# Using the State Curriculum: Algebra/Data Analysis, High School

## State Curriculum TOOLKIT

Tools aligned to State Curriculum expectations.

Additional Topics is content that may be appropriate for the curriculum but is not included in the Core Learning Goals.
• Skill Statements
Describes how a student demonstrates an understanding of an indicator
 Goal 1 Goal 3

## Goal 1

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

##### Indicators
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
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.
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.
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

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

##### Indicators
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.
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.
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.
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.
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.

June 2007