Minnesota High School MCA-II, GRAD & MCA-Modified
Minnesota High School MCA-II, GRAD & MCA-Modified
2003 Math Strands & Standards
STRAND / SUBSTRAND/STANDARD9.I
Mathematical Reasoning / 9.I.-
Apply skills of mathematical representation, communication & reasoning throughout the remaining content standards.
9.II
Number Sense, Computation & Operations / 9.II.A Number Sense
Use real number, represented in a variety of ways, to quantify information & to solve real-world & mathematical problems.
9.II.B Computation & Operations
Appropriately use calculators & other technologies to solve algebraic, geometric, probabilistic & statistical problems.
9.III
Patterns, Functions & Algebra / 9.III.A Patterns & Functions
Represent & analyze real-world & mathematical problems using numeric, graphic & symbolic methods for a variety of functions.
9.III.B Algebra (Algebraic Thinking)
Solve simple equations & inequalities numerically, graphically, & symbolically. Use recursion to model & solve real-world & mathematical problems.
9.IV
Data Analysis, Statistics & Probability / 9.IV.A Data & Statistics
Represent data & use various measures associated with data to draw conclusions & identify trends. Understand the effects of display distortion & measurement error on the interpretation of data.
9.IV.B Probability
Use appropriate counting procedures, calculate probabilities in various ways and apply theoretical probability concepts to solve real-world and mathematical problems.
9.V
Spatial Sense, Geometry & Measurement / 9.V.A Spatial Sense
Use models to represent and understand two- and three-dimensional shapes and how various motions affect them. Recognize the relationship between different representations of the same shape.
9.V.B Geometry
Apply basic theorems of plane geometry, right triangle trigonometry, coordinate geometry and a variety of visualization tools to solve real-world and mathematical problems.
9.V.C Measurement
Use the interconnectedness of geometry, algebra and measurement to explore real-world and mathematical problems.
High School—Mathematical Reasoning Strand
with MCA-II, GRAD & MCA-Modified Test Specifications
2003 MN Math Standard to Benchmarks
SUBSTRAND / STANDARD / BENCHMARK9.I
Mathematical Reasoning / 9.I.-
Apply skills of mathematical representation, communication & reasoning throughout the remaining content strands. / 9.I.-.1
Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of solutions in a given context & rejecting extraneous solutions.
9.I.-.2
Appropriately use examples & counterexamples to make & test conjectures, justify solutions, & explain results.
9.I.-.3
Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically & interpret the result in the original context.
9.I.-.4
Support mathematical results by explaining why the steps in a solution are valid & why a particular method is appropriate.
9.I.-.5
Determine whether or not relevant information is missing from a problem & if so, decide how to best express the results that can be obtained without that information.
9.I.-.6
Know & use the relationship that exists among a logical implication of the form “if A, then B,” its converse “if B, then A,” its inverse “if not A, then not B,” & its contrapositive “if not B, then not A.”
High School—Number Sense, Computation & Operations
with MCA-II, GRAD & MCA-Modified Test Specifications
2003 MN Math Standard to Benchmarks
(GRAD 5-8 items)
*Item Type—Multiple Choice (MC) or Gridded Response (GR)
*Cognitive Levels—Knowing (A), Understanding (B), Application, Analysis Synthesis & Evaluation (C)
* Calculator Use—Item appears in calculator section of assessment (CL), Calculator Neutral, item appears in either section of assessment (CN)
SUBSTRAND / STANDARD / * / BENCHMARK9.II.A
Number Sense / 9.II.A
Use real numbers, represented in a variety of ways, to quantify information & to solve real-world & mathematical problems. / MC/GR
ABC
CL / 9.II.A.-
N/A
· These benchmarks are continued from grade 8 & embedded in algebra, probability & geometry in grade 11.
9.II.B
Computation & Operations
GRAD
5-8 items / 9.II.B
Appropriately use calculators & other technologies to solve algebraic, geometric, probabilistic & statistical problems. / MC/GR
ABC
CL / 9.II.B.1
Apply the correct order of operations & grouping symbols when using calculators & other technologies.
MCA-II
· This benchmark is assessed in grade 8
· It is embedded in other grade 11 items
9.II.B.2
Know, use & translate calculator notational conventions to mathematical notation.
MCA-II
· Assessed only at the classroom level
MC/GR
ABC
CL / 9.II.B.3
Recognize the impact of units such as degrees & radians on calculations.
