Florida Algebra 2 EOC: Solving Systems of Linear Equations and Function Notation, Exams of Algebra

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DRAFT

Algebra 2 EOC

Item Specifications

Florida Standards Assessments

The draft Florida Standards Assessments (FSA) Test Item Specifications

( Specifications) are based upon the Florida Standards and the Florida Course

Descriptions as provided in CPALMs. The Specifications are a resource that defines

the content and format of the test and test items for item writers and reviewers.

Each grade-level and course Specifications document indicates the alignment of

items with the Florida Standards. It also serves to provide all stakeholders with

information about the scope and function of the FSA.

Item Specifications Definitions

Also assesses refers to standard(s) closely related to the primary standard

statement.

Clarification statements explain what students are expected to do when

responding to the question.

Assessment limits define the range of content knowledge and degree of difficulty

that should be assessed in the assessment items for the standard.

Item types describe the characteristics of the question.

Context defines types of stimulus materials that can be used in the assessment

items.

Florida Standards Assessments

Mathematical Practices:

The Mathematical Practices are a part of each course description for Grades 3-8, Algebra 1,

Geometry, and Algebra 2. These practices are an important part of the curriculum. The

Mathematical Practices will be assessed throughout.

MAFS.K12.MP.1.1:

Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the

meaning of a problem and looking for entry points to its solution. They

analyze givens, constraints, relationships, and goals. They make

conjectures about the form and meaning of the solution and plan a

solution pathway rather than simply jumping into a solution attempt.

They consider analogous problems, and try special cases and simpler

forms of the original problem in order to gain insight into its solution.

They monitor and evaluate their progress and change course if

necessary. Older students might, depending on the context of the

problem, transform algebraic expressions or change the viewing window

on their graphing calculator to get the information they need.

Mathematically proficient students can explain correspondences

between equations, verbal descriptions, tables, and graphs or draw

diagrams of important features and relationships, graph data, and

search for regularity or trends. Younger students might rely on using

concrete objects or pictures to help conceptualize and solve a problem.

Mathematically proficient students check their answers to problems

using a different method, and they continually ask themselves, “Does

this make sense?” They can understand the approaches of others to

solving complex problems and identify correspondences between

different approaches.

MAFS.K12.MP.2.1:

Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their

relationships in problem situations. They bring two complementary

abilities to bear on problems involving quantitative relationships: the

ability to decontextualize—to abstract a given situation and represent it

symbolically and manipulate the representing symbols as if they have a

life of their own, without necessarily attending to their referents—and

the ability to contextualize, to pause as needed during the manipulation

process in order to probe into the referents for the symbols involved.

Quantitative reasoning entails habits of creating a coherent

Florida Standards Assessments

MAFS.K12.MP.3.1:

representation of the problem at hand; considering the units involved;

attending to the meaning of quantities, not just how to compute them;

and knowing and flexibly using different properties of operations and

objects.

Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated

assumptions, definitions, and previously established results in

constructing arguments. They make conjectures and build a logical

progression of statements to explore the truth of their conjectures. They

are able to analyze situations by breaking them into cases, and can

recognize and use counterexamples. They justify their conclusions,

communicate them to others, and respond to the arguments of others.

They reason inductively about data, making plausible arguments that

take into account the context from which the data arose.

Mathematically proficient students are also able to compare the

effectiveness of two plausible arguments, distinguish correct logic or

reasoning from that which is flawed, and—if there is a flaw in an

argument—explain what it is. Elementary students can construct

arguments using concrete referents such as objects, drawings, diagrams,

and actions. Such arguments can make sense and be correct, even

though they are not generalized or made formal until later grades. Later,

students learn to determine domains to which an argument applies.

Students at all grades can listen or read the arguments of others, decide

whether they make sense, and ask useful questions to clarify or improve

the arguments.

MAFS.K12.MP.4.1:

Model with mathematics.

