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Algebra I Mathematics– Evidence Statements

Overview of the Maryland Comprehensive Assessment Program (MCAP)

The MCAP includes a coherent set of summative mathematics assessments aligned to the Maryland College and Career Ready Standards for

Mathematics (MCCRSM). Students are required to take an MCAP mathematics assessment at the end of grades 3 – 8 and at the end of

the grain size of the evidence that the MCAP mathematics assessments will yield. Assessment items are designed to elicit evidence of a student’s

level of proficiency for each claim.

MCAP MATHEMATICS CLAIMS STRUCTURE

The student is college and career ready or is on track to being college and career ready in mathematics.

Content - The student solves problems related to all content of the grade/course related to the Standards for Mathematical Practice.

Reasoning - The student expresses grade/course level appropriate mathematical reasoning.

Modeling - The student solves real-world problems with a degree of difficulty appropriate to the grade/course.

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Type III items assess a student’s ability to apply their

understanding of mathematics when solving real-world

contextual problems.

Modeling

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The MCAP Mathematics Evidence Statements for the Content Sub-Claim are organized using the same structure as the Maryland College and

Career Ready Standards for Mathematics. The Algebra I, Geometry and Algebra II Content Evidence Statements are organized by Conceptual

Category, Domains, Clusters, and then Standards.

Evidence statements are provided for each standard to describe the type of evidence that a task addressing the standard should elicit. In some

cases, the standard clearly describes the type of evidence that an aligned task should elicit. The Evidence Statement for such standards will read “As

stated in the standard”. In cases where the wording of a standard does not adequately describe the type of evidence that should be elicited, the

Evidence Statement will attempt to better describe the type of evidence items should elicit. In cases where a standard is taught in both Algebra I

and Algebra II, the Evidence Statement and/or Item Specification will seek to describe how the items might differ between the two courses.

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Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a

Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol («).

The last column of each table found in the Content Sub-Claim Evidence Statement tables identifies whether items that assess a given standard will

allow the use of a calculator. The codes are identified in the Calculator Key below.

Calculator Key:

Y – Yes. A calculator will be available on the tool bar when this standard is assessed.

N – No. A calculator will NOT be available on the tool bar when this standard is assessed.

X – The calculator designation will be dependent on the task and will be determined as a Yes or No during content review.

The MCAP Mathematics Evidence Statements for the Modeling Sub-Claim have a different structure than the Content Evidence Statements. The

codes for the Modeling Evidence Statements begin with either A1, G or A2 that correspond to Algebra I, Geometry or Algebra II. The letter “M”

appears after the course designation in the code to indicate that the statement is a Modeling Evidence Statement. The Modeling Evidence

Statements may apply to both machine-scored and constructed response items, unless otherwise noted. Modeling items may align to any of the

content standards from a given course.

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These practice rest on important “processes and proficiencies” with longstanding importance in mathematics education.

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

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N.RN The Real Number System

N.RN.B Use properties of rational and irrational numbers.

N.RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is

irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Evidence Statement:

• Apply properties of rational and irrational numbers to identify rational and irrational numbers.

Clarification:

• Assess at the cluster level (for example, items may include addition, subtraction, and multiplication of irrational numbers).

• Simplification of radicals not required.

• Division of radicals not assessed.

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N.Q.A.1  Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in

formulas; choose and interpret the scale and the origin in graphs and data displays.

Evidence Statement:

• Determine an appropriate scale for a graph.

• Use dimensional analysis to convert units.

Clarifications:

• Items must have real-world context.

Calculator Code: Y

N.Q.A.2  Define appropriate quantities for the purpose of descriptive modeling.

*This standard is also taught in Algebra II*

• Select an appropriate quantity for a real-world context.

Not assessed. This is an instructional standard only.

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A.SSE.A Interpret the structure of expressions.

A.SSE.A.1  Interpret expressions that represent a quantity in terms of its real-world context.

1a. Interpret parts of an expression, such as terms, factors, and coefficients.

Note: (A.SSE.A.1a-1 focuses on linear, A.SSE.A.1a-2 focuses on quadratic, A.SSE.A.1a-3 focuses on exponential)

Evidence Statement:

• Interpret parts of linear, quadratic, or exponential expressions that represent a quantity in terms of real-world context.

