Elementary Education K–6
Subtest 4: Mathematics (604)

Test Competencies and Skills Worksheet

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Competency 1—Knowledge of integers, decimals, and fractions in base-10

  • Approximate Percentage of Total Subtest Questions: 29%
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This section of the worksheet allows users to map the test competencies and skills to the curriculum by entering up to six courses in the course name fields, and checking the boxes if the content of the course covers the information described by the test skills in the rows below.
Skills Course 1:
 Course 2:
 Course 3:
 Course 4:
 Course 5:
 Course 6:
1. Apply concepts of prime and composite numbers, multiples, and factors in performing arithmetic operations with integers and fractions.
2. Identify and apply arithmetic strategies based on place value (e.g., composing, decomposing, regrouping, compensating) to perform multidigit operations.
3. Compare integers, decimals, and fractions (e.g., integers and positive fractions with positive exponents, rounding) and identify their positions on a number line.
4. Apply the four arithmetic operations to solve problems involving integers, decimals, fractions, and percentages, represented by visual models, equations, and algorithms.
5. Identify and apply strategies for building fluency with addition, subtraction, and multiplication of multidigit whole numbers (e.g.,  visual models, partial sums and products, arrays and area models, compensation, inverse relationship between addition and subtraction and between multiplication and division).
6. Select appropriate representations (e.g., number line, area, set model) for problems or solutions involving fractions.
Notes on Competency 1:

Competency 2—Knowledge of algebraic reasoning

  • Approximate Percentage of Total Subtest Questions: 15%
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Check this box if the course listed above covers the content described by this skill
Check this box if the course listed above covers the content described by this skill
This section of the worksheet allows users to map the test competencies and skills to the curriculum by entering up to six courses in the course name fields, and checking the boxes if the content of the course covers the information described by the test skills in the rows below.
Skills Course 1:
 Course 2:
 Course 3:
 Course 4:
 Course 5:
 Course 6:
1. Interpret and extend multiple representations of numerical patterns and linear relationships represented by tables, graphs, equations, expressions, and verbal descriptions.
2. Select an algebraic expression, equation, or inequality that represents a real-world situation.
3. Apply operations (e.g., associative, commutative, distributive properties) and the properties of equality to solve single-variable equations and inequalities, and determine whether two algebraic expressions are equivalent.
4. Apply the concept of substitution to evaluate algebraic expressions with integer coefficients (e.g., expressions with exponents, expressions with nested parentheses).
5. Analyze and apply methods (e.g., models, estimation, reasonableness of solutions) to solve mathematical and real-world multistep problems (e.g., fractions, decimals, interpreting remainders within context) involving any of the four arithmetic operations.
6. Solve mathematical and real-world problems involving comparisons, mixtures, measurement conversions, percentages, rates and unit rates, using ratios to represent relationships between numerical quantities.
Notes on Competency 2:

Competency 3—Knowledge of measurement, data analysis, and statistics

  • Approximate Percentage of Total Subtest Questions: 14%
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Check this box if the course listed above covers the content described by this skill
This section of the worksheet allows users to map the test competencies and skills to the curriculum by entering up to six courses in the course name fields, and checking the boxes if the content of the course covers the information described by the test skills in the rows below.
Skills Course 1:
 Course 2:
 Course 3:
 Course 4:
 Course 5:
 Course 6:
1. Calculate and evaluate the appropriateness of statistical measures of central tendency and variability based on real-world context and the shape of the data distribution.
2. Analyze and interpret rational number data presented in various ways (i.e., stem-and-leaf plots, box plots, line plots, histograms, tables, bar graphs, circle graphs).
3. Convert standard measurement units within the same measurement system (e.g., metric, U.S. customary) to solve single- and multi-step, mathematical, and real-world problems.
4. Select appropriate units to solve problems involving measurement and estimation of time, money, distance, volume, mass/weight, and temperature.
Notes on Competency 3:

Competency 4—Knowledge of geometric concepts

  • Approximate Percentage of Total Subtest Questions: 15%
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Check this box if the course listed above covers the content described by this skill
Check this box if the course listed above covers the content described by this skill
Check this box if the course listed above covers the content described by this skill
This section of the worksheet allows users to map the test competencies and skills to the curriculum by entering up to six courses in the course name fields, and checking the boxes if the content of the course covers the information described by the test skills in the rows below.
Skills Course 1:
 Course 2:
 Course 3:
 Course 4:
 Course 5:
 Course 6:
1. Apply geometric properties and relationships to solve real-world problems involving perimeter and area of triangles and quadrilaterals (e.g., figures that can be decomposed into triangles and quadrilaterals; figures with decimal, fractional, or unknown side lengths).
2. Apply geometric properties and relationships to solve real-world problems involving volume and surface area of right rectangular prisms and right rectangular pyramids using nets and volume of right rectangular prisms (e.g., figures with decimal, fractional, or unknown side lengths, decomposing figures into right rectangular prisms and pyramids).
3. Select ordered pairs of rational numbers, and determine the perimeter and area of rectangles plotted on the coordinate plane by calculating distances between two points with a common coordinate.
4. Classify attributes (e.g., number of sides, lengths of sides, right angles, lines of symmetry) of 2D figures in a hierarchy based on mathematical properties (e.g., a rectangle is also a trapezoid).
5. Classify attributes (e.g., number of faces, lengths of edges, straight or curved edges) of 3D figures (e.g., prisms, pyramids, cylinders, spheres), using mathematical terms (e.g., faces, edges, vertices).
6. Identify and evaluate angles (e.g., the use of the additive property of angle measure to determine unknown angle measures) and relationships between lines, using mathematical terminology (e.g., acute, obtuse, straight, reflex, parallel, perpendicular).
Notes on Competency 4:

Competency 5—Knowledge of student reasoning and instructional practices

  • Approximate Percentage of Total Subtest Questions: 27%
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Check this box if the course listed above covers the content described by this skill
Check this box if the course listed above covers the content described by this skill
Check this box if the course listed above covers the content described by this skill
Check this box if the course listed above covers the content described by this skill
This section of the worksheet allows users to map the test competencies and skills to the curriculum by entering up to six courses in the course name fields, and checking the boxes if the content of the course covers the information described by the test skills in the rows below.
Skills Course 1:
 Course 2:
 Course 3:
 Course 4:
 Course 5:
 Course 6:
1. Identify and apply appropriate mathematical concepts, procedures, skills, and professional vocabulary to evaluate student work.
2. Analyze and interpret individual student mathematics assessment data (e.g., diagnostic, formative, progress monitoring, summative) to guide instructional decisions and differentiate instruction.
3. Select and analyze instructional methods and tools, including technology (e.g., interactive whiteboards, computers), for small and large groups of students according to the cognitive complexity of a task and students’ needs.
4. Analyze learning progressions to demonstrate how students’ mathematical knowledge and skills develop over time among concrete, representational, and abstract modes of understanding.
5. Distinguish among the stages of students’ mathematical fluency (i.e., exploration, procedural reliability, procedural fluency) and recognize the role played by automaticity in each of those stages.
6. Identify and apply the use of mathematical thinking (e.g., use of patterns, structures, real-world contexts, and multiple representations; assessing the reasonableness of solutions).
7. Identify and apply instructional methods to reinforce connections between mathematical topics within a grade level, across subject areas within a grade level, and the progression of mathematical topics from one grade level to the next.
8. Identify and apply appropriate instructional strategies for problem solving (e.g., drawing a picture, making a table, acting it out, writing an expression or equation).
Notes on Competency 5:

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