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<TotalMTotal%OO=Warning Text?Warning Text%XTableStyleMedium9PivotStyleLight16`InformationmMA03MA04@MA05;MA06MA07_MA08$MA09\MA10 (Colorado Student Assessment Program 2009Grade 3 Mathematics Item Map"Order of difficulty (easy to hard)LocationTest/ SessionItem No.Point for CR Item Item Type!Content Standard/ Subcontent Area BenchmarkDOKAssessment ObjectiveG3 MA S1MCCS 11.1b\Identify the fractional part of a drawing or a set (restricted to halves, thirds, fourths). G3 MA S21 of 3CRCS 66.1axUsing pictures, diagrams, numbers or words, demonstrate addition and subtraction of whole numbers with 2digit numbers. CS 4/55.1csChoose the appropriate tool to measure familiar objects/situations containing length, weight, temperature or time. 4.2caIdentify three dimensional figures (for example, cubes, spheres, cylinders, cones and pyramids). CS 2/32.1bSUse a pattern to find missing elements (for example, multiples of 2, 3, 4, 5, 10). 1 of 24.1bMIdentify a line of symmetry for regular polygons and other familiar objects. 3.2b>Use various displays of data, interpret and draw conclusions. 6.3aUDemonstrate understanding of basic multiplication facts of 1 s, 2 s, 3 s, 5 s, 10 s. 5.3apMeasure the length of objects including the sides of rectangles and squares to the nearest inch and centimeter. 3.3aDetermine which outcomes are the most likely, least likely, or equally likely when using a chance device (for example, a spinner). 5.1bkRead and interpret pictorial representations of measurements of length, weight, temperature, and capacity. 1.2baRead the number words for selected numbers from zero to nine thousand, nine hundred ninetynine. 5.1aEUse an analog and digital clock, tell time to the nearest 5 minutes. 1.2dGenerate equivalent representations for the same number up to a 4 digit number (for example; 25=20+5 or 10+15 or 2 tens and 5 ones). 4.3a!Find the perimeter of a polygon. 6.4aUse estimation strategies with whole numbers prior to performing the operations of addition and subtraction (for example, frontend estimation, estimation by rounding, friendly numbers, flexible rounding, clustering). 6.5aqGiven a real world problemsolving situation, sue addition, subtraction, or multiplication to solve the problem. 4.2aIdentify the characteristics of twodimensional figures (for example, number of sides or vertices, contains a right angle, contains parallel sides). 2.4aUsing whole numbers, determine how the change in one quantity affects the change in the other by addition or subtraction (for example, one bicycle has 2 wheels, 2 bicycles have 4 wheels, and 3 bicycles have 6 wheels. How many wheels do 4 bicycles have? 2 of 31.1c[Using concrete materials or pictures identify different combinations of coins up to $0.99. 2.3b,Given numbers in a table, extend the table. 1.3amLocate, label, or count forward from any even number by 2 s and from any number by 10 s and 100 s up to 999. 3.4aGiven pictures, determine all the possible combinations of matching a set containing two elements with a set containing three elements. 6.4bDemonstrate three basic operations of whole numbers (for example, addition and subtraction of three digits, and multiplication of multiples of ten by 1, 2, 3, 5). 2 of 26.2bvUsing money notation, add and subtract commonly used decimals in which sums and differences should not exceed $10.00. 4.2eCreate and identify the results of combining or subdividing given geometric shapes (for example, pattern blocks, tangrams). 1.4bSolve addition and subtraction problems using commutative and associative properties (for example, 2+3+6=6+3+2; the words commutative and associative will not be used in test items). 4.2dIdentify right angles. 5.2adCompare objects according to the measurable attributes of length, capacity, weight, or temperature. 2.3a_Identify a rule using addition or subtraction patterns and solve a new problem using the rule. 1.5aTUse estimation strategies to determine the reasonableness of solutions to problems. 5.4auApproximate the measurement of familiar objects using standards units (for example, a paper clip is about one inch). 3 of 3Mathematics Item MapsPurpose of Item Maps
The item maps contain information that may be of some assistance examining a school or district's adopted curricular alignment to the state standards. They are not an instructional tool, and cannot be used to develop curriculum.