MCA-II
· This benchmark is embedded in grade 11 items from Strand V
9.II.B.4
Recognize that applying an inverse function with a calculator may lead to extraneous or incomplete solutions.
MCA-II
· Assessed only at the classroom level
9.II.B.5
Understand the limitations of calculators such as missing or additional features on graphs due to viewing parameters or misleading representations of zero or very large numbers.
MCA-II
· Assessed only at the classroom level
9.II.B.6
Understand that use of a calculator requires appropriate mathematical reasoning & does not replace the need for mental computation.
MCA-II
· Assessed only at the classroom level
MC
CL
GRAD
2-3 items / 9.II.B.G7
Students will apply the correct order of operations to simplify & evaluate numeric expressions.
GRAD
· Items must use positive rational numbers
· Items will use addition, subtraction, multiplication, division & grouping symbols only
· Fraction denominators are limited to 2, 3, 4, 5, 6, 8, 10 & 12
· Subtraction cannot be a mixed number minus a mixed number requiring regrouping (e.g., is not acceptable)
· Multiplication may be expressed as a raised dot, x, or ( ) (e.g., )
· Division may be expressed using division symbol or fraction bar (e.g., or )
· Division items must have a whole number divisor
· For multiplication & division items, mixed numbers must be expressed as improper fractions
· No nested grouping symbols are allowed (e.g., is not allowed)
· Items may require the identification of the correct order of operations shown (calculation not required)
· Items may require integer approximations of square roots of positive numbers
· Items may include exponents
· Problems may include context
MC
CL
GRAD
0-1 items / 9.II.B.G8
Students will use rational numbers in complex ways to solve multi-step real-world & mathematical problems.
GRAD
· Rationals are limited to positive rationals
· Non-integer rationals will be represented in decimal form
· Items may require integer approximations of square roots of positive integers
· Squares must be less than or equal to 150
MC
CL
GRAD
1-2 items / 9.II.B.G9
Students will use fractions, decimals & percents in multiple representations for estimation & computation to solve real-world & mathematical problems.
GRAD
· Fraction denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25 & 100. Restrictions on denominators apply to problem and answer options (e.g., 1/3 + 1/5 is not allowed; 1/15 – 1/3 is not allowed)
· Items may include positive & negative fractions, decimals & percents
MC
CL
GRAD
2-3 items / 9.II.B.G10
Students will use proportional reasoning to solve real-world & mathematical problems.
GRAD
· Items may involve:
· rates
· scale drawings & maps
· similar figures
· ratio
· unit pricing
· showing how changing one or more dimensions affect change in area
· Shapes are limited to circles, parallelograms & triangles
· Items are limited to two-dimensional figures
· Pictures or diagrams may be used but are note required
· Similarity may be shown using similarity symbol () or using markings on figures
· Items may include context
High School—Patterns, Functions & Algebra
with MCA-II, GRAD & MCA-Modified Test Specifications
2003 MN Math Standard to Benchmarks
(MCA-II 19-21 items)
(GRAD 12-19 items)
(MCA-Modified 16-18 items)
*Item Type—Multiple Choice (MC) or Gridded Response (GR)
*Cognitive Levels—Knowing (A), Understanding (B), Application, Analysis Synthesis & Evaluation (C)
* Calculator Use—Item appears in calculator section of assessment (CL), Calculator Neutral, item appears in either section of assessment (CN)
SUBSTRAND / STANDARD / * / BENCHMARK9.III.A
Patterns & Functions
MCA-II
7-9 items
GRAD
5-7 items
MCA-M
6-7 items / 9.III.A
Represent & analyze real-world & mathematical problems using numeric, graphic & symbolic methods for a variety of functions. / MC
ABC
CL
MCA-II/ GRAD
1-2 items
MCA-M
1-2 items / 9.III.A.1
Students will know the numeric, graphic & symbolic properties of linear, step, absolute value & quadratic functions.
MCA-II/MCA-M
· Items may include rates of change, intercepts, maxima & minima
· Items may include intersection between two graphs
· Step functions must model real-world situations
· Step functions will not be represented symbolically
GRAD
· Items may not include step or absolute value functions
· Items may include rates of change & intercepts
· Items that assess quadratics are limited to graphical properties
· Increments of x & y axes must be integers
MC
ABC
CL
MCA-II/ GRAD
1-2 items
MCA-M
1-2 items / 9.III.A.2
Students will model exponential growth & decay.
