School Improvement in Maryland

Using the Core Learning Goals: Mathematics

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CLG Toolkit

Tools aligned to CLG expectations and/or indicators.

  • Skill Statements
    Describes how a student demonstrates an understanding of an indicator
  • Public Release Items
    HSA items and annotated student responses as appropriate
  • Lesson Plans
    Written by Maryland educators for teaching the concepts
Functions & Algebra

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 limit:

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.