Please refer to the Standards for Educational and Psychological testing relative to the ethical and appropraite use of assessment data, including item maps. How to Use Item Maps
Item maps are linked to a specific form and year of the test. They are useful in a broader sense of ensuring curricular and or programmatic alignment to the standards and benchmarks assessed on that particular form of the assessment.
Use item maps in conjunction with student performance data to ask questions about a district s adopted curriculum and program of instruction.
For District and School administration:
Is this benchmark included in key concepts within your adopted district curriculum?
For Teachers:
Is this benchmark taught within the larger scope of concepts included in the district adopted curriculum?
How have I assessed this concept?
Can students demonstrate understanding of these broader concepts contained within the benchmarks and standards in a variety of ways?
To Examine curricular alignment:
How are the varying leels of DOK reflected in curriculum and instruction?
Classroom/school/district level adopted curricular inventory
Cautions
Item maps must not be used to create yearly instructional targets. Please keep in mind that objectives are assessed on a cyclical basis, and item focused instruction based on item map information is not only ineffective, it is an unethical use of the information provided.PItem Number:
Indicates the actual item number within the test booklet. If an item # is missing, one of two things could be true:
1. Reading/Writing tests  Writing contains Item #s 1 and 2, then Reading contains #3 and so on. If an item # is missing from either Reading or Writing, it may be found in the other content area.
2. A missing item may have been suppressed. An item is suppressed, or removed from the calculations, if it is recognized as not operational as a quality measure of the assessment objective. Any suppressed items are not used in calculations of student scores.
%Order of Difficulty:
Indicates the level of difficulty based on actual student performance. It may be thought of this way: more actual students ans< wered correctly items at the lowest level of difficulty and fewer actual students answer correctly the items at the highest level of difficulty.}Test Session:
Indicates the session in which the item was located.
For example: G5 MA S1 is Grade 5, Mathematics, Session 1:Item Type:
MC = Multiple Choice
CR = Constructed ResponsePoints for Item:
1 of ' x' means that 1 point out of 'x' possible points for constructed response items. Example: 1 of 3, 2 of 3, 3 of 3. The first time the item occurs in the list indicates the scale location of 67 percent of students scoring 1 point on that item; the second time indicates the scale location of 67 percent of students scoring 2 points on that item, and so on.
See Content Rubrics: http://www.cde.state.co.us/cdeassess/documents/csap/csap_scoring.htmlDOK (Depth of Knowledge)
Indicates the Depth of Knowledge (complexity) the item requires of students. This is not item difficulty.
(See Depth of Knowledge on CDE website:
http://www.cde.state.co.us/cdeassess/documents/csap/csap_plds.html#DOK ).
Note: The DOK level is assigned to each ITEM and not to each score point. This means that an item may have one point that requires a low complexity, but has an overall DOK level that is high level because there are score points requiring more complex skills.wSubcontent Areas
Items are developed to measure each Assessment Objective within a Standard. Following test construction, each item is reviewed for their alignment to subcontent areas. Subcontent areas are required to have a minimum of ten points on each test. Given the small number of points assigned within each subcontent area, the standard error of measurement is too large to accurately diagnose an individual student need, but may be used to point educators in the direction of need for more indepth diagnostic assessments to be used at the school and classroom level. These areas are provided to enable districts and schools to further diagnose the needs at a curricular or program level where large numbers of students will reduce the standard error of measurement.
Subcontent area information is available in the GRT layout file on the CDE website in the CSAP Fact Sheets.Scale Location:
Performance levels were used as a standard setting tool for individuals that set cut points for overall proficiency levels. This does not guide interpretation of current results and does not reflect student performance on the items. Benchmark:
Indicates the Assessment Objective the item is measuring. In Writing, the Extended and Paragraph Writing may be assigned a Standard rather than a single Assessment Objective.