Mathematically proficient students can apply the mathematics they

know to solve problems arising in everyday life, society, and the

workplace. In early grades, this might be as simple as writing an addition

equation to describe a situation. In middle grades, a student might apply

proportional reasoning to plan a school event or analyze a problem in

the community. By high school, a student might use geometry to solve a

design problem or use a function to describe how one quantity of

interest depends on another. Mathematically proficient students who

can apply what they know are comfortable making assumptions and

approximations to simplify a complicated situation, realizing that these

may need revision later. They are able to identify important quantities in

a practical situation and map their relationships using such tools as

diagrams, two-way tables, graphs, flowcharts and formulas. They can

analyze those relationships mathematically to draw conclusions. They

routinely interpret their mathematical results in the context of the

Florida Standards Assessments

MAFS.K12.MP.7.1:

Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or

structure. Young students, for example, might notice that three and

seven more is the same amount as seven and three more, or they may

sort a collection of shapes according to how many sides the shapes

have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7

× 3, in preparation for learning about the distributive property. In the

expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9

as 2 + 7. They recognize the significance of an existing line in a geometric

figure and can use the strategy of drawing an auxiliary line for solving

problems. They also can step back for an overview and shift perspective.

They can see complicated things, such as some algebraic expressions, as

single objects or as being composed of several objects. For example,

they can see 5 – 3(x – y)² as 5 minus a positive number times a square

and use that to realize that its value cannot be more than 5 for any real

numbers x and y.

MAFS.K12.MP.8.1:

Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated,

and look both for general methods and for shortcuts. Upper elementary

students might notice when dividing 25 by 11 that they are repeating

the same calculations over and over again, and conclude they have a

repeating decimal. By paying attention to the calculation of slope as they

repeatedly check whether points are on the line through (1, 2) with

slope 3, middle school students might abstract the equation (y – 2)/(x –

1) = 3. Noticing the regularity in the way terms cancel when expanding (x

• 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them

to the general formula for the sum of a geometric series. As they work

to solve a problem, mathematically proficient students maintain

oversight of the process, while attending to the details. They continually

evaluate the reasonableness of their intermediate results.

Florida Standards Assessments

Technology-Enhanced Item Descriptions:

The Florida Standards Assessments (FSA) are composed of test items that include traditional

multiple- choice items, items that require students to type or write a response, and

technology-enhanced items (TEI). Technology-enhanced items are computer-delivered items

that require students to interact with test content to select, construct, and/or support their

answers.

Currently, there are nine types of TEIs that may appear on computer-based assessments for

FSA Mathematics. For students with an IEP or 504 plan that specifies a paper-based

accommodation, TEIs will be modified or replaced with test items that can be scanned and

scored electronically.

For samples of each of the item types described below, see the FSA Training Tests.

Technology-Enhanced Item Types – Mathematics

1. Editing Task Choice – The student clicks a highlighted word or phrase, which reveals a

drop-down menu containing options for correcting an error as well as the highlighted

word or phrase as it is shown in the sentence to indicate that no correction is needed.

The student then selects the correct word or phrase from the drop-down menu. For

paper-based assessments, the item is modified so that it can be scanned and scored

electronically. The student fills in a circle to indicate the correct word or phrase.

2. Editing Task – The student clicks on a highlighted word or phrase that may be incorrect,

which reveals a text box. The directions in the text box direct the student to replace the

highlighted word or phrase with the correct word or phrase. For paper-based

assessments, this item type may be replaced with another item type that assesses the

same standard and can be scanned and scored electronically.

3. Hot Text –

a. Selectable Hot Text – Excerpted sentences from the text are presented in this

item type. When the student hovers over certain words, phrases, or sentences,

the options highlight. This indicates that the text is selectable (“hot”). The

student can then click on an option to select it. For paper- based assessments, a

“selectable” hot text item is modified so that it can be scanned and scored

electronically. In this version, the student fills in a circle to indicate a selection.

