Iowa K-12 Core Content Standards and Benchmarks Corresponding to the Iowa Tests: Math Content Standards	NAEP Grade 8 Mathematics Format: Contains both selected response and constructed response items (NAGB, not dated)		ITBS Level 14 Mathematics Total comprised of two subtests: Math Concepts and Estimation Skills (49 questions) and Math Problem Solving and Data Interpretation Skills (32 questions) Format: Contains selected response items only (ITP, 2003)		ICAM: Eighth-Grade Mathematics includes 7 modules: Problem-Solving Strategies and Process; Number Concepts and Operations; Measurement; Geometry; Data Interpretation, Statistics, and Probability; Patterns, Functions, and Algebra; Solving Work-Related Math Problems Format: Contains both selected response and constructed response items (ICM, 2003)		ITBS Constructed Response Supplement: Thinking about Mathematics, Level 14 Format: Contains constructed response items only (ITP, not dated)
A. Students can understand and apply a variety of math concepts.	Number Sense, Properties, and Operations	25%-60%	Number Properties and Operations	15 questions	Number Concepts and Operations	18 points	Concepts/Estimation	11 questions
	Relate counting, grouping, and place value -Use place value to model and describe whole numbers and decimals -Use scientific notation in meaningful contexts		Represent, compare, and order numbers (4 questions) Describe and apply properties of number (5 questions) Use place value and write numbers in expanded and exponential form (1 question)		Understands basic number concepts associated with the rational number system (Number Concepts and Operations, 3-4 points) Understands the characteristics and uses of roots, exponents, and scientific notation and the relationships among them and their equivalent representations (Number Concepts and Operations, 2 points)
	Represent numbers and operations in a variety of equivalent forms using models, diagrams, and symbols - Model numbers using number lines -Use two- and three-dimensional region models to describe numbers -Use other models as appropriate -Read write, rename, order, and compare numbers
	Compute with numbers (that is, add, subtract, multiply, divide) -Apply basic properties of operations -Describe features of algorithms -Select appropriate computation method		Classify numbers by divisibility (2 questions) Perform operations (3 questions)		Understands the properties of operations with rational numbers and the correct order of operations for performing arithmetic computations (Number Concepts and Operations, 1-2 points)
A1. Understand and apply number properties and operations. B. Students can understand and apply methods of estimations. C. Students can solve a variety of math problems.	Use computation and estimation in applications -Round whole numbers, decimals, and fractions in meaningful contexts -Make estimates appropriate to a given situation -Select appropriate method of estimation -Solve application problems involving numbers and operations using exact answers or estimates as appropriate -Interpret round-off errors using calculators/computers -Verify solutions and determine the reasonableness of results		Estimation Use standard rounding (3 questions) Use order of magnitude (2 questions) Use number sense (7 questions) Problem Solving Multiple-step (14 questions) Approaches and Procedures Identify insufficient information (2 questions) Choose solution methods (3 questions)	12 questions 14 questions 5 questions	Solves problems using number concepts (Number Concepts and Operations, 6 points) Problem-Solving Strategies and Process Understands the relationship between the language of mathematics and real-word situations (Problem-Solving Strategies and Process, 2-3 points) Uses strategies to understand and solve problems (Problem-Solving Strategies and Process, 8-9 points) Identifies relevant, irrelevant, and missing information needed to solve the problems (Problem-Solving Strategies and Process, 3 points) Uses informal deductive reasoning and inductive reasoning to justify reasoning process and methods of solutions to problems (Problem-Solving Strategies and Process, 6 points) Solving Work-Related Math Problems Solves work-related mathematics problems using a variety of mathematical concepts and computations (Solving Work-Related Math Problems (20 points)	20 points 20 points	Problem Solving/Data Interpretation/Reasoning	13 questions
	Apply ratios and proportional thinking in a variety of situation -Use ratios to describe situations -Use proportions to model problems -Use Proportional thinking to solve problems -Understand the meaning of percentage -Solve problems involving percentages				Understands the concepts of fraction, ratio, proportion, and percent and the relationships among them and their equivalent representations (Number Concepts and Operations, 5 points)
	Use elementary number theory -Describe odd and even numbers and their characteristics -Describe number patterns -Use factors and multiples to model and solve problems -Describe prime numbers -Use divisibility and remainders in problem settings (including simple modular arithmetic)
A4. Students can understand and apply concepts of measurement.	Measurement	15%	Measurement	4 questions	Measurement	18 points
	Estimate the size of an object with respect to a given measurement attribute (e.g., length or perimeter).
