line using proximity to the data and the context of the data.

· Model data in context using variables and parameters.

Rate of Change

The student will be able to:

o Compute the average rate of change from tabular data including the appropriate units.

o Apply the average rate of change to interpolate and extrapolate from tabular data including the appropriate units.

o Interpret the meaning of slope and intercepts in the context of authentic application problems. Interpret slope in diverse settings and types of functions.

o Calculate rate of change using [f(b)-f(a)]/(b-a) and interpret results with a context. [bad choice. it should be delta y/ delta x]

Formulas and Geometry

The student will be able to:

· Evaluate formulas (input variables one side, output variable isolated)

· Report lengths, areas and volumes using the correct units.

· Choose correctly whether to use length, area or volume in a problem.

· Estimate lengths and volumes in UWS standard and metric units

· Calculate using UWS standard and metric units reporting answers with the correct units.

· Calculate perimeters, areas, volumes (in U.S. Standard or metric units) of basic and irregular shapes.

Recognize Patterns and Generalize

The student will be able to:

Ü Predict and analyze trends using patterns in data.

PROBABILITY AND STATISTICS

Basic Probability

The student will be able to:

o Identify the sample space of an experiment.

o Use basic rules of probability to calculate the probability of an event, including unions, intersections, and complement.

Central Tendency and Variability

The student will be able to:

· Calculate measures of central tendency and variation.

· Recognize the differences between measures of central tendency, which measure is most appropriate to use and how to use multiple measures for better communication.

· Use measures of central tendency, measures of variation, and mathematical models to explain and/or interpret data.

Graphical Representations

The student will be able to:

o Recognize when graph scales can lead to misinterpretation of data, and how to correctly construct graph scales for basic situations.

o Use statistical graphs and charts to identify and extract data and interpret their meaning

o Be able to read and make decisions based upon data from lines graphs, bar graphs, histograms, box and whisker plots, scatterplots and pie charts (circle graph).

o Construct an appropriate graphical representation of a set of data. [use technology]

o Be able to organize and display (discrete or continuous) data using a spreadsheet, and use the spreadsheet to create an appropriate chart or graph.