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.]

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”

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.



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.

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


Concept 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.


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.