Grade 4 Mathematics Item MapG4 MA S1 CS 1 SA 11.1aUsing concrete materials and visual representations, compare, order, and represent decimal fractions with like and unlike denominators such as: halves, fourths, and tenths (for example, may use baseten blocks, pictures, fraction strips, fraction circles)G4 MA S34.1a*Identify and give examples of congruency. CS 2 SA 2YDetermine the missing element in a pattern using pictures, geometric shapes, or numbers. CS 33.3bqDetermine and support which outcomes are most likely, least likely or equally likely when using a chance device. G4 MA S2CS 4/5 SA 3Compare objects according to measurable attributes of length, area, volume, capacity, weight, and/or temperature in US customary and/or metric units. 1 of 41.2a@Read, write, and order numerals and number words from 099,999. Identify a rule using addition, subtraction, or multiplication and solve a problem using the rule (for example, function boxes, input/output boxes, T charts). Using whole numbers, determine how the change in one quantity affects the change in the other by addition, subtraction, or multiplication (for example, Maria is making ladybugs. For 1 ladybug she needs 6 black dots, for 2 ladybugs she needs 12 dots. How m`Tell time in hours and minutes, including a.m. and p.m. using both analog and digital displays. 1.2cGenerate equivalent representations for whole numbers up to 99,9999 (for example; 87459 = 7,000 + 400 + 50 + 9 or 36 = 30 + 6 or 2 tens +16 ones). 2 of 4Given a realworld problem solving situation, use an appropriate operation (any four basic math operation) and an appropriate method (paperpencil, mental math, estimation, calculator, computer) to solve the problem. 4.4aQLocate objects on a coordinate grid (1st quadrant only) and label ordered pairs. Using paper and pencil, demonstrate the four basic operations of whole numbers including: addition; subtraction; multiplication of 2 or 3digit numbers by a 1digit number; division of 2digit number by a 1digit divisor. 5.5aChoose appropriate units of measure for length, area, volume, capacity, weight, temperature, and/or time to solve problems. 1Identify one line of symmetry for a given shape. RSolve for perimeter and area of rectangles and squares using a drawing on a grid. CS 2 CS 6 SA 1Demonstrate the conceptual meaning (using pictures, words, diagrams, or numbers) of addition, subtraction, multiplication, and division of whole numbers. 6.3bMContinue to demonstrate proficiency of basic addition and subtraction facts. iUsing money notation, add and subtract decimals in which sums and differences should not exceed $100.00. 3 of 4nPredict the outcomes of flipping a coin, spinning a spinner with four congruent sectors and/or a number cube. lUse estimation strategies to determine the reasonableness of solutions involving the four basic operations. 6.2aUsing pictures, demonstrate addition and subtraction of commonly used fractions with the same denominators where sums/differences are equal or less than a whole (1/2, 1/3, 1/4, 1/8, 1/10). 2.2a7Display numbers in tables or graphs, to show patterns. Use reasonable estimation techniques before performing basic math operations (for example, frontend estimation, estimation by rounding, friendly numbers, compatible numbers, flexible rounding, clustering). 3.2a,Draw conclusions from a given data display. 3.1aiOrganize, construct, read and interpret a table, line plot, bar graph and/or pictograph from given data. Identify, classify, and compare 2dimensional shapes and use vocabulary to describe the attributes (for example, number of sides, vertices, angles, parallel sides). FDemonstrate understanding of basic multiplication and division facts. tUse number properties with any of the four basic operations (commutative, associative, properties of zero and one). 5.3b9Determine the areas of squares and rectangles on a grid. &Identify place value through 99,9999. TMeasure and determine perimeter of polygons to the nearest half inch or centimeter. Relate units of measurement of length, area, volume, capacity, weight, and/or temperature in US customary and/or metric units to every day objects or situations (for example, yard to a stride, liter to a quart). 4 of 4jIdentify 2 and 3dimensional figures; such as, trapezoids, parallelograms, rhombuses and other polygons. YGiven pictures, describe all possible combinations of matching the elements of two sets. 2.1aUReproduce, extend, and create patterns, using pictures, geometric shapes or numbers. NFind the median, mode, the smallest and the largest element in a set of data. Grade 5 Mathematics Item MapG5 MA S1 CS 3 SA 33.1cERead, interpret, and draw conclusions from various displays of data. G5 MA S31.4aDemonstrate the equivalent relationships among commonly used fractions, decimals, and percents using pictorial or concrete materials. 3.1bOrganize, construct, and interpret displays of data including tables, charts, pictographs, line plots, bar graphs, and line graphs. Read, write, and order positive rational numbers, including commonlyused fractions and terminating decimals through hundredths. 6.4czGiven a math sentence, use any one of the four operations with whole numbers, create and illustrate a realworld problem. Analyze data and draw conclusions based on data displays such a< s tables, charts, line graphs, bar graphs, pictographs, and line plots. G5 MA S2QRepresent, describe, and analyze geometric and numeric patterns (whole numbers). Use concrete materials or pictures, determine commonly used percentages (for example, 25%, 50%) in problemsolving situations. 6.2c~Demonstrate proficiency of addition, subtraction, multiplication and division of whole numbers in problemsolving situations. 2.5avUse tables, charts, concrete objects, or pictures to solve problems involving linear relationships and whole numbers. 6.2d}Use and explain strategies to add and subtract commonly used fractions with like denominators in problemsolving situations. 6.2eeUse and explain strategies to add and subtract commonlyused decimals in problemsolving situations. QDemonstrate the meaning of square numbers using pictorial or concrete materials. 4.6a[Predict and describe the results of flipping, sliding, or turning a twodimensional shape. WSolve problems by representing and analyzing patterns using words, tables, and graphs. 4.5a4Solve problems involving the perimeter of polygons. 1.6bUse appropriate techniques to estimate, determine, and then justify the reasonableness of solutions to problems involving whole numbers. 6.4dIn a problemsolving situation, determine whether the results are reasonable and justify those results with correct computations. 1.5bpUse number properties (commutative, associative, identity) to evaluate numeric expressions and solve equations. 5.1dREstimate the measures of angles (for example, 90, less than 90, more than 90). nUse and explain strategies to add, subtract, multiply and divide whole numbers in problemsolving situations. ODescribe how a change in one quantity results in a change in another quantity. 4.5b=Solve problems involving the area of rectangles and squares. Demonstrate how changing one of the dimensions of a rectangle affects its perimeter (using concrete materials or graph paper). :Identify factors, multiples, and prime/composite numbers. =Read and interpret scales on number lines, graphs, and maps. 4.4cdUse maps and grids to locate points, create paths and measure distances within a coordinate system. 1.3bRecognize equivalent representations for the same number and generate them by decomposing and composing numbers (for example,36 can be represented as 30+6, 20+16, 9x4, 404, three dozen and/or the square of 6). 1.3cSDescribe numbers by their characteristics (for example, even, odd, prime, square). 5.6bhMeasure the sides of rectangles, squares, and triangles to the nearest 1/4 inch and nearest centimeter. 3.6bNMake predications based on data obtained from simple probability experiments. 4.4b@Choose the coordinate graph, which represents a given data set. 1.6aUse number sense to estimate sums and differences of fractions and decimals using benchmarks (for example, 5/6 + 7/8 must be equal to an amount less than 2, since each fraction is less than 1). tDetermine the appropriate unit of measure (metric and US customary) when estimating distance, capacity, and weight. FUse and explain a variety of estimation techniques to solve problems. DRecognize that a variable is used to represent an unknown quantity. Using concrete materials, demonstrate the equivalence of commonlyused fractions, terminating decimals, and percents (for example, 7/10 = 0.7 = 70%). &Determine the range of a set of data. 4.6b/Show lines of symmetry for geometrical shapes. ACompare commonlyused proper fractions and terminating decimals. Locate commonly used positive rational numbers including terminating decimals through hundredths, fractions (halves, thirds, fourths, eighths, and tenths), mixed numbers, and percents on a number line. sDevelop, test, and explain conjectures about properties of whole numbers and commonlyused fractions and decimals. 9Distinguish between the median and mode of a data sheet. 3.5aDescribe events such as likely or unlikely and explain the degree of likelihood using words, such as certain, equally likely, and impossible. Identify, compare, and analyze the attributes of twoand threedimensional shapes and develop vocabulary to describe the attributes (for example, acute, obtuse, right angle, parallel lines, perpendicular lines, intersecting lines, and line segments). 5.5b{Demonstrate how change in one of the dimensions of a rectangle affects its area (using concrete materials or graph paper). 