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AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. PO 1. Make models that represent improper fractions. PO CLARIFICATION Match improper fractions to representative models. CONCEPT SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. 2. Identify symbols, words, or models that represent improper fractions. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 1 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. PO 3. Use improper fractions in contextual situations. PO CLARIFICATION At this grade level, this PO is defined as using word problems that do not require an operation. CONCEPT SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Micah had two whole pizzas cut into 6 equal pieces. He ate 4 pieces of pizza. What improper fraction represents the amount of pizza left? A 8 4 B C 6 2 8 6 D 12 4 Arizona Department of Education Page 2 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. 4. Compare two proper fractions or improper fractions with like denominators. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 3 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. 5. Order three or more unit fractions, proper or improper fractions with like denominators, or mixed numbers with like denominators. CONCEPT PO A unit fraction has a “1” as the numerator and any number as the 1 1 1 1 denominator (e.g., , , , ). 2 7 23 50 PO CLARIFICATION There are several ways to address this PO other than the suggested sample(s) presented here. SAMPLE MC ITEM Which of the following lists the mixed numbers in order from least to greatest? A 7 1 7 4 3 7 2 4 7 1 6 7 B 5 2 7 6 1 7 6 5 7 7 3 7 C 2 3 7 2 1 7 3 4 7 4 2 7 D 6 2 7 3 3 7 3 5 7 5 4 7 Arizona Department of Education Page 4 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. 6. Compare two whole numbers, fractions, and decimals (e.g., 1/2 to 0.6). CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. PO 7. Order whole numbers, fractions, and decimals. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Arizona Department of Education Page 5 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. 8. Determine the equivalency between and among fractions, decimals, and percents in contextual situations. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. The table below shows how much of a group report each student completed. Joe 25% Carrie 1/3 Ben 1/4 Ally 30% Who completed equal amounts of the report? A Ally and Joe B Joe and Ben C Carrie and Ben D Ally and Carrie Arizona Department of Education Page 6 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. 9. Identify all whole number factors and pairs of factors for a number. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. CONCEPT PO 10. Recognize that 1 is neither a prime nor a composite number. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 7 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT 1: Number Sense and Operations 1: Number Sense: Understand and apply numbers, ways of representing numbers, the relationships among numbers and different number systems. PO 11. Sort whole numbers (through 50) into sets containing only prime numbers or only composite numbers. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 8 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another 1. Select the grade-level appropriate operation to solve word problems. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another 2. Solve word problems using grade-level appropriate operations and numbers. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 9 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 3. Multiply whole numbers. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 4. Divide with whole numbers. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT CONCEPT Arizona Department of Education Page 10 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another 5. Demonstrate the distributive property of multiplication over addition. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Study the expression below. 5(10 + 2) Which of these is equivalent to the expression? A (5 + 10) × (5 + 2) B (5 × 10) × (5 × 2) C (5 × 10) + (5 × 2) D (5 + 10) + (5 + 2) Arizona Department of Education Page 11 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another 6. Demonstrate the addition and multiplication properties of equality. At this grade level, this PO is defined as demonstrating the addition and multiplication properties of equality as follows: PO CLARIFICATION If a = b, then a + c = b + c If a = b, then ac = bc SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 12 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another 7. Apply grade-level appropriate properties to assist in computation. PO CLARIFICATION At this grade level, this PO is defined as using associative and commutative properties. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 8. Apply the symbol “[ ]” to represent grouping. PO CLARIFICATION No clarification needed. CONCEPT SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 13 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 9. Use grade-level appropriate mathematical terminology. PO CLARIFICATION At this grade level, this PO is defined as using the terms quotient, divisor, sum, addend, product, factor, difference, etc. CONCEPT SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. In the equation below, identify which number is the divisor? 25 ÷ 6 = 4 R1 A 1 B 4 C 6 D 25 STRAND CONCEPT 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 10. Simplify fractions to lowest terms. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 14 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 11. Add or subtract proper fractions and mixed numbers with like denominators with regrouping. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another CONCEPT PO 12. Add or subtract decimals. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 15 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 13. Multiply decimals. PO CLARIFICATION No clarification needed SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another CONCEPT PO 14. Divide decimals. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. What is the value of the expression below? 242.2 ÷ 7 A 34.6 B 34 r6 C 340 r6 D 3.46 Arizona Department of Education Page 16 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT 1: Number Sense and Operations 2: Numerical Operations: Understand and apply numerical operations and their relationship to one another PO 15. Simplify numerical expressions using the order of operations with grade-appropriate operations on number sets. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 1: Number Sense and Operations CONCEPT 3: Estimation: Use estimation strategies reasonably and fluently. PO 1. Solve grade-level appropriate problems using estimation. PO CLARIFICATION At this grade level, this PO is defined as estimating to solve problems, using the four basic operations with whole numbers and decimals. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 17 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations CONCEPT 3: Estimation: Use estimation strategies reasonably and fluently. 2. Use estimation to verify the reasonableness of a calculation (e.g., “Is 4.1 x 2.7 about 12?”). PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 1: Number Sense and Operations CONCEPT 3: Estimation: Use estimation strategies reasonably and fluently. PO 3. Round to estimate quantities. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 18 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations CONCEPT 3: Estimation: Use estimation strategies reasonably and fluently. PO 4. Estimate and measure for area and perimeter. PO CLARIFICATION At this grade level, this PO is defined as either estimating or measuring either area or perimeter (i.e., estimate area, estimate perimeter, measure area, and measure perimeter). SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 19 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 1: Number Sense and Operations CONCEPT 3: Estimation: Use estimation strategies reasonably and fluently. 5. Compare estimated measurements between U.S. customary and metric systems (e.g., A yard is about a meter.). PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. PO 1. Formulate questions to collect data in contextual situations. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Arizona Department of Education Page 20 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. 2. Construct a double-bar graph, line plot, frequency table, or three-set Venn diagram with appropriate labels and title from organized data. CONCEPT PO PO CLARIFICATION At this grade level, this PO is defined as identifying correctly constructed graphic organizers based on given data. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 21 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. 3. Interpret graphical representations and data displays including bar graphs (including double-bar), circle graphs, frequency tables, three-set Venn diagrams, and line graphs that display continuous data. CONCEPT PO PO CLARIFICATION SAMPLE MC ITEM Arizona Department of Education At this grade level, this PO is defined as the ability to correctly read a display, and answer questions based on that display. There are several ways to address this PO other than the suggested sample(s) presented here. Page 22 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. 4. Answer questions based on graphical representations, and data displays including bar graphs (including double-bar), circle graphs, frequency tables, three-set Venn diagrams, and line graphs that display continuous data. CONCEPT PO PO CLARIFICATION SAMPLE MC ITEM Arizona Department of Education At this grade level, this PO is defined as the ability to perform mathematical operations based on data from a graphical representation; and answer questions based on the outcome of those operations. There are several ways to address this PO other than the suggested sample(s) presented here. Page 23 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. PO 5. Identify the mode(s) and mean (average) of given data. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Arizona Department of Education Page 24 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. PO 6. Formulate reasonable predictions from a given set of data. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Arizona Department of Education Page 25 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. PO 7. Compare two sets of data related to the same investigation. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. CONCEPT No sample available STRAND 2: Data Analysis, Probability, and Discrete Mathematics 1: Data Analysis (Statistics): Understand and apply data collection, organization and representation to analyze and sort data. PO 8. Solve contextual problems using graphs, charts, and tables. PO CLARIFICATION No clarification needed SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Arizona Department of Education Page 26 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. PO 1. Name the possible outcomes for a probability experiment. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Rick will spin the spinner shown below. 2 1 3 7 4 6 5 What is the possibility that the spinner will stop on an odd numbered space? A. certain B. impossible C. more likely to stop on an even number D. more likely to stop on an odd number Arizona Department of Education Page 27 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. 2. Describe the probability of events as being: • certain (represented by “1”), • impossible, (represented by “0”), or • neither certain nor impossible (represented by a fraction less than 1). PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 28 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. 3. Predict the outcome of a grade-level appropriate probability experiment. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 29 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. 4. Record the data from performing a grade-level appropriate probability experiment. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND CONCEPT PO 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. 5. Compare the outcome of an experiment to predictions made prior to performing the experiment. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 30 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. 6. Make predictions from the results of student-generated experiments using objects (e.g., coins, spinners, number cubes). PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 2: Data Analysis, Probability, and Discrete Mathematics 2: Probability: Understand and apply the basic concepts of probability. 7. Compare the results of two repetitions of the same grade-level appropriate probability experiment. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 31 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 2: Data Analysis, Probability, and Discrete Mathematics 3: Discrete Mathematics – Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes. 1. Find all possible combinations when one item is selected from each of two sets of different items, using a systematic approach. (e.g., shirts: tee shirt, tank top, sweatshirt; pants: shorts, jeans). CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 32 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO PO CLARIFICATION SAMPLE MC ITEM Arizona Department of Education 2: Data Analysis, Probability, and Discrete Mathematics 4: Vertex-Edge Graphs: Understand and apply vertex-edge graphs. 1. Color maps with the least number of colors so that no common edges share the same color (increased complexity throughout grade levels). At this grade level, this PO is defined as coloring maps or pictures with 12 or fewer sections. There are several ways to address this PO other than the suggested sample(s) presented here. Page 33 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 3: Patterns, Algebra, and Functions 1: Patterns: Identify patterns and apply pattern recognition to reason mathematically. 1. Communicate a grade-level appropriate iterative pattern, using symbols or numbers. At this grade level, this PO is defined as: PO CLARIFICATION Iterative pattern, meaning a pattern generated by using an initial value and repeatedly applying the same operation/s SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 34 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 3: Patterns, Algebra, and Functions 1: Patterns: Identify patterns and apply pattern recognition to reason mathematically. PO 2. Extend a grade-level appropriate iterative pattern. PO CLARIFICATION At this grade level, this PO is defined as determining the subsequent terms of an iterative pattern, using positive whole numbers with one operation. CONCEPT (An iterative pattern is a pattern which is generated by using an initial value and repeatedly applying the same operation.) SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Celia used a rule to make the number pattern below: 92, 88, 44, 40, 20, ___ What will be the next number in the pattern? A 16 B 12 C 10 D 8 Arizona Department of Education Page 35 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 3: Patterns, Algebra, and Functions 1: Patterns: Identify patterns and apply pattern recognition to reason mathematically. PO 3. Solve grade-level appropriate iterative pattern problems. PO CLARIFICATION At this grade level, this PO is defined as either identifying the rule, or applying the rule to determine a specified term using up to two operations in an iterative pattern. CONCEPT (An iterative pattern is a pattern which is generated by using an initial value and repeatedly applying the same operations.) SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 36 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 3: Patterns, Algebra, and Functions 2: Functions and Relationships: Describe and model functions and their relationships. 1. Describe the rule used in a simple grade-level appropriate function (e.g., T-chart, input/output model). PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 37 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 3: Patterns, Algebra, and Functions 3: Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations. 1. Evaluate expressions involving the four basic operations by substituting given decimals for the variable. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. What is the value of the expression below when n = 5.1? 4xn A 9.1 B 9.5 C 20.4 D 20.5 STRAND 3: Patterns, Algebra, and Functions 3: Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations. PO 2. Use variables in contextual situations. PO CLARIFICATION At this grade level, this PO is defined as identifying a variable in word problems. CONCEPT SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 38 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 3: Patterns, Algebra, and Functions 3: Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations. 3. Solve one-step equations with one variable represented by a letter or symbol (e.g., 15 = 45 ÷ n). CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 39 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO 3: Patterns, Algebra, and Functions 4: Analysis of Change: Analyze change in a variable over time and in various contexts. 1. Describe patterns of change: • constant rate (speed of movement of the hands on a clock), and • increasing or decreasing rate (rate of plant growth) PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 40 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 1. Recognize regular polygons. PO CLARIFICATION At this grade level, this PO is defined as identifying regular polygons having all sides congruent and all angles congruent. CONCEPT SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Regular polygons have: A some congruent sides B some congruent angles C no congruent sides or no congruent angles D all congruent sides and all congruent angles STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. 2. Draw 2-dimensional figures by applying significant properties of each (e.g., Draw a quadrilateral with two sets of parallel sides and four right angles.). CONCEPT PO PO CLARIFICATION At this grade level, this PO is defined as identifying 2-dimensional figures by their attributes. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 41 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 3. Sketch prisms, pyramids, cones, and cylinders. PO CLARIFICATION At this grade level, this PO is defined as identifying prisms, pyramids, cones, and cylinders from pictures. CONCEPT SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. 4. Identify the properties of 2- and 3-dimensional geometric figures using appropriate terminology and vocabulary. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 42 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. 5. Draw points, lines, line segments, rays, and angles with appropriate labels. CONCEPT PO PO CLARIFICATION At this grade level, this PO is defined as identifying points, lines, line segments, rays, and angles from illustrations; and correctly choosing appropriate labels. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 6. Recognize that all pairs of vertical angles are congruent. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. CONCEPT No sample available Arizona Department of Education Page 43 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 7. Classify triangles as scalene, isosceles, or equilateral. PO CLARIFICATION At this grade level, this PO is defined as identifying types of triangles. CONCEPT SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 44 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 8. Recognize that a circle is a 360º rotation about a point. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. CONCEPT Study the circle below. 1 2 How many degrees are there in section 2 of the circle? A 360° B 270° C 180° D 90° Arizona Department of Education Page 45 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 9. Identify the diameter, radius, and circumference of a circle. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. CONCEPT No sample available STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. CONCEPT PO 10. Understand that the sum of the angles of a triangle is 180°. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND CONCEPT 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 11. Draw two congruent geometric figures. PO CLARIFICATION At this grade level, this PO is defined as identifying two congruent figures (i.e., same size, same shape). SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 46 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. CONCEPT PO 12. Draw two similar geometric figures. PO CLARIFICATION At this grade level, this PO is defined as identifying two similar figures (i.e., same shape, not same size). SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND CONCEPT 4: Geometry and Measurement 1: Geometric Properties: Analyze the attributes and properties of 2- and 3-dimensional shapes and develop mathematical arguments about their relationships. PO 13. Identify the lines of symmetry in a 2-dimensional shape. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 47 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 2: Transformation of Shapes: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. PO 1. Demonstrate reflections using geometric figures. PO CLARIFICATION At this grade level, this PO is defined as identifying reflections (flips). CONCEPT SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 48 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 2: Transformation of Shapes: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. PO 2. Describe the transformations that created a tessellation. PO CLARIFICATION At this grade level, this PO is defined as a tessellation having geometric shapes that cover a plane with no gaps or overlapping. CONCEPT SAMPLE MC ITEM Arizona Department of Education There are several ways to address this PO other than the suggested sample(s) presented here. Page 49 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 3: Coordinate Geometry: Specify and describe spatial relationships using coordinate geometry and other representational systems. 