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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

## 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 = x
^{2}+ c (simple quadratic), y = x^{3}+ 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), x^{2} (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.