Clarifications:

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• Limit to linear and quadratic functions.

equation 𝑓 ; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find

successive approximations. Include cases where and/or are linear, polynomial, rational, absolute value, exponential, and

*This standard is also taught in Algebra II*

Evidence Statement:

• Approximate the solutions to an equation of the form 𝑓 using the point(s) of intersection of the graphs of the

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• If the graphs of the two equations are provided with clearly identified points of intersection, then combinations of linear,

graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Evidence Statement:

Calculator Code: N

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F.IF.A Understand the concept of a function and use function notation.

F.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain

to the input x. The graph of f is the graph of the equation

Evidence Statement:

• As stated in the standard.

Clarifications:

• Items may require students to identify the domain and/or range of a function.

Calculator Code: X

F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a

real-world context.

Evidence Statement:

• As stated in the standard.

Evidence Statement:

• Identify a given sequence as arithmetic or geometric

• Match a given sequence to a given algebraic representation for the sequence.

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• Given a recursive or explicit rule, evaluate the expression to find the value for a specified term in the sequence

• Create an explicit function rule for a sequence.

• Limit sequences to simple arithmetic or geometric sequences.

F.IF.B Interpret functions that arise in applications in terms of the real-world context.

F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the

quantities, and sketch graphs showing key features given a verbal description of the relationship

*This standard is also taught in Algebra II*

• Limit items to linear, quadratic, square root functions, piecewise-defined (including step functions, and absolute-value

• Items may include determining and/or interpreting the slope/rate of change of a linear function from table or graph.

Calculator Code: X

F.IF.B. Relate the domain of a function to a graph and, where applicable, to the quantitative relationship it describes.

Evidence Statement:

• As stated in the standard.

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• Limit items to linear, quadratic, square root, piecewise-defined (including step functions, and absolute-value functions), and

• An item containing a graph, equation or verbal description is acceptable to assess this standard.

Estimate the rate of change from a graph.

*This standard is also taught in Algebra II*

Evidence Statement:

• As stated in the standard.

Clarifications:

• Items must have real-world context.

• Limit functions to linear, quadratic, and exponential functions.

• Limit exponential functions to those with integer domains.

Calculator Code: X

complicated cases.

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• As stated in the standard.

• N/A

• As stated in the standard.

Clarifications:

• N/A

Calculator Code: X

F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

8a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of

the graph, and interpret these in terms of a real-world context.

Evidence Statement:

• As stated in the standard.

Clarifications:

• Items must have real-world context.

*This standard is also taught in Algebra II*

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• As stated in the standard.

• Function types are limited to linear, quadratic, square root, cube root, piecewise-defined (including step functions and absolute

• Items may or may not have real world context.

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1a. Determine an explicit expression, a recursive process, or steps for calculation from a real-world context.

Note: (F.BF.A.1a-1 focuses on linear, F.BF.A.1a-2 focus on exponential, F.BF.A.1a-3 focus on quadratic)

*This standard is also taught in Algebra II*

Evidence Statement:

• Write a function based on an observed pattern in a real-world scenario.

Clarifications:

• Items must have real-world context.

• Limit to linear, quadratic and exponential functions with domains in the integers.

• Similar to creating a function from a scatterplot but for this standard the relationship between the two quantities is clear from

F.BF.B.3 Identify the effect on the graph of replacing by , , , and for specific values of k (both positive

• As stated in the standard.

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• Limit to linear and quadratic functions.

• Even and odd functions are not assessed In Algebra I.

• The experiment part of the standard is instructional only. This aspect of the standard is not assessed.

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1a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors

Clarifications:

1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Evidence Statement:

• Identify the relationship between two quantities in a given contextual situation where the rate of change over equal intervals

• Items must have real-world context.

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• Identify a correct method and justification given two or more chains of reasoning.

• Items may involve two or more steps in a single reasoning chain.

Clarifications:

• N/A

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• Express reasoning about transformations of functions.

• Content scope: F-BF.3 excluding even and odd functions.

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• Four items from this grouping will appear on each assessment.

• Items are 4 points per item.

• Calculators are allowed on all reasoning items.

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• Validate a given model and make improvement.

Clarifications:

• Limit to linear functions, linear inequalities, systems of linear equations or inequalities, quadratic functions, and exponential

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• Compare the result from a model with real world data.

• Limit to linear functions, linear inequalities, systems of linear equations or inequalities, quadratic functions, and exponential

Clarifications:

Clarifications:

A1.M.8 Evidence Statement:

Clarifications: