Core Learning Goals for Algebra/Data Analysis

The objectives assessed on MSA at each grade level are embedded in the Core Learning Goals (CLG). They are identified with the notation, Assessment limit. Assessment limits provide clarification about the specific skills and content that students are expected to have learned for each assessed objective. Even though some objectives in the VSC may not have an Assessment limit at a given grade-level, these non-assessed objectives still must be included in instruction. They introduce important concepts in preparation for assessed skills and content at subsequent grade levels.

Print Mathematics:

Goal 1 Functions and Algebra

The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra.

Expectation 1.1

The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

Indicator

• 1.1.1 The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.

Assessment limits:
• The given pattern must represent a relationship of the form y = mx + b (linear), y = x2 + c (simple quadratic), y = x3 + c (simple cubic), simple arithmetic progression, or simple geometric progression with all exponents being positive.
• The student will not be asked to draw three-dimensional figures.
• Algebraic description of patterns is in indicator 1.1.2

Indicator

• 1.1.2 The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

Assessment limits:
• The given pattern must represent a relationship of the form mx + b (linear), x2 (simple quadratic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

Indicator

• 1.1.3 The student will apply addition, subtraction, multiplication, and/or division of algebraic expressions to mathematical and real-world problems.

Assessment limits:
• The algebraic expression is a polynomial in one variable.
• The polynomial is not simplified.

Indicator

• 1.1.4 The student will describe the graph of a non-linear function and discuss its appearance in terms of the basic concepts of maxima and minima, zeros (roots), rate of change, domain and range, and continuity.

Assessment limits:
• A coordinate graph will be given with easily read coordinates.
• “Zeros” refers to the x-intercepts of a graph, “roots” refers to the solution of an equation in the form p(x) = 0.
• Problems will not involve a real-world context.

Expectation 1.2

The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

Indicator

• 1.2.1 The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

Assessment limits:
• Functions are to have no more than two variables with rational coefficients.
• Linear equations will be given in the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
• Vertical lines are included.
• The majority of these items should be in real-world context.

Indicator

• 1.2.2 The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

Assessment limits:
• Inequalities will have no more than two variables with rational coefficients.
• Acceptable forms of the problem or solution are the following:
Ax + By < C, Ax + By < C, Ax + By > C, Ax + By > C, Ax + By + C < 0, Ax + By + C < 0, Ax + By + C > 0, Ax + By + C > 0, y < mx + b, y < mx + b, y > mx + b, y > mx + b, y < b, y < b, y > b, y > b, x < b, x < b, x > b, x > b, a < x < b, a < x < b, a < x < b, a < x < b, a < x + c < b, a < x + c < b, a < x + c < b, a < x + c < b.
• The majority of these items should be in real-world context.
• Systems of linear inequalities will not be included.
• Compound inequalities will be included.
• Disjoint inequalities will not be included.
• Absolute value inequalities will not be included.

Indicator

• 1.2.3 The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

Assessment limits:
• Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
• All coefficients will be rational.
• Vertical lines will be included.
• Systems of linear functions will include coincident, parallel, or intersecting lines.
• The majority of these items should be in real-world context.

Indicator

• 1.2.4 The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.

Assessment limits:
• The problem is to be in a real-world context.
• The function will be represented by a graph.
• The equation of the function may be given.
• The features of the graph may include maxima/minima, zeros (roots), rate of change over a given interval (increasing/decreasing), continuity, or domain and range.
• “Zeros” refers to the x-intercepts of a graph, “roots” refers to the solution of an equation in the form p(x) = 0.
• Functions may include step, absolute value, or piece-wise functions.

Indicator

• 1.2.5 The student will apply formulas and/or use matrices (arrays of numbers) to solve real-world problems.

Assessment limits:
• Formulas will be provided in the problem or on the reference sheet.
• Formulas may express linear or non-linear relationships.
• The students will be expected to solve for first degree variables only.
• Matrices will represent data in tables.
• Matrix addition, subtraction, and/or scalar multiplication may be necessary.
• Inverse and determinants of matrices will not be required.

Goal 3 Data Analysis And Probability

The student will demonstrate the ability to apply probability and statistical methods for representing and interpreting data and communicating results, using technology when needed.

Expectation 3.1

The student will collect, organize, analyze, and present data.

Indicator

• 3.1.1 The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

Assessment limits:
• The student will design investigations stating how data will be collected and justify the method.
• Types of investigations may include: simple random sampling, representative sampling, and probability simulations.
• Probability simulations may include the use of spinners, number cubes, or random number generators.
• In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations.

Indicator

• 3.1.2 The student will use the measures of central tendency and/or variability to make informed conclusions.

Assessment limits:
• Measures of central tendency include mean, median, and mode.
• Measures of variability include range, interquartile range, and quartiles.
• Data may be displayed in a variety of representations which may include: frequency tables, box and whisker plots, and other displays.

Indicator

• 3.1.3 The student will calculate theoretical probability or use simulations or statistical inference from data to estimate the probability of an event.

Assessment limits:
• This indicator does not include finding probabilities of dependent events.

Expectation 3.2

The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations.

Indicator

• 3.2.1 The student will make informed decisions and predictions based upon the results of simulations and data from research.

Indicator

• 3.2.2 The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.

Assessment limits:
• Items should include a definition of the data and what it represents.
• Data will be given when a line of best fit is required.
• Equation or graph will be given when a curve of best fit is required.

Indicator

• 3.2.3 The student will communicate the use and misuse of statistics.

Assessment limits:
• Examples of “misuse of statistics” include the following:
• misuse of scaling on a graph
• misuse of measures of central tendency and variability to represent data,
• using three-dimensional figures inappropriately
• using data to sway interpretation to a predetermined conclusion
• using incorrect sampling techniques
• using data from simulations incorrectly
• predicting well beyond the data set.