22.1cyIdentify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers. Given a realworld problem, use and appropriate method (mental arithmetic, estimation, paperandpencil, calculator) to correctly solve the problem. Grade 6 Mathematics Item MapG6 MA S1eRead, interpret and draw conclusions from a line graph, bar graph, circle graph and frequency table. Predict and describe how a change in one quantity results in a change in another quantity in a linear relationship (for example, A creature gains 3 oz. a day, how much will it have gained over 10 days?) G6 MA S2G6 MA S3Analyze data and draw conclusions to predict outcomes based on data displays such as line graphs, bar graphs, or frequency tables. }Represent, describe, and analyze geometric and numeric patterns using tables, words, symbols, concrete objects, or pictures. nSolve problems using tables, concrete objects, or pictures involving linear relationships with whole numbers. 3.6aUsing a chance device, such as a number cube or spinner, design a fair game and an unfair game, and explain why they are fair and unfair respectively. JIdentify congruent shapes using reflections, rotations, and translations. `Solve problems involving area of polygons (square, rectangle, parallelogram, rhombus, triangle) 3.6cDescribe an event as likely or unlikely and explain the degree of likelihood using words such as certain, very likely, not likely, or impossible. 4.2bnMake and test conjectures about geometric relationships and develop logical arguments to justify conclusions. LDemonstrate proficiency with the four basic operations using whole numbers. 5.4bUse formulas and/or procedures to solve problems involving the area of squares, rectangles, parallelograms, rhombus, and triangles. Use and explain strategies to add/subtract decimals and fractions in problem solving situations (common fractions with like and unlike denominators, mixed numbers, and decimals to thousandth.) Demonstrate equivalence relationships among fractions, decimals and percents in problem solving situations (for example, two students out of eight is the same as 25%) tDetermine the appropriate unit of measure, metric and US customary, when estimating distance, capacity, and weight. Apply appropriate computation methods to solve problems involving whole numbers, common fractions, and decimals (use only addition and subtraction of fractions and decimals). Develop, apply and explain a variety of different estimation strategies in problem solving situations and explain why an estimate may be acceptable in place of an exact answer. _Read, write, order and compare common fractions, decimals, and percents in a variety of forms. Using physical materials or pictures to demonstrate the meaning and equivalence of commonlyused fractions and/or percents (for example, write the fractions, decimal, and percent value for the shaded portion of a partially shaded circle). Estimate the area of a polygon. sFind and use the range from a given set of data (for example, find the range from 2 to 12. Note: the range is 10). XDescribe numbers by characteristics (divisibility, even, odd, prime, composite, square. LFind and use measures of central tendency including mean, median, and mode. WUse formulas and/or procedures to solve problems involving the perimeter of a polygon. Use concrete materials or pictures to determine commonl< y used percentages (for example, 25%, 50%) in problemsolving situations. YIdentify and use the concepts of factor, multiple, prime, composite, and square numbers. >Use a variable to represent an unknown (letter, box, symbol). MMake predictions based on data obtained from simple probability experiments. Use number sense to estimate, determine, and justify the reasonableness of solutions involving whole numbers, decimals, and common fractions (only sums and differences for fractions and decimals). For example: Is 1/2 + 1/3 closer to 0, 1/2 or 1? Develop, test, and explain conjectures about properties of numbers (associative, commutative, identity, distributive multiplicative property of zero on whole and rational numbers.) 4Show lines of symmetry on a twodimensional figure. Demonstrate how changing one of the dimensions of a rectangle or triangle affects its perimeter and area using concrete materials or graph paper. 