Florida Standards Assessments

Reference Sheets:

• Reference sheets and z-tables will be available as online references (in a pop-up window). A paper

version will be available for paper-based tests.

• Reference sheets with conversions will be provided for FSA Mathematics assessments in Grades

4–8 and EOC Mathematics assessments.

• There is no reference sheet for Grade 3.
• For Grades 4, 6, and 7, Geometry, and Algebra 2, some formulas will be provided on the reference

sheet.

• For Grade 5 and Algebra 1, some formulas may be included with the test item if needed to meet

the intent of the standard being assessed.

• For Grade 8, no formulas will be provided; however, conversions will be available on a reference

sheet.

• For Algebra 2, a z-table will be available.

Grade Conversions Some Formulas z-table

3 No No No

4 On Reference Sheet On Reference Sheet No

5 On Reference Sheet With Item No

6 On Reference Sheet On Reference Sheet No

7 On Reference Sheet On Reference Sheet No

8 On Reference Sheet No No

Algebra 1 On Reference Sheet With Item No

Algebra 2 On Reference Sheet On Reference Sheet Yes

Geometry On Reference Sheet On Reference Sheet No

Florida Standards Assessments MAFS.912.A-APR.1.1 Understand that polynomials form a system analogous to theintegers; namely, they are closed under the operations of addition, Also assesses subtraction, and multiplication; add, subtract, and multiplypolynomials. MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagoreantriples. Item Types Editing Task Choice– May require choosing steps in an informal argument. Equation Editor – May require creating a value or an expression. GRID – May require dragging and dropping graphics to construct a proof or ordering steps in a proof. Hot Text – May require ordering steps in a proof. Matching Item – May require matching equivalent expressions. Multiple Choice – May require selecting a value, an expression, or a statement from a list. Multiselect – May require selecting all equivalent expressions. Open Response – May require explaining the steps used in generating a polynomial identity. Clarifications Students will apply their understanding of closure to adding,subtracting, and multiplying polynomials. Students will add, subtract, and multiply polynomials with rationalcoefficients. Students will use polynomial identities to describe numerical relationships. Students will use the structure of algebra to complete an algebraicproof of a polynomial identity. Assessment Limits Items set in a real-world context should not result in a nonreal answerif the polynomial is solved. In items that require addition and subtraction, polynomials are limited to polynomials with no more than 5 terms. The simplifiedpolynomial should contain no more than 8 terms.

Florida Standards Assessments MAFS.912.A-APR.4.6 Rewrite simple rational expressions in different forms; writein the form q ( x ) + r ( x )/ b ( x ), where a ( x ), b ( x ), q ( x ), and r ( x ) are a ( x )/ b ( x ) polynomials with the degree ofinspection, long division, or, for the more complicated examples, a r ( x ) less than the degree of b ( x ), using Also assesses computer algebra system. MAFS.912.A-APR.2.2 Know and apply the Remainder Theorem: For a polynomial p ( x ) and a numberonly if ( x a – , the remainder on division by a ) is a factor of p ( x ). x – a is p ( a ), so p ( a ) = 0 if and Item Types Equation Editor – May require creating an expression or a value. GRID – May require dragging and dropping graphics to complete longdivision. Hot Text – May require completing long division. Multiple Choice – May require identifying an expression or a value. Multiselect – May require choosing factors from a list. Open Response – May require explaining what a value means. Clarifications Students will rewrite a rational expression as the quotient in the formof a polynomial added to the remainder divided by the divisor. Students will use polynomial long division to divide a polynomial by a polynomial. Students will use the Remainder Theorem to determine if ( x – a ) is a factor of a polynomial. Students will use the Remainder Theorem to determine theremainder of p ( x )/( x – a ). Assessment Limits The polynomial that is the dividend should have a degree no less than3 and no greater than 6. The polynomial that is the divisor should have a degree of 1, 2, or 3. In items that require the Remainder Theorem, the value of a in ( x – a ), the divisor, may be a rational number. Stimulus Attributes Items should be set in a mathematical context. Items may use function notation. Response Attribute Items may require the student to provide sub-steps to complete polynomial long division. Calculator No