	Select and use appropriate measurement instruments such as ruler, meter stick, clock, thermometer, or other scaled instruments.				Uses measurement tools appropriately for given situations (Measurement, 1-2 points)
	Select and use appropriate units of measurement according type and size of unit		Measure length/distance, time, temperature, weight, mass, and volume (2 questions) Identify and use appropriate units of measurement (1 question)		Understands the relationships among linear dimensions, area, and volume, uses appropriate units of measure, and solves problems involving units of measurement and converts units as appropriate (Measurement, 4 points)
	Estimate, calculate or compare perimeter, area, volume, and surface area in meaningful contexts to solve mathematical and real-world problems -Solve problems involving perimeter and area -Solve problems involving volume and surface area		Apply concepts of perimeter, area, and volume (Geometry, 2 questions) Estimate measurements with appropriate precision (1 question)		Solves problems involving perimeter, area, and volume of geometric shapes (Measurement, 6-7 points) Estimates quantities and measurements (Measurement, 2 points)
	Apply given measurement formulas for perimeter, area, volume, and surface area in problem settings
	Convert from one measurement to another within the same system
	Determine precision, accuracy, and error -Apply significant digits in meaningful contexts -Determine appropriate size of unit of measurement in problem situation -Apply concepts of accuracy of measurement in problem situations -Apply absolute and relative error in problem situations
	Make and read scale drawings
	Select appropriate methods of measurement (such as direct or indirect)
	Apply the concept of rate to measurement situations				Understand the basic concept of rate as a measure (Measurement, 4 points)
A3. Students can understand and apply concepts of geometry.	Geometry	20%	Geometry	6 questions	Geometry	20 points
	Describe, visualize, draw, and construct geometric figures -Draw or sketch a figure given a verbal description (open-ended items) -Given a figure, write a verbal description of its geometric qualities		Identify, classify and compare geometric figures (2 questions)		Understands the properties of lines, angles, planes, and two- and three-dimensional figures and knows geometric language for describing and naming them (Geometry, 6-7 points)
	Investigate and predict results of combining, subdividing, and changing shapes
	Identify the relationship (congruence, similarity) between a figure and its image under a transformation -Use motion geometry -Use transofrmations				Understands the geometric concepts of similarity, congruency, and symmetry (Geometry, 2-3 points) Understands geometric transformations of figures (Geometry, 2 points)
	Describe the intersection of two or more geometric figures -two dimensional -Planar cross-section of a solid
	Classify figures in terms of congruence and similarity, and informally apply these relationships using proportional reasoning where appropriate
	Apply geometric properties and relationship in solving problems -Use concepts of “between,” “inside,” “on,” and “outside” -Use the Pythagorean relationship to solve problems -Apply properties of ratio and proportion with respect to similarity
	Establish and explain relationships involving geometric concepts -Make conjectures -Validate and justify conclusions and generalizations -Use informal induction and deduction		Describe geometric properties, patterns, and relationships (2 questions)
	Represent problem situations with geometric models and apply properties of figures in meaningful contexts to solve mathematical and real-world problems				Solves problems using properties of and relationships among geometric figures (Geometry, 2-4 points)
	Represent geometric figures and properties algebraically using coordinates and vectors -Use properties of lines to describe figures algebraically				Uses the x-y coordinate system to model and solve basic problems (Geometry, 6 points)
A5. Students can understand and apply concepts in probability and statistics.	Data Analysis, Statistics, and Probability	15%	Probability and Statistics