3.7aDetermine the number of possible outcomes for simple events using a variety of methods such as: organized lists or tree diagrams. Grade 7 Mathematics Item MapG7 MA S3Represent, describe, and analyze numeric or geometric patterns involving common positive rational numbers or integers using tables, graphs, rules, or symbols. G7 MA S1CS 1/6}Use concrete materials or pictures to explain how ratios, proportion, and percents can be used to solve real world problems. KAdd, subtract, multiply, and divide positive rational numbers or integers. G7 MA S2CS 4/5 SA 2fSolve problems involving the areas of circles, triangles, and parallelograms (formulas not provided). yAnalyze data and draw conclusions to predict outcomes based on data displays such as histograms and stem and leaf plots. tPredict and describe how a change in one quantity results in a change in another quantity in a linear relationship. AConstruct a histogram or stem and leaf from a set of given data. Solve problems by representing and analyzing patterns involving positive rational numbers or integers using tables, graphs, or rules. Describe how a change in an object s linear dimensions affects its perimeter and area (for example, how a change in the radius or diameter will affect the circumference and area of a circle). CS 1/6 SA 1"Use models to represent integers. @Locate positive rational numbers and integers on a number line. Create a situation that matches a given number sentence involving positive rational numbers or integers, excluding division of fractions and decimals. 3Make predictions based on theoretical probability. ZUse reflections, translations, and/or rotations, to determine congruence between figures. Describe, analyze and reason informally about the attributes of two and threedimensional shapes (for example, angles, sides, edges, faces, vertices). KRecognize and use equivalent representations of positive rational numbers. NIdentify and compare similar shapes using ratio, proportion, or scale factor. 2.5buTranslate written words to algebraic expressions/equations and conversely, algebraic expressions/equations to words. Given a display of data (for example, line plot, stem and leaf plot, list of data), determine the mean, mode, median and range. Select the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph or intervals on a histogram). Read and interpret scales on number lines, graphs and maps (for example, given a map and a scale, determine the distance between two points on the map). WEstimate the area of irregular shapes, angle measurement, or weight of common objects. mRead, interpret and draw conclusions from histograms, circle graphs, stem and leaf plots, and scatter plots. IReport the probability of an even in fraction, decimal and percent form. SConstruct a coordinate graph and plot ordered integer pairs in all four quadrants. Develop and use procedures or formulas to solve problems involving area of polygons (for example, trapezoids, regular hexagons, regular octagons). OApply order of operations (including exponents with positive rational numbers. Use the relationships among fractions, decimals and percents including the concepts of ratio and proportion in problem solving situations. yEstimate, solve and justify the reasonableness of solutions to problems involving positive rational numbers or integers. wSolve simple linear equations in problem solving situations using a variety of methods (informal, formal, or graphic). lDescribe numbers by their characteristics (for example, even, odd, prime, composite, divisibility, square). Determine the number of possible outcomes for a given event using a variety of strategies, such as: tree diagrams, or organized lists. 4.5cYSolve problems involving the surface area of rectangular prisms (formulas not provided). PSolve problems involving the circumference of a circle (formulas not provided). ZEstimate, make and use direct and indirect measurements to describe and make comparisons. 5.6aSelect and use appropriate units and tools to measure to the degree of accuracy required in a particular problemsolving situation (for example, reconstruct a replica of a given figure). Grade 8 Mathematics Item MapBlueprint TextG8 MA S3 CS 2 SA 1kDescribe patterns using variables, expressions, equations, and inequalities in problem solving situations. G8 MA S2Solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions (include right prisms and cylinders). Describe, analyze and reason informally about properties (for example, parallelism, perpendicularity, congruence, and similarity) of two and threedimensional figures. G8 MA S1?Recognize the misuse of statistical data in written arguments. Display and use measures of central tendency, (such as mean, median, and mode) and measures of variability, (such as range and quartiles) in problem solving situations. Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how a person s height changes over time). }Use a model (list, tree diagram, area model) to determine theoretical probabilities to solve problems involving uncertainty. HApply order of operations to evaluate simple expressions with integers. Recognize and use equivalent representations of positive rational numbers and common irrational numbers (for example, locate rational numbers on a number line and demonstrate the meaning of square roots and perfect squares). dTransform geometric figures using reflections, translations, and rotations to determine congruence. bDevelop and test conjectures about properties of integers (Does 35 = 53?) and rational numbers. Represent, describe, and analyze patterns (for example, geometric and numeric) and relationships using tables, graphs, verbal rules, and standard algebraic notation. xSolve simple linear equations in problem solving situations using a variety of methods (informal, formal, and graphic). Read and construct displays of data using appropriate techniques (for example, circle graphs, scatter plots, box and whisker plots, stemandleaf plots). pConvert from one functional representation (table, graph, verbal rule, standard algebraic notation) to another. ^Formulate hypotheses, draw conclusions, and make convincing arguments based on data analysis. CS 1/6 SA 2Use the relationships among fractions, decimals and percents including the concepts of ratio and proportion in problem solving situations (similarity, scale factor, unit rate). Develop and use procedures or formulas to solve problems involving measurement (for example, distance, area, surface area, and volume of right prisms< and cylinders). CS 3 SA 2GMake predictions using theoretical probability in realworld problems. rSolve problems in realworld situations using coordinate geometry (for example, maps, distance on a number line). VApply the concept of ratio, proportion, and similarity in problem solving situations. Use a model or counting techniques to determine all the possible outcomes from an experiment (for example, the number of ways students can line up to have their picture taken). fUse models to explain how ratios, proportions, and percents can be used to solve realworld problems. Apply computational methods (including ration and proportion) to solve problems involving commonly used fractions, decimals, percents, and integers (for example, discount, tax, sale price, unit price) and determine whether the results are reasonable.] 6.1b<Convert from one set of units to another using proportions. Estimate, make and use direct and indirect measurements to describe and make comparisons (for example, use a proportion to find the height of a flag pole). qApply number theory concepts (for example, primes, factors, multiples, exponents) in problem solving situations. Describe how a change in an object s linear dimensions affects its perimeter, area and volume (for example, how the area of a circle changes as the radius increases). fEstimate and use measures of area, volume, capacity, weight, and angle comparisons to solve problems. <Apply the Pythagorean Theorem to solve realworld problems. Grade 9 Mathematics Item MapG9 MA S22.2b7Convert from one functional representation to another. G9 MA S3Select and use an appropriate display to represent and describe a set of data (for example, scatter plot, line graph and histogram). G9 MA S1 CS 3 SA 1qFit curves to scatter plots using informal methods or appropriate technology to make predictions about the data. 2.4bMUsing a graph, identify the maximum and minimum value within a given domain. Represent functional relationships using written explanations, tables, equations, and graphs, and describe the connections among these representations. Model real world phenomena involving linear and nonlinear relationships using multiple representations of rules that can take the form of recursive processes, functions, equations, or inequalities. CS 4/5 SA 1Use measurement to solve realworld problems involving rate of change (for example, distance traveled using rate and time). Fit curves to scatter plots using informal methods or appropriate technology to determine the type (positive, negative, or nonexistent) of relationship between two data sets. CAnalyze a graph, table, or summary for misleading characteristics. 2.4cAnalyze the effects of change in the leading coefficient and/or the vertical translation (for example, given y = kx + c, how do changes in k and/or c affect the graphs? 3.5c3.5b3.2ctDescribe how data can be interpreted in more than one way or be used to support more than one position in a debate. aSolve problems involving perimeter, area, and volume of regular and irregular geometric figures. 4.3bQUse coordinate geometry to solve problems involving shapes and their properties. Solve realworld problems with informal use of combinations and permutations (for example, determining the number of possible meals at a restaurant featuring a given number of side dishes). Make and test conjectures about geometric shapes and their properties (for example, parallelism, perpendicularity, similarity, congruence, symmetry). aApply appropriate computational methods to solve multistep problems involving rational numbers. :Use the Pythagorean theorem to solve realworld problems. cUse ratios, proportions, and percents in problem solving situations that involve rational numbers. [Compare and order sets of rational numbers and common irrational numbers ("2, "5, and .). Use appropriate measurements to solve problems indirectly (for example, find the height of a flagpole using similar