1. Graph points in the first quadrant on a grid using ordered pairs. CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 50 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. 1. PO State an appropriate measure of accuracy for a contextual situation (e.g., What unit of measurement would you use to measure the top of your desk?). PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. 2. PO PO CLARIFICATION SAMPLE MC ITEM Draw 2-dimensional figures to specifications using the appropriate tools (e.g., Draw a circle with a 2-inch radius.). At this grade level, this PO is defined as identifying which tool to use (e.g., protractor, compass, ruler, etc.) or which graphic was drawn with certain specifications. There are several ways to address this PO other than the suggested sample(s) presented here. To measure the size of an angle you would use: A compass B protractor C ruler D thermometer Arizona Department of Education Page 51 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. 3. PO Determine relationships including volume (e.g., pints and quarts, milliliters and liters). PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. 4. PO Convert measurement units to equivalent units within a given system (U.S. customary and metric) (e.g., 12 inches = 1 foot; 10 decimeters = 1 meter). PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. The ceiling in Ms. Alexander’s classroom is 7 feet high. How high is the ceiling in inches? 7 feet = _?_ inches A 14 B 21 C 49 D 84 Arizona Department of Education Page 52 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 5. PO CLARIFICATION At this grade level, this PO is defined as convex polygons having all diagonals lie inside of the polygon. SAMPLE MC ITEM Arizona Department of Education Solve problems involving the perimeter of convex polygons. There are several ways to address this PO other than the suggested sample(s) presented here. Page 53 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT PO Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. 6. Determine the area of figures composed of two or more rectangles on a grid. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. Arizona Department of Education Page 54 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 7. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. Solve problems involving the area of simple polygons. No sample available STRAND 4: Geometry and Measurement 4: Measurement - Units of Measure - Geometric Objects CONCEPT PO Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. 8. Describe the change in perimeter or area when one attribute (length, width) of a rectangle is altered. PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 55 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND CONCEPT PO PO CLARIFICATION SAMPLE MC ITEM Arizona Department of Education 5: Structure and Logic 1: Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems in contextual situations. 1. Discriminate necessary information from unnecessary information in a given grade-level appropriate word problem. At this grade level, this PO is defined as using the four basic operations with whole numbers or decimals to determine the suitability of information in a word problem. There are several ways to address this PO other than the suggested sample(s) presented here. Page 56 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 5: Structure and Logic 1: Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems in contextual situations. PO 2. Design simple algorithms using whole numbers. PO CLARIFICATION At this grade level, this PO is defined as identifying algorithms. SAMPLE MC ITEM No sample item is available for this PO. CONCEPT No sample available STRAND CONCEPT PO 5: Structure and Logic 1: Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems in contextual situations. 3. Develop an algorithm or formula to calculate areas of simple polygons. PO CLARIFICATION At this grade level, this PO is defined as identifying algorithms or formulas from word problems. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 57 of 58 March 6, 2007 AIMS Item Specifications 5th Grade Mathematics STRAND 5: Structure and Logic 2: Logic, Reasoning, Arguments, and Mathematical Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications. PO 1. Construct if…then statements. PO CLARIFICATION At this grade level, this PO is defined as identifying or completing the correct if…then statement when given the condition (if). CONCEPT SAMPLE MC ITEM There are several ways to address this PO other than the suggested sample(s) presented here. All the students in Mr. Tate’s class brought chips to school on Monday. Luis brought only an apple to school on Monday. Based on this information, which of the following is true? A If Luis brought only an apple, then he was not in school on Monday. B If Luis brought only an apple, then he is in Mr. May’s class. C If Luis brought only an apple, then he is in Mr. Tate’s class D If Luis brought only an apple, then he is not in Mr. Tate’s class. STRAND 5: Structure and Logic 2: Logic, Reasoning, Arguments, and Mathematical Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions and recognize their applications. 2. Identify simple valid arguments using if … then statements based on graphic organizers (e.g., 3-set Venn diagrams and pictures). CONCEPT PO PO CLARIFICATION No clarification needed. SAMPLE MC ITEM No sample item is available for this PO. No sample available Arizona Department of Education Page 58 of 58 March 6, 2007