Sample Item See Appendix for the practice test item aligned to group. a standard in this

Florida Standards Assessments

Florida Standards Assessments In items that require the student to solve literal equations andformulas, the term of interest may be quadratic, a cubic in a monomial term, a linear term in the denominator of rationalequation, a linear term in a square root equation, or a linear term as the base of an exponential equation with a rational number as thevalue for the exponent. For A-CED.1.4, items should not require more than six proceduralsteps to isolate the variable of interest. Items will not assess inequalities. Stimulus Attributes For A-CED.1.1 and A-CED.1.4, items should be set in a real-worldcontext. For A-REI.1.2, items may be set in a mathematical or real-world context. Items may use function notation. Items may require the student to choose and interpret units. Response Attributes For A-CED.1.1 and A-CED.1.4, items may require the student to apply the basic modeling cycle. Items may require the student to recognize equivalent expressions. Calculator Sample Item NeutralSee Appendix for the practice test item aligned to a standard in this group.

Florida Standards Assessments MAFS.912.A-CED.1. Also assesses MAFS.912.A-CED.1.

Also assessesMAFS.912.A-REI.3. Also assessesMAFS.912.A-REI.3.

Create equations in two or more variables to represent relationshipsbetween quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities and by systems ofequations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinationsof different foods. Solve systems of linear equations exactly and approximately (e.g., withgraphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. find the points of intersection between the line y = -3 x and the circle x² For example,

• y² = 3_._ Item Types Editing Task Choice variable. – May require choosing the correct definition of a Equation Editor – May require creating a set of equations, a set ofinequalities, or giving an ordered pair. GRID – May require graphing a representation of a set of equations, a set of inequalities, or an ordered pair, or selecting a solution region. Hot Text – May require selecting a solution or constraints. Multiple Choice – May require identifying an equation or a value from a list of four possible choices, identifying graphs, or identifyinginequalities. Multiselect – May require identifying equations or inequalities, orselecting constraints, or variable definitions. Open Response – May require defining a variable or interpreting a solution. Clarifications Students will identify the quantities in a real-world situation thatshould be represented by distinct variables. Students will write constraints for a real-world context usingequations, inequalities, a system of equations, or a system of inequalities. Students will write a system of equations given a real-world situation. Students will graph a system of equations that represents a real-worldcontext using appropriate axis labels and scale.

Florida Standards Assessments Items may require the student to graph a circle whose center is (0, 0). Items may require the student to choose and interpret units. Calculator Neutral Sample Item See Appendix for the practice test item aligned to a standard in thisgroup.

Florida Standards Assessments MAFS.912.A-REI.1.1 Explain each step in solving a simple equation as following from theequality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct aviable argument to justify a solution method. Item Types Editing Task Choice – May require correcting a step in an informalargument. Equation Editor – May require creating an expression. GRID – May require dragging and dropping steps, equations, and/or justifications to create a viable argument. Hot Text – May require rearranging equations or justifications. Multiple Choice – May require identifying expressions or statements. Open Response – May require creating a written response, justifying a solution method. Clarifications Students will complete an algebraic proof to explain steps for solvinga simple equation. Students will construct a viable argument to justify a solutionmethod. Assessment Limits Items should not assess linear equations. Items will not require the student to recall names of properties frommemory. Stimulus Attributes Items should be set in a mathematical context. Items may use function notation. Coefficients may be a rational number or a variable that represents Response Attributes any real number.Items may ask the student to complete steps in a viable argument. Items will not ask the student to provide the solution. Calculator No Sample Item See Appendix for the practice test item aligned to this standard.