triangles. QSolve simple systems of equations using algebraic, graphical or numeric methods. eConvert from one set of units to another using proportions (for example, feet/minute to miles/hour). YExpress the perimeter, area and volume relationships of geometric figures algebraically. wUsing large populations, formulate hypothesis, draw conclusions, and make convincing arguments based on data analysis. Use number sense to estimate and justify the reasonableness of solutions to problems involving rational numbers and common irrational numbers (for example, circumference, area of a circle, and Pythagorean Theorem). Determine, analyze, and use measure of central tendency (such as mean, median, and mode) and measures of variability (such as range and quartiles) in problem solving situations. 2.2c@Interpret a graphical representation of a realworld situation. GIdentify and interpret x and y intercepts in the context of a problem. 2.3cySolve equations with more than one variable for a given variable (for example, solve for p in 1= prt or for r in C=2pr). Describe how changing one attribute of a shape affects its angle measure, perimeter, circumference, area, surface area and volume. 3.4bUse averages (including averages per trial, expected value) to draw conclusions about distributions of data (for example, if there are 10 people with one five dollar bill and one dollar bill in their wallets and they each randomly place one of the bills ioUse very large and very small numbers in real life situations to solve problems (scientific notation, powers). aGraph solutions to equations and inequalities in oneand twodimensions and determine solutions. Recognize and use equivalent representations of rational numbers and common irrational numbers ("2, "5, and .), including scientific notation. Find and analyze relationships among geometric figures using transformation (for example, reflections, translation, rotations, dilation) in coordinate systems. Grade 10 Mathematics Item Map G10 MA S23.3c)Predict values using a line of best fit. G10 MA S1VDraw conclusions about a large population based upon a properly chosen random sample. RGiven the rate of change, model realworld problems algebraically or graphically. G10 MA S3Use very large and very small numbers in real life situations to solve problems (for example, understanding the size of the national debt). 3.3eNRecognize which model, linear or nonlinear, fits the data most appropriately. kSolve problems involving functions and relations using calculators, graphs, tables, and algebraic methods. 3.5daCalculate the probability of event A and B occurring and the probability event A or B occurring. mUse number sense to estimate and justify the reasonableness of solutions to problems involving real numbers. KUse the Pythagorean theorem and its converse to solve realworld problems. xDemonstrate horizontal and vertical translations on graphs of functions and their meanings in the context of a problem. Model real world phenomena involving linear, quadratic and exponential relationships using multiple representations of rules that can take the form of a recursive process, a function, an equation, or an inequality. (Compare and order sets of real numbers. Apply appropriate computational methods to solve multistep problems involving all types of numbers from the real number system. 6.1c6Apply direct variation to problem solving situations. 2.4d)Recognize when a relation is a function. YDistinguish between experimental and theoretical probability and use each appropriately. KUse properties of polygons to find areas of regular and i<rregular figures. ZDifferentiate between mean, median, and mode and demonstrate the appropriate use of each. >Use right triangle trigonometry to solve realworld problems. Determine when estimation is an appropriate method to solve a problem and describe what error might result from estimation. IGraph solutions to equations and inequalities in oneand twodimensions. Select and use an appropriate display to represent and describe a set of data (for example, scatter plot*, line graph and histogram). Recognize and use equivalent representations of real numbers in a variety of forms including scientific notation, radicals, and other irrational numbers such as p. 3.4dhDemonstrate how outliers might affect various representations of data and measures of central tendency. 4.1c?Use coordinate geometry and/or tessellations to solve problems DDescribe and apply the properties of similar and congruent figures. nApply organized counting techniques to determine combinations and permutations in problem solving situations. pUse properties of geometric solids to find volumes and surface areas of regular and irregular geometric solids. 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CDE InformationMA03MA04MA05MA06MA07MA08MA09MA10Worksheets
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