MCA-II/MCA-M
· Models may be numeric, graphic & symbolic
· When calculation is required, exponents must be integers
· Items may have real-world context (e.g., bacterial growth, half-life, compound interest)
GRAD
· Models may be numeric or graphic
· Items may have real-world context (e.g., bacterial growth, half-life, compound interest)
MC
ABC
CL
MCA-II
1-2 items
MCA-M
1-2 items / 9.III.A.3
Students will analyze the effects of coefficient changes on linear & quadratic functions & their graphs.
MCA-II/MCA-M
· Changes to coefficients in are limited to a & c
MC/GR
ABC
CL
MCA-II/ GRAD
1-2 items
MCA-M
1-2 items / 9.III.A.4
Students will apply basic concepts of linear, quadratic & exponential expressions or equations in real-world problems.
MCA-II/MCA-M
· Exponents must be integers
GRAD
· Items will be limited to linear & exponential
· Expressions & equations must be able to be solved numerically. Table or graph required
· Items will not require expressions or equations to be solved symbolically
MC
A
CN
MCA-II
1-2 items
MCA-M
1-2 items / 9.III.A.5
Students will distinguish functions from other relations using graphic & symbolic methods.
MCA-II/MCA-M
· Not more than 10 increments on either side of axes
MC
CL
GRAD
1-2 items / 9.III.A.G6
Students will generate a table of values from a formula or equation. Students will graph the result of a formula or linear equations in ordered pair format on a grid.
GRAD
· x & y axes may have different scales
· items do not require students to graph or generate a table of a non-linear relation
· formulas will only have unknowns to the first degree
· items may not require generating a linear equation from a table of values
· items may include real-world context (e.g., converting temperature)
· given a continuous (i.e., individual points not indicated) linear graph, student will generate a table of values
· linear equations will be given in form
MC
CL
GRAD
1-2 items / 9.III.A.G7
Students will translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically & interpret the result in the original context.
GRAD
· items may include real-world context
9.III.B
Algebra (Algebraic Thinking)
MCA-II
12-14 items
GRAD
7-12 items
MCA-M
10-11 items / 9.III.B
Solve simple equations & inequalities numerically, graphically & symbolically. Use recursion to model & solve real-world & mathematical problems. / MC
A
CN
MCA-II/ GRAD
1-2 items
MCA-M
1-2 items / 9.III.B.1
Students will translate among equivalent forms of expressions.
MCA-II/MCA-M
· Items may include:
· simplifying algebraic expressions involving nested pairs of parentheses & brackets
· simplifying rational expressions
· factoring a common monomial term from an expression
· applying associative, commutative & distributive laws
· A simplified expression should contain, at most, four terms with, at most, two variables per term
GRAD
· Items may include:
· simplifying algebraic expressions involving nested pairs of parentheses & brackets
· simplifying rational expressions
· factoring a common monomial term from an expression
· applying associative, commutative & distributive laws
· When applying distributive law, expressions may not contain 2 binomials
· Expressions may not include nested pairs of parentheses or brackets
· A simplified expression should contain at most two terms with at most one variable per term
MC
AB
CN
MCA-II
1-2 items
MCA-M
1-2 items / 9.III.B.2
Students will understand the relationship between absolute value & distance on the number line. Students will graph simple expressions involving absolute value.
MCA-II/MCA-M
· At most, one absolute value on each side of the equation or inequality
· Absolute values will be in the form of (e.g., or )
MC
AB
CN
MCA-II/ GRAD
1-2 items
MCA-M
1-2 items / 9.III.B.3
Students will find equations of a line.
MCA-II/MCA-M
· Items will provide two points on the line, a point & the slope of the line or the slope & y-intercept of the line
· All answer options will be given in the same form within a MC item, either slope-intercept () or standard form ()
GRAD
· Items may require the student to generate the equation from the graph or identify the graph given the equation
· Items will provide the slope & y-intercept of the line, when graph is not provided
· Equations must be presented in slope-intercept form
MC
AB
CN
MCA-II
1-2 items
MCA-M
1-2 items / 9.III.B.4
Students will translate among equivalent forms of linear equations & inequalities.
MCA-II/MCA-M
· Translating may require simplification (e.g., translates to )
· Equivalent forms may be slope-intercept, standard or two-point
· All answer options will be given in the same form within a MC item, either slope-intercept () or standard form ()
MC
ABC
CN
MCA-II
2-3 items
MCA-M
1-2 items / 9.III.B.5
Students will use a variety of models to represent functions & patterns in real